<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019cd8ad-1309-7f0f-858f-a7579c067000,g:75573232-2e63-4f6c-896a-3e1764721cb3-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/all" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#all"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#hypercube-dimension"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-default"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-domain"/>
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/domain-member" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#domain-member"/>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/CondensedConsolidatedStatementsofChangesinStockholdersEquityUnaudited" xlink:type="simple" xlink:href="ades-20260331.xsd#CondensedConsolidatedStatementsofChangesinStockholdersEquityUnaudited"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/CondensedConsolidatedStatementsofChangesinStockholdersEquityUnaudited" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems_019cd8ad-143d-7014-a799-cdf9689a1d17" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable_019cd8ad-143d-7e74-bd07-16868297fb43" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_StatementLineItems_019cd8ad-143d-7014-a799-cdf9689a1d17" xlink:to="loc_us-gaap_StatementTable_019cd8ad-143d-7e74-bd07-16868297fb43" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis_019cd8ad-143d-77d4-a1e5-4d7ec305b0b3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_StatementTable_019cd8ad-143d-7e74-bd07-16868297fb43" xlink:to="loc_us-gaap_StatementEquityComponentsAxis_019cd8ad-143d-77d4-a1e5-4d7ec305b0b3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_019cd8ad-143d-77d4-a1e5-4d7ec305b0b3_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_019cd8ad-143d-77d4-a1e5-4d7ec305b0b3" xlink:to="loc_us-gaap_EquityComponentDomain_019cd8ad-143d-77d4-a1e5-4d7ec305b0b3_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain_019cd8ad-143d-71c2-bd7e-001f7ceebe41" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_StatementEquityComponentsAxis_019cd8ad-143d-77d4-a1e5-4d7ec305b0b3" xlink:to="loc_us-gaap_EquityComponentDomain_019cd8ad-143d-71c2-bd7e-001f7ceebe41" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember_019cd8ad-143d-78b2-9fde-1b3eb2986cc9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_019cd8ad-143d-71c2-bd7e-001f7ceebe41" xlink:to="loc_us-gaap_CommonStockMember_019cd8ad-143d-78b2-9fde-1b3eb2986cc9" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember_019cd8ad-143d-7288-a1f3-5b6caef1719d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_019cd8ad-143d-71c2-bd7e-001f7ceebe41" xlink:to="loc_us-gaap_TreasuryStockCommonMember_019cd8ad-143d-7288-a1f3-5b6caef1719d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember_019cd8ad-143d-7b6e-9649-0531687ee661" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_019cd8ad-143d-71c2-bd7e-001f7ceebe41" xlink:to="loc_us-gaap_AdditionalPaidInCapitalMember_019cd8ad-143d-7b6e-9649-0531687ee661" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember_019cd8ad-143d-7c05-913a-3418ea5c1d21" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_EquityComponentDomain_019cd8ad-143d-71c2-bd7e-001f7ceebe41" xlink:to="loc_us-gaap_RetainedEarningsMember_019cd8ad-143d-7c05-913a-3418ea5c1d21" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_StatementLineItems_019cd8ad-143d-7014-a799-cdf9689a1d17" xlink:to="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesOutstanding_019cd8ad-143d-7d28-88af-82e51305e613" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesOutstanding"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:to="loc_us-gaap_SharesOutstanding_019cd8ad-143d-7d28-88af-82e51305e613" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_019cd8ad-143d-7433-9e0c-3c8dea661d14" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:to="loc_us-gaap_StockholdersEquity_019cd8ad-143d-7433-9e0c-3c8dea661d14" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares_019cd8ad-143d-792e-bf9b-7c953cf46193" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:to="loc_us-gaap_TreasuryStockCommonShares_019cd8ad-143d-792e-bf9b-7c953cf46193" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_019cd8ad-143d-7aab-b73b-4c8da64097c9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:to="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_019cd8ad-143d-7aab-b73b-4c8da64097c9" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_019cd8ad-143d-79fe-b39d-b7452af16428" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:to="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_019cd8ad-143d-79fe-b39d-b7452af16428" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_019cd8ad-143d-7520-8910-8c08ba4b2491" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:to="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_019cd8ad-143d-7520-8910-8c08ba4b2491" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_019cd8ad-143d-77cc-a5ad-85f13aed55aa" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:to="loc_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_019cd8ad-143d-77cc-a5ad-85f13aed55aa" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss_019cd8ad-143d-7187-bb8d-b27707d223e3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019cd8ad-143d-7428-9490-16ec880e279a" xlink:to="loc_us-gaap_NetIncomeLoss_019cd8ad-143d-7187-bb8d-b27707d223e3" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesOutstanding_019cd8ad-143d-72aa-b534-30f0b98f0c81" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesOutstanding"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity_019cd8ad-143d-702b-ba27-c7a438246e1b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares_019cd8ad-143d-761a-9b87-923983441574" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonShares"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/RevenueAdditionalInformationDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#RevenueAdditionalInformationDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/RevenueAdditionalInformationDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems_019cd8ad-143e-7116-9545-4269f9f8bfca" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsNotesAndLoansReceivableLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable_019cd8ad-143e-76ea-b400-3eef60a3a748" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems_019cd8ad-143e-7116-9545-4269f9f8bfca" xlink:to="loc_us-gaap_DisaggregationOfRevenueTable_019cd8ad-143e-76ea-b400-3eef60a3a748" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationAxis_019cd8ad-143e-7f3f-8077-8956797cc4b0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BalanceSheetLocationAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable_019cd8ad-143e-76ea-b400-3eef60a3a748" xlink:to="loc_us-gaap_BalanceSheetLocationAxis_019cd8ad-143e-7f3f-8077-8956797cc4b0" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationDomain_019cd8ad-143e-7f3f-8077-8956797cc4b0_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BalanceSheetLocationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BalanceSheetLocationAxis_019cd8ad-143e-7f3f-8077-8956797cc4b0" xlink:to="loc_us-gaap_BalanceSheetLocationDomain_019cd8ad-143e-7f3f-8077-8956797cc4b0_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationDomain_019cd8ad-143e-7a2e-8d85-f8999b3926c2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BalanceSheetLocationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BalanceSheetLocationAxis_019cd8ad-143e-7f3f-8077-8956797cc4b0" xlink:to="loc_us-gaap_BalanceSheetLocationDomain_019cd8ad-143e-7a2e-8d85-f8999b3926c2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_UnbilledReceivablesMember_019cd8ad-143e-75f1-a7d9-278e5b37b742" xlink:href="ades-20260331.xsd#ades_UnbilledReceivablesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BalanceSheetLocationDomain_019cd8ad-143e-7a2e-8d85-f8999b3926c2" xlink:to="loc_ades_UnbilledReceivablesMember_019cd8ad-143e-75f1-a7d9-278e5b37b742" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesMember_019cd8ad-143e-73e0-ba78-4d7facf7a716" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BalanceSheetLocationDomain_019cd8ad-143e-7a2e-8d85-f8999b3926c2" xlink:to="loc_us-gaap_OtherLiabilitiesMember_019cd8ad-143e-73e0-ba78-4d7facf7a716" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019d8fb9-f73a-7003-a3a2-4d894581c9ce" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable_019cd8ad-143e-76ea-b400-3eef60a3a748" xlink:to="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019d8fb9-f73a-7003-a3a2-4d894581c9ce" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain_019d8fb9-f73a-7003-a3a2-4d894581c9ce_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019d8fb9-f73a-7003-a3a2-4d894581c9ce" xlink:to="loc_us-gaap_ReceivableTypeDomain_019d8fb9-f73a-7003-a3a2-4d894581c9ce_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain_019d8fb9-f73a-7c0f-b301-db0ec9b26ca5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019d8fb9-f73a-7003-a3a2-4d894581c9ce" xlink:to="loc_us-gaap_ReceivableTypeDomain_019d8fb9-f73a-7c0f-b301-db0ec9b26ca5" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeAccountsReceivableMember_019d8fb9-f73a-7a6a-9bfa-2ef542c6bb5b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradeAccountsReceivableMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReceivableTypeDomain_019d8fb9-f73a-7c0f-b301-db0ec9b26ca5" xlink:to="loc_us-gaap_TradeAccountsReceivableMember_019d8fb9-f73a-7a6a-9bfa-2ef542c6bb5b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetNet_019cd8ad-143e-7e44-8f9f-69dd4d49ec50" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerAssetNet"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems_019cd8ad-143e-7116-9545-4269f9f8bfca" xlink:to="loc_us-gaap_ContractWithCustomerAssetNet_019cd8ad-143e-7e44-8f9f-69dd4d49ec50" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent_019d8fb9-f73a-78e2-8ebe-9ad2a4a61910" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems_019cd8ad-143e-7116-9545-4269f9f8bfca" xlink:to="loc_us-gaap_AccountsReceivableNetCurrent_019d8fb9-f73a-78e2-8ebe-9ad2a4a61910" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherReceivablesNetCurrent_019d8fb9-f73a-71ce-bfcf-c1c44249ff40" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherReceivablesNetCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems_019cd8ad-143e-7116-9545-4269f9f8bfca" xlink:to="loc_us-gaap_OtherReceivablesNetCurrent_019d8fb9-f73a-71ce-bfcf-c1c44249ff40" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/RevenueScheduleofAccountsReceivablesDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#RevenueScheduleofAccountsReceivablesDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/RevenueScheduleofAccountsReceivablesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems_019cd8ad-143e-7ad8-9ad7-8327b2fbc8eb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsNotesAndLoansReceivableLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_019cd8ad-143e-7a24-8605-41612f32780c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems_019cd8ad-143e-7ad8-9ad7-8327b2fbc8eb" xlink:to="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_019cd8ad-143e-7a24-8605-41612f32780c" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019cd8ad-143e-7ca3-8d4e-9cb6ae9ce0f0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_019cd8ad-143e-7a24-8605-41612f32780c" xlink:to="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019cd8ad-143e-7ca3-8d4e-9cb6ae9ce0f0" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain_019cd8ad-143e-7ca3-8d4e-9cb6ae9ce0f0_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019cd8ad-143e-7ca3-8d4e-9cb6ae9ce0f0" xlink:to="loc_us-gaap_ReceivableTypeDomain_019cd8ad-143e-7ca3-8d4e-9cb6ae9ce0f0_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain_019cd8ad-143e-7339-b2e5-f893dee0faf7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019cd8ad-143e-7ca3-8d4e-9cb6ae9ce0f0" xlink:to="loc_us-gaap_ReceivableTypeDomain_019cd8ad-143e-7339-b2e5-f893dee0faf7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeAccountsReceivableMember_019cd8ad-143e-7f83-9fc6-524a357a0e33" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradeAccountsReceivableMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ReceivableTypeDomain_019cd8ad-143e-7339-b2e5-f893dee0faf7" xlink:to="loc_us-gaap_TradeAccountsReceivableMember_019cd8ad-143e-7f83-9fc6-524a357a0e33" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent_019cd8ad-143e-70a6-9a06-cb83b838837b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems_019cd8ad-143e-7ad8-9ad7-8327b2fbc8eb" xlink:to="loc_us-gaap_AccountsReceivableNetCurrent_019cd8ad-143e-70a6-9a06-cb83b838837b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherReceivablesNetCurrent_019cd8ad-143e-7da5-a08d-0bf9010d3fdb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherReceivablesNetCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems_019cd8ad-143e-7ad8-9ad7-8327b2fbc8eb" xlink:to="loc_us-gaap_OtherReceivablesNetCurrent_019cd8ad-143e-7da5-a08d-0bf9010d3fdb" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/DebtObligationsScheduleofDebtDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#DebtObligationsScheduleofDebtDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/DebtObligationsScheduleofDebtDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-723f-bf2e-97bd6a36f943" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-723f-bf2e-97bd6a36f943" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis_019cd8ad-143e-77ee-b5ce-efd4fcc6a174" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-723f-bf2e-97bd6a36f943" xlink:to="loc_us-gaap_DebtInstrumentAxis_019cd8ad-143e-77ee-b5ce-efd4fcc6a174" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-77ee-b5ce-efd4fcc6a174_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DebtInstrumentAxis_019cd8ad-143e-77ee-b5ce-efd4fcc6a174" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-77ee-b5ce-efd4fcc6a174_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7964-a9f8-ac2d6f346eed" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DebtInstrumentAxis_019cd8ad-143e-77ee-b5ce-efd4fcc6a174" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7964-a9f8-ac2d6f346eed" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_SecuredRevolvingCreditFacilityMember_019cd8ad-143e-7823-9e17-9a5cf1d2a9ae" xlink:href="ades-20260331.xsd#ades_SecuredRevolvingCreditFacilityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7964-a9f8-ac2d6f346eed" xlink:to="loc_ades_SecuredRevolvingCreditFacilityMember_019cd8ad-143e-7823-9e17-9a5cf1d2a9ae" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_CTBLoanDueJanuary2036Member_019cd8ad-143e-7659-8c7b-d73e73c31d77" xlink:href="ades-20260331.xsd#ades_CTBLoanDueJanuary2036Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7964-a9f8-ac2d6f346eed" xlink:to="loc_ades_CTBLoanDueJanuary2036Member_019cd8ad-143e-7659-8c7b-d73e73c31d77" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount_019cd8ad-143e-7921-acdb-6031e28c7800" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_DebtInstrumentCarryingAmount_019cd8ad-143e-7921-acdb-6031e28c7800" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiability_019cd8ad-143e-7f7d-8110-67cc0ba42902" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_FinanceLeaseLiability_019cd8ad-143e-7f7d-8110-67cc0ba42902" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLongTermDebt_019cd8ad-143e-7ff1-bdf8-c9b1a3710f76" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLongTermDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_OtherLongTermDebt_019cd8ad-143e-7ff1-bdf8-c9b1a3710f76" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt_019cd8ad-143e-746e-ad63-4090bd9af9c1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_LongTermDebt_019cd8ad-143e-746e-ad63-4090bd9af9c1" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscount_019cd8ad-143e-7324-9fa0-5b46ca34bc1c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentUnamortizedDiscount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_DebtInstrumentUnamortizedDiscount_019cd8ad-143e-7324-9fa0-5b46ca34bc1c" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnamortizedDebtIssuanceExpense_019cd8ad-143e-7491-bef5-45c365bff36f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnamortizedDebtIssuanceExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_UnamortizedDebtIssuanceExpense_019cd8ad-143e-7491-bef5-45c365bff36f" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities_019cd8ad-143e-77cc-8e4f-92c585a97fdb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities_019cd8ad-143e-77cc-8e4f-92c585a97fdb" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtCurrent_019cd8ad-143e-709a-9270-d78ac017f403" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_LongTermDebtCurrent_019cd8ad-143e-709a-9270-d78ac017f403" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtNoncurrent_019cd8ad-143e-7258-9b63-752d1aece572" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_LongTermDebtNoncurrent_019cd8ad-143e-7258-9b63-752d1aece572" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityStatementOfFinancialPositionExtensibleList_019d3308-276a-78d6-a3ec-e71b1de6a8d5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityStatementOfFinancialPositionExtensibleList"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7611-93cb-b98b83f3b5db" xlink:to="loc_us-gaap_FinanceLeaseLiabilityStatementOfFinancialPositionExtensibleList_019d3308-276a-78d6-a3ec-e71b1de6a8d5" xlink:type="arc" order="9"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/DebtObligationsNarrativeDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#DebtObligationsNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/DebtObligationsNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-743d-b1e6-4391fd3576fb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-743d-b1e6-4391fd3576fb" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis_019cd8ad-143e-7b30-94e5-37bbe5328de2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-743d-b1e6-4391fd3576fb" xlink:to="loc_us-gaap_CreditFacilityAxis_019cd8ad-143e-7b30-94e5-37bbe5328de2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain_019cd8ad-143e-7b30-94e5-37bbe5328de2_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_CreditFacilityAxis_019cd8ad-143e-7b30-94e5-37bbe5328de2" xlink:to="loc_us-gaap_CreditFacilityDomain_019cd8ad-143e-7b30-94e5-37bbe5328de2_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain_019cd8ad-143e-7a00-ac4f-90794df55384" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_CreditFacilityAxis_019cd8ad-143e-7b30-94e5-37bbe5328de2" xlink:to="loc_us-gaap_CreditFacilityDomain_019cd8ad-143e-7a00-ac4f-90794df55384" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember_019cd8ad-143e-7b52-9e22-717a97ed9352" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CreditFacilityDomain_019cd8ad-143e-7a00-ac4f-90794df55384" xlink:to="loc_us-gaap_RevolvingCreditFacilityMember_019cd8ad-143e-7b52-9e22-717a97ed9352" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis_019cd8ad-143e-7e29-8d8c-de3f563c53b4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-743d-b1e6-4391fd3576fb" xlink:to="loc_us-gaap_LongtermDebtTypeAxis_019cd8ad-143e-7e29-8d8c-de3f563c53b4" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-143e-7e29-8d8c-de3f563c53b4_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_019cd8ad-143e-7e29-8d8c-de3f563c53b4" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-143e-7e29-8d8c-de3f563c53b4_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-143e-7f09-9071-38d99d855e32" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_019cd8ad-143e-7e29-8d8c-de3f563c53b4" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-143e-7f09-9071-38d99d855e32" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember_019cd8ad-143e-7972-b9fb-8defb27a58ec" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredDebtMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-143e-7f09-9071-38d99d855e32" xlink:to="loc_us-gaap_SecuredDebtMember_019cd8ad-143e-7972-b9fb-8defb27a58ec" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateAxis_019cd8ad-143e-7cdb-86ed-b57705cdaab3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableRateAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-743d-b1e6-4391fd3576fb" xlink:to="loc_us-gaap_VariableRateAxis_019cd8ad-143e-7cdb-86ed-b57705cdaab3" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateDomain_019cd8ad-143e-7cdb-86ed-b57705cdaab3_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableRateDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_VariableRateAxis_019cd8ad-143e-7cdb-86ed-b57705cdaab3" xlink:to="loc_us-gaap_VariableRateDomain_019cd8ad-143e-7cdb-86ed-b57705cdaab3_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateDomain_019cd8ad-143e-7274-9949-351e6822aca6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableRateDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_VariableRateAxis_019cd8ad-143e-7cdb-86ed-b57705cdaab3" xlink:to="loc_us-gaap_VariableRateDomain_019cd8ad-143e-7274-9949-351e6822aca6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredOvernightFinancingRateSofrMember_019cd8ad-143e-7b7d-9b39-1a3bd81b3e54" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredOvernightFinancingRateSofrMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableRateDomain_019cd8ad-143e-7274-9949-351e6822aca6" xlink:to="loc_us-gaap_SecuredOvernightFinancingRateSofrMember_019cd8ad-143e-7b7d-9b39-1a3bd81b3e54" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrimeRateMember_019cd8ad-143e-7de0-a122-ef642c21c690" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrimeRateMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_VariableRateDomain_019cd8ad-143e-7274-9949-351e6822aca6" xlink:to="loc_us-gaap_PrimeRateMember_019cd8ad-143e-7de0-a122-ef642c21c690" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventAxis_019cd8ad-143e-7981-b5ad-a20b3a34bb02" xlink:href="ades-20260331.xsd#ades_TriggeringEventAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-743d-b1e6-4391fd3576fb" xlink:to="loc_ades_TriggeringEventAxis_019cd8ad-143e-7981-b5ad-a20b3a34bb02" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventDomain_019cd8ad-143e-7981-b5ad-a20b3a34bb02_default" xlink:href="ades-20260331.xsd#ades_TriggeringEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_ades_TriggeringEventAxis_019cd8ad-143e-7981-b5ad-a20b3a34bb02" xlink:to="loc_ades_TriggeringEventDomain_019cd8ad-143e-7981-b5ad-a20b3a34bb02_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventDomain_019cd8ad-143e-7ee1-a3a1-3369d6736625" xlink:href="ades-20260331.xsd#ades_TriggeringEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_ades_TriggeringEventAxis_019cd8ad-143e-7981-b5ad-a20b3a34bb02" xlink:to="loc_ades_TriggeringEventDomain_019cd8ad-143e-7ee1-a3a1-3369d6736625" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TrancheYearOneMember_019cd8ad-143e-7de9-8aa8-a5f69cc76c58" xlink:href="ades-20260331.xsd#ades_TrancheYearOneMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventDomain_019cd8ad-143e-7ee1-a3a1-3369d6736625" xlink:to="loc_ades_TrancheYearOneMember_019cd8ad-143e-7de9-8aa8-a5f69cc76c58" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TrancheYearTwoMember_019cd8ad-143e-73d4-9f86-a5f3b3ce3a69" xlink:href="ades-20260331.xsd#ades_TrancheYearTwoMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventDomain_019cd8ad-143e-7ee1-a3a1-3369d6736625" xlink:to="loc_ades_TrancheYearTwoMember_019cd8ad-143e-73d4-9f86-a5f3b3ce3a69" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TrancheYearThreeMember_019cd8ad-143e-7e30-ac1a-f6d0bd896d79" xlink:href="ades-20260331.xsd#ades_TrancheYearThreeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventDomain_019cd8ad-143e-7ee1-a3a1-3369d6736625" xlink:to="loc_ades_TrancheYearThreeMember_019cd8ad-143e-7e30-ac1a-f6d0bd896d79" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TrancheYearThereafterMember_019cd8ad-143e-7255-aa85-89ae004a6b4c" xlink:href="ades-20260331.xsd#ades_TrancheYearThereafterMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventDomain_019cd8ad-143e-7ee1-a3a1-3369d6736625" xlink:to="loc_ades_TrancheYearThereafterMember_019cd8ad-143e-7255-aa85-89ae004a6b4c" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_ThroughJanuary2026Member_019cd8ad-143e-7195-b0b8-a364f80e5ec5" xlink:href="ades-20260331.xsd#ades_ThroughJanuary2026Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventDomain_019cd8ad-143e-7ee1-a3a1-3369d6736625" xlink:to="loc_ades_ThroughJanuary2026Member_019cd8ad-143e-7195-b0b8-a364f80e5ec5" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_AfterJanuary2026Member_019cd8ad-143e-7a7a-ae34-944731defc53" xlink:href="ades-20260331.xsd#ades_AfterJanuary2026Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventDomain_019cd8ad-143e-7ee1-a3a1-3369d6736625" xlink:to="loc_ades_AfterJanuary2026Member_019cd8ad-143e-7a7a-ae34-944731defc53" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_PenaltyYear2026Member_019cd8ad-143e-7ac0-8cca-c8d80505b3e6" xlink:href="ades-20260331.xsd#ades_PenaltyYear2026Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventDomain_019cd8ad-143e-7ee1-a3a1-3369d6736625" xlink:to="loc_ades_PenaltyYear2026Member_019cd8ad-143e-7ac0-8cca-c8d80505b3e6" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis_019cd8ad-143e-7faf-9ff2-568fb46aee08" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-743d-b1e6-4391fd3576fb" xlink:to="loc_us-gaap_BusinessAcquisitionAxis_019cd8ad-143e-7faf-9ff2-568fb46aee08" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_019cd8ad-143e-7faf-9ff2-568fb46aee08_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_019cd8ad-143e-7faf-9ff2-568fb46aee08" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_019cd8ad-143e-7faf-9ff2-568fb46aee08_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain_019cd8ad-143e-7c06-ba97-a27c202d734e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_BusinessAcquisitionAxis_019cd8ad-143e-7faf-9ff2-568fb46aee08" xlink:to="loc_us-gaap_BusinessAcquisitionAcquireeDomain_019cd8ad-143e-7c06-ba97-a27c202d734e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_ArqLimitedMember_019cd8ad-143e-7558-b98f-4c2947a5a655" xlink:href="ades-20260331.xsd#ades_ArqLimitedMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain_019cd8ad-143e-7c06-ba97-a27c202d734e" xlink:to="loc_ades_ArqLimitedMember_019cd8ad-143e-7558-b98f-4c2947a5a655" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis_019cd8ad-143e-73af-bcff-8f1d851ef5ff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-743d-b1e6-4391fd3576fb" xlink:to="loc_us-gaap_DebtInstrumentAxis_019cd8ad-143e-73af-bcff-8f1d851ef5ff" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-73af-bcff-8f1d851ef5ff_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_DebtInstrumentAxis_019cd8ad-143e-73af-bcff-8f1d851ef5ff" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-73af-bcff-8f1d851ef5ff_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7fa3-bed8-c9905a830464" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_DebtInstrumentAxis_019cd8ad-143e-73af-bcff-8f1d851ef5ff" xlink:to="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7fa3-bed8-c9905a830464" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_CTBLoanMember_019cd8ad-143e-7a73-87ab-cc06a40114cd" xlink:href="ades-20260331.xsd#ades_CTBLoanMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7fa3-bed8-c9905a830464" xlink:to="loc_ades_CTBLoanMember_019cd8ad-143e-7a73-87ab-cc06a40114cd" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_CFGLoanMember_019cd8ad-143e-7ef7-9c73-c2542a1643c7" xlink:href="ades-20260331.xsd#ades_CFGLoanMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7fa3-bed8-c9905a830464" xlink:to="loc_ades_CFGLoanMember_019cd8ad-143e-7ef7-9c73-c2542a1643c7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_PromissoryNoteAMember_019cd8ad-143e-7bd2-bbff-437752d52053" xlink:href="ades-20260331.xsd#ades_PromissoryNoteAMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7fa3-bed8-c9905a830464" xlink:to="loc_ades_PromissoryNoteAMember_019cd8ad-143e-7bd2-bbff-437752d52053" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_PromissoryNoteBMember_019cd8ad-143e-7acb-90cb-7b7556c100d8" xlink:href="ades-20260331.xsd#ades_PromissoryNoteBMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentNameDomain_019cd8ad-143e-7fa3-bed8-c9905a830464" xlink:to="loc_ades_PromissoryNoteBMember_019cd8ad-143e-7acb-90cb-7b7556c100d8" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis_019d8e04-406f-756d-9a4f-e5c235bb48b1" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementScenarioAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-143e-743d-b1e6-4391fd3576fb" xlink:to="loc_srt_StatementScenarioAxis_019d8e04-406f-756d-9a4f-e5c235bb48b1" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain_019d8e04-406f-756d-9a4f-e5c235bb48b1_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioUnspecifiedDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_StatementScenarioAxis_019d8e04-406f-756d-9a4f-e5c235bb48b1" xlink:to="loc_srt_ScenarioUnspecifiedDomain_019d8e04-406f-756d-9a4f-e5c235bb48b1_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain_019d8e04-406f-75b4-81ad-a577603a13e9" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioUnspecifiedDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_StatementScenarioAxis_019d8e04-406f-756d-9a4f-e5c235bb48b1" xlink:to="loc_srt_ScenarioUnspecifiedDomain_019d8e04-406f-75b4-81ad-a577603a13e9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioForecastMember_019d8e04-406f-73ef-b346-8840440d0bb6" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioForecastMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ScenarioUnspecifiedDomain_019d8e04-406f-75b4-81ad-a577603a13e9" xlink:to="loc_srt_ScenarioForecastMember_019d8e04-406f-73ef-b346-8840440d0bb6" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm_019cd8ad-143e-7b79-afdb-8f093471b184" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentTerm_019cd8ad-143e-7b79-afdb-8f093471b184" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019cd8ad-143e-7f23-9518-51ba047501ed" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019cd8ad-143e-7f23-9518-51ba047501ed" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019cd8ad-143e-71d0-b877-3451860fabeb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019cd8ad-143e-71d0-b877-3451860fabeb" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_DebtInstrumentBasisSpreadOnVariableRateFloor_019cd8ad-143e-70fd-b3c4-89b4a3ccda01" xlink:href="ades-20260331.xsd#ades_DebtInstrumentBasisSpreadOnVariableRateFloor"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_ades_DebtInstrumentBasisSpreadOnVariableRateFloor_019cd8ad-143e-70fd-b3c4-89b4a3ccda01" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_019cd8ad-143e-7058-84a6-2d26d6bec34c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_019cd8ad-143e-7058-84a6-2d26d6bec34c" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_LineOfCreditFacilityPercentageOfCollateralManagementFeeOfOutstandingBalance_019cd8ad-143e-7450-9566-127975292327" xlink:href="ades-20260331.xsd#ades_LineOfCreditFacilityPercentageOfCollateralManagementFeeOfOutstandingBalance"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_ades_LineOfCreditFacilityPercentageOfCollateralManagementFeeOfOutstandingBalance_019cd8ad-143e-7450-9566-127975292327" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_LineOfCreditFacilityPreclosureFeePercentage_019cd8ad-143e-70a6-b7e1-6045e272ad3b" xlink:href="ades-20260331.xsd#ades_LineOfCreditFacilityPreclosureFeePercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_ades_LineOfCreditFacilityPreclosureFeePercentage_019cd8ad-143e-70a6-b7e1-6045e272ad3b" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_DebtCovenantMinimumCashBalanceRequirement_019cd8ad-143e-75ee-a7d1-ef952a9628f4" xlink:href="ades-20260331.xsd#ades_DebtCovenantMinimumCashBalanceRequirement"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_ades_DebtCovenantMinimumCashBalanceRequirement_019cd8ad-143e-75ee-a7d1-ef952a9628f4" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount_019cd8ad-143e-78e4-8c47-2c0d92754adb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentCarryingAmount_019cd8ad-143e-78e4-8c47-2c0d92754adb" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount_019cd8ad-143e-726d-8d59-85ecf1b81449" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentFaceAmount_019cd8ad-143e-726d-8d59-85ecf1b81449" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFairValue_019cd8ad-143e-7f0b-b559-5b53224cec85" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentFairValue_019cd8ad-143e-7f0b-b559-5b53224cec85" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscount_019cd8ad-143e-7b7b-a239-b64a7cd56091" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentUnamortizedDiscount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentUnamortizedDiscount_019cd8ad-143e-7b7b-a239-b64a7cd56091" xlink:type="arc" order="11"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_DebtInstrumentNumberOfInstruments_019cd8ad-143e-736e-81b1-344ba0833ed8" xlink:href="ades-20260331.xsd#ades_DebtInstrumentNumberOfInstruments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_ades_DebtInstrumentNumberOfInstruments_019cd8ad-143e-736e-81b1-344ba0833ed8" xlink:type="arc" order="12"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_019cd8ad-143e-769e-b02b-1f08d2b559b0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage_019cd8ad-143e-769e-b02b-1f08d2b559b0" xlink:type="arc" order="13"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentPeriodicPaymentPrincipal_019cd8ad-143e-7a72-95fb-b91e84e1aa07" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentPeriodicPaymentPrincipal"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentPeriodicPaymentPrincipal_019cd8ad-143e-7a72-95fb-b91e84e1aa07" xlink:type="arc" order="14"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_DebtInstrumentPrepaymentPenaltyPercentage_019cd8ad-143e-7e2f-9bf8-5567fa0deb4d" xlink:href="ades-20260331.xsd#ades_DebtInstrumentPrepaymentPenaltyPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_ades_DebtInstrumentPrepaymentPenaltyPercentage_019cd8ad-143e-7e2f-9bf8-5567fa0deb4d" xlink:type="arc" order="15"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_DebtInstrumentCovenantIndebtednessToNetWorth_019cd8ad-143e-7349-b50c-f6ec2e5f3a08" xlink:href="ades-20260331.xsd#ades_DebtInstrumentCovenantIndebtednessToNetWorth"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_ades_DebtInstrumentCovenantIndebtednessToNetWorth_019cd8ad-143e-7349-b50c-f6ec2e5f3a08" xlink:type="arc" order="16"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateIncreaseDecrease_019cd8ad-143e-7f53-a782-bbd2360f32e6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateIncreaseDecrease"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentInterestRateIncreaseDecrease_019cd8ad-143e-7f53-a782-bbd2360f32e6" xlink:type="arc" order="17"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentConvertibleConversionRatio1_019cd8ad-143e-79d0-8f3b-35aae9aa0016" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentConvertibleConversionRatio1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-143e-7e70-b2e8-bcf20caaf301" xlink:to="loc_us-gaap_DebtInstrumentConvertibleConversionRatio1_019cd8ad-143e-79d0-8f3b-35aae9aa0016" xlink:type="arc" order="18"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/LeasesNarrativeDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#LeasesNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/LeasesNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionLineItems_019cd8ad-143e-7850-af1c-f1e9f438f820" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeaseDescriptionLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionTable_019cd8ad-143e-70f2-8ade-e238ca746147" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeaseDescriptionTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems_019cd8ad-143e-7850-af1c-f1e9f438f820" xlink:to="loc_us-gaap_LesseeLeaseDescriptionTable_019cd8ad-143e-70f2-8ade-e238ca746147" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis_019cd8ad-143e-7fbe-9b57-02543cf05846" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductOrServiceAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable_019cd8ad-143e-70f2-8ade-e238ca746147" xlink:to="loc_srt_ProductOrServiceAxis_019cd8ad-143e-7fbe-9b57-02543cf05846" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain_019cd8ad-143e-7fbe-9b57-02543cf05846_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ProductOrServiceAxis_019cd8ad-143e-7fbe-9b57-02543cf05846" xlink:to="loc_srt_ProductsAndServicesDomain_019cd8ad-143e-7fbe-9b57-02543cf05846_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain_019cd8ad-143e-7b9a-a167-d623beed9d8a" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ProductOrServiceAxis_019cd8ad-143e-7fbe-9b57-02543cf05846" xlink:to="loc_srt_ProductsAndServicesDomain_019cd8ad-143e-7b9a-a167-d623beed9d8a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_ConsumablesMember_019cd8ad-143e-7bee-836c-cf90ec1963fc" xlink:href="ades-20260331.xsd#ades_ConsumablesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_ProductsAndServicesDomain_019cd8ad-143e-7b9a-a167-d623beed9d8a" xlink:to="loc_ades_ConsumablesMember_019cd8ad-143e-7bee-836c-cf90ec1963fc" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis_019cd8ad-143e-70fe-8dce-7d067e4b1e93" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable_019cd8ad-143e-70f2-8ade-e238ca746147" xlink:to="loc_us-gaap_IncomeStatementLocationAxis_019cd8ad-143e-70fe-8dce-7d067e4b1e93" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-143e-70fe-8dce-7d067e4b1e93_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_IncomeStatementLocationAxis_019cd8ad-143e-70fe-8dce-7d067e4b1e93" xlink:to="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-143e-70fe-8dce-7d067e4b1e93_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-143e-727b-b934-cbba284f4bd3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_IncomeStatementLocationAxis_019cd8ad-143e-70fe-8dce-7d067e4b1e93" xlink:to="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-143e-727b-b934-cbba284f4bd3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpenseMember_019cd8ad-143e-7090-9813-27a0434826ff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpenseMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-143e-727b-b934-cbba284f4bd3" xlink:to="loc_us-gaap_GeneralAndAdministrativeExpenseMember_019cd8ad-143e-7090-9813-27a0434826ff" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingGeneralAndAdministrativeExpensesMember_019cd8ad-143e-783b-a94c-02af4c1975a6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpensesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-143e-727b-b934-cbba284f4bd3" xlink:to="loc_us-gaap_SellingGeneralAndAdministrativeExpensesMember_019cd8ad-143e-783b-a94c-02af4c1975a6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis_019d8730-d7db-75e1-b195-68885c700968" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable_019cd8ad-143e-70f2-8ade-e238ca746147" xlink:to="loc_srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis_019d8730-d7db-75e1-b195-68885c700968" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_019d8730-d7db-75e1-b195-68885c700968_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis_019d8730-d7db-75e1-b195-68885c700968" xlink:to="loc_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_019d8730-d7db-75e1-b195-68885c700968_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_019d8730-d7db-70a2-9d62-5086c71498ea" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis_019d8730-d7db-75e1-b195-68885c700968" xlink:to="loc_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_019d8730-d7db-70a2-9d62-5086c71498ea" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_CorbinFacilityMember_019d8730-d7db-7412-b311-a328ac5aace5" xlink:href="ades-20260331.xsd#ades_CorbinFacilityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_019d8730-d7db-70a2-9d62-5086c71498ea" xlink:to="loc_ades_CorbinFacilityMember_019d8730-d7db-7412-b311-a328ac5aace5" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_019cd8ad-143e-74ff-af72-c542f90fa485" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems_019cd8ad-143e-7850-af1c-f1e9f438f820" xlink:to="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_019cd8ad-143e-74ff-af72-c542f90fa485" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_019cd8ad-143e-7936-a21a-1122ce1798a6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems_019cd8ad-143e-7850-af1c-f1e9f438f820" xlink:to="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_019cd8ad-143e-7936-a21a-1122ce1798a6" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_019cd8ad-143e-717a-b3ad-d346a68260dc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems_019cd8ad-143e-7850-af1c-f1e9f438f820" xlink:to="loc_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_019cd8ad-143e-717a-b3ad-d346a68260dc" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseExpense_019cd8ad-143e-7cac-b802-3fc31f7ee3b4" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems_019cd8ad-143e-7850-af1c-f1e9f438f820" xlink:to="loc_us-gaap_OperatingLeaseExpense_019cd8ad-143e-7cac-b802-3fc31f7ee3b4" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseRenewalTerm_019de493-4e06-7c23-8c94-051f0b01ceac" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseRenewalTerm"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems_019cd8ad-143e-7850-af1c-f1e9f438f820" xlink:to="loc_us-gaap_LesseeOperatingLeaseRenewalTerm_019de493-4e06-7c23-8c94-051f0b01ceac" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_019d8730-d7db-7e3d-b65f-469c42dd90c0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems_019cd8ad-143e-7850-af1c-f1e9f438f820" xlink:to="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_019d8730-d7db-7e3d-b65f-469c42dd90c0" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_OperatingLeaseRightOfUseLiabilityPeriodicReduction_019d8730-d7db-76b0-a5e0-ac4de91ac00e" xlink:href="ades-20260331.xsd#ades_OperatingLeaseRightOfUseLiabilityPeriodicReduction"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems_019cd8ad-143e-7850-af1c-f1e9f438f820" xlink:to="loc_ades_OperatingLeaseRightOfUseLiabilityPeriodicReduction_019d8730-d7db-76b0-a5e0-ac4de91ac00e" xlink:type="arc" order="6"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/CommitmentsandContingenciesDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#CommitmentsandContingenciesDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/CommitmentsandContingenciesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsLineItems_019cd8ad-14e3-7106-955e-879b99243ec1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsTable_019cd8ad-143e-77ef-bbac-5ab14ae995c2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_OtherCommitmentsLineItems_019cd8ad-14e3-7106-955e-879b99243ec1" xlink:to="loc_us-gaap_OtherCommitmentsTable_019cd8ad-143e-77ef-bbac-5ab14ae995c2" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis_019cd8ad-143e-7b6c-adcb-69cf52991c6d" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CounterpartyNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_OtherCommitmentsTable_019cd8ad-143e-77ef-bbac-5ab14ae995c2" xlink:to="loc_srt_CounterpartyNameAxis_019cd8ad-143e-7b6c-adcb-69cf52991c6d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain_019cd8ad-143e-7b6c-adcb-69cf52991c6d_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_CounterpartyNameAxis_019cd8ad-143e-7b6c-adcb-69cf52991c6d" xlink:to="loc_srt_RepurchaseAgreementCounterpartyNameDomain_019cd8ad-143e-7b6c-adcb-69cf52991c6d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain_019cd8ad-143e-7ee7-b18f-7d3b6f77b607" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_CounterpartyNameAxis_019cd8ad-143e-7b6c-adcb-69cf52991c6d" xlink:to="loc_srt_RepurchaseAgreementCounterpartyNameDomain_019cd8ad-143e-7ee7-b18f-7d3b6f77b607" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_FiveForksMineMember_019cd8ad-143e-784c-9c24-c71ca8084aae" xlink:href="ades-20260331.xsd#ades_FiveForksMineMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain_019cd8ad-143e-7ee7-b18f-7d3b6f77b607" xlink:to="loc_ades_FiveForksMineMember_019cd8ad-143e-784c-9c24-c71ca8084aae" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_CorbinFacilitiesMember_019cd8ad-143e-7856-b462-717a37562800" xlink:href="ades-20260331.xsd#ades_CorbinFacilitiesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain_019cd8ad-143e-7ee7-b18f-7d3b6f77b607" xlink:to="loc_ades_CorbinFacilitiesMember_019cd8ad-143e-7856-b462-717a37562800" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_WestVirginiaMine4Member_019cd8ad-143e-7ecf-ab31-f7ca48939413" xlink:href="ades-20260331.xsd#ades_WestVirginiaMine4Member"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain_019cd8ad-143e-7ee7-b18f-7d3b6f77b607" xlink:to="loc_ades_WestVirginiaMine4Member_019cd8ad-143e-7ecf-ab31-f7ca48939413" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis_019cd8ad-143e-7c43-8525-73b30244b01f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_OtherCommitmentsTable_019cd8ad-143e-77ef-bbac-5ab14ae995c2" xlink:to="loc_us-gaap_RelatedPartyTransactionAxis_019cd8ad-143e-7c43-8525-73b30244b01f" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain_019cd8ad-143e-7c43-8525-73b30244b01f_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis_019cd8ad-143e-7c43-8525-73b30244b01f" xlink:to="loc_us-gaap_RelatedPartyTransactionDomain_019cd8ad-143e-7c43-8525-73b30244b01f_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain_019cd8ad-14e3-7b94-b224-453462bcf4e3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis_019cd8ad-143e-7c43-8525-73b30244b01f" xlink:to="loc_us-gaap_RelatedPartyTransactionDomain_019cd8ad-14e3-7b94-b224-453462bcf4e3" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TinuumGroupLLCMember_019cd8ad-14e3-7f4f-9641-f90c53e406ce" xlink:href="ades-20260331.xsd#ades_TinuumGroupLLCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain_019cd8ad-14e3-7b94-b224-453462bcf4e3" xlink:to="loc_ades_TinuumGroupLLCMember_019cd8ad-14e3-7f4f-9641-f90c53e406ce" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-71ab-8591-a4bbc0dff35e" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_OtherCommitmentsTable_019cd8ad-143e-77ef-bbac-5ab14ae995c2" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-71ab-8591-a4bbc0dff35e" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-71ab-8591-a4bbc0dff35e_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-71ab-8591-a4bbc0dff35e" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-71ab-8591-a4bbc0dff35e_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-754f-8dac-00943148ed17" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-71ab-8591-a4bbc0dff35e" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-754f-8dac-00943148ed17" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TinuumGroupLLCMember_019cd8ad-14e3-7356-86aa-9347923cd802" xlink:href="ades-20260331.xsd#ades_TinuumGroupLLCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-754f-8dac-00943148ed17" xlink:to="loc_ades_TinuumGroupLLCMember_019cd8ad-14e3-7356-86aa-9347923cd802" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_SuretyAgreementBondAmount_019cd8ad-14e3-7dac-b378-1093bc8c3027" xlink:href="ades-20260331.xsd#ades_SuretyAgreementBondAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherCommitmentsLineItems_019cd8ad-14e3-7106-955e-879b99243ec1" xlink:to="loc_ades_SuretyAgreementBondAmount_019cd8ad-14e3-7dac-b378-1093bc8c3027" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashNoncurrent_019cd8ad-14e3-7e00-8a28-0f817c2e7cd9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherCommitmentsLineItems_019cd8ad-14e3-7106-955e-879b99243ec1" xlink:to="loc_us-gaap_RestrictedCashNoncurrent_019cd8ad-14e3-7e00-8a28-0f817c2e7cd9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_SupplyAgreementPerformanceBond_019cd8ad-14e3-72c7-b3f9-91cebdfc56ed" xlink:href="ades-20260331.xsd#ades_SupplyAgreementPerformanceBond"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherCommitmentsLineItems_019cd8ad-14e3-7106-955e-879b99243ec1" xlink:to="loc_ades_SupplyAgreementPerformanceBond_019cd8ad-14e3-72c7-b3f9-91cebdfc56ed" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_SupplyAgreementPerformanceBondOutstandingAmount_019d8733-1b4a-7429-9828-605259db15d0" xlink:href="ades-20260331.xsd#ades_SupplyAgreementPerformanceBondOutstandingAmount"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherCommitmentsLineItems_019cd8ad-14e3-7106-955e-879b99243ec1" xlink:to="loc_ades_SupplyAgreementPerformanceBondOutstandingAmount_019d8733-1b4a-7429-9828-605259db15d0" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_LimitedGuarantees.Percent_019cd8ad-14e3-7e54-9823-9d7d71a01634" xlink:href="ades-20260331.xsd#ades_LimitedGuarantees.Percent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherCommitmentsLineItems_019cd8ad-14e3-7106-955e-879b99243ec1" xlink:to="loc_ades_LimitedGuarantees.Percent_019cd8ad-14e3-7e54-9823-9d7d71a01634" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/SupplementalFinancialInformationScheduleofOtherLongTermAssetsDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#SupplementalFinancialInformationScheduleofOtherLongTermAssetsDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/SupplementalFinancialInformationScheduleofOtherLongTermAssetsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-14e3-75db-a37b-f1566ad4d107" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable_019cd8ad-14e3-750a-9c67-b0d0d70d0bd6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-14e3-75db-a37b-f1566ad4d107" xlink:to="loc_us-gaap_DebtInstrumentTable_019cd8ad-14e3-750a-9c67-b0d0d70d0bd6" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis_019cd8ad-14e3-7f8a-8975-96c49d98a070" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-14e3-750a-9c67-b0d0d70d0bd6" xlink:to="loc_us-gaap_CreditFacilityAxis_019cd8ad-14e3-7f8a-8975-96c49d98a070" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain_019cd8ad-14e3-7f8a-8975-96c49d98a070_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_CreditFacilityAxis_019cd8ad-14e3-7f8a-8975-96c49d98a070" xlink:to="loc_us-gaap_CreditFacilityDomain_019cd8ad-14e3-7f8a-8975-96c49d98a070_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain_019cd8ad-14e3-7ecd-9a02-56b58c0226f9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_CreditFacilityAxis_019cd8ad-14e3-7f8a-8975-96c49d98a070" xlink:to="loc_us-gaap_CreditFacilityDomain_019cd8ad-14e3-7ecd-9a02-56b58c0226f9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember_019cd8ad-14e3-7dde-86c7-0ebfe63cb4e8" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_CreditFacilityDomain_019cd8ad-14e3-7ecd-9a02-56b58c0226f9" xlink:to="loc_us-gaap_RevolvingCreditFacilityMember_019cd8ad-14e3-7dde-86c7-0ebfe63cb4e8" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis_019cd8ad-14e3-736f-8c6e-8a5b276355ce" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_DebtInstrumentTable_019cd8ad-14e3-750a-9c67-b0d0d70d0bd6" xlink:to="loc_us-gaap_LongtermDebtTypeAxis_019cd8ad-14e3-736f-8c6e-8a5b276355ce" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-14e3-736f-8c6e-8a5b276355ce_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_019cd8ad-14e3-736f-8c6e-8a5b276355ce" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-14e3-736f-8c6e-8a5b276355ce_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-14e3-7e6a-8fad-57ccdf3e17dd" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_LongtermDebtTypeAxis_019cd8ad-14e3-736f-8c6e-8a5b276355ce" xlink:to="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-14e3-7e6a-8fad-57ccdf3e17dd" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember_019cd8ad-14e3-7e49-97cf-c09334ed7f32" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredDebtMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LongtermDebtTypeDomain_019cd8ad-14e3-7e6a-8fad-57ccdf3e17dd" xlink:to="loc_us-gaap_SecuredDebtMember_019cd8ad-14e3-7e49-97cf-c09334ed7f32" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_019cd8ad-14e3-79bc-840b-3c85531faf2b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-14e3-75db-a37b-f1566ad4d107" xlink:to="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_019cd8ad-14e3-79bc-840b-3c85531faf2b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseCurrent_019cd8ad-14e3-777c-b771-e54aca77ae09" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidExpenseCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_019cd8ad-14e3-79bc-840b-3c85531faf2b" xlink:to="loc_us-gaap_PrepaidExpenseCurrent_019cd8ad-14e3-777c-b771-e54aca77ae09" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_PrepaidLenderFeesCurrent_019cd8ad-14e3-7403-bc48-4a250803b3d0" xlink:href="ades-20260331.xsd#ades_PrepaidLenderFeesCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_019cd8ad-14e3-79bc-840b-3c85531faf2b" xlink:to="loc_ades_PrepaidLenderFeesCurrent_019cd8ad-14e3-7403-bc48-4a250803b3d0" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidTaxes_019cd8ad-14e3-7fb1-94ce-f741d95b0d71" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidTaxes"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_019cd8ad-14e3-79bc-840b-3c85531faf2b" xlink:to="loc_us-gaap_PrepaidTaxes_019cd8ad-14e3-7fb1-94ce-f741d95b0d71" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsCurrent_019cd8ad-14e3-730f-a80e-bbc31f8f06ca" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_019cd8ad-14e3-79bc-840b-3c85531faf2b" xlink:to="loc_us-gaap_OtherAssetsCurrent_019cd8ad-14e3-730f-a80e-bbc31f8f06ca" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019cd8ad-14e3-7049-be9f-245e40da3f2d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_019cd8ad-14e3-79bc-840b-3c85531faf2b" xlink:to="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019cd8ad-14e3-7049-be9f-245e40da3f2d" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsNoncurrentAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_DebtInstrumentLineItems_019cd8ad-14e3-75db-a37b-f1566ad4d107" xlink:to="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInventoriesSpareParts_019cd8ad-14e3-7145-a371-1f4e07728884" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInventoriesSpareParts"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_us-gaap_OtherInventoriesSpareParts_019cd8ad-14e3-7145-a371-1f4e07728884" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_MineDevelopmentCost_019cd8ad-14e3-7e33-99e8-559b7ba9c307" xlink:href="ades-20260331.xsd#ades_MineDevelopmentCost"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_ades_MineDevelopmentCost_019cd8ad-14e3-7e33-99e8-559b7ba9c307" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset_019cd8ad-14e3-762f-a902-ea85aa53f0c6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_us-gaap_OperatingLeaseRightOfUseAsset_019cd8ad-14e3-762f-a902-ea85aa53f0c6" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_UpfrontPaymentsFromContractWithCustomer_019cd8ad-14e3-72ad-95aa-83dcb4845aa4" xlink:href="ades-20260331.xsd#ades_UpfrontPaymentsFromContractWithCustomer"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_ades_UpfrontPaymentsFromContractWithCustomer_019cd8ad-14e3-72ad-95aa-83dcb4845aa4" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_MineReclamationAsset_019cd8ad-14e3-7e9d-8c61-11d936050818" xlink:href="ades-20260331.xsd#ades_MineReclamationAsset"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_ades_MineReclamationAsset_019cd8ad-14e3-7e9d-8c61-11d936050818" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill_019cd8ad-14e3-70e2-9bb6-7e229762512e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill_019cd8ad-14e3-70e2-9bb6-7e229762512e" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_OtherAssetsNoncurrentOther_019cd8ad-14e3-7e34-8cb4-985f3b0c1b13" xlink:href="ades-20260331.xsd#ades_OtherAssetsNoncurrentOther"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_ades_OtherAssetsNoncurrentOther_019cd8ad-14e3-7e34-8cb4-985f3b0c1b13" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_019d331c-3562-7e1f-a36d-dca04d3bcab1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_019d331c-3562-7e1f-a36d-dca04d3bcab1" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent_019cd8ad-14e3-7baa-8bd9-4ba9175db075" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_us-gaap_OtherAssetsNoncurrent_019cd8ad-14e3-7baa-8bd9-4ba9175db075" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm_019cd8ad-14e3-745a-8630-9e590dc81ffa" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_us-gaap_DebtInstrumentTerm_019cd8ad-14e3-745a-8630-9e590dc81ffa" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_ContractWithCustomerTermOfContract_019cd8ad-14e3-7c16-bb31-c3c267095371" xlink:href="ades-20260331.xsd#ades_ContractWithCustomerTermOfContract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract_019cd8ad-14e3-7d2b-b02a-6d6bf8a94651" xlink:to="loc_ades_ContractWithCustomerTermOfContract_019cd8ad-14e3-7c16-bb31-c3c267095371" xlink:type="arc" order="11"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/SupplementalFinancialInformationNarrativeDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#SupplementalFinancialInformationNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/SupplementalFinancialInformationNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems_019cd8ad-14e3-731d-8a5d-8686d9593d04" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019cd8ad-14e3-75f5-83ee-7cc5127e4a06" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_019cd8ad-14e3-731d-8a5d-8686d9593d04" xlink:to="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019cd8ad-14e3-75f5-83ee-7cc5127e4a06" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-7cd3-9bef-4e3af2e8ebc2" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019cd8ad-14e3-75f5-83ee-7cc5127e4a06" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-7cd3-9bef-4e3af2e8ebc2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-7cd3-9bef-4e3af2e8ebc2_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-7cd3-9bef-4e3af2e8ebc2" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-7cd3-9bef-4e3af2e8ebc2_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-7984-ba7d-c338ff7e9782" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-7cd3-9bef-4e3af2e8ebc2" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-7984-ba7d-c338ff7e9782" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_HighviewEnterprisesLimitedMember_019cd8ad-14e3-7209-b2c5-42ff003b9c5b" xlink:href="ades-20260331.xsd#ades_HighviewEnterprisesLimitedMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-7984-ba7d-c338ff7e9782" xlink:to="loc_ades_HighviewEnterprisesLimitedMember_019cd8ad-14e3-7209-b2c5-42ff003b9c5b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TinuumGroupLLCMember_019cd8ad-14e3-7166-aa4f-d0d76f5a0f4f" xlink:href="ades-20260331.xsd#ades_TinuumGroupLLCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-7984-ba7d-c338ff7e9782" xlink:to="loc_ades_TinuumGroupLLCMember_019cd8ad-14e3-7166-aa4f-d0d76f5a0f4f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis_019cd8ad-14e3-74c1-9e2f-7adab73204ec" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019cd8ad-14e3-75f5-83ee-7cc5127e4a06" xlink:to="loc_us-gaap_IncomeStatementLocationAxis_019cd8ad-14e3-74c1-9e2f-7adab73204ec" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-14e3-74c1-9e2f-7adab73204ec_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_IncomeStatementLocationAxis_019cd8ad-14e3-74c1-9e2f-7adab73204ec" xlink:to="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-14e3-74c1-9e2f-7adab73204ec_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-14e3-7745-aea4-04c77bd49e09" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_IncomeStatementLocationAxis_019cd8ad-14e3-74c1-9e2f-7adab73204ec" xlink:to="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-14e3-7745-aea4-04c77bd49e09" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfSalesMember_019cd8ad-14e3-73f8-906e-5f893dfdae1e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfSalesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_IncomeStatementLocationDomain_019cd8ad-14e3-7745-aea4-04c77bd49e09" xlink:to="loc_us-gaap_CostOfSalesMember_019cd8ad-14e3-73f8-906e-5f893dfdae1e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments_019cd8ad-14e3-7a2d-a503-40d423a1697b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_019cd8ad-14e3-731d-8a5d-8686d9593d04" xlink:to="loc_us-gaap_EquityMethodInvestments_019cd8ad-14e3-7a2d-a503-40d423a1697b" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage_019cd8ad-14e3-73eb-b751-ad03bcddf728" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_019cd8ad-14e3-731d-8a5d-8686d9593d04" xlink:to="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage_019cd8ad-14e3-73eb-b751-ad03bcddf728" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments_019cd8ad-14e3-7279-a7f2-ec6cff0dfbbc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems_019cd8ad-14e3-731d-8a5d-8686d9593d04" xlink:to="loc_us-gaap_IncomeLossFromEquityMethodInvestments_019cd8ad-14e3-7279-a7f2-ec6cff0dfbbc" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/SupplementalFinancialInformationScheduleofOtherLiabilitiesDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#SupplementalFinancialInformationScheduleofOtherLiabilitiesDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/SupplementalFinancialInformationScheduleofOtherLiabilitiesDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems_019cd8ad-14e3-7087-9230-43618d02a9cf" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_019cd8ad-14e3-7af8-a371-ca50f95b3dd9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems_019cd8ad-14e3-7087-9230-43618d02a9cf" xlink:to="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_019cd8ad-14e3-7af8-a371-ca50f95b3dd9" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-7bba-a7de-c23b68fadd4d" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_019cd8ad-14e3-7af8-a371-ca50f95b3dd9" xlink:to="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-7bba-a7de-c23b68fadd4d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-7bba-a7de-c23b68fadd4d_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-7bba-a7de-c23b68fadd4d" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-7bba-a7de-c23b68fadd4d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-78af-b36f-4e2e4e8073bf" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019cd8ad-14e3-7bba-a7de-c23b68fadd4d" xlink:to="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-78af-b36f-4e2e4e8073bf" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TinuumGroupLLCMember_019cd8ad-14e3-7265-9629-61b863dc91d6" xlink:href="ades-20260331.xsd#ades_TinuumGroupLLCMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_EquityMethodInvesteeNameDomain_019cd8ad-14e3-78af-b36f-4e2e4e8073bf" xlink:to="loc_ades_TinuumGroupLLCMember_019cd8ad-14e3-7265-9629-61b863dc91d6" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrentAbstract_019cd8ad-14e3-747b-99e2-8a24fad9373d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesCurrentAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems_019cd8ad-14e3-7087-9230-43618d02a9cf" xlink:to="loc_us-gaap_OtherLiabilitiesCurrentAbstract_019cd8ad-14e3-747b-99e2-8a24fad9373d" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrent_019cd8ad-14e3-7639-807d-42da844510c9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherLiabilitiesCurrentAbstract_019cd8ad-14e3-747b-99e2-8a24fad9373d" xlink:to="loc_us-gaap_OperatingLeaseLiabilityCurrent_019cd8ad-14e3-7639-807d-42da844510c9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetRetirementObligationCurrent_019cd8ad-14e3-7937-a13a-2ec76eacec69" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetRetirementObligationCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherLiabilitiesCurrentAbstract_019cd8ad-14e3-747b-99e2-8a24fad9373d" xlink:to="loc_us-gaap_AssetRetirementObligationCurrent_019cd8ad-14e3-7937-a13a-2ec76eacec69" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxesPayableCurrent_019cd8ad-14e3-77a0-b468-e728e900983b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TaxesPayableCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherLiabilitiesCurrentAbstract_019cd8ad-14e3-747b-99e2-8a24fad9373d" xlink:to="loc_us-gaap_TaxesPayableCurrent_019cd8ad-14e3-77a0-b468-e728e900983b" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_OtherLiabilitiesCurrentOther_019cd8ad-14e3-737d-87ed-0a7c90768849" xlink:href="ades-20260331.xsd#ades_OtherLiabilitiesCurrentOther"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherLiabilitiesCurrentAbstract_019cd8ad-14e3-747b-99e2-8a24fad9373d" xlink:to="loc_ades_OtherLiabilitiesCurrentOther_019cd8ad-14e3-737d-87ed-0a7c90768849" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent_019cd8ad-14e3-7151-acde-e8ec5f90cc40" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherLiabilitiesCurrentAbstract_019cd8ad-14e3-747b-99e2-8a24fad9373d" xlink:to="loc_us-gaap_OtherLiabilitiesCurrent_019cd8ad-14e3-7151-acde-e8ec5f90cc40" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrentAbstract_019cd8ad-14e3-7aeb-93b3-f43d07c90881" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesNoncurrentAbstract"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems_019cd8ad-14e3-7087-9230-43618d02a9cf" xlink:to="loc_us-gaap_OtherLiabilitiesNoncurrentAbstract_019cd8ad-14e3-7aeb-93b3-f43d07c90881" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MineReclamationAndClosingLiabilityNoncurrent_019cd8ad-14e3-7b9c-b5f0-45d94aff9857" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MineReclamationAndClosingLiabilityNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrentAbstract_019cd8ad-14e3-7aeb-93b3-f43d07c90881" xlink:to="loc_us-gaap_MineReclamationAndClosingLiabilityNoncurrent_019cd8ad-14e3-7b9c-b5f0-45d94aff9857" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent_019cd8ad-14e3-7f3f-982b-0c63030ad74d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrentAbstract_019cd8ad-14e3-7aeb-93b3-f43d07c90881" xlink:to="loc_us-gaap_OperatingLeaseLiabilityNoncurrent_019cd8ad-14e3-7f3f-982b-0c63030ad74d" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_OtherLongTermLiabilities_019cd8ad-14e3-7848-bdff-10c6c126f56a" xlink:href="ades-20260331.xsd#ades_OtherLongTermLiabilities"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrentAbstract_019cd8ad-14e3-7aeb-93b3-f43d07c90881" xlink:to="loc_ades_OtherLongTermLiabilities_019cd8ad-14e3-7848-bdff-10c6c126f56a" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent_019cd8ad-14e3-73b1-9382-50ecf2105ddc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrentAbstract_019cd8ad-14e3-7aeb-93b3-f43d07c90881" xlink:to="loc_us-gaap_OtherLiabilitiesNoncurrent_019cd8ad-14e3-73b1-9382-50ecf2105ddc" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_019cd8ad-14e3-79e6-b0ae-02a0c4c632cd" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems_019cd8ad-14e3-7087-9230-43618d02a9cf" xlink:to="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_019cd8ad-14e3-79e6-b0ae-02a0c4c632cd" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_019cd8ad-14e3-7967-a6bb-33609c36a491" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems_019cd8ad-14e3-7087-9230-43618d02a9cf" xlink:to="loc_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_019cd8ad-14e3-7967-a6bb-33609c36a491" xlink:type="arc" order="3"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/StockholdersEquityDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#StockholdersEquityDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/StockholdersEquityDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems_019cd8ad-14e3-778a-998e-08b86374b07f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable_019cd8ad-14e3-7bb5-8628-5b4125a79f43" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ClassOfStockLineItems_019cd8ad-14e3-778a-998e-08b86374b07f" xlink:to="loc_us-gaap_ScheduleOfStockByClassTable_019cd8ad-14e3-7bb5-8628-5b4125a79f43" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_019cd8ad-14e3-7441-9aca-056862fb8ca8" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable_019cd8ad-14e3-7bb5-8628-5b4125a79f43" xlink:to="loc_srt_RangeAxis_019cd8ad-14e3-7441-9aca-056862fb8ca8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_019cd8ad-14e3-7441-9aca-056862fb8ca8_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_019cd8ad-14e3-7441-9aca-056862fb8ca8" xlink:to="loc_srt_RangeMember_019cd8ad-14e3-7441-9aca-056862fb8ca8_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_019cd8ad-14e3-75c9-bd50-85a0c85b37a8" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_019cd8ad-14e3-7441-9aca-056862fb8ca8" xlink:to="loc_srt_RangeMember_019cd8ad-14e3-75c9-bd50-85a0c85b37a8" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_019cd8ad-14e3-7996-9218-9a124fd81bbb" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_019cd8ad-14e3-75c9-bd50-85a0c85b37a8" xlink:to="loc_srt_MaximumMember_019cd8ad-14e3-7996-9218-9a124fd81bbb" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_RequirementToOwnSharesOutstandingAsPercent_019cd8ad-14e3-7361-95d6-84b581eeca65" xlink:href="ades-20260331.xsd#ades_RequirementToOwnSharesOutstandingAsPercent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ClassOfStockLineItems_019cd8ad-14e3-778a-998e-08b86374b07f" xlink:to="loc_ades_RequirementToOwnSharesOutstandingAsPercent_019cd8ad-14e3-7361-95d6-84b581eeca65" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofAllocationofCompensationExpenseDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#StockBasedCompensationScheduleofAllocationofCompensationExpenseDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofAllocationofCompensationExpenseDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-717a-8cd6-e7c5b01bee7c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7665-8f51-954f12390046" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-717a-8cd6-e7c5b01bee7c" xlink:to="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7665-8f51-954f12390046" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7250-a984-88c2dacfb523" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7665-8f51-954f12390046" xlink:to="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7250-a984-88c2dacfb523" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7250-a984-88c2dacfb523_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7250-a984-88c2dacfb523" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7250-a984-88c2dacfb523_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7129-baa9-944264046472" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7250-a984-88c2dacfb523" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7129-baa9-944264046472" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember_019cd8ad-14e3-7f2b-b33d-bf6bf0b03c2f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7129-baa9-944264046472" xlink:to="loc_us-gaap_RestrictedStockMember_019cd8ad-14e3-7f2b-b33d-bf6bf0b03c2f" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformanceSharesMember_019cd8ad-14e3-7f92-ac12-de149bcd10c2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PerformanceSharesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7129-baa9-944264046472" xlink:to="loc_us-gaap_PerformanceSharesMember_019cd8ad-14e3-7f92-ac12-de149bcd10c2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember_019cd8ad-14e3-74fa-9061-a7457548c013" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7129-baa9-944264046472" xlink:to="loc_us-gaap_EmployeeStockOptionMember_019cd8ad-14e3-74fa-9061-a7457548c013" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense_019cd8ad-14e3-74d5-8921-ba5bc418f7fa" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-717a-8cd6-e7c5b01bee7c" xlink:to="loc_us-gaap_AllocatedShareBasedCompensationExpense_019cd8ad-14e3-74d5-8921-ba5bc418f7fa" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofUnrecognizedCompensationCostDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#StockBasedCompensationScheduleofUnrecognizedCompensationCostDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofUnrecognizedCompensationCostDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b2f-9a85-03d2711b275d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7c7d-806a-0daa104c6ccc" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b2f-9a85-03d2711b275d" xlink:to="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7c7d-806a-0daa104c6ccc" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-71d9-a48d-ba8b40e4375f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7c7d-806a-0daa104c6ccc" xlink:to="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-71d9-a48d-ba8b40e4375f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-71d9-a48d-ba8b40e4375f_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-71d9-a48d-ba8b40e4375f" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-71d9-a48d-ba8b40e4375f_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7e59-afa4-8bfe5f77f142" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-71d9-a48d-ba8b40e4375f" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7e59-afa4-8bfe5f77f142" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember_019cd8ad-14e3-72ea-9d00-d6eb90133e03" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7e59-afa4-8bfe5f77f142" xlink:to="loc_us-gaap_RestrictedStockMember_019cd8ad-14e3-72ea-9d00-d6eb90133e03" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformanceSharesMember_019cd8ad-14e3-7cde-8277-b35cd05b344c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PerformanceSharesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7e59-afa4-8bfe5f77f142" xlink:to="loc_us-gaap_PerformanceSharesMember_019cd8ad-14e3-7cde-8277-b35cd05b344c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember_019cd8ad-14e3-75c9-be11-4471227082ad" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7e59-afa4-8bfe5f77f142" xlink:to="loc_us-gaap_EmployeeStockOptionMember_019cd8ad-14e3-75c9-be11-4471227082ad" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_019cd8ad-14e3-7a87-820b-22ca93bcf5a3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b2f-9a85-03d2711b275d" xlink:to="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_019cd8ad-14e3-7a87-820b-22ca93bcf5a3" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_019cd8ad-14e3-7b9e-854d-10b2ef196114" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b2f-9a85-03d2711b275d" xlink:to="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_019cd8ad-14e3-7b9e-854d-10b2ef196114" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/StockBasedCompensationNarrativeDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#StockBasedCompensationNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/StockBasedCompensationNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-724a-b6bf-d04f2d83d033" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7a24-991e-30e72c73e69b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-724a-b6bf-d04f2d83d033" xlink:to="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7a24-991e-30e72c73e69b" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7a70-bfc9-58ed9bad439a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7a24-991e-30e72c73e69b" xlink:to="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7a70-bfc9-58ed9bad439a" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7a70-bfc9-58ed9bad439a_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7a70-bfc9-58ed9bad439a" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7a70-bfc9-58ed9bad439a_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7d20-bc08-b1e6f1906777" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7a70-bfc9-58ed9bad439a" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7d20-bc08-b1e6f1906777" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember_019cd8ad-14e3-74df-9c09-15b5ed39af3e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7d20-bc08-b1e6f1906777" xlink:to="loc_us-gaap_RestrictedStockMember_019cd8ad-14e3-74df-9c09-15b5ed39af3e" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformanceSharesMember_019cd8ad-14e3-775d-8d87-5ae7da421a24" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PerformanceSharesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7d20-bc08-b1e6f1906777" xlink:to="loc_us-gaap_PerformanceSharesMember_019cd8ad-14e3-775d-8d87-5ae7da421a24" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember_019cd8ad-14e3-7599-8366-f6a729f9467b" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7d20-bc08-b1e6f1906777" xlink:to="loc_us-gaap_EmployeeStockOptionMember_019cd8ad-14e3-7599-8366-f6a729f9467b" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_019cd8ad-14e3-7c46-970e-18a22b428789" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7a24-991e-30e72c73e69b" xlink:to="loc_srt_RangeAxis_019cd8ad-14e3-7c46-970e-18a22b428789" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_019cd8ad-14e3-7c46-970e-18a22b428789_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_019cd8ad-14e3-7c46-970e-18a22b428789" xlink:to="loc_srt_RangeMember_019cd8ad-14e3-7c46-970e-18a22b428789_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_019cd8ad-14e3-7d63-a636-909cffe4fb5f" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_019cd8ad-14e3-7c46-970e-18a22b428789" xlink:to="loc_srt_RangeMember_019cd8ad-14e3-7d63-a636-909cffe4fb5f" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_019cd8ad-14e3-79de-a775-8a811a345788" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_019cd8ad-14e3-7d63-a636-909cffe4fb5f" xlink:to="loc_srt_MaximumMember_019cd8ad-14e3-79de-a775-8a811a345788" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_019cd8ad-14e3-72ad-98c6-9b68ba6490c7" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-724a-b6bf-d04f2d83d033" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_019cd8ad-14e3-72ad-98c6-9b68ba6490c7" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_019cd8ad-14e3-7577-aed0-f9d7eb8b3c05" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-724a-b6bf-d04f2d83d033" xlink:to="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_019cd8ad-14e3-7577-aed0-f9d7eb8b3c05" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_019cd8ad-14e3-78c9-aa6c-a0f01d962d72" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-724a-b6bf-d04f2d83d033" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_019cd8ad-14e3-78c9-aa6c-a0f01d962d72" xlink:type="arc" order="2"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofRestrictedStockActivityDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#StockBasedCompensationScheduleofRestrictedStockActivityDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofRestrictedStockActivityDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b76-b129-583a1d567216" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7b97-83bb-1bba8784156a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b76-b129-583a1d567216" xlink:to="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7b97-83bb-1bba8784156a" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-721a-9c7d-abb565b26172" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-7b97-83bb-1bba8784156a" xlink:to="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-721a-9c7d-abb565b26172" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-721a-9c7d-abb565b26172_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-721a-9c7d-abb565b26172" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-721a-9c7d-abb565b26172_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-74f5-a232-9ef95a5a1917" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-721a-9c7d-abb565b26172" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-74f5-a232-9ef95a5a1917" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember_019cd8ad-14e3-7d3a-964f-c172fff18d06" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-74f5-a232-9ef95a5a1917" xlink:to="loc_us-gaap_RestrictedStockMember_019cd8ad-14e3-7d3a-964f-c172fff18d06" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7379-ac8c-2eca9b64630a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b76-b129-583a1d567216" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7379-ac8c-2eca9b64630a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019cd8ad-14e3-74cb-a113-cfce7e0ade60" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7379-ac8c-2eca9b64630a" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019cd8ad-14e3-74cb-a113-cfce7e0ade60" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_019cd8ad-14e3-704e-8581-ffde5cd3b3df" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7379-ac8c-2eca9b64630a" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_019cd8ad-14e3-704e-8581-ffde5cd3b3df" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_019cd8ad-14e3-7163-ab42-9b200faa1442" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7379-ac8c-2eca9b64630a" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_019cd8ad-14e3-7163-ab42-9b200faa1442" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_019cd8ad-14e3-71bf-9b94-b77527a8ad86" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7379-ac8c-2eca9b64630a" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_019cd8ad-14e3-71bf-9b94-b77527a8ad86" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019cd8ad-14e3-7ef2-b019-cbc85d699078" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-762c-9290-b719f9d09da9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b76-b129-583a1d567216" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-762c-9290-b719f9d09da9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019cd8ad-14e3-783f-8296-edf402baba57" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-762c-9290-b719f9d09da9" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019cd8ad-14e3-783f-8296-edf402baba57" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_019cd8ad-14e3-71de-bb30-e9359ac17032" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-762c-9290-b719f9d09da9" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_019cd8ad-14e3-71de-bb30-e9359ac17032" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_019cd8ad-14e3-7f24-ab34-7aa13a42c9c3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-762c-9290-b719f9d09da9" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_019cd8ad-14e3-7f24-ab34-7aa13a42c9c3" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_019cd8ad-14e3-7bbd-8854-a09a27f2d83d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-762c-9290-b719f9d09da9" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_019cd8ad-14e3-7bbd-8854-a09a27f2d83d" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019cd8ad-14e3-7580-8d9e-f7fa85eb7736" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofPerformanceSharesUnitsDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#StockBasedCompensationScheduleofPerformanceSharesUnitsDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofPerformanceSharesUnitsDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b39-b635-b341892dbb59" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-78ab-9a89-817849e8eefd" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b39-b635-b341892dbb59" xlink:to="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-78ab-9a89-817849e8eefd" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7428-b7b0-ca25abffd66d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-78ab-9a89-817849e8eefd" xlink:to="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7428-b7b0-ca25abffd66d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7428-b7b0-ca25abffd66d_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7428-b7b0-ca25abffd66d" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7428-b7b0-ca25abffd66d_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-71f1-9f8e-76130bbb5a45" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-7428-b7b0-ca25abffd66d" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-71f1-9f8e-76130bbb5a45" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformanceSharesMember_019cd8ad-14e3-7651-b9c1-49f4618ec43a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PerformanceSharesMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-71f1-9f8e-76130bbb5a45" xlink:to="loc_us-gaap_PerformanceSharesMember_019cd8ad-14e3-7651-b9c1-49f4618ec43a" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventAxis_019cd8ad-14e3-7218-90a3-b6bfbf0263e4" xlink:href="ades-20260331.xsd#ades_TriggeringEventAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-78ab-9a89-817849e8eefd" xlink:to="loc_ades_TriggeringEventAxis_019cd8ad-14e3-7218-90a3-b6bfbf0263e4" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7218-90a3-b6bfbf0263e4_default" xlink:href="ades-20260331.xsd#ades_TriggeringEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_ades_TriggeringEventAxis_019cd8ad-14e3-7218-90a3-b6bfbf0263e4" xlink:to="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7218-90a3-b6bfbf0263e4_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7139-adc4-8fe3e2951df7" xlink:href="ades-20260331.xsd#ades_TriggeringEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_ades_TriggeringEventAxis_019cd8ad-14e3-7218-90a3-b6bfbf0263e4" xlink:to="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7139-adc4-8fe3e2951df7" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_IssuedUponVestingOfPSUsMember_019cd8ad-14e3-7761-8a1d-6e01ec610c5d" xlink:href="ades-20260331.xsd#ades_IssuedUponVestingOfPSUsMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7139-adc4-8fe3e2951df7" xlink:to="loc_ades_IssuedUponVestingOfPSUsMember_019cd8ad-14e3-7761-8a1d-6e01ec610c5d" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis_019cd8ad-14e3-706d-91f8-717f352e1398" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-78ab-9a89-817849e8eefd" xlink:to="loc_srt_RangeAxis_019cd8ad-14e3-706d-91f8-717f352e1398" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_019cd8ad-14e3-706d-91f8-717f352e1398_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_RangeAxis_019cd8ad-14e3-706d-91f8-717f352e1398" xlink:to="loc_srt_RangeMember_019cd8ad-14e3-706d-91f8-717f352e1398_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember_019cd8ad-14e3-722d-b18c-55af0e44e9f9" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_RangeAxis_019cd8ad-14e3-706d-91f8-717f352e1398" xlink:to="loc_srt_RangeMember_019cd8ad-14e3-722d-b18c-55af0e44e9f9" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember_019cd8ad-14e3-7574-a36a-8a513a195a10" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_019cd8ad-14e3-722d-b18c-55af0e44e9f9" xlink:to="loc_srt_MinimumMember_019cd8ad-14e3-7574-a36a-8a513a195a10" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember_019cd8ad-14e3-7b66-aefb-57a781427751" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_RangeMember_019cd8ad-14e3-722d-b18c-55af0e44e9f9" xlink:to="loc_srt_MaximumMember_019cd8ad-14e3-7b66-aefb-57a781427751" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7099-94c8-3fc0aa9601df" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b39-b635-b341892dbb59" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7099-94c8-3fc0aa9601df" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019cd8ad-14e3-76b0-be64-6dc5ea5efc50" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7099-94c8-3fc0aa9601df" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019cd8ad-14e3-76b0-be64-6dc5ea5efc50" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_019cd8ad-14e3-741d-b119-093af04133b3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7099-94c8-3fc0aa9601df" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_019cd8ad-14e3-741d-b119-093af04133b3" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_019cd8ad-14e3-7924-8647-d41825bb296a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7099-94c8-3fc0aa9601df" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_019cd8ad-14e3-7924-8647-d41825bb296a" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_019cd8ad-14e3-7dab-8a62-082d8ecafd2a" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019cd8ad-14e3-7099-94c8-3fc0aa9601df" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_019cd8ad-14e3-7dab-8a62-082d8ecafd2a" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019cd8ad-14e3-70ef-baba-aa445e72384d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-773c-9dfe-1a27d1f5fdd0" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b39-b635-b341892dbb59" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-773c-9dfe-1a27d1f5fdd0" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019cd8ad-14e3-79ca-bf9a-85e34d88d18c" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-773c-9dfe-1a27d1f5fdd0" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019cd8ad-14e3-79ca-bf9a-85e34d88d18c" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_019cd8ad-14e3-7186-b419-eb7c0bec9c29" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-773c-9dfe-1a27d1f5fdd0" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_019cd8ad-14e3-7186-b419-eb7c0bec9c29" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_019cd8ad-14e3-7d07-8d69-404965053990" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-773c-9dfe-1a27d1f5fdd0" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_019cd8ad-14e3-7d07-8d69-404965053990" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_019cd8ad-14e3-7676-bd4e-a600bc780e51" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019cd8ad-14e3-773c-9dfe-1a27d1f5fdd0" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_019cd8ad-14e3-7676-bd4e-a600bc780e51" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019cd8ad-14e3-7bf2-b647-c506e0932e52" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding_019cd8ad-14e3-7bc0-b512-4c1303a75b80" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b39-b635-b341892dbb59" xlink:to="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding_019cd8ad-14e3-7bc0-b512-4c1303a75b80" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsOutstandingWeightedAverageRemainingContractualTerms_019cd8ad-14e3-7a27-900c-62fff209f9a1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsOutstandingWeightedAverageRemainingContractualTerms"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b39-b635-b341892dbb59" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsOutstandingWeightedAverageRemainingContractualTerms_019cd8ad-14e3-7a27-900c-62fff209f9a1" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_019cd8ad-14e3-76de-bd03-d4e13c6f6b92" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-7b39-b635-b341892dbb59" xlink:to="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_019cd8ad-14e3-76de-bd03-d4e13c6f6b92" xlink:type="arc" order="4"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofOptionActivityDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#StockBasedCompensationScheduleofOptionActivityDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/StockBasedCompensationScheduleofOptionActivityDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-731e-b8fe-215ba96c561d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-731e-b8fe-215ba96c561d" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-71cd-a797-55ba1f60d763" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019cd8ad-14e3-731e-b8fe-215ba96c561d" xlink:to="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-71cd-a797-55ba1f60d763" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-71cd-a797-55ba1f60d763_default" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-71cd-a797-55ba1f60d763" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-71cd-a797-55ba1f60d763_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7a52-8ade-18d18685c32e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_us-gaap_AwardTypeAxis_019cd8ad-14e3-71cd-a797-55ba1f60d763" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7a52-8ade-18d18685c32e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember_019cd8ad-14e3-7df9-bc2c-bde357dd96a5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019cd8ad-14e3-7a52-8ade-18d18685c32e" xlink:to="loc_us-gaap_EmployeeStockOptionMember_019cd8ad-14e3-7df9-bc2c-bde357dd96a5" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_019cd8ad-14e3-77b5-8e75-b55c531fe66f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_019cd8ad-14e3-77b5-8e75-b55c531fe66f" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_019cd8ad-14e3-7d55-80c2-c9bc0de6335d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_019cd8ad-14e3-77b5-8e75-b55c531fe66f" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_019cd8ad-14e3-7d55-80c2-c9bc0de6335d" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_019cd8ad-14e3-72c8-ba92-39afc0436e68" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_019cd8ad-14e3-77b5-8e75-b55c531fe66f" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_019cd8ad-14e3-72c8-ba92-39afc0436e68" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_019cd8ad-14e3-78ca-92b8-b31cb9814ec1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_019cd8ad-14e3-77b5-8e75-b55c531fe66f" xlink:to="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_019cd8ad-14e3-78ca-92b8-b31cb9814ec1" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod_019cd8ad-14e3-70b7-bfcf-04d41c3528da" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_019cd8ad-14e3-77b5-8e75-b55c531fe66f" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod_019cd8ad-14e3-70b7-bfcf-04d41c3528da" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_019cd8ad-14e3-738f-80c5-d5f4990c5f62" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_019cd8ad-14e3-7257-8546-724ea42df903" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_019cd8ad-14e3-7257-8546-724ea42df903" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_019cd8ad-14e3-78cc-aa2f-a5e50a6b1e81" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_019cd8ad-14e3-7257-8546-724ea42df903" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_019cd8ad-14e3-78cc-aa2f-a5e50a6b1e81" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_019cd8ad-14e3-78f1-a5e4-198ae7bb8d08" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_019cd8ad-14e3-7257-8546-724ea42df903" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_019cd8ad-14e3-78f1-a5e4-198ae7bb8d08" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_019cd8ad-14e3-7f87-9176-d0dd66738e73" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_019cd8ad-14e3-7257-8546-724ea42df903" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_019cd8ad-14e3-7f87-9176-d0dd66738e73" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice_019cd8ad-14e3-76c8-920a-5ec2857891f1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_019cd8ad-14e3-7257-8546-724ea42df903" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice_019cd8ad-14e3-76c8-920a-5ec2857891f1" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_019cd8ad-14e3-717d-86b4-46e762afb428" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_019cd8ad-14e3-70b9-ade5-c43a6ca60cd6" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_019cd8ad-14e3-70b9-ade5-c43a6ca60cd6" xlink:type="arc" order="2"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_019cd8ad-14e3-733c-a3f6-07b8041ed780" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_019cd8ad-14e3-733c-a3f6-07b8041ed780" xlink:type="arc" order="3"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_019cd8ad-14e3-7176-82fd-ee8d243475c1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_019cd8ad-14e3-7176-82fd-ee8d243475c1" xlink:type="arc" order="4"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_019cd8ad-14e3-7e41-ba02-c29852c92089" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_019cd8ad-14e3-7e41-ba02-c29852c92089" xlink:type="arc" order="5"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_019cd8ad-14e3-764c-9437-ab116e5410d5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_019cd8ad-14e3-764c-9437-ab116e5410d5" xlink:type="arc" order="6"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice_019cd8ad-14e3-7a50-be0d-3bc91d956dd9" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice_019cd8ad-14e3-7a50-be0d-3bc91d956dd9" xlink:type="arc" order="7"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_019cd8ad-14e3-7b45-8de5-c6217dd0bd82" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_019cd8ad-14e3-7b45-8de5-c6217dd0bd82" xlink:type="arc" order="8"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue_019cd8ad-14e3-71ee-a187-32c390804a79" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue_019cd8ad-14e3-71ee-a187-32c390804a79" xlink:type="arc" order="9"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1_019cd8ad-14e3-7ab6-91b2-2cd927b8568e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1_019cd8ad-14e3-7ab6-91b2-2cd927b8568e" xlink:type="arc" order="10"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_019cd8ad-14e3-74f4-8279-1fc07412ef0e" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019cd8ad-14e3-79dc-b305-4f86a0e3f171" xlink:to="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_019cd8ad-14e3-74f4-8279-1fc07412ef0e" xlink:type="arc" order="11"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/IncomeTaxesNarrativeDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#IncomeTaxesNarrativeDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/IncomeTaxesNarrativeDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventLineItems_019cd8ad-14e3-787f-86fa-ce26fe0a09ee" xlink:href="ades-20260331.xsd#ades_TriggeringEventLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventTable_019cd8ad-14e3-7727-bc65-39d1db34c039" xlink:href="ades-20260331.xsd#ades_TriggeringEventTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_ades_TriggeringEventLineItems_019cd8ad-14e3-787f-86fa-ce26fe0a09ee" xlink:to="loc_ades_TriggeringEventTable_019cd8ad-14e3-7727-bc65-39d1db34c039" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventAxis_019cd8ad-14e3-7f81-8e00-c605a52aa8bb" xlink:href="ades-20260331.xsd#ades_TriggeringEventAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_ades_TriggeringEventTable_019cd8ad-14e3-7727-bc65-39d1db34c039" xlink:to="loc_ades_TriggeringEventAxis_019cd8ad-14e3-7f81-8e00-c605a52aa8bb" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7f81-8e00-c605a52aa8bb_default" xlink:href="ades-20260331.xsd#ades_TriggeringEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_ades_TriggeringEventAxis_019cd8ad-14e3-7f81-8e00-c605a52aa8bb" xlink:to="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7f81-8e00-c605a52aa8bb_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7c00-8980-ecab6faee6eb" xlink:href="ades-20260331.xsd#ades_TriggeringEventDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_ades_TriggeringEventAxis_019cd8ad-14e3-7f81-8e00-c605a52aa8bb" xlink:to="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7c00-8980-ecab6faee6eb" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_ades_BeforeOutOfPeriodStateIncomeTaxExpenseMember_019cd8ad-14e3-720e-902c-0a31d0eafc31" xlink:href="ades-20260331.xsd#ades_BeforeOutOfPeriodStateIncomeTaxExpenseMember"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventDomain_019cd8ad-14e3-7c00-8980-ecab6faee6eb" xlink:to="loc_ades_BeforeOutOfPeriodStateIncomeTaxExpenseMember_019cd8ad-14e3-720e-902c-0a31d0eafc31" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit_019cd8ad-14e3-7b09-89f8-770722779029" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventLineItems_019cd8ad-14e3-787f-86fa-ce26fe0a09ee" xlink:to="loc_us-gaap_IncomeTaxExpenseBenefit_019cd8ad-14e3-7b09-89f8-770722779029" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations_019cd8ad-14e3-76a5-8e7e-bbd1bbc3492d" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_ades_TriggeringEventLineItems_019cd8ad-14e3-787f-86fa-ce26fe0a09ee" xlink:to="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations_019cd8ad-14e3-76a5-8e7e-bbd1bbc3492d" xlink:type="arc" order="1"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://www.advancedemissionssolutions.com/role/SegmentReportingScheduleofRevenuefromExternalCustomersAttributedbycountryDetails" xlink:type="simple" xlink:href="ades-20260331.xsd#SegmentReportingScheduleofRevenuefromExternalCustomersAttributedbycountryDetails"/>
  <link:definitionLink xlink:role="http://www.advancedemissionssolutions.com/role/SegmentReportingScheduleofRevenuefromExternalCustomersAttributedbycountryDetails" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems_019cd8ad-14e3-730b-ba0f-f2cd2dd7fdeb" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019cd8ad-14e3-772c-8805-388cd836358f" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_019cd8ad-14e3-730b-ba0f-f2cd2dd7fdeb" xlink:to="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019cd8ad-14e3-772c-8805-388cd836358f" xlink:type="arc" order="1" xbrldt:closed="true" xbrldt:contextElement="segment"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis_019cd8ad-14e3-7844-a96f-1ae26f334ed2" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019cd8ad-14e3-772c-8805-388cd836358f" xlink:to="loc_srt_StatementGeographicalAxis_019cd8ad-14e3-7844-a96f-1ae26f334ed2" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain_019cd8ad-14e3-7844-a96f-1ae26f334ed2_default" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="loc_srt_StatementGeographicalAxis_019cd8ad-14e3-7844-a96f-1ae26f334ed2" xlink:to="loc_srt_SegmentGeographicalDomain_019cd8ad-14e3-7844-a96f-1ae26f334ed2_default" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain_019cd8ad-14e3-7192-86c4-1a681d6512bb" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="loc_srt_StatementGeographicalAxis_019cd8ad-14e3-7844-a96f-1ae26f334ed2" xlink:to="loc_srt_SegmentGeographicalDomain_019cd8ad-14e3-7192-86c4-1a681d6512bb" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_country_US_019cd8ad-14e3-7175-94ad-e31f8b83cfd8" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_US"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_SegmentGeographicalDomain_019cd8ad-14e3-7192-86c4-1a681d6512bb" xlink:to="loc_country_US_019cd8ad-14e3-7175-94ad-e31f8b83cfd8" xlink:type="arc" order="0"/>
    <link:loc xlink:type="locator" xlink:label="loc_country_CA_019cd8ad-14e3-789d-879f-86ba5133e33e" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_CA"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_srt_SegmentGeographicalDomain_019cd8ad-14e3-7192-86c4-1a681d6512bb" xlink:to="loc_country_CA_019cd8ad-14e3-789d-879f-86ba5133e33e" xlink:type="arc" order="1"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_019cd8ad-14e3-7235-a577-24ac8d3f56d5" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems_019cd8ad-14e3-730b-ba0f-f2cd2dd7fdeb" xlink:to="loc_us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_019cd8ad-14e3-7235-a577-24ac8d3f56d5" xlink:type="arc" order="0"/>
  </link:definitionLink>
  <link:roleRef roleURI="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists" xlink:type="simple" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-roles-2025.xsd#eedm"/>
  <link:definitionLink xlink:role="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiability"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="loc_us-gaap_FinanceLeaseLiability" xlink:type="arc" order="31"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:definitionArc xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="loc_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="101"/>
  </link:definitionLink>
</link:linkbase>
