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Share-Based Compensation - Schedule of company's compensation cost allocated to employees (Details) - USD ($) $ in Millions | 3 Months Ended | 6 Months Ended
--- | --- | ---
Mar. 31, 2022 | Mar. 31, 2021 | Mar. 31, 2022 | Mar. 31, 2021
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Share-Based Compensation Expense | $ 3.9 | $ 2.9 | $ 8.5 | $ 6.7
Tax benefit associated with share-based compensation costs recognized | 1.0 | 0.7 | 2.0 | 1.6
Cost of products sold |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Share-Based Compensation Expense | 0.7 | 0.6 | 1.7 | 1.5
Selling and administrative expense |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Share-Based Compensation Expense | 2.8 | 1.7 | 5.7 | 3.9
Research and development expense |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Share-Based Compensation Expense | $ 0.4 | $ 0.6 | $ 1.1 | $ 1.3

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- Definition Amount of expense for award under share-based payment arrangement. Excludes amount capitalized. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 1 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5047-113901 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 14.F) -URI http://asc.fasb.org/extlink&oid=122041274&loc=d3e301413-122809 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
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- Definition Amount of tax benefit for recognition of expense of award under share-based payment arrangement. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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