Analytical solutions for helium bubble

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1、118JournalofNuclearMaterials131(1985)11X-125~ortk-command.AmsterdamANALYTICALSOLUTIONSFORHELIUMBUBBLEANDCRITICALRADIUSPARAMETERSUSINGAHARDSPHEREEQUATIONOFSTATER.E.STOLLER*andG.R.ODETTEDepartmentofChemicalandNuclearEngineering,~n~versi~~ofCalifornia.SuntaBarbara,CA93

2、106,USAReceived10October1984;accepted10December1984Considerabletheoreticalandexperimentalworkhasverifiedtheroleofhelium-stabilizedbubblesastheprecursortovoidformationinfastneutronirradiatedstainlesssteels.Theconceptofthecriticalbubbleradiusorcriticalheliumnumberforb

3、ubble-to-voidconversionhasreceivedparticularattention.Ahardsphereequationofstateisusedtocomputetheseparametersforavarietyofirradiationconditionsandtheresultsarecomparedwiththosecomputedusingtheidealgaslaw.Simplifiedanalyticalsolutionsaredevelopedwhichpermitthecalcul

4、ationofthebubbleradiusandthecriticalbubbleparameterswithoutresortingtoiterativetechniquesandyetretaintheaccuracyofthehardsphereequationofstate.Theuseofthesesolutionsisillustratedusingaratetheorymodelofvoidsyellingwhichhasbeencalibratedusingfastreactorswellingdata.th

5、anthosewhicharecomputeusingamorecom-plicatedequationofstate.Thisisparticul~lytruewhenTransmutantheliumwassuspectedofplayingakeythecriticalradiusissmall(e.g.forT<5OOC,r*<2.5roleinpromotingthevoidswellingofstainlesssteelnm)leadingtohighcompressibilities.However,theuse

6、whenthisphenomenonwasfirstdiscoveredinthelateofarealgasequationofstategenerallyrequiresmore1960s[1,2].Subsequentresearchhasgenerallyestab-complexnumericalsolutionstoobtainthecriticalradiuslishedthatonemajorinfluenceofheliumistoincreaseorcriticalnumber.Iterativesolut

7、ionsarealsorequiredthecavitydensitybystabilizingsmallvacancyclusterstoobtainthebubbleradiusasafunctionofitsheliumagainstthermalannealing[3-51.Theseclusterscancon-content.Hence,theuseofarealisticequationofstatetinuetogrowbyheliumandvacancyabsorptionuntilcomplicatesbo

8、thparametricstudiesofthecriticaltheyreachacriticalsize[6,7]atwhichtheynolongerheliumbubbleparametersandmoredetailedmodelingrequirestabiliz