훐맺쳥쫓톧폫춼쿱럖컶ꆡ2001쓪3퓂ꆡ뗚6뻭ꆡ뗚1웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆤ46ꆤꆡꆡ컄헂뇠뫅:1007-1482(2001)01-0046-04닄쇏쿔캢ퟩ횯죽캬맛닢폫믹폚춼쿱뗄쒣탍퇐뺿쇵맺좨,헅ꆡ폭,쟘쿦룳,낲쾣훐,쇵뾡폑(놱뺩뿆벼듳톧닄쇏뿆톧폫릤돌톧풺,놱뺩100083)햪ꆡ튪:뛳튪움쫶쇋닄쇏캢맛죽캬탎첬횱뷓맛달ꆢ죽캬뚨솿뇭헷벼쫵폫죽캬쿔캢ퟩ횯럂헦뗈쇬폲뷼쓪살뗄퇐뺿뷸햹,뻍웤훐뗄튻킩컊쳢폫뷢뻶춾뺶뷸탐쇋퇐쳖ꆣ맘볼듊:닄쇏쒣탍뮯;죽캬쿔캢ퟩ횯;뚨솿뷰쿠톧;쳥쫓톧;춼쿱럖컶;볆쯣믺럂헦훐춼럖샠뫅:TG115121(TP39119)ꆡꆡꆡꆡꆡ컄쿗뇪쪶싫:AONTHREE-DIMENSIONALMEASUREMENTSANDIMAGE-BASEDMODELSOFMICROSTRUCTURESINMATERIALSLIUGuo-quan,ZHANGYu,QINXiang-ge,ANXi-zhong,LIUJun-you(SchoolofMaterialsScienceandEngineering,UniversityofScienceandTechnologyBeijing,Beijing100083,China)Abstract:Recentdevelopmentandstate-of-artoffollowingscientificareasareverybrieflyreviewedinthisarticle:(1)Directobservationofthree-dimensionalmorphologyofmicrostructuresinmateri2als;(2)Three-dimensionalquantitativecharacterizationtechniquesincludingstereology;(3):materialsmodeling;three-dimensionalmicrostructure;quantitativematerialography;stereology;imageanalysis;computersimulation1ꆡ틽퇔쓑ꆣ뻸듳뛠쫽닄쇏뫍컯훊뗄늻춸쏷탔웈쪹죋쏇뻖쿞폚뛔닄쇏쿔캢ퟩ횯뗄뛾캬(2D)뷘쏦믲놡쒤퇹욷뷸닄쇏캢맛ퟩ횯뷡릹뗄죽캬(3D)맛닢폫뚨솿뇭탐춶펰맛닢,뛸헢샠맛닢퓚쳡릩탅쾢뗄춬쪱튲뎣뎣헷튻횱쫇닄쇏뿆톧폫릤돌쇬폲뗄붹뗣뫍쓑뗣ꆣ듓닄룸죋쏇뛔닄쇏3Dퟩ횯뷡릹뗄에뛏듸살컳뷢ꆣ쇏릤돌뷇뛈돶랢,붨솢죎튻닄쇏ퟩ횯폫탔쓜횮볤뗄튻룶훘튪뗄쪵샽쫇,떱뷱맺쓚췢훚뛠컯샭튱뷰뚨솿맘쾵뻹튪쟳쫗쿈쪵쿖뛔닄쇏3Dퟩ횯뷡릹뗄쇋톧(뷰쫴톧)뷌닄뫍컄쿗훐죔맣랺죏캪뺧솣돟듧럖늼뷢,뛸붨솢닄쇏릤틕뿘훆쒣탍뫍닄쇏뫪맛닣듎쒣탍뗄ퟔ쿠쯆탔쫇3D뺧솣솬탸뎤듳맽돌뗄믹놾쳘헷,쪱돽춨맽뛔쪵퇩쫽뻝믘맩럖컶믱뗃붨쒣뗄믹놾탅쾢뛸ퟮ뷼ퟷ헟벰웤뫏ퟷ헟틑횤쏷헢튻룅쓮쫇늻ힼ좷췢,룼탨튪뫃뗄쿔캢ퟩ횯쒣탍틔믱뗃믹폚컯샭뫍뮯뗄,틲캪웤믹뒡뷶쿞폚평뺧솣2D뷘쏦돟듧럖늼ퟔ톧뗄탅쾢폫뷢쫍,샽죧캢뫏뷰뮯룟잿뛈뗍뫏뷰쿠쯆탔뗄맛닢뷡맻쿲3D뿕볤뷸탐늻뫏샭뗄췆룖\[1,2\]ꆣ듓닄쇏뿆톧뷇뛈뛸퇔,웤훘튪탔룼쫇늻퇔맣\[3\],헢킩뻹룼춹쿔돶3D맛닢폫뚨솿뇭헷뗄뇘튪뛸폷ꆣ닄쇏쿔캢ퟩ횯뗄뛠뇤탔쪹뗃뛔웤뺲첬뫍뚯첬탔뫍웈쟐탔ꆣ놾컄뛳튪움쫶쇋룃쇬폲뷼쓪살뗄튻킩3D벸뫎탎쎲뗄뚨솿뇭헷뇈뺧쳥뷡릹뗄뇭헷룼캪삧뷸햹ꆣ쫕룥죕웚:2001-03-022ꆡ닄쇏3Dퟩ횯뗄횱뷓돉쿱폫쪵퇩맛닢믹뷰쿮쒿:맺볒ퟔ좻뿆톧믹뷰(59872003뫍59771070)벰뷌폽늿뿧쫀볍폅탣죋닅믹뷰훺쿮쒿짮쪴램ꆢ뺧솣믲뗚뛾쿠럖샫램ꆢ짤쿟헕쿠램ꆢ솢ퟷ헟볲뷩:쇵맺좨(1952-),쓐,몺ퟥ,즽뚫샖쇪쫐죋,뷌쫚,늩쳥쫓뻵ꆢ릲뻛붹쿔캢뺵ꆢ풭ퟓ솦쿔캢뺵ꆢ뎡샫ퟓ쿔캢쪿,늩쪿짺떼쪦,퇐뺿랽쿲:닄쇏럂헦폫짨볆
ꆡ2001쓪뗚6뻭뗚1웚ꆡꆡꆡꆡꆡꆡ쇵맺좨뗈:닄쇏쿔캢ퟩ횯죽캬맛닢폫믹폚춼쿱뗄쒣탍퇐뺿ꆡꆡꆡꆡꆡꆡꆤ47ꆤ뺵ꆢCT벰쿠맘벼쫵ꆢ듓쾵쇐뷘쏦춼쿱훘붨3Dퟩ횯뗄뛾캬컞욫볆쫽뿲,내헕컞욫좡퇹맦퓲뛔뿲쓚솣ퟓ뷡릹뗈랽램뻹퓸놻폃폚닄쇏3Dퟩ횯뗄횱뷓돉쿱폫뷸탐톡좡,뛔웤훐캴퓚쇭튻뷘쏦짏춬쪱돶쿖뗄솣ퟓ쪵퇩맛닢ꆣ떫듳뛠쫽믲뷶쫊폃폚벫쳘쫢뗄쟩뿶,믲뷸탐볆쫽,볇캪N,퓲퇹욷훐솣ퟓ룶쫽쳥쏜뛈캪NV릤ퟷ솿벫듳,믲횻쓜뛔퇹욷뇭쏦돉쿱뫍맛닢ꆣ웤훐,=N/Ah뗄뛠듎닢솿횵뗄욽뻹횵ꆣ룶쫽좨훘욽뻹릤튵CT벼쫵뛔닄쇏쓚늿뻟폐쏷쿔쏜뛈닮틬뗄뷏듳쳥믽퓲평쿂쪽믱뗃:VN=N-1Vꆣ돟듧좱쿝뗄컞쯰볬닢뫜폐킧,헢폐뿉쓜돉캪튻룶탂쇵맺좨뗈틑붫솣ퟓ쮫뷘쏦쳥램돉릦췘햹펦폃폚뗄퇐뺿랢햹랽쿲,떫폃폚닄쇏3D쿔캢ퟩ횯뷡릹뗄돤싺죽캬뿕볤뛠뺧쳥훐뗄뺧솣룶쫽쳥쏜뛈뫍룶쫽좨맛닢쪱럖뇦싊짐듽쳡룟ꆣ떱폐뿉쓜춨맽쪵퇩믱좡쾵훘욽뻹쳥믽뗄쪵퇩닢뚨,캪닄쇏뿆톧쿔캢ퟩ횯뚨솿쇐뷘쏦춼쿱쪱,3D훘붨뛔폚3D횱뷓맛달퓲뫜폐냯뇭헷쳡릩쇋튻쳵탂춾뺶\[5,7\]ꆣ훺ꆣ쇭췢,횱뷓맛달늢늻ퟜ쫇틢캶ퟅ뿉틔횱뷓닢솿ꆣ(2)뗣좡뷘뻠램(point-sampledinter2횵뗃힢틢뗄쫇,퓚캴쓜쪵쿖닄쇏ퟩ횯3D뿉쫓뮯믲cepts)ꆪꆪꆪ폃폚닢좡솣ퟓ뗄쳥믽좨훘욽뻹쳥믽쯤틑뿉쫓뮯떫짐컞램믱뗃웤뚨솿뇭헷쫽뻝뗄쟩뿶믹놾닙ퟷ:퓚튻룶뷰쿠쒥쏦짏죷실튻ퟩ쯦믺뗣,쿂,쳥쫓톧럖컶뿉틔폃뫜킡뗄듺볛믱뗃3Dퟩ횯뷡맽실퓚솣ퟓ뷘쏦쓚뗄훮뗣ퟷ쯦믺뷘쿟늢닢웤뷘뻠,릹뗄컞욫뗄뚨솿닢솿,듓뛸쫇닄쇏뿆톧폫릤돌늻뿉좻뫳룹뻝춹탍믲낼탍솣ퟓ좷뚨솣ퟓ쳥믽좨훘욽뻹쳥좱짙뗄ퟩ횯뚨솿럖컶폫뇭헷뗄릤뻟\[2,4,5\]ꆣ믽뗄뻟쳥볆쯣릫쪽ꆣ샽죧,춹탍솣ퟓ뗄쳥믽좨훘욽뻹쳥믽볆쯣릫쪽캪3:VV(convex)=ꛐ(l1+3l2+ꆭ3ꆡ닄쇏3Dퟩ횯뚨솿럖컶폫쫽횵뇭헷+3lk)/3k,쪽훐k캪좡퇹뗣뗄쫽쒿ꆣ떱CVN(V)닄쇏캢맛춼쿱뗄믱좡ꆢ듦뒢뫍뒫쫤탂랽램,춼쿱<뗄쟩뿶쿂,틲캪춬튻ퟩ뺧솣뗄VV뫍VN뗄쿠뒦샭폫춼쿱럖컶죭볾벰펲볾뗄늻뛏돶쿖뫍룄뷸,쳥뛔닮틬킡폚10%,듓뛸퓚튪쟳늻룟쪱뿉쪹폃뗣좡뷘쫓톧톧뿆뗄랢햹뫍펦폃,볆쯣믺탔쓜뗄량쯙쳡룟뻹뻠램닢뚨뗄VV쫽횵ퟷ캪솣ퟓ뗄룶쫽좨훘욽뻹쳥믽캪닄쇏쿔캢ퟩ횯탎첬톧평뚨탔뇭헷쿲뚨솿뇭헷ꆢ평VN뗄뷼쯆횵ꆣ2D맛닢쿲3D탅쾢믱좡랽램뗄랢햹뫍펦폃쳡릩쇋룃램틠뿉폃폚폫쮫뷘쏦쳥램솪뫏닢좡솣ퟓ뗄룶쓑뗃뗄믺폶ꆣ쫽좨훘쳥믽럖늼뗄럖늼뿭뛈,믲폃폚폫퓱뫏램솪뫏쳥쫓톧(stereology)쫇평뛔3D뷡릹뗄뷘쏦믲춶닢좡떥룶솣ퟓ뗄쳥믽뫍솣ퟓ뗄룶쫽좨훘욽뻹쳥믽ꆣ펰춼맛닢믱뗃3D뚨솿탅쾢믲훘붨3D뷡릹뗄튻룶(3)뗣좡뷘뻠폫쮫뷘쏦쳥솪뫏램뿆톧럖횧,쫇닄쇏ퟩ횯뚨솿탎첬톧뗄믹뒡\[2,4ꆫ6\]ꆣ웤닢좡솣ퟓ룶쫽좨훘쳥믽럖늼뿭뛈횮볆쯣릫쪽쳥쫓톧퓚닄쇏볬닢뫍뇭헷훐뗄훘튪ퟷ폃쯦ퟅ쿠맘뗄캪:ASTM뫍ISO뗈뇪ힼ뗄늻뛏붨솢뛸춹쿔돶살ꆣ놾CV/2N(V)=[(VV/VN)-11]컄ퟷ헟(쇵맺좨)쒿잰ퟷ캪쿠맘ISO뇪ힼ릤ퟷퟩ뗄쇵맺좨뗈쫗듎닉폃듋램돉릦쪵퇩닢뚨쇋튻훖뗍훐맺볒돉풱닎폫쇋뇪ힼ뗄훆뚨탞룄릤ퟷꆣ컒맺맘첼룖퓚1050ꇦ놣컂ꆫ50min쳵볾쿂냂쫏쳥뺧솣폚닄쇏쿔캢ퟩ횯뚨솿럖컶뗄맺볒뇪ힼꆢ탐튵뇪ힼ훐뎤듳뗄맦싉,랢쿖퇹욷뗄뺧솣룶쫽좨훘쳥믽럖늼뿭튲풽살풽훘쫓쳥쫓톧풭샭폫춼쿱럖컶벼쫵뗄펦폃,뛈CVN(V)평퓶볓훁,풶풶룟폚잰컄쯹쟒틑솢쿮훆뚨쇋탂뗄폐맘뇪ힼꆣ쫶뗄ꆣ듋쪱늻쓜폃쳥믽좨훘욽뻹뺧솣쳥믽쫽횵훐컄컄쿗\[4\뛔]뺭뗤쳥쫓톧뷸탐쇋쾵춳뷩짜,웤뷼쯆룶쫽쳥믽좨훘욽뻹쳥믽,틲캪듋쪱춬튻퇹욷뗄쯼쳥쫓톧훸훐튻냣튲폐뷏뛠뷩짜,놾컄늻폨훘뢴ꆣ쳥믽좨훘욽뻹뺧솣쳥믽쫽횵뿉쓜듯떽룶쫽쳥믽좨훘뛸뷼20폠쓪살ퟮ횵뗃튻쳡뗄3D쿔캢ퟩ횯뚨솿탎욽뻹쳥믽뗄뷼놶\[7\]!첬톧퇐뺿뗄춻웆탔뷸햹쫇튻쾵쇐믹폚짨볆뗄쳥쫓톧(4)퓱뫏램(selector)ꆪꆪꆪ쮫뷘쏦쳥램횮튻훖,좡퇹뫍닢솿랽램뗄컊쫀\[5ꆫ9\],웤훐쮫뷘쏦쳥램캪웤늻탨횪뗀솽룶뷘쏦횮볤뻠ퟮ훘튪뗄뫋탄ꆣ샽죧:퓱뫏램믹놾닙ퟷ럖3룶늽훨:폃disector램톡(1)쮫뷘쏦쳥램(disector)ꆪꆪꆪ폃폚닢좡솣ퟓ룶좡솣ퟓvi,퓚맛달쏦짏쯹톡솣ퟓ뷘쏦Ai쓚톡좡뗣쫽쳥쏜뛈NV믲솣ퟓ뗄룶쫽좨훘욽뻹쳥믽VNQi,맽룷Qi닢좡솣ퟓ뷘쏦싖삪횮뷘뻠li,떥룶솣ퟓ믹놾닙ퟷ:퓚퇹욷짏좡웤볤뻠h틑횪뗄솽룶욽쳥믽Vi=ꛐ33(l1+l2+ꆭ+3lm)/3m,웤훐m캪룃탐뷘쏦(맛달쏦뫍뫋닩쏦),퓚튻룶쏦짏훃쏦믽캪A솣ퟓ쯹뗃뗣좡뷘뻠뗄ퟜ쫽ꆣ
ꆡꆡꆡꆡꆡꆡꆡꆤꆡ48ꆡꆤꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ훐맺쳥쫓톧폫춼쿱럖컶ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2001쓪뗚6뻭뗚1웚룃램쫇쮫뷘쏦쳥램뫍뗣좡뷘뻠램뗄뷡뫏,뿉폃쯣(CALPHAD)램뿉틔볆쯣룸뚨쳵볾쿂뫏뷰쳥쾵훐폚믱뗃떥룶솣ퟓ뗄룶쫽좨훘쳥믽,폖뿉폃폚믱뗃솣뿉쓜돶쿖뗄룷쿠쫽솿,듓맣틥짏붲틠뿉죏캪쫇놾닣ퟓ뗄룶쫽좨훘쳥믽욽뻹횵ꆣ힢틢:럇룷쿲춬탔ퟩ횯듎뗄튻훖볆쯣믺쒣쓢랽램ꆣ(4)뫪맛닣듎:믹폚솬탸쳵볾쿂늻쓜퓙쪹폃욽탐뷘쏦ꆣ뷩훊볙짨뷸탐,죧폐쿞풪램(FEM램)ꆢ폐쿞닮럖램(5)뒹횱뷘쏦램(verticalsectioning)ꆪꆪꆪ폃폚뗈,뿉폃폚닄쇏훆놸뫍룄탔맽돌훐컂뛈뎡ꆢ얨뛈뎡ꆢ룷쿲틬탔퇹욷쳥쫓톧좡퇹뫍뛠훖닎솿뗄닢좡펦솦뎡ꆢ쇷뎡뗈뗄볆쯣폫쒣쓢뗈ꆣ샽죧,샻폃떥룶뒹횱뷘쏦뿉닢좡뇭쏦믽쳥쏜뛈ꆢ틔짏쎿룶돟뛈닣듎뗄볆쯣믺럂헦뻹폐웤뻖쿞쳥믽럖쫽ꆢ솣ퟓ쳥믽좨훘욽뻹쳥믽ꆢ탇쳥믽벰웤룷쿲탔,맊쒿잰랢햹랽쿲쫇뷸탐닄쇏뗄뛠돟뛈럂헦(mul2틬탔ꆢ쿟뷓뒥뻠샫럖늼ꆢ쳥쳘헷컯뗄뿕볤럖늼쏨쫶ti-scalesimulation),벴퓚뷸튻늽랢햹폫췪짆떥튻돟뗈,샻폃쮫뒹횱뷘쏦믲뫱냥퇹욷퓲뿉폃폚닢좡솣ퟓ뛈볆쯣믺쒣쓢랽램뫍펦폃뗄춬쪱,솦쟳붫늻춬돟뛈룶쫽쏜뛈ꆢ쿟뎤쳥쏜뛈ꆢ솬춨탔쏜뛈ꆢ욽뻹솣ퟓ쳥믽ꆢ뗄쒣쓢랽램뫏,틔룼뫃뗘쫊펦닄쇏뿆톧퇐뺿뗄탨솣ퟓ쳥믽룶쫽럖늼뗄랽닮ꆢ솣ퟓ3D뿕볤럖늼,뗈튪ꆣ뗈ꆣꆡ쿔캢ퟩ횯럂헦쒣탍틔짏룷훖컞욫쳥쫓톧랽램틑퓚짺컯튽톧뗈쇬폲닄쇏쿔캢ퟩ횯럂헦쒣탍벴캪쇋쳘뚨쒿뗄붫틔쪵믱뗃쿠떱뛠뗄펦폃ꆣ컒쏇뛔헢킩랽램퓚닄쇏ퟩ횯뚨볊닄쇏쿔캢ퟩ횯캪풭탍(Prototype)뗄쒳킩탅쾢볲솿탎첬톧훐뗄펦폃쯹뷸탐뗄쾵춳탔뛔뇈쪵퇩퇩횤뇭쯵ꆢ쳡솶뛸릹퓬뗄풭탍쳦듺컯ꆣ닉폃볆쯣믺뛔닄쇏쏷,쯼쏇춬퇹쫊폃폚닄쇏뿆톧폫릤돌쇬폲\[7,8\]ꆣ헦쪵캢맛ퟩ횯뗄탎돉뫍퇝뇤뷸탐뫏샭럂헦,붨솢폫쇭췢,쳥쫓톧볒쏇뮹쳡돶쇋trisector,point-쳘뚨샠탍쿔캢ퟩ횯벫캪쿠뷼뗄ퟩ횯쒣탍늢폃폚닄쇏sampledarea,fractionator,orientator,isector,nucle2뿆톧퇐뺿뫍닄쇏릤돌펦폃,쫇닄쇏뿆톧훐뛠돟뛈럂ator,starvolume뗈컞욫좡퇹뫍닢솿풭샭ꆢ랽램폫닎헦퇐뺿뗄훘튪ퟩ돉늿럖,뷼쓪살틑훰붥쫜떽훘쫓늢솿,틔벰죴룉뛾뷗쳥쫓톧(secondarystereology)랽믱뗃쇋튻뚨뷸햹ꆣ춼1캪놾컄ퟷ헟췪돉뗄늿럖닄쇏램ꆣ퓚헢랽쏦,횵뗃췆볶뗄튻놾볦뻟좨췾탔뫍쪵폃쓚늿ퟩ횯뷡릹럂헦쒣탍뗄쪵샽ꆣ탔뗄쳥쫓톧ퟮ탂훸쫇평쏀맺훸쏻춼쿱럖컶볒늻춬폚닄쇏믲컯훊뗄뺧쳥뷡릹뇭헷쓇퇹죝틗붨뷌쫚뫍쫀뷧훸쏻쳥쫓톧볒솢웰뿕볤벸뫎쒣탍,닄쇏믲컯훊쿔캢ퟩ횯뗄뛠뇤탔뷌쫚뫏훸뗄ꆶPracticalStereologyꆷ(뗚뛾냦,ISBN0뻶뚨쇋늻뿉쓜붨솢웰룷훖닄쇏3Dퟩ횯뷡릹뗄춳튻-306-46476-4,2000쓪11퓂돶냦,릲382쒣탍ꆣ컄쿗\[10\ퟛ]뫏움쫶쇋돤싺뿕볤뗄3D뺧솣쒣튳\[9\])ꆣ룃쫩뗄틲쳘췸뗘횷캪:.탍뗄퇐뺿뷸햹,냼삨붨솢쒣탍뗄믹놾ힼ퓲ꆢKelvin뫍nl/
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