ON THE COMPONENT DISTRIBUTION COEFFICIENTS AND SOME REGULARITIES OF THE CRYSTALLIZATION OF SOLID SOLUTION ALLOYS IN MULTICOMPONENT SYSTEMS*

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1 METL , Hradec nad Mravicí ON THE OMPONENT DISTRIUTION OEFFIIENTS ND SOME REGULRITIES OF THE RYSTLLIZTION OF SOLID SOLUTION LLOYS IN MULTIOMPONENT SYSTEMS* Eugenij V.Sidrv a, M.V.Pikunv b, Jarmír.Drápala c a Vladimir Sae Universiy, Grky S., 87, Vladimir, , Russian Federain,. (49) 7 98, ferrmag@vsne.ru b Mscw Sae Insiue f Seel and llys (Technlgical Universiy), Lenin venue, 4, Mscw, 999, Russian Federain c Vyská škla báňská Technical Universiy f Osrava, v. 7. lispad, 5, 708 Osrava Pruba, zech Republic, Jarmir.Drapala@vsb.cz bsrac The rai f he cmpnen cnen in he liquid and slid phases in hree-, fur- and mulicmpnen slid sluin sysems fr differen cmpsiins has been sudied. mplicaed regulariies f he cmpnen redisribuin in he slid and liquid phases during crysallizain have been revealed. I is shwn ha during he crysallizain f a number f allys he equilibrium disribuin cefficien f sme cmpnens can have he value frm < = and furher >. mre cmplex cmpnen redisribuin in he micrand macrvlumes in he prcess f he nnequilibrium crysallizain has been revealed. new mehd f he graphical analysis f he crysallizain prcesses f he mulicmpnen allys allwing deermine impran characerisics f hese allys has been prpsed. T analyze crysallizain f allys i is cusmary use equilibrium disribuin cefficiens ( ), which are deermined n he basis f he phase diagrams as he relain = sl / liq a he emperaure l s. Here l and s are liquidus and slidus emperaures crrespndingly. sl and liq are he allying cmpnen cnens in he cexising slid and liquid phases a he emperaure. The cmpnen wih he lesser cnen is cusmary assumed he allying cmpnen. On he basis f he binary phase diagrams ne can easily deermine equilibrium disribuin cefficiens f he allying cmpnen in he prcess f he equilibrium crysallizain f allys. In he binary sysem he disribuin cefficien f he hard-ing allying cmpnen f any ally is always mre han a uniy ( >) and he disribuin cefficien f he ligh-ing cmpnen is always less han a uniy ( <). This allws predic he curse f he inracrysalline r dendrie liquain in he prcess f he nnequilibrium crysallizain f ally and he cmpnen disribuin in he direcinally slidified ing wih he plane frn. The dendrie liquain cefficien ( l ) in allys is usually deermined as he relain l = bund / cen, where bund is he cmpnen cnen n he dendrie cell bundary, cen is he cmpnen cnen in he dendrie cell cenre. In he ernary sysem (Fig.), where he cmpnen ing emperaures are relaed as > >, he equilibrium disribuin cefficien f he cmpnen (he ms hard-ing ne) in all allys is mre han a uniy ( >), he equilibrium disribuin cefficien f he cmpnen (he ms ligh-ing ne) in all allys is less han a uniy ( <). T speak abu he disribuin cefficien f he cmpnen (having he inermediae ing emperaure) in his sysem is cnsiderably mre difficul. In [] prbably fr he firs ime he auhrs succeeded shw ha in such sysems here exiss regin α b (Fig.), in which allys wih he changing disribuin cefficien f he

2 METL , Hradec nad Mravicí cmpnen are lcaed: a he beginning f he crysallizain clse he liquidus emperaure f hese allys <, a he emperaure equal =, a he end f he prcess clse he slidus emperaure >. The saed regin is deermined by he ishermal secin f he diagram a he ing emperaure f he cmpnen. he equilibrium crysallizain f allys lcaed in he regin b he disribuin cefficien f he cmpnen is less han a uniy ( <) and he disribuin cefficien f he cmpnen f allys lcaed in he regin α is mre han a uniy ( >). * In his paper cninuus slid sluins wihu minimums and maximums are cnsidered. Fig. mpsiins f he liquid ( liq ) and slid ( sl ) phases a he equilibrium crysallizain f allys and he ishermal secins a he liquidus emperaures f allys, and wihin he crysallizain inerval f ally. Ishermal and plyhermal secins f ernary phase diagrams are used sudy hreecmpnen allys. In hese secins i is impssible wihu experimens and special calculains deermine he psiin f he cnid cnnecing he cmpsiins f he cexising phases. In his cnnecin i is raher difficul bserve he prcess f he equilibrium and especially nnequilibrium crysallizain f hree-cmpnen allys. Fr he same reasn he equilibrium disribuin cefficiens f he cmpnens urn u be unknwn which des n allw safey enugh predic he evluin f he micrnnhmgeneiy f he ernary slid sluin cmpsiin afer he nnequilibrium crysallizain. T slve such prblems while invesigaing hree-cmpnen and mre cmpund allys we can ffer he fllwing mehd: fr he ally cmpsiin, which is being invesigaed, pl secins f hypheic binary phase diagrams in which he sum f all cmpnens excep ne will be assumed as he basis f he ally and cnsider exacly his cmpnen, in urn,

3 METL , Hradec nad Mravicí he allying cmpnen. The number f such hypheic binary diagram secins fr ne ally cmpsiin urns u be equal he number f his ally cmpnens. In hese hypheic binary phase diagrams he liquidus and slidus emperaures f he allys are shwn. On he hriznal axis he iniial ally cmpsiin fr ne f he cmpnens is indicaed and als he change f he liquid and slid phase cncenrain fr he given ally cmpnen is shwn. In Fig.a he principle f pling he binary hypheic phase diagram f he ally (4% % %) as per Fig. is presened. In his diagram i is assumed ha 750, = 70, = = 700. The liquidus and slidus emperaures f he ally are 75 and 75 crrespndingly. The liquid and slid phase cmpsiins and he equilibrium disribuin cefficiens a he liquidus and slidus emperaures and als in he crysallizain inerval are he fllwing: Temperaure ( ) Phases mpnen cnen ( %) Equilibrium disribuin cefficiens Slid,0 50,0 9,0 = l =75 Liquid,0,0 4,0 0,64,5 0,85 Slid,0 46,0,0 =7 Liquid 6,5 9,0 4,5 0,6,6 0,9 Slid,0 4,0 4,0 =70 Liquid 4,0 5,0 4,0 0,56,7,0 Slid 9,0 6,5 4,5 4 =77 Liquid 46,0,0,0 0,6,66,08 Slid,0,0 4,0 5 = s =75 Liquid 49,8,0 9, 0,67,57,6 In Fig.a he change f he liquid and slid phase cnen a he equilibrium crysallizain is shwn. The lengh f he perpendiculars drpped n he side f he cncenrain riangle is prprinae he cmpnen cnen. he equilibrium crysallizain a lile lwer l = 75 a slid phase wih he cmpsiin sl precipiaes u f he cmpsiin, he cmpnen cnen f his phase is deermined by he lengh sls which crrespnds 9%. This cmpnen cnen mus be refleced in he hypheic binary phase diagram a l (Fig.b). he emperaure = 7 he slid phase cmpsiin will crrespnd and he liquid phase cmpsiin. The cmpnen cnen in sl hese phases will be equal he lenghs S (%) and sl liq liql (4,5%) crrespndingly. These values are als pled n he hypheic binary diagram (Fig.b). he emperaure = 70 he cnid becmes parallel he side f he cncenrain riangle and herefre he cmpnen cnen in he liquid and slid phases is he same and equal (4%). rrespndingly in he hypheical binary phase diagram a here will be ne cmpsiin fr he liquid and slid phases. 4 = 77 he cmpnen cnen in he 4 4 slid phase becmes mre (he perpendicular lengh S ) han ha in he liquid phase (he 4 4 perpendicular lengh liql ) and hese changes are clearly seen in he hypheic binary diagram. The equilibrium crysallizain will end a he equilibrium slidus emperaure s = 5 75 when he slid phase cnen is equal and he liquid phase cnen is equal which crrespnds he perpendicular lengh 5 5 liq l. In ha way he hypheic binary diagrams fr he and cmpnens were pled. sl liq

4 METL , Hradec nad Mravicí Fig. mpsiins f he liquid ( liq ) and slid ( sl ) phases a he equilibrium crysallizain f he ally accrding Fig. a), and he hypheic binary diagram f he ally depicing he change f he cmpnen phase cmpsiins б). s i was menined, he ms ineresing prcesses are bserved a he ally crysallizain frm he regin α b (Fig.) where he disribuin cefficien f he cmpnen a sme definie mmen urns u be equal a uniy ( =). This manifess iself in ha a he cmpnen ing emperaure he cnid liq sl becmes parallel he side f he cncenrain riangle and he cmpnen cnen will be, accrdingly, he same bh in he liquid and slid phases. s i was menined earlier, all allys having he slidus emperaure higher han he disribuin cefficien <, all allys wih he liquidus emperaure lwer han >. The pssibiliy f changing he cmpnen equilibrium cefficien frm < > will be ypically manifesed a he cmpleely nnequilibrium crysallizain f allys and he effec can be revealed afer he direcinal slidificain f he ing in he presence f he plane frn and a he absence f he diffusin in he slid phase and a he presence f he unlimied diffusin in he liquid phase and he cnvecin sirring f he. Fr he ally wih he cmpsiin 90% 6% 4% he cmpnen disribuin depending n he slidified fracin f he ing (m) is shwn in Fig.. 4

5 METL , Hradec nad Mravicí I can be seen frm Fig. ha he cmpnen cnen gradually decreases and he cmpnen cnen gradually increases depending n he slidified ing fracin.the cmpnen cnen a firs increases and reaches he maximum value apprximaely 0% afer he 0,8 ing fracin slidificain and hen decreases again. Wih his, he equilibrium disribuin cefficiens f he cmpnens and are he same and are equal apprximaely 0,5-0,6. Fig. Disribuin f he cmpnens f he ally (90% 6% 4% ) depending n he fracin f he direcinally slidified ing wih he plane crysallizain frn a D sl = 0, D liq. regular erahedrn was used deermine he equilibrium disribuin cefficiens and invesigae he equilibrium and nnequilibrium crysallizain f he fur-cmpnen ally. In his Figure he erahedrn apexes crrespnd pure cmpnens, six edges binary sysems, fur sides ernary sysems and he inner space f he erahedrn quaernary sysems [,]. Fur cmpnens which ing emperaures are relaed as > > > D were chsen fr analysis. The equilibrium crysallizain f varius cmpsiins was sudied. Fr each emperaure he space was pled in he erahedrn crrespnding he w-phase regin (LIQ SOL). The cnid direcins was deermined prceeding frm he principle f heir gradual changing frm ne erahedrn edge anher, frm ne side anher. y he cnids he cmpnen cnen in he liquid and slid phases fr differen allys was fund and accrdingly he equilibrium disribuin cefficiens f he cmpnens wihin he equilibrium crysallizain inerval. In Fig.4 he ishermal secin f he phase diagram a he ing emperaure f he cmpnen is shwn and als he direcin f he cnids in w-, hree- and fur-cmpnen sysems and he equilibrium disribuin cefficien values f he cmpnens in hese sysems a he given emperaure. The equilibrium crysallizain f varius cmpsiins f he D sysem furcmpnen allys was examined. I was fund ha in he fur-cmpnen sysem he equilibrium disribuin cefficien f he ms hard-ing cmpnen () is always mre han a uniy ( >) fr any cmpsiin and he equilibrium disribuin cefficien f he ms ligh-ing cmpnen (D) is always less han a uniy ( <). The equilibrium D 5

6 METL , Hradec nad Mravicí cefficiens f he cmpnens wih he inermediae ing emperaures (,) can be bh mre r less han a uniy and als can change heir values frm he value less han a uniy he value mre han a uniy depending n he ally cmpsiin. These cmpsiin regins are defined by he frm f he equilibrium phase diagram f he fur-cmpnen ally. If he ally cmpsiin ges in he w-phase regin frmed a he ing emperaure f he cmpnen having he inermediae ing emperaure, hen in his ally he equilibrium disribuin cefficien f his cmpnen will cerainly change is value frm < > like in he hree-cmpnen sysem. The ishermal secin shwn in Fig.4 is characerized by he equal amun f he cmpnen cnen bh in he liquid and slid phases fr all cmpsiins f he w-phase regin f he fur-cmpnen ally since all cnids a he given emperaure are parallel he side D f he erahedrn and he equilibrium cefficien f he cmpnen, crrespndingly, is equal a uniy ( =). he emperaures a lile higher han >. < and a he emperaures a lile lwer han Fig.4 Ishermal secins in he quaernary ally D a he ing emperaure f he cmpnen. 6

7 METL , Hradec nad Mravicí In he ishermal secin a he ing emperaure f he cmpnen all cnids becme parallel he side D f he erahedrn, and he cmpnen cnen bh in he liquid and slid phases will be he same fr all cmpsiins frm his w-phase regin, and he equilibrium disribuin cefficien f he cmpnen will be equal a uniy ( =). he emperaures a lile higher han han <, a he emperaures a lile lwer >. The equilibrium cefficiens f he mre hard-ing cmpnens ( and ) in hese cmpsiins will exceed a uniy and he equilibrium cefficien f he mre lighing cmpnen (D) will be less han a uniy. If we cnsider he direcinal cnrlled slidificain f he ing in he presence f he plane frn and he absence f he diffusin in he slid phase and in he presence f he unlimied diffusin in he liquid phase and wih he cnvecin sirring f he f he furcmpnen ally frm he regin mre rich in he ms hard-ing cmpnen (ally 85% 6% 5% 4%D), we will ge he cmpnen disribuin presened in Fig.5. Fig.5 Disribuin f he cmpnens f he ally (85% 6% 5% 4% D) depending n he fracin f he direcinally slidified ing wih he plane crysallizain frn a D sl = 0, D liq. Prceeding frm he described abve hereical invesigains f he hree- and furcmpnen ally crysallizain we can frmulae he rule f deermining he values f he equilibrium disribuin cefficiens f any cmpnen in he mulicmpnen ally cninuus slid sluin (in he absence f maximums and minimums in he sysem) based n he knwledge f he ing emperaures f he cmpnens frming he ally cmpsiin and als he equilibrium liquidus and slidus emperaures f he ally under cnsiderain. In he mulicmpnen ally slid sluin he cmpnens wih he ing emperaure higher han he liquidus emperaure f he ally have he equilibrium disribuin cefficiens mre han a uniy, he cmpnens wih he ing emperaure less han he slidus emperaure f he ally have he equilibrium disribuin cefficiens less han a uniy and he cmpnens, which ing emperaure is in he crysallizain inerval f he ally, have he equilibrium disribuin cefficiens a firs less han a uniy, hen equal a uniy and hen mre han a uniy. 7

8 METL , Hradec nad Mravicí In Fig.6 w-, hree- and fur-cmpnen sysems wih differen ally cmpsiins in hese sysems and, accrdingly, wih differen liquidus and slidus emperaures and he equilibrium disribuin cefficiens deermined by he described abve rule are shwn., В пл С пл А пл D пл >, < >, < >, D < -, -, -D based w-cmpnen allys >, <, < >, >, < >, >, < < В-С-А based hree-cmpnen allys >, <, D <, < > >,, <, D < В-С-А-D based fur-cmpnen allys >, >, <, D < >, >, >, D < >, >, >, D < < < Fig. 6 Deerminain f he equilibrium disribuin cefficiens f he cmpnens in he slid sluin allys by he liquidus and slidus emperaures. REFERENES [] SIDOROV, E.V., PIUNOV, M.V. Peculiariies f he nnequilibrium crysallizain f he hree-cmpnen slid sluin allys and he arising dendrie liquain. Meals, 994, N. 6, p. 7-. [] NOSOV, V.Ya., OZEROV, M.I., FILOV, Yu.Ya. The bases f he physicchemical analysis. Publishing huse Science. Mscw, 976, p.504. [] PETROV, D.. Quaernary sysems. nvel apprach he pling and analysis. Mscw, Meallurgy, 99, p

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