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1、%A=Cb=xa%B=Ac=xb%C=Ba=xccabxxa+xb+xc=AB=BC=CAbac’b’%A%C双线法abc双线法4Thefollowingfeaturesareofinterestinconnectionwithcompositionalaspectsofternarysystems.(1)IfastraightlinesuchasCDisdrawnfromonecornerofthetriangle(i.e.fromcomponentC)tointersecttheoppositeside(i.e.AB),th
2、entheratiooftheothertwocomponents(i.e.AandB)isconstantinalloysrepresentedbypointslyingontheline.ConsideringalloycompositionsalongCD,asthecompositionpointbecomesprogressivelyfurtherawayfromCthepercentageofCpresentinthealloysdecreases,buttherelativeamountsofBandAremain
3、thesame.SomerulesPGH等比例规则：CD线上A、B组元的含量之比是一定值。Speciallineson线：A组元的含量相等。Am线：B,C两组元含量之比为一常数。6(3)Iftwoalloys(twophases)(e.g.dande)aremixedtogether,thecompositionoftheresultingmixtureliesonastraightlinejoiningthecompositionsofthetwoalloys(co-linearprinciple).Thetotalcompo
4、sitionliesatthepointdividingthelineintosegmentsinverselyproportionaltotheratioofthequantitiesoftheoriginalalloys.共线规则（杠杆规则）7M（a1b1c1)N(a2b2c2)P（xyz）8Thisistheso-called'leverprinciple'or'leverrule'whichfindsanimportantapplicationin'tie-lines'whenanalloydecomposesintoa
5、two-phasemixture.Then,usingweightpercentages:杠杆规则9(4)Ifthreealloys(phases)a,b,andcaremixedtogether,thecompositionofthemixture,o,lieswithinthetriangleformedbyjoiningthecompositionsofthealloysbystraightlines.Usingthe'centreofgravity'principle,thetrianglemaybeconsidered
6、asbeingsupportedonapointfulcrumatoandhavingmassesatitscornersproportionaltotheamountsofthealloys.Then,inequilibrium,thepositionofoissuchthatthepercentagesofthethreealloysinthemixturearegivenby%a=a’o/aa’×100%%b=b’o/bb’×100%%c=c’o/cc’×100%Theapplicationofthisprinciplei
7、n'tie-triangles',representingthree-phasesinequilibrium.ABCαβLaa'cc'bb'o重心规则10Procedure:L:xα:yγ:z=1-x-yx×50%+y×85%+(1-x-y)×10%=40%x×40%+y×10%+(1-x-y)×20%=30%x=55.3%%;y=10.5%;z=34.2%Answer:~55%liquid,10%α,35%γ.(b)Procedure:L:0α:50%γ:50%A:aB:bC:c=1-a-ba=0×50%+0.5×85%+0.
8、5×10%=47.5%b=0×40%+0.5×10%+0.5×20%=15%Answer:~48%A,15%B,37%C.InasystemABC,aternaryalloyofcomposition30wt%Band30wt%Cconsistsataparti
