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1、,%A= Cb=xa %B= Ac=xb %C= Ba=xc,c,a,b,x,xa+xb+xc =AB=BC=CA,b,a,c,b,%A,%C,双线法,a,b,c,双线法,4,The following features are of interest in connection with compositional aspects of ternary systems. (1) If a straight line such as CD is drawn from one corner of the triangle (i.e. from component C) to intersect
2、the opposite side (i.e. AB), then the ratio of the other two components (i.e. A and B) is constant in alloys represented by points lying on the line. Considering alloy compositions along CD, as the composition point becomes progressively further away from C the percentage of C present in the alloys
3、decreases, but the relative amounts of B and A remain the same.,Some rules,等比例规则：CD线上A、B组元的含量之比是一定值。,Special lines,on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) If two alloys (two phases) (e.g. d and e) are mixed together, the composition of the resulting mixture lies on a straight line joining the compos
4、itions of the two alloys (co-linear principle). The total composition lies at the point dividing the line into segments inversely proportional to the ratio of the quantities of the original alloys.,共线规则（杠杆规则）,7,M（a1 b1 c1) N(a2 b2 c2) P（xyz）,8,This is the so-called lever principle or lever rule whic
5、h finds an important application in tie-lines when an alloy decomposes into a two-phase mixture.,Then, using weight percentages:,杠杆规则,9,(4) If three alloys (phases) a, b, and c are mixed together, the composition of the mixture, o, lies within the triangle formed by joining the compositions of the a
6、lloys by straight lines. Using the centre of gravity principle, the triangle may be considered as being supported on a point fulcrum at o and having masses at its corners proportional to the amounts of the alloys. Then, in equilibrium, the position of o is such that the percentages of the three allo
7、ys in the mixture are given by %a = ao /aa 100% %b = bo /bb 100% %c = co / cc 100% The application of this principle in tie-triangles, representing three-phases in equilibrium.,重心规则,10,Procedure: L:x :y :z=1-x-y x50%+y85%+(1-x-y) 10%=40% x40%+y10%+(1-x-y) 20%=30% x=55.3%; y=10.5%;z=34.2% Answer: 55%
8、 liquid, 10 %, 35 %. (b) Procedure: L:0 :50% :50% A:a B:b C:c=1-a-b a=050%+0.585%+0.510%=47.5% b=040%+0.510%+0.520%=15% Answer: 48%A, 15%B, 37 %C.,In a system ABC, a ternary alloy of composition 30 wt % B and 30 wt % C consists at a particular temperature of three phases of equilibrium compositions
9、as follows: Liquid phase 50% A, 40% B, 10% C solid solution 85% A, 10% B, 5% C solid solution 10% A, 20% B, 70% C,课堂练习,1. 确定合金I、II、III、IV的成分,I 点：,A%=60% B%=30% C%=10%,课堂练习,1. 确定合金I、II、III、IV的成分,II点：,A%=20% B%=50% C%=30%,课堂练习,1. 确定合金I、II、III、IV的成分,III 点：,A%=20% B%=20% C%=60%,课堂练习,1. 确定合金I、II、III、IV的成
10、分,IV 点：,A%=40% B%=0% C%=60%,2. 标出75%A+10%B+15%C的合金,课堂练习,3. 标出50%A+20%B+30%C的合金,课堂练习,课堂练习,4. 绘出A 40%的合金,5. 绘出C 30%的合金,6. 绘出C / B 1/3的合金,课堂练习,7. 绘出A / C 1/4的合金,19,共轭曲线及直线规则,共轭曲线,共轭连线,固相中高熔点的组元含量通常比液相高。,20,A,B,C,s,o,s1,s,s2,s1,s2,l1,l2,l,s,o,s1,s2,l1,l2,l,l,l2,l1,平衡结晶过程分析,22,5.3 Ternary eutectic phase
11、diagrams The classification of four phases equilibrium in a ternary system: Eutectic reaction: L +（共晶） Peritectic reaction: L +(a) （包晶） or: L + (b) Monotectic reaction: L1 L2 +（偏晶） Eutectoid reaction: +（共析） Peritectoid reaction: +（包析）,23,单相区：4个 两相区：3个 三相区：4个 四相区：1个,24,投影图,A,B,C,相图分析,液相面,固相面,液相线,固溶面,
12、固相面,固溶面,三相平衡,f =C-P+1=4-3=1，T确定，则f =0 根据相区接触法则，三相区在L+ 、 L+之下，+之上的空间中。,三相平衡时，每两个相都平衡，因此在等温截面上，三条共轭连线形成共轭三角形。,共轭三角形的三个顶点表示三个平衡相的成分点。 可用重心法则确定三个相的质量分数。,A,B,C,te温度： L0+ 为三元系的共晶反应 注意：是在一个温度范围内进行的。,L,L,L+,L+,L+,L+,共晶型,包晶型,具有四相平衡反应的三元相图,A-B，B-C，C-A两两组成共晶相图。 组元在固态有限溶解的共晶相图,液相面 固相面(组成) 面： 二相共晶面 三相共晶面 溶解度曲面：6
13、个 两相区：6个 区： 单相区：4个 三相区：4个 四相区：1个,相图分析,四相平衡区,f =C-P+1=3-4-1=0 因此，四相平衡在三元相图中为一具有特定形状的水平面。,L,发生四相共晶反应： L + + ,四相共晶反应,投影图,液相区投影,A,C,B,E,e1,e2,e3,A,C,B,e1,e2,e3,固相区投影,A,C,B,l,l,l,m,n,p,变温截面图,L,L+,L+,L+,+,+,+,L,L+,L+,L+,+,+,+,L+,38,39,Solution: 1. Ternary invariant reactions: 1585: L + M3C2 Graphite + M7C
14、3 1415: L + M23C6 M7C3 + 1275: L + + M7C3 1230: L + Graphite + M7C3 M3C 1160: L + M7C3 +M3C 1155: L + M3C +graphite,三元相图小结,1 三元合金相图的表示方法 浓度三角形，浓度三角形中具有特定意义的直线 2 三元匀晶相图 相图分析：水平截面，垂直截面，液相面投影 典型合金的结晶过程 3 三元共晶相图 三组元固态互不相溶，具有共晶转变的相图： 相图分析、水平截面， 截线法则，垂直截面，投影图 三组元固态有限互溶，具有共晶转变的相图：组元间固态有限互溶时 相图的基本特点，截面及投影图，典型合金结晶过程分析,
