材料热力学练习三：各种热力学性质的计算

1、新型材料设计及其热力学与动力学The excess Gibbs energies of bcc solidsolutionof (Fe,Cr) and fcc solid solution of(Fe,Cr) is represented by the following expressions:Gex (bcc)/J xCr xFe (25104 11.7152 T);Gex (fcc)/J xCr xFe (13108 31.823 T 2.748 T log eT)For the bcc phase, please do the following calculations using

2、one calculator.(a) Calculate the partial Gibbs energy expressions for Fe and Cr(b) Plot the integral and partial Gibbs energies as a function of composition at 873 K(c)Plot the activities (aCr and a Fe) as a function of composition at 873K(d) What are the Henryslaw constants for Fe and Cr?For the fc

3、c phase, please do the calculations (a) to (b) by using your own code翻译：BCC （ Fe ，Cr ）固溶体的过剩吉布斯自由能和fcc 固溶体（ Fe，Cr ）的吉布斯自由能表达式如下：Gex (bcc)/J x Cr xFe (25104 11.7152 T);Gex (fcc)/J x Cr x Fe (13108 31.823 T 2.748 T ln T) G ex /J对于体心立方相，请使用计算器做下面的计算。（ a） 计算 Fe 和 Cr 的局部吉布斯能量表达式；（ b ）画出 873K 时局部吉布斯自由能和整体

4、吉布斯自由能的复合函数图。（ c） 画出 873K 时 Fe 和 Cr 反应的活度图。（ d ） Fe 和 Cr 亨利定律常数是什么？对于 fcc, 请用你自己的符号计算a 和 b 。（ a）由 exGj = ex G m + ex Gm/x j - xiex Gm /x i 可得exGFe = XcrX Feex G(bcc)+XCr ex Gm (bcc)-XFe X Cr ex G+X Cr XFe ex G=XcrX Fe (25104 11.7152 T)+X Cr (25104 11.7152 T) -X Fe X Cr (25104 11.7152 T) +X Cr X Fe (

5、25104 11.7152 T) =X 2Cr (25104 11.7152 T)同理；可得 ;ex GCr =X 2Fe (25104 11.7152 T)(b) 当 T=873K时，Gex (bcc) x Crx Fe (25104 11.7152 T)= x Cr xFe 14876.6304J设 xCr =X ，则 X Fe =1-Xex GFe= X 2 14876.6304 J（ T=873K ）ex GCr =（ 1-X ） 2 14876.6304 J（ T=873K ）0.00.20.40.60.8exGFe1.0160001600014000140001200012000)

6、1000010000J(80008000eFGx60006000e400040002000200000-2000-20000.00.20.40.60.81.0X图一exGFe-X 图)J(eFGxeGxe0.00.20.40.60.8exGFe1.016000160001400014000120001200010000100008000800060006000400040002000200000-2000-20000.00.20.40.60.81.0X图二 exGcr-X图0.00.20.40.60.8exG1.04000400035003000300025002000200015001000

7、10000.00.30.60.9x图三exG-X 图（C ） am =X m fmaB = x B expX 2 oL /(RT)exG (bcc)/J xCr xFe oLo L=25104 11.7152 T因而2a Fe = (1-X) expX (25104 11.7152 T) /(RT) （ T=873K ）2a Cr= X exp(1-X) (25104 11.7152 T) /(RT)（T=873K ）0aFe1.0e0.5a F0.000.00.51.0x图三aCr X 图0aCr0.00.4rCa0.800.00.51.0x图五aFeX 图(d)f b = expoL /RT所以 :f Fe =fCr = exp25104 11.7152 T /RTfcc:ex G Fe = X 2Cr (13108 31.823 T 2.748 T In T)ex G Cr = X 2Fe (13108 31.823 T 2.748