材料熱力學(xué)練習(xí)三各種熱力學(xué)性質(zhì)的計(jì)算

1、新型材料設(shè)計(jì)及其熱力學(xué)與動(dòng)力學(xué) The excess Gibbs energies of bcc solid solution of (Fe,Cr) and fcc solid solution of (Fe,Cr) is represented by the following expressions:Gex(bcc)/JxCrxFe (2510411.7152T); Gex(fcc)/JxCrxFe (1310831.823T2.748T logeT)For the bcc phase, please do the following calculations using one calc

2、ulator.(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 aFe) as a function of composition at 873K(d) What are the Henrys law constants for Fe and Cr? For the fcc phas

3、e, please do the calculations (a) to (b) by using your own code 翻譯：BCC（Fe，Cr）固溶體的過(guò)剩吉布斯自由能和fcc固溶體（Fe，Cr）的吉布斯自由能表達(dá)式如下：Gex(bcc)/JxCrxFe (2510411.7152T); Gex(fcc)/JxCrxFe (1310831.823T2.748T lnT) Gex/J對(duì)于體心立方相，請(qǐng)使用計(jì)算器做下面的計(jì)算。（a） 計(jì)算Fe和Cr的局部吉布斯能量表達(dá)式；（b） 畫(huà)出873K時(shí)局部吉布斯自由能和整體吉布斯自由能的復(fù)合函數(shù)圖。（c） 畫(huà)出873K時(shí)Fe和Cr反應(yīng)的活度圖。（

4、d） Fe和Cr亨利定律常數(shù)是什么？對(duì)于fcc,請(qǐng)用你自己的符號(hào)計(jì)算a和b。（a）由exGj = exGm + ¶exGm/ ¶ xj - å xi ¶exGm/ ¶ xi可得 exGFe=XcrX FeexG(bcc)+XCr exGm(bcc)-XFeXCr exG+XCrXFe exG =XcrX Fe (2510411.7152T) +XCr (2510411.7152T) -XFeXCr(2510411.7152T) +XCrXFe (2510411.7152T) =X2Cr (2510411.7152T)同理；可得;exGCr=X2

5、Fe(2510411.7152T)(b)當(dāng)T=873K時(shí)，Gex(bcc)xCrxFe (2510411.7152T)= xCrxFe 14876.6304 J設(shè)xCr =X，則XFe=1-XexGFe=X2·14876.6304 J （T=873K）exGCr=（1-X）2·14876.6304 J （T=873K）圖一 exGFe-X圖圖二 exGcr-X圖圖三 exG-X圖（C）am=Xm·fm aB = xB expX2·oL /(RT) exG (bcc)/JxCrxFe oL oL=2510411.7152T因而 aFe= (1-X)· expX2·(2510411.7152T) /(RT)（T=873K）aCr= X· exp(1-X)2·(2510411.7152T) /(RT) （T=873K）圖三 aCr X圖圖五 aFeX圖(d) fb = expoL /RT所以:fFe =fCr = exp2510411.7152T /RTfcc:exGFe = X2Cr (1310831.823T2.748T InT)exGCr = X2Fe (1310831.823T2.748T lnT