简介概要

RE-X二元合金相图的热力学数据库

来源期刊:中国有色金属学报2011年第4期

论文作者:刘兴军 张红玲 王书亮 王翠萍 潘复生 汤爱涛 赵栋梁

文章页码:865 - 874

关键词:稀土合金;相图;热力学计算

Key words:rare earth alloys; phase diagrams; thermodynamic modeling

摘    要:利用CALPHAD方法,采用亚正规溶体模型、亚点阵模型以及理想气体模型来描述RE-X (Ag, Bi, Cr, Mn, Mo, V, Zn)中二元系各相的Gibbs自由能,并结合相平衡及热力学性质的实验结果,对Ag-RE (RE: Sc, Y, Nd, Sm, Gd, Tb, Ho, Er)、Bi-RE (RE: Nd, Tm, Er, Ho, Pr, Gd)、Cr-RE (RE: Ce, Nd, Sm, Lu)、Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu)、Mo-RE (RE: Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu)、V-RE (RE: La, Ce, Pr, Nd, Ho, Lu)和Zn-RE (RE: Y, Ce, Pr, Nd, Sm ) 各二元系相图进行热力学优化与计算。计算结果与实验数据取得很好的一致性,并结合其他相关稀土二元系相图热力学计算,初步建立部分稀土二元合金相图的热力学数据库。该热力学数据库可以提供相平衡及热力学性质等多种信息,为外推计算稀土多组元体系的相平衡提供理论基础,并为高性能稀土合金材料的设计及制备提供重要的理论指导。

Abstract: The thermodynamic assessments of phase diagrams in the Ag-RE (RE: Sc, Y, Nd, Sm, Gd, Tb, Ho, Er), Bi-RE (RE: Nd, Tm, Er, Ho, Pr, Gd), Cr-RE (RE: Ce, Nd, Sm, Lu), Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu), Mo-RE (RE: Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu), V-RE (RE: La, Ce, Pr, Nd, Ho, Lu) and Zn-RE (RE: Y, Ce, Pr, Nd, Sm) binary alloy systems were carried out by using calculation of phase diagrams (CALPHAD) method on the basis of the experimental data including thermodynamic properties and phase equilibria. The Gibbs free energies of the solution phases were described by the subregular solution model with Redlich–Kister equation, and those of the intermetallic compounds and gas phase were, respectively, described by sublattice model and ideal gas model. A consistent set of thermodynamic parameters were derived to describe the Gibbs free energies of each solution phase and intermetallic compound. The calculated phase diagrams and thermodynamic properties are in good agreement with the experimental data. The primary thermodynamic database of rare earth alloys is developed, which will provide important information including phase diagrams and various thermodynamic properties for development of rare earth alloy materials.



详情信息展示

文章编号:1004-0609(2011)04-0865-10

RE-X二元合金相图的热力学数据库

刘兴军1,张红玲1,王书亮1,王翠萍1,潘复生2,汤爱涛2,赵栋梁3

(1. 厦门大学 材料学院,厦门 361005;

2. 重庆大学 材料科学与工程学院,重庆 400045;

3. 北京钢铁研究总院,北京 100081)

摘  要:利用CALPHAD方法,采用亚正规溶体模型、亚点阵模型以及理想气体模型来描述RE-X (Ag, Bi, Cr, Mn, Mo, V, Zn)中二元系各相的Gibbs自由能,并结合相平衡及热力学性质的实验结果,对Ag-RE (RE: Sc, Y, Nd, Sm, Gd, Tb, Ho, Er)、Bi-RE (RE: Nd, Tm, Er, Ho, Pr, Gd)、Cr-RE (RE: Ce, Nd, Sm, Lu)、Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu)、Mo-RE (RE: Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu)、V-RE (RE: La, Ce, Pr, Nd, Ho, Lu)和Zn-RE (RE: Y, Ce, Pr, Nd, Sm ) 各二元系相图进行热力学优化与计算。计算结果与实验数据取得很好的一致性,并结合其他相关稀土二元系相图热力学计算,初步建立部分稀土二元合金相图的热力学数据库。该热力学数据库可以提供相平衡及热力学性质等多种信息,为外推计算稀土多组元体系的相平衡提供理论基础,并为高性能稀土合金材料的设计及制备提供重要的理论指导。

关键词:稀土合金;相图;热力学计算

中图分类号:TG 113.14       文献标志码:A

Thermodynamic database of phase diagram in RE-X binary alloy systems

LIU Xing-jun1, ZHANG Hong-ling1, WANG Shu-liang1, WANG Cui-ping1, PAN Fu-sheng2,

TANG Ai-tao2, ZHAO Dong-liang3

(1. College of Materials, Xiamen University, Xiamen 361005, China;

2. College of Material Science and Engineering, Chongqing University, Chongqing 400045, China;

3. Beijing General Iron and Steel Research Institute, Beijing 100081, China)

Abstract: The thermodynamic assessments of phase diagrams in the Ag-RE (RE: Sc, Y, Nd, Sm, Gd, Tb, Ho, Er), Bi-RE (RE: Nd, Tm, Er, Ho, Pr, Gd), Cr-RE (RE: Ce, Nd, Sm, Lu), Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu), Mo-RE (RE: Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu), V-RE (RE: La, Ce, Pr, Nd, Ho, Lu) and Zn-RE (RE: Y, Ce, Pr, Nd, Sm) binary alloy systems were carried out by using calculation of phase diagrams (CALPHAD) method on the basis of the experimental data including thermodynamic properties and phase equilibria. The Gibbs free energies of the solution phases were described by the subregular solution model with Redlich–Kister equation, and those of the intermetallic compounds and gas phase were, respectively, described by sublattice model and ideal gas model. A consistent set of thermodynamic parameters were derived to describe the Gibbs free energies of each solution phase and intermetallic compound. The calculated phase diagrams and thermodynamic properties are in good agreement with the experimental data. The primary thermodynamic database of rare earth alloys is developed, which will provide important information including phase diagrams and various thermodynamic properties for development of rare earth alloy materials.

Key words: rare earth alloys; phase diagrams; thermodynamic modeling

稀土元素由于其结构的特殊性而具有诸多其他元素所不具备的光、电、磁、热等性能,从而可以制备成许多能用于高新技术的新材料[1]。中国是稀土资源大国,稀土材料的开发具有重要的战略意义。相图作为材料设计的“地图”,对稀土材料的开发具有重要的指导意义。因此,有效地利用稀土二元合金的实验相图及热力学性能等相关信息,开展相图的热力学计算并建立稀土合金的热力学设计系统,实现稀土合金的成分与组织的精确设计,将是一项具有重要理论价值的研究工作。

相图计算的CALPHAD技术[2]是通过建立热力学模型来计算体系的相图和热力学性质,其特点是通过二元和三元等低组元系的实验数据为主建立的热力学模型和多元系的少量关键实验数据相结合,可以预测实用多元合金的相平衡、热力学性质、组元的活度和蒸汽压、相变驱动力等合金的性质等。CALPHAD方法[2]已经成为多元合金设计的有效手段。

本研究利用CALPHAD方法,结合各种实验数据对Ag-RE (RE: Sc, Y, Nd, Sm, Gd, Tb, Ho, Er)、Bi-RE (RE: Nd, Tm, Er, Ho, Pr, Gd)、Cr-RE (RE: Ce, Nd, Sm, Lu)、Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu)、Mo-RE (RE: Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu)、V-RE (RE: La, Ce, Pr, Nd, Ho, Lu)和Zn-RE (RE: Y, Ce, Pr, Nd, Sm)各二元系相图进行热力学优化与计算,获得一组自洽合理的描述各相自由能的热力学参数,并结合其他相关稀土二元系相图热力学计算的文献报道[3-12],初步建立 RE-X 二元合金相图的热力学数据库。

1  热力学模型

1.1  液相和端际固溶体相

液相和端际固溶体相的Gibbs自由能都是采用亚正规溶体模型[13]描述的,其摩尔Gibbs自由能表示为

      (1)

式中:xi相中组分i的摩尔分数;为纯组分i的相摩尔Gibbs自由能;相的摩尔过剩自由能,用Redlich-Kister多项式描述:

(2)

式中:表示二元相互作用参数,可采用如下形式:

                        (3)

式中:a、b和c是待优化的热力学参数。

是磁性对Gibbs自由能的贡献,用如下等式描述:

                    (4)

式中:是归一化温度()的函数;是磁有序的临界温度;β是与总磁熵有关的量。大多数情况下,设它等于每摩尔原子的玻尔(Bohr)磁矩。

本研究在计算Mn-RE各二元系相图时,考虑磁性自由能对相变的影响。

1.2  理想气体模型

在RE-X二元系中存在气相时,采用理想气体模型[14]来描述气相的自由能。Ggas表示气相自由能,用如下等式描述:

    (5)

式中:xi为气相中组分i的摩尔分数;P­0为标准大气压;P为体系的实际压力;为纯组分i的气相摩尔Gibbs自由能。

1.3  金属间化合物相

在RE-X体系中,线性化合物相采用通式AmBn表示,该类化合物相的Gibbs自由能采用亚点阵模  型[15]来描述。其摩尔Gibbs自由能采用AmBn的亚点阵模型,表达式如下:

                           (6)

式中:为该化合物标准形成自由能;分别为纯组元A和B的摩尔自由能;参数是待优化的热力学参数;是磁性自由能,也用式(4)描述。

2  RE-X二元系相图热力学数据库的建立

本研究利用相图计算的CALPHAD方法[2],结合相平衡和热力学性质的相关实验数据,对Ag-RE (RE: Sc[16], Y[17], Nd[18], Sm, Gd[18], Tb, Ho, Er)、Bi-RE (RE: Nd[19], Tm[19], Er, Ho, Pr, Gd)、Cr-RE (RE: Ce, Nd, Sm, Lu)、Mn-RE (RE: Pr[20], Nd, Sm[21], Eu, Tb, Dy[20], Ho[21], Er, Tm, Yb, Lu)、Mo-RE (RE: Sc, Y, La[22], Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu)、V-RE (RE: La, Ce, Pr, Nd, Ho, Lu)和Zn-RE (RE: Y[23], Ce[24], Pr[24], Nd[25], Sm[25])各二元系相图进行了热力学优化与计算,具体的工作是在 SUNDMAN等[2]开发的Thermo-Calc软件上完成的。其中,液相和端际固溶体相的Gibbs自由能采用亚正规溶体模型来描述,金属间化合物相的Gibbs自由能采用亚点阵模型来描述,而气相的Gibbs自由能采用理想气体模型来描述。计算结果与实验值取得了较好的一致性,得到一组合理的、用于描述RE-X各二元系中各相自由能的热力学参数。

本课题组的最终研究目标是建立稀土合金的热力学设计系统。目前已初步建立RE-X二元合金相图的热力学数据库。该数据库可以提供相平衡及热力学性质等多种信息,例如稳定和亚稳相图的计算、热力学性质(生成焓、Gibbs自由能、活度、熵等)的计算以及相分数与体积分数的计算等。同时,RE-X二元系相图的热力学数据库将为稀土合金三元及多元系合金相图的热力学计算提供重要的基础热力学参数。

3  热力学数据库的应用

3.1  RE-X二元系相图

利用本研究建立的RE-X二元合金相图的热力学数据库,计算的部分RE-X二元系相图如图1所示。


图1  RE-X二元系相图的计算结果

Fig.1  Calculated results of phase diagram in RE-X binary systems: (a) Ag-Sc system; (b) Ag-Nd system; (c) Mo-Ho system;     (d) Mo-Eu system; (e) Mn-Sm system; (f) Mn-Tm system

图1(a)和(b)所示分别为Ag-Sc和Ag-Nd二元系相图的计算结果与实验数据。在Ag-Sc和Ag-Nd二元系中都存在多个线性化合物相,包含多个不变系反应,都呈现出比较复杂的相平衡关系,并利用该热力学数据库可以准确地计算出Ag-Sc和Ag-Nd二元系的相平衡,本研究优化计算结果与实验值取得了较好的一致性。图1(c)所示为Mo-Ho二元系的计算相图,该体系中在高温存在稳定的液相两相分离,并在2 517 ℃下发生偏晶反应L2?L1+(Mo),图1(c)中的虚线所示为计算的亚稳液相两相分离的相界限。图1(d)所示为Mo-Eu二元系相图的计算结果,在该体系中利用理想气体模型对气相的相界线进行了计算,如图1(d) 所示,该体系的相平衡关系可以通过热力学计算得以准确地再现。图1(e)和(f)所示分别为Mn-Sm和Mn-Tm二元系相图的计算结果,在计算Mn-Sm和Mn-Tm二元系相图时,考虑了磁性自由能的贡献,如图1(e)和(f)所示,本研究优化计算的结果与实验值取得了较好的一致性。

3.2  RE-X热力学性质的计算

利用本研究得到的RE-X二元系的热力学参数计算的部分热力学性质如图2(a)~(d)所示。图2(a)所示为Mn-Sm二元系中化合物相在1 024 ℃的形成焓的计算结果(参考态为α-Mn和α-Sm)。图2(b)所示为Ag-Nd二元系中化合物相在1 073 ℃时形成的Gibbs自由能的计算结果(参考态为液相Ag和液相Nd)。图2(c)所示为Ag-Nd二元系中组元Ag和Nd在液相中的活度的计算结果(参考态为液相Ag和液相Nd)。图2(d)所示为Zn-Y二元系中线性化合物相在500 ℃时形成熵的计算结果(参考态为α-Y和液相Zn)。由计算结果可见,该热力学数据库不仅可以很好地再现各个二元系的相平衡关系,也可以计算出各个体系中各相的不同的热力学性质。


图2  RE-X 二元系热力学性质的计算结果

Fig.2  Calculated results of thermodynamic properties in RE-X binary systems: (a) Calculated enthalpies of intermetallic compounds formation at 1 024 ℃ in Mn-Sm system; (b) Calculated Gibbs free energies of formation at 1 073 ℃ in Ag-Nd system;   (c) Calculated activity of components at 1 073 ℃ in Ag-Nd system; (d) Calculated entropy of formation at 5 00 ℃ in Zn-Y system



3.3  稀土合金三元系相图的热力学计算

利用本研究建立的RE-X二元合金相图的热力学数据库,可以为稀土多元系合金相图的热力学优化与计算提供重要的基础热力学参数。图3所示为计算的Zn-Al-Ce[26]三元系在320 ℃时的等温截面相图,计算结果与实验点基本吻合。图4所示为计算的Zn-CeAl2的垂直截面相图与实验数据。可见,计算结果与大部分实验点吻合。


图3  Zn-Al-Ce三元系在320 ℃等温截面的计算结果与实验数据的比较[26]

Fig.3  Comparison of calculated data of isothermal section of Zn-Al-Ce system at 320 ℃ with experimental data[26]

图4  Zn-Al-Ce三元系Zn-CeAl2垂直截面的计算结果与实验数据的比较

Fig.4  Comparison of calculated data of vertical section along Zn-CeAl2 of Zn-Al-Ce system with experimental data


图5(a)和(b)所示分别为计算的Co-Mn-Pr[27]三元系在397 ℃和597 ℃时的等温截面相图。由于该三元系中仅有Co-Mn(597 ℃)及Co-Pr(397 ℃)侧的部分实验信息,本研究利用3个基础二元系的热力学参数,外推计算了整个成分范围内的相平衡。

图6(a)和(b)所示分别为仅利用基础二元系的热力


图5  Co-Mn-Pr三元系在不同温度时等温截面与实验数据的比较[27]

Fig.5  Comparison of calculated data of isothermal section of Co-Mn-Pr ternary system at different temperatures with experimental data[27]: (a) 397 ℃; (b) 597 ℃



学参数计算的Co-Mn-Dy[27]三元系在600 ℃和800 ℃时的等温截面相图。由于Co-Dy和Mn-Dy二元系中均存在多个线性化合物相,因此Co-Mn-Dy三元系的各等温截面相图较为复杂,其中均出现多个三相平衡区域。在图6(b)中出现了较大范围的液相区域,这说明Dy元素可明显降低Co-Mn基合金的熔点。上述外推计算的结果需要进一步的实验验证,但这些计算结果可为稀土合金相图的进一步研究和稀土材料的合金设计提供一定的理论参考。

图7(a)~(c)所示分别为计算的Dy含量为0.1%、


图6  计算的Co-Mn-Dy三元系在不同温度时等温截面[27]

Fig.6  Calculated isothermal section of Co-Mn-Dy ternary system at different temperatures[27]: (a) 600 ℃; (b) 800 ℃



图7  计算的Sn-Bi-Dy三元系在不同Dy含量时的垂直截面相图

Fig.7  Calculated vertical section diagrams at different Dy contents in Sn-Bi-Dy system: (a) x(Dy)=0.1%; (b) x(Dy)=0.2%;       (c) x(Dy)=0.3%


0.2%和0.3%(摩尔分数)时Sn-Bi-Dy三元系的垂直截面相图。从计算结果可以看出,当微量稀土元素Dy加到0.3%时,液相先析出初晶相BiDy,然后再发生共晶反应,即由液相生成固溶体相β-Sn和(Bi)。

图8所示为计算的Sn-Bi-Dy三元系的液相面和各个液相等温线。从图中发现两个共晶反应,一个是(E1



图8  计算的Sn-Bi-Dy三元系的液相面

Fig.8  Calculated liquidus project of Sn-Bi-Dy system


点)在1 177.58 ℃时发生的L?α-Dy+Sn3Dy5+Bi3Dy5,其中反应成分是x(Sn)=9.1%, x(Bi)=3.9%;另一个是(E2点)在140.22 ℃时发生的L?BiDy+β-Sn+(Bi),其中反应成分是x(Sn)=58.7%,x(Bi)=41.1%。把计算的Sn-Bi-Dy三元系低温共晶反应E2的反应温度(140.22 ℃)和计算的Sn-Bi二元系的共晶反应温度(140.6 ℃)比较,发现加入微量的稀土Dy(0.2%)基本没有对共晶点处的反应温度产生影响。但是,从图7(a)~(c)可看出,当微量稀土元素Dy加到0.3%时,液相先析出初晶相BiDy,然后再发生共晶反应,即由液相生成固溶体相β-Sn和(Bi),这将对焊料组织形态产生一定的影响。有研究结果显示[28-30]:加入稀土可以细化焊料的组织,也将对焊料的铺展面积和润湿性产生影响,这些有待于以后的实验研究中解决。

4  结论

1) 本研究利用CALPHAD法,对Ag-RE (RE: Sc, Y, Nd, Sm, Gd, Tb, Dy, Ho, Er)、Bi-RE (RE: Nd, Tm, Er, Ho, Pr, Gd)、Cr-RE (RE: Ce, Nd, Sm, Lu)、Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu)、Mo-RE (RE: Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu)、V-RE (RE: La, Ce, Pr, Nd, Ho, Lu)和Zn-RE (RE: Y, Ce, Pr, Nd, Sm)各二元系的相图进行热力学优化与计算,计算结果与实验值取得了较好的一致性,并初步建立RE-X二元合金相图的热力学数据库。

2) 该热力学数据库将为稀土多元合金相图的热力学计算提供重要的基础热力学参数,同时为稀土合金设计提供重要的理论指导。

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(编辑 李艳红)


                                 

基金项目:国家自然科学基金资助项目(50771087)

收稿日期:2010-06-20;修订日期:2010-09-20

通信作者:王翠萍,教授,博士;电话:0592-2180606;E-mail: wangcp@xmu.edu.cn

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