铝合金中关键二元、三元体系热力学和弹性性质的实验和计算研究
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摘要
当今材料界普遍认识到材料设计与材料合成的耦合是高效制备新材料的最佳途径,而对材料性能的预测是材料设计的核心。材料性能预测已成为一门系统性、综合性和理论性很强的学科,同时它也是实现传统材料和先进材料性能重大突破的关键之一。精确的热力学和弹性性质是设计材料所需的两种重要物性参数,而当前国际上缺乏对铝基合金体系热力学和弹性性质的系统研究。
本论文以多组元商业铝合金体系为研究对象,力求为建立一个基于关键实验,相图热力学和第一原理计算的热力学和弹性性质的自洽的铝合金数据库奠定基础。本工作的总体思路是：首先集成关键实验、计算相图(CALPHAD, CALculation of PHAase Diagram)与第一原理计算方法来获得多组元铝合金中两个关键三元系Al-Mg-Mn和Cu-Si-Zn体系精准的相图热力学数据库；然后使用第一原理计算研究多组元铝合金体系中含铝化合物在0K和有限温度下的热力学性质,并预测含铝化合物的弹性性质和合金元素对铝的弹性性质的影响。本工作建立了一种综合考虑关键实验,相图热力学和第一原理计算方法对多组元铝合金体系的热力学和弹性性质进行精确描述的研究方法。该方法对其它多元合金体系的热力学和弹性性质的研究提供了一种可借鉴的方法。本研究工作取得以下重要成果：
(1)由于λ-A14Mn的形核障碍,文献中关于λ-A14Mn熔化行为的报道一直有争议。本工作利用精确设计的静态法和动态法相结合的关键实验重新研究了Al-Mn体系富Al端的相平衡,首次明确了λ-A14Mn的熔化行为,而且发现了两个新的零变量平衡。根据晶体结构数据,将A18Mn5的亚点阵模型由Al12Mn4(A1,Mn)10修改为A112Mn5(A1,Mn)9,同时也给出A111Mn4的高温相的热力学模型。在考虑当前实验数据和可靠的文献数据的基础上,获得了能够精确描述Al-Mn和Al-Mg-Mn体系相图热力学数据的热力学参数。计算和实验数据的比较表明,本工作的热力学参数能够很好地描述几乎所有的合理的实验数据。
(2)多组元A1合金热力学数据库中γ相模型的兼容性问题限制了A1合金热力学数据的应用。为了使Cu-Si-Zn体系的热力学描述与已有的多组元A1合金数据库相匹配,使用了新的亚点阵模型(Zn)4(Cu,Zn)1(Cu,Zn)8来描述Cu-Zn体系的γ相,并重新优化了Cu-Zn体系的热力学参数。使用15个关键合金研究了Cu-Si-Zn体系600℃等温截面。本实验测定了5个三相区,没有发现三元化合物。澄清了文献中关于600℃时富Cu角α,β,γ-Cu5Zn8和κ-Cu7Si之间相关系的争议。基于本工作得到的Cu-Zn体系热力学参数,结合文献中的和本工作的实验数据,使用CALPHAD方法重新优化了Cu-Si-Zn体系,获得了一套可以在482到847℃C温度范围内和整个成分范围内合理描述该体系相图的热力学参数。
(3)使用第一原理计算预测了A1基化合物的能量-体积关系(物态方程),形成焓和弹性常数。基于预测的弹性常数,研究了每个化合物的稳定性(波恩判据)及多晶内聚性质,如体模量、剪切模量、B/G比率和各向异性比率等。计算得到的绝大部分化合物的形成焓与实验数据吻合,并和Al基多组元热力学数据库相一致。计算的单晶和多晶弹性性质与文献数据相吻合。本工作系统地给出了A1基化合物的能量基准和弹性性质,为A1合金设计提供了重要的物性参数。
(4)基于第一原理计算,在准谐近似下,考虑晶格振动和价电子热激发对能量的贡献,系统研究了在工业中非常重要的铝基合金化合物的热力学性质。计算得到的热力学性质和文献中报道的实验数据及相图热力学计算结果符合较好。同时发现CALPHAD方法中常用于描述化合物热容Cp的Neumann-Kopp定律对很多体系并不适合,因此需要改进CALPHAD方法中部分化合物Cp的描述。本工作预测的热力学性质为更精确的铝合金体系热力学模拟提供了坚实的基础。
(5)文献中没有合金元素对A1的弹性性质影响的系统报道。本工作使用第一原理计算研究了15种合金元素对Al的弹性性质的影响。计算得到的晶格常数、局域晶格畸变和弹性常数与已有的实验数据相吻合。基于得到的弹性常数,获得了合金的体模量,剪切模量,杨氏模量和B/G比。经分析发现Al合金的体模量随摩尔体积、合金原子与Al原子之间距离的增加而减小；随合金元素自身体模量的增加而增加；且A1合金的体模量与合金的摩尔体积和电荷密度之间的线性关系为：nAl31χ=1.0594+0.0207√B/Vm。
It is well known that an efficient way to develop new materials is the integration of materials design and materials synthesis, while the key factor for materials design is the prediction of material properties. The prediction of the properties for materials has been developed to be a systematic, comprehensive and theoretical science, which is also the key factor to significantly improve the properties of traditional and advanced materials. Accurate descriptions of thermodynamic and elastic properties are important information for materials design. However, there is a lack of systematic description on the thermodynamic and elastic properties in Al-based alloy systems.
The object of the present dissertation is about multi-component commercial Al alloy system, aiming at establishing the basis of a systematic thermodynamic and elastic properties database by integrating data from key experiments, CALPHAD (CALculation of PHAse Diagram) and first-principles calculations. The overall idea of the present work is:A hybrid approach of key experiments, first-principles calculations and CALPHAD was firstly employed to establish the accurate thermodynamic databases of the Al-Mg-Mn and Cu-Si-Zn systems, and first-principles calculations was then utilized to predict the thermodynamic properties of Al-contained compounds in the multi-component alloys at both0K and finite temperatures, and the elastic properties of the Al-contained compounds and the effects of alloying elements to the elastic properties of Al systematically. A scientific integration of the key experiments, CALPHAD method and first-principles calculations was established in the present work to accurately describe the thermodynamic and elastic properties Al alloys, and can serve as the guidance for accurate description of the thermodynamic and elastic properties for other alloy systems. The major content of the present dissertation is summarized as follows:
(1) The melting behavior of λ-Al4Mn is contradictory in the literature due to the nucleation barrier. The phase equilibria in the Al-rich side of the Al-Mn system have been reinvestigated by precisely designed key experiments, the melting behavior of λ-Al4Mn was correctly elucidated for the first time, and two invariant reactions associated with λ-Al4Mn were observed. The model Al12Mn4(Al,Mn)10previously used for Al8Mn5was modified to be Al12Mn5(Al,Mn)9based on crystal structure data. In addition, the high-temperature form of Al11Mn4was included in the present assessment. Based on the present experimental data and reliable literature data, a new set of thermodynamic description for the Al-Mn system and Al-Mg-Mn system was obtained in the present work. Comprehensive comparisons show that the experimental data are well accounted for by the present descriptions and significant improvements were found when compared with previous assessments.
(2) The application of the Al thermodynamic databases is restricted by the model inconsistence of the y phase. In an effort to provide a compatible thermodynamic description of the Cu-Si-Zn system for the multi-component Al-based thermodynamic database, the Cu-Zn binary system was remodeled using the CALPHAD approach with a new sublattice model Zn4(Cu,Zn)1(Cu,Zn)8for the y-Cu5Zn8phase. In addition, the isothermal section of the Cu-Si-Zn ternary system at600℃was experimentally determined by preparing fifteen alloys with their composition selection guided by computational predictions. At600℃, no ternary compounds were observed, and five three-phase equilibria were well determined. In particular, the longstanding controversy regarding the four three-phase equilibria in the Cu-rich corner involving the phases a,(3, γ-Cu5Zn8, and K-Cu7Si was resolved experimentally in the present work. Subsequently, a thermodynamic description of the Cu-Si-Zn system was obtained over the studied temperature range and the entire composition range based on the presently modeled Cu-Zn system and the experimental data from the literature and the present measurements.
(3) A systematic first-principles calculations of energy vs. volume (E-V) equations of state (EOS), enthalpy of formation and single crystal elastic stiffness constants (cij's) has been performed for Al-based binary and ternary compounds. The calculated enthalpies of formation, and cij's of these compounds were compared with the available experimental data in the literature. In addition, elastic properties of polycrystalline aggregates including bulk modulus (B), shear modulus (G), Young's modulus (E), B/G ratio, and anisotropy ratio were also determined and compared with the experimental and theoretical results available in the literature. All the compounds studied in the present work are mechanical stable based on Born's criteria. The systematic predictions of elastic properties and enthalpies of formation for Al compounds provide helpful insight into the understanding and design of Al-based alloys.
(4) The finite-temperature thermodynamic properties for the technologically important Al compounds have been studied based on first-principles calculations. The thermodynamic properties were predicted in terms of the quasiharmonic approach by considering both the lattice vibrational and thermal electronic contributions. When possible, the predicted properties were compared with data from experiments and thermodynamic modeling, and a good agreement is found. It is also found the Neumann-Kopp law, which is commonly used to estimate the Cp for compounds in CALPHAD method, is not valiad for some of the investigated compounds. The predicted thermodynamic properties herein provide robust foundation for thermodynamic modeling of Al systems studied herein.
(5) The effects of fifteen alloying elements on elastic properties of Al have been investigated using first-principles calculations. A good agreement is obtained between calculated and available experimental data. Lattice parameters of the studied Al alloys are found to be dependent on atomic radii of solute atoms. The elastic properties of polycrystalline aggregates including bulk modulus, shear modulus, Young's modulus, and the B/G ratio are also determined based on the calculated elastic constants. It is found that the bulk modulus of Al alloys decreases with increasing volume due to the addition of alloying elements and they also related to the total molar volume (Vm) and electron density (nAl31X)with the relationship of nAl31X=1.0594+0.0207(?)
本论文以多组元商业铝合金体系为研究对象,力求为建立一个基于关键实验,相图热力学和第一原理计算的热力学和弹性性质的自洽的铝合金数据库奠定基础。本工作的总体思路是：首先集成关键实验、计算相图(CALPHAD, CALculation of PHAase Diagram)与第一原理计算方法来获得多组元铝合金中两个关键三元系Al-Mg-Mn和Cu-Si-Zn体系精准的相图热力学数据库；然后使用第一原理计算研究多组元铝合金体系中含铝化合物在0K和有限温度下的热力学性质,并预测含铝化合物的弹性性质和合金元素对铝的弹性性质的影响。本工作建立了一种综合考虑关键实验,相图热力学和第一原理计算方法对多组元铝合金体系的热力学和弹性性质进行精确描述的研究方法。该方法对其它多元合金体系的热力学和弹性性质的研究提供了一种可借鉴的方法。本研究工作取得以下重要成果：
(1)由于λ-A14Mn的形核障碍,文献中关于λ-A14Mn熔化行为的报道一直有争议。本工作利用精确设计的静态法和动态法相结合的关键实验重新研究了Al-Mn体系富Al端的相平衡,首次明确了λ-A14Mn的熔化行为,而且发现了两个新的零变量平衡。根据晶体结构数据,将A18Mn5的亚点阵模型由Al12Mn4(A1,Mn)10修改为A112Mn5(A1,Mn)9,同时也给出A111Mn4的高温相的热力学模型。在考虑当前实验数据和可靠的文献数据的基础上,获得了能够精确描述Al-Mn和Al-Mg-Mn体系相图热力学数据的热力学参数。计算和实验数据的比较表明,本工作的热力学参数能够很好地描述几乎所有的合理的实验数据。
(2)多组元A1合金热力学数据库中γ相模型的兼容性问题限制了A1合金热力学数据的应用。为了使Cu-Si-Zn体系的热力学描述与已有的多组元A1合金数据库相匹配,使用了新的亚点阵模型(Zn)4(Cu,Zn)1(Cu,Zn)8来描述Cu-Zn体系的γ相,并重新优化了Cu-Zn体系的热力学参数。使用15个关键合金研究了Cu-Si-Zn体系600℃等温截面。本实验测定了5个三相区,没有发现三元化合物。澄清了文献中关于600℃时富Cu角α,β,γ-Cu5Zn8和κ-Cu7Si之间相关系的争议。基于本工作得到的Cu-Zn体系热力学参数,结合文献中的和本工作的实验数据,使用CALPHAD方法重新优化了Cu-Si-Zn体系,获得了一套可以在482到847℃C温度范围内和整个成分范围内合理描述该体系相图的热力学参数。
(3)使用第一原理计算预测了A1基化合物的能量-体积关系(物态方程),形成焓和弹性常数。基于预测的弹性常数,研究了每个化合物的稳定性(波恩判据)及多晶内聚性质,如体模量、剪切模量、B/G比率和各向异性比率等。计算得到的绝大部分化合物的形成焓与实验数据吻合,并和Al基多组元热力学数据库相一致。计算的单晶和多晶弹性性质与文献数据相吻合。本工作系统地给出了A1基化合物的能量基准和弹性性质,为A1合金设计提供了重要的物性参数。
(4)基于第一原理计算,在准谐近似下,考虑晶格振动和价电子热激发对能量的贡献,系统研究了在工业中非常重要的铝基合金化合物的热力学性质。计算得到的热力学性质和文献中报道的实验数据及相图热力学计算结果符合较好。同时发现CALPHAD方法中常用于描述化合物热容Cp的Neumann-Kopp定律对很多体系并不适合,因此需要改进CALPHAD方法中部分化合物Cp的描述。本工作预测的热力学性质为更精确的铝合金体系热力学模拟提供了坚实的基础。
(5)文献中没有合金元素对A1的弹性性质影响的系统报道。本工作使用第一原理计算研究了15种合金元素对Al的弹性性质的影响。计算得到的晶格常数、局域晶格畸变和弹性常数与已有的实验数据相吻合。基于得到的弹性常数,获得了合金的体模量,剪切模量,杨氏模量和B/G比。经分析发现Al合金的体模量随摩尔体积、合金原子与Al原子之间距离的增加而减小；随合金元素自身体模量的增加而增加；且A1合金的体模量与合金的摩尔体积和电荷密度之间的线性关系为：nAl31χ=1.0594+0.0207√B/Vm。
It is well known that an efficient way to develop new materials is the integration of materials design and materials synthesis, while the key factor for materials design is the prediction of material properties. The prediction of the properties for materials has been developed to be a systematic, comprehensive and theoretical science, which is also the key factor to significantly improve the properties of traditional and advanced materials. Accurate descriptions of thermodynamic and elastic properties are important information for materials design. However, there is a lack of systematic description on the thermodynamic and elastic properties in Al-based alloy systems.
The object of the present dissertation is about multi-component commercial Al alloy system, aiming at establishing the basis of a systematic thermodynamic and elastic properties database by integrating data from key experiments, CALPHAD (CALculation of PHAse Diagram) and first-principles calculations. The overall idea of the present work is:A hybrid approach of key experiments, first-principles calculations and CALPHAD was firstly employed to establish the accurate thermodynamic databases of the Al-Mg-Mn and Cu-Si-Zn systems, and first-principles calculations was then utilized to predict the thermodynamic properties of Al-contained compounds in the multi-component alloys at both0K and finite temperatures, and the elastic properties of the Al-contained compounds and the effects of alloying elements to the elastic properties of Al systematically. A scientific integration of the key experiments, CALPHAD method and first-principles calculations was established in the present work to accurately describe the thermodynamic and elastic properties Al alloys, and can serve as the guidance for accurate description of the thermodynamic and elastic properties for other alloy systems. The major content of the present dissertation is summarized as follows:
(1) The melting behavior of λ-Al4Mn is contradictory in the literature due to the nucleation barrier. The phase equilibria in the Al-rich side of the Al-Mn system have been reinvestigated by precisely designed key experiments, the melting behavior of λ-Al4Mn was correctly elucidated for the first time, and two invariant reactions associated with λ-Al4Mn were observed. The model Al12Mn4(Al,Mn)10previously used for Al8Mn5was modified to be Al12Mn5(Al,Mn)9based on crystal structure data. In addition, the high-temperature form of Al11Mn4was included in the present assessment. Based on the present experimental data and reliable literature data, a new set of thermodynamic description for the Al-Mn system and Al-Mg-Mn system was obtained in the present work. Comprehensive comparisons show that the experimental data are well accounted for by the present descriptions and significant improvements were found when compared with previous assessments.
(2) The application of the Al thermodynamic databases is restricted by the model inconsistence of the y phase. In an effort to provide a compatible thermodynamic description of the Cu-Si-Zn system for the multi-component Al-based thermodynamic database, the Cu-Zn binary system was remodeled using the CALPHAD approach with a new sublattice model Zn4(Cu,Zn)1(Cu,Zn)8for the y-Cu5Zn8phase. In addition, the isothermal section of the Cu-Si-Zn ternary system at600℃was experimentally determined by preparing fifteen alloys with their composition selection guided by computational predictions. At600℃, no ternary compounds were observed, and five three-phase equilibria were well determined. In particular, the longstanding controversy regarding the four three-phase equilibria in the Cu-rich corner involving the phases a,(3, γ-Cu5Zn8, and K-Cu7Si was resolved experimentally in the present work. Subsequently, a thermodynamic description of the Cu-Si-Zn system was obtained over the studied temperature range and the entire composition range based on the presently modeled Cu-Zn system and the experimental data from the literature and the present measurements.
(3) A systematic first-principles calculations of energy vs. volume (E-V) equations of state (EOS), enthalpy of formation and single crystal elastic stiffness constants (cij's) has been performed for Al-based binary and ternary compounds. The calculated enthalpies of formation, and cij's of these compounds were compared with the available experimental data in the literature. In addition, elastic properties of polycrystalline aggregates including bulk modulus (B), shear modulus (G), Young's modulus (E), B/G ratio, and anisotropy ratio were also determined and compared with the experimental and theoretical results available in the literature. All the compounds studied in the present work are mechanical stable based on Born's criteria. The systematic predictions of elastic properties and enthalpies of formation for Al compounds provide helpful insight into the understanding and design of Al-based alloys.
(4) The finite-temperature thermodynamic properties for the technologically important Al compounds have been studied based on first-principles calculations. The thermodynamic properties were predicted in terms of the quasiharmonic approach by considering both the lattice vibrational and thermal electronic contributions. When possible, the predicted properties were compared with data from experiments and thermodynamic modeling, and a good agreement is found. It is also found the Neumann-Kopp law, which is commonly used to estimate the Cp for compounds in CALPHAD method, is not valiad for some of the investigated compounds. The predicted thermodynamic properties herein provide robust foundation for thermodynamic modeling of Al systems studied herein.
(5) The effects of fifteen alloying elements on elastic properties of Al have been investigated using first-principles calculations. A good agreement is obtained between calculated and available experimental data. Lattice parameters of the studied Al alloys are found to be dependent on atomic radii of solute atoms. The elastic properties of polycrystalline aggregates including bulk modulus, shear modulus, Young's modulus, and the B/G ratio are also determined based on the calculated elastic constants. It is found that the bulk modulus of Al alloys decreases with increasing volume due to the addition of alloying elements and they also related to the total molar volume (Vm) and electron density (nAl31X)with the relationship of nAl31X=1.0594+0.0207(?)
引文
[1]Totten G E, D.S. M, Handbook of Aluminum[M], New York:Marcel Dekker; 2003.
[2]Zolotorevsky V S, Belov N A, Glazoff M V, Casting Aluminum Alloys[M], Amsterdam:Elsevier; 2007.
[3]潘复生,张丁非,铝合金及应用[M],化学工业出版社；2006.
[4]王祝堂,新的变形铝合金的成分与简明性能[J].轻合金加工技术,2001；29：1-4.
[5]张君尧,铝合金材料的新进展[J].轻合金加工技术,1998；26：1-10.
[6]http://market.cnal.com/statistics/2012/02-21/1329785236266980.shtml
[7]http://market.cnal.com/statistics/2012/02-21/1329784946266975.shtml
[8]Integrated Computational Materials Engineering:A Transformational Discipline for Improved Competitivies and National Security[M], Washinton, D.C.:The National Academies Press; 2008.
[9]http://www.whitehouse.gov/blog/2011/06/24/materials-genome-initiative-renaissa nce-american-manufacturing
[10]Kaufman L, Bernstein H, Computer Calculations of Phase Diagrams[M], New York:Academic Press; 1970.
[11]Andersson J O, Helander T, Hoeglund L, et al., THERMO-CALC and DICTRA, Computational Tools for Materials Science[J]. CALPHAD,2002; 26(2): 273-312.
[12]Du Y, Wang J, Ouyang Y F, et al., An Approach to Determine Enthalpies of Formation for Ternary Compounds[J]. J. Min. Metall. Sect. B-Metall.,2010; 46: 1-9.
[13]Du Y, Liu S H, Zhang L J, et al., An overview on phase equilibria and thermodynamic modeling in multicomponent Al alloys:Focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system[J]. CALPHAD,2011; 35:427-445.
[14]Kohn W, Sham L J, Self-Consistent Equations Including Exchange and Correlation Effects[J]. Phys. Rev. A,1965; 140(2):1133-1138.
[15]Wang Y, Liu Z K, Chen L Q, Thermodynamic properties of Al, Ni, NiAl, and Ni3Al from first-principles calculations [J]. Acta Mater.,2004; 52:2665-2671.
[16]乔芝郁,郝士明,相图计算研究的进展[J].材料与冶金学报,2005；4(2)83-89.
[17]徐祖耀,材料热力学[M],北京：高等教育出版社；2009.
[18]张圣弼,李道子,相图-原理、计算及在冶金中的应用[M],北京：冶金工业出版社：1986.
[19]Kodentsov A A, Bastin G F, van Loo F J J, The diffusion couple technique in phase diagram determination [J]. J. Alloys Compd.,2001; 320:207-217.
[20]Girchner G, Larbo G, Uhrenius B, Distribution of chromium and manganese between ferrite and austenite using experimental measurements and thermodynamic calculations[J]. Prakt. Metall.,1971; 8:641-654.
[21]Hasebe M, Nishizawa T, Applications of phase diagrams in metallurgy and ceramics[M], Washington:National Bureau of Standards SP-496; 1978.
[22]Jin Z P, A study of the range of stability of sigma phase in some ternary system [J]. Scand. J. Metall.,1981; 10:178-187.
[23]Xu H H, Du Y, Huang B Y, et al., Phase diagram of the Co-Cu-Ti system at 850 ℃[J]. Z. Metallkd.,2006; 97:140-144.
[24]Zhao J C, The diffusion-multiple approach to designing alloys[J]. Ann. Rev. Mater. Res.,2005; 35:51-73.
[25]Zhao J C, Combinatorial approaches as effective tools in the study of phase diagrams and composition-structure-property relationships [J]. Prog. Mater. Sci., 2006; 51:557-631.
[26]王培铭,许乾慰,材料研究方法[M],北京：科学出版社；2005.
[27]Du Y, Schuster J C, An effective approach to describe growths of binary intermediate phases with narrow ranges of homogeneity [J]. Metall. Mater. Trans. A,2001; 32(9):2396-2400.
[28]http://www.calphad.org/
[29]Turchi P E A, Abrikosov I A, Burton B, et al., Interface between quantum-mechanical-based approaches, experiments, and CALPHAD methodology [J]. CALPHAD,2007; 31:4-27.
[30]冯端,师昌绪,刘治国,材料科学导论[M],北京：化学工业出版社；2002.
[31]http://www.thermocalc.com
[32]Hillert M, Phase Equilibria, Phase Diagrams and Phase Transformations:Their Thermodynamic Basis[M], UK:Cambridge University Press; 1998.
[33]郝士明,材料热力学[M],北京：化学工业出版社；2003.
[34]Curtarolo S, Kolmogorov A N, Cocks F H, High-throughput ab initio analysis of the Bi-In, Bi-Mg, Bi-Sb, In-Mg, In-Sb and Mg-Sb systems[J]. CALPHAD,2005; 29:155-161.
[35]Gonzales-Ormeno P G, Petrilli H M, Schon C G, Ab initio calculation of the bcc Mo-Al (Molybdenum-aluminium) phase diagram:Implications for the nature of the z2-MoAl phase[J]. Scripta Mater.,2005; 53:751-756.
[36]Lechermann F, Faehnle M, Sanchez J M, First-Principles Investigation of the Ni-Fe-Al System[J]. Intermetallics,2005; 13(10):1096-1109.
[37]Kaufman L, Fahnle M, Turchi P E A, et al., Thermodynamics of the Cr-Ta-W system by combing the ab initio and CALPHAD methods[J]. CALPHAD,2002; 25:419-433.
[38]Chvatalova K, Fahnle M, Houserova J, et al., First-principles calculations of energetics of sigma phase formation and thermodynamic modeling in Fe-Ni-Cr system[J]. J. Alloys Compd.,2004; 378:71-74.
[39]Ohtani H, Fahnle M, Yamano M, et al., Thermodynamic analysis of the Co-Al-C and Ni-Al-C systems by incorporating ab initio energetic calculations into the CALPHAD approach[J]. CALPHAD,2004; 28:177-190.
[40]Jiang C, Gleeson B, A Combined First-Principles/CALPHAD Modeling of the Al-Ir System[J]. Acta Mater.,2006; 54(15):4101-4110.
[41]Du Y, Wang J, Zhao J R, et al., Reassessment of the Al-Mn system and a thermodynamic description of the Al-Mg-Mn system[J]. Int. J. Mater. Res.,2007; 98:855-871.
[42]Zhang L J, Wang J, Du Y, et al., Thermodynamic properties of the Al-Fe-Ni system acquired via a hybrid approach combining calorimetry, first-principles and CALPHAD[J]. Acta Mater.,2009; 57:5324-5341.
[43]Dinsdale A T, SGTE Data for Pure Elements[J]. CALPHAD,1991; 15:317-425.
[44]Wang Y, Curtarolo S, Jiang C, et al., Ab initio lattice stability in comparison with CALPHAD lattice stability[J]. CALPHAD,2004; 28:79-90.
[45]Sluiter M H F, Ab initio lattice stabilities of some elemental complex structures[J]. CALPHAD,2006; 30:357-366.
[46]Redlich O, Kister A T, Algebraic Representation of Thermodynamic Properties and the Classification of Solutions[J]. Ind. Eng. Chem.,1948; 40:345-348.
[47]Hillert M, Staffans.Li, Regular Solution Model for Stoichiometric Phases and Ionic Melts[J]. Acta Chem. Scand.,1970; 24:3618-3626.
[48]Bragg W L, Williams E J, The Effect of Thermal Agitation on Atomic Arrangement in Alloys[J]. Proc. Roy. Soc. Lond. A,1934; 145:699-730.
[49]Bragg W L, Williams E J, The Effect of Thermal Agitation on Atomic Arrangement in Alloys. Ⅱ[J]. Proc. Roy. Soc. Lond. A,1935; 151:540-566.
[50]Pelton A, Blander M, Thermodynamic analysis of ordered liquid solutions by a modified quasichemical approach-Application to silicate slags[J]. Metall. Mater. Trans. B,1986; 17:805-815.
[51]Hildebrand J H, Eastman E D, The Vapor Pressure of Thallium Amalgams[J]. J. Am. Chem. Soc.,1915; 37:2452-2459.
[52]Yuan X, Sun W, Du Y, et al., Thermodynamic modeling of the Mg-Si system with the Kaptay equation for the excess Gibbs energy of the liquid phase [J]. CALPHAD,2009; 33:673-678.
[53]Kaptay G, A new equation for the temperature dependence of the excess Gibbs energy of solution phases [J]. CALPHAD,2004; 28:115-124.
[54]Hillert M, Jarl M, A model for alloying in ferromagnetic metals[J]. CALPHAD, 1978; 2:227-238.
[55]Ansara I, Sundman B, Willemin P, Thermodynamic modeling of ordered phases in the Ni-Al system[J]. Acta Metallurgica,1988; 36:977-982.
[56]Ansara I, Dupin N, Lukas H L, et al., Thermodynamic assessment of the Al-Ni system[J]. J. Alloy. Compd.,1997; 247:20-30.
[57]http://cst-www.nrl.navy.mil/lattice/
[58]Massalski T B, Okamoto H, Subramanian P R, et al., Binary Alloy Phase Diagrams[M], ASM International; 1990.
[59]罗伯编著D,项金钟,吴兴惠译,计算材料学[M],北京：化学工业出版社；2002.
[60]Frenkel, Smit,汪文川等译,分子模拟-从算法到应用[M],北京：化学工业出版社;2002.
[61]Born M, Oppenheimer J R, Concerning the Quantum Theory of Molecules[J]. Ann. Phys-new. York.,1927; 84:457-484.
[62]Hartree D R, The wave mechanics of an atom with a non-Coulomb central field[J]. Proc. Cambridge. Philos. Soc.,1928; 24:89-110.
[63]黄昆原著,韩汝琦改编,固体物理学[M],北京：高等教育出版社；1988.
[64]Fock V, Naherungsmethode zur Losung des quanten-mechanischen Mehrkorper-probleme[J]. Z. Phys.,1930; 61:126-148.
[65]谢希德,陆栋,固体能带理论[M],上海：复旦大学出版社；1998.
[66]Thomas L H, The calculation of atomic fields[J]. Proc. Cambridge. Philos. Soc., 1927; 23:542-548.
[67]Fermi E, A statistical method for the determination of some properties of atoms. II. Application to the periodic system of the elements[J]. Z. Phys.,1928,48. 73-79.
[68]Dirac P A M, Note on exchange phenomena in the Thomas atom[J]. Proc. Cambridge. Philos. Soc.,1930; 26:376-385.
[69]Hohenberg P, Kohn W, Inhomogeneous Electron Gas[J]. Phys. Rev. B,1964; 136: B864-B871.
[70]Kohn W, Sham L J, Self-Consistent Equations Including Exchange and Correlatioin Effects[J]. Physical Review,1965; 140:A1133-A1138.
[71]Perdew J P, Wang Y, Accurate and Simple Analytic Representation of the Electron-Gas Correlation-Energy [J]. Phys. Rev. B,1992; 45:13244-13249.
[72]Slater J C, A simplification of the Hartree-Fock method[J]. Phys. Rev.,1951; 81: 385-390.
[73]Mahan G D, Many particle physics[M], New York:Plenum Publishing; 1990.
[74]Slater J C, Wilson T M, Wood J H, Comparison of several exchange potentials for electrons in the Cu+ ion[J]. Phys. Rev.,1969; 179:28-38.
[75]Hedin L, Lundqvis.Bi, Explicit local exchange correlaiton potentials[J]. J Phys C Solid State Phys,1971; 4:2064-2083.
[76]Vosko S H, Wilk L, Nusair M, Accurate spin-dependent electron liquid correlation energies for local spin density calculations:a critical analysis[J]. Can. J. Phys.,1980; 58:1200-1211.
[77]Perdew J P, Zunger A, Self-interaction correction to density-functional approximations for many-electron systems[J]. Phys. Rev. B,1981; 23: 5048-5079.
[78]Ceperley D M, Alder B J, Ground-state of the Electron Gas by a Stochastic Method[J]. Phys. Rev. Lett.,1980; 45:566-569.
[79]Becke A D, Density-functional exchange-energy approximation with correct asymptotic behavior[J]. Physical Review A,1988; 38:3098-3100.
[80]Becke A D, Density functional calculations of molecular bond energies[J]. J. Chem. Phys.,1986; 84:4524-4529.
[81]Lee C T, Yang W T, Parr R G, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density [J]. Physical Review B,1988; 37:785-789.
[82]Perdew J P, Burke K, Ernzerhof M, Generalized gradient approximation made simple[J]. Physical Review Letters,1996; 77:3865-3868.
[83]Kohn W, Nobel Lecture:Electronic structure of matter-wave functions and density functionals[J]. Rev. Mod. Phys.,1999; 71:1253-1266.
[84]Monkhorst H J, Pack J D, Special Points for Brillouin-Zone Integrations [J]. Phys. Rev. B,1976; 13:5188-5192.
[85]Pack J D, Monkhorst H J, Special points for Brillouin-zone integrations-a reply[J]. Phys. Rev. B,1977; 16:1748-1749.
[86]Payne M C, Teter M P, Allan D C, et al., Iterative minimization techniques for ab initio total-energy calculations-molecular-dynamics and conjugate gradients[J]. Rev. Mod. Phys.,1992; 64:1045-1097.
[87]Fermi E. Nuovo Cimento,1934; 11:157.
[88]Hellmann H. Acta Physiochimica URSS,1935; 1:913.
[89]Hamann D R, Schluter M, Chiang C, Norm-Conserving Pseudopotentials[J]. Phys. Rev. Lett.,1979; 43:1494-1497.
[90]Vanderbilt D, Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism[J]. Phys. Rev. B,1990; 41:7892-7895.
[91]Blochl P E, Projector Augmented-Wave Method[J]. Phys. Rev. B,1994; 50: 17953-17979.
[92]Hellmann H, Einfuhrung in die Quantumchemie[M], Leipzig:Deuticke; 1937.
[93]Feynman R P, Forces in molecules[J]. Phys. Rev.,1939; 56:340-343.
[94]Press W H, Teukolsky S A, Vetterling W T, et al., Numerical recipes:the art of scientific computing[M], Cambridge:Cambridge University Press; 1986.
[95]Kresse G, Hafner J, Abinitio Molecular-Dynamics for Liquid-Metals.[J]. Phys. Rev. B,1993; 47:558-561.
[96]Kresse G, Furthmuller J, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[J]. Comp. Mater. Sci., 1996; 6:15-50.
[97]Kresse G, Furthmuller J, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J]. Phys. Rev. B,1996; 54: 11169-11186.
[98]Kresse G, Joubert D, From ultrasoft pseudopotentials to the projector augmented-wave method[J]. Phys. Rev. B,1999; 59:1758-1775.
[99]Kresse G, Hafner J, Norm-Conserving and Ultrasoft Pseudopotentials for First-Row and Transition-Elements[J]. J. Phys-condens. Mat.,1994; 6: 8245-8257.
[100]Davidson E R, Methods in computational molecular physics, Vol 113 of NATO Advanced Study Institute, Series C:Mathematical and Physical Sciences[M], New York:Plenum Press.
[101]Pulay P, Convergence acceleration of iterative sequences-the case of scf iteration[J]. Chem. Phys. Lett.,1980; 73:393-398.
[102]Jepsen O, Andersen O K, The electronic-structure of hcp ytterbium[J]. Solid State Commun.,1993; 88:871-875.
[103]Blochl P E, Jepsen O, Andersen O K, Improved Tetrahedron Method for Brillouin-Zone Integrations[J]. Phys. Rev. B,1994; 49:16223-16233.
[104]Fu C L, Ho K M, First-principles calculation of the equilibrium ground-state properties of transition metals:Applications to Nb and Mo[J]. Phys. Rev. B, 1983; 28:5480-5486.
[105]Methfessel M, Paxton A T, High-Pricision Sampling for Brillouin-Zone Integration in Metals[J]. Phys. Rev. B,1989; 40:3616-3621.
[106]Liang P, Su H L, Donnadieu P, et al., Experimental investigation and thermodynamic calculation of the central part of the Mg-Al phase diagram[J]. Z. Metallkd.,1998; 89:536-540.
[107]Grobner J, Mirkovic D, Ohno M, et al., Experimental investigation and thermodynamic calculation of binary Mg-Mn phase equilibria[J]. J. Phase. Equilib. Diffus.,2005; 26:234-239.
[108]Villars P, Calvert L D, Pearson's Handbook of Crystallographic Data for Intermetallic Phases,2nd Edition[M], Materials Park, Ohio, USA:ASM International; 1991.
[109]Ellner M, The Structure of the High-Temperature Phase Mnal(H) and the Displacive Transformation from Mnal(H) into Mn5Al8[J]. Metall. Mater. Trans. A,1990; 21:1669-1672.
[110]Kreiner G, Franzen H F, The crystal structure of lambda-Al4Mn[J]. J. Alloy. Compd.,1997; 261:83-104.
[111]Ohno M, Schmid-Fetzer R, Thermodynamic assessment of Mg-Al-Mn phase equilibria, focusing on Mg-rich alloys[J]. Z. Metallkd.,2005; 96:857-869.
[112]Liu X J, Ohnuma I, Kainuma R, et al., Thermodynamic assessment of the aluminum-manganese (Al-Mn) binary phase diagram[J]. J. Phase. Equilib., 1999; 20:45-56.
[113]Jansson A, A Thermodynamic Evaluation of the Al-Mn System[J]. Metall. Mater. Trans. A,1992; 23:2953-2962.
[114]Dix E H, Fink W L, Willey L A, Equilibrium Relations in Aluminum-Manganese Alloys of High Purity, II[J]. Trans. AIME,1933; 104: 335-352.
[115]Godecke T, Koster W, Supplement to constitution of Aluminium-Manganese system[J]. Z. Metallkd.,1971; 62:727-732.
[116]Thornton M C. Unpublished research work, Alcan International Ltd, Banbury Laboratory, USA,1996.
[117]Weitzer F, Rogl P, Hayes F H, et al., In:F Aldinger, H Mughrabi editors Werkstoff Woche'96, Materialwissenschaftliche Grundlagen, Deutsche Gesellschaft fur Materialkunde, Germany [M]; 1996, pp.185-190.
[118]Taylor M A, Intermetallic Phases in the Aluminium-Manganese Binary System[J]. Acta Metallurgica,1960; 8:256-262.
[119]Murray J L, McAlister A J, Schaefer R J, et al., Stable and Metastable Phase-Equilibria in the Al-Mn System[J]. Metall. Mater. Trans. A,1987; 18: 385-392.
[120]Robinson J A J, Hayes F H, Serneels A, et al., In:COST 507:Definition of thermochemical and thermophysical properties to provide a database for the development of new light alloys, Vol.1, COST Secretariat[M], Brussels, Belgium; 1998, p.230.
[121]Hanawalt J D, Nelson C E, Peloubet J A, Corrosion studies of magnesium and its alloys[J]. Trans. AIME,1942; 147:273-298.
[122]Nelson C E, Transactions of the American Foundrymen's Society[M], American Foundrymen's Society; 1948.
[123]Ran Q S, In:G Effenberg, F Aldinger, L Rokhlin editors Graphischer Betrieb Konrad Triltsch, D-07070 Wurzburg[M]; 1999.
[124]Ansara I, Dinsdale A T, Rand M H, COST 507:Thermochemical database for light metal alloys[M], Office for Official Publications of the European Communities; 1998.
[125]McAlister A, Murray J, The (Al-Mn) Aluminum-Manganese system[J]. J. Phase. Equilib.,1987; 8:438-447.
[126]Kuznetsov G M, Barsukov A D, Abas M I,Study of manganese, chromium, titanium, and zirconium solubility in solid aluminum[J]. Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall.,1983; 96-100.
[127]Minamino Y, Yamane T, Araki H, et al., Solid Solubilities of Manganese and Titanium in Aluminum at 0.1-Mpa and 2.1-Gpa[J]. Metall. Mater. Trans. A, 1991; 22:783-786.
[128]Chastel R, Saito M, Bergman C, Thermodynamic Investigation on All-Xmnx Melts by Knudsen Cell Mass-Spectrometry[J]. J. Alloy. Compd.,1994; 205: 39-43.
[129]Meschel S V, Kleppa O J, The standard enthalpies of formation of some 3d transition metal aluminides by high-temperature direct synthesis calorimetry[J]. NATO ASI SER., SER. E,1994; 256:103-113.
[130]Sigli C, In:CALPHAD XXIV, Kyoto, Japan; 1995.
[131]Matuo M, Muramatsu T, Asanuma A, et al., Estimation of solute Fe and Mn concentration in aluminum alloys by phenol filtrate analysis[J]. Keikinzoku, 1997; 47:15-20.
[132]Dix E H, Jr., Keith W D, Equilibrium Relations in Aluminum-Manganese Alloys of High Purity[J]. Trans. AIME,1927; No.1633-E:315-335.
[133]Fahrenhorst E, Hofmann W, The solubility of manganese in aluminum containing up to 2% magnesium[J]. Metallwirtsch,1940; 19:891-893.
[134]Phillips H W L, The constitution of alloys of Aluminium with Manganese, Silicon, and Iron. I. The binary system:Aluminium-Manganese. Ⅱ. The ternary systems:Aluminium-Manganese-Silicon and Aluminium-Manganese-iron[J]. J Inst. Met.,1943; 69:275-316.
[135]Butchers E, Humerothery W, The solubility of manganese in aluminium[J]. J Inst. Met.,1945; 71:87-91.
[136]Obinata I, Yamaji K, Hata E, Subcooled aluminum-manganese alloys. I[J]. Nippon Kinzoku Gakkaishi,1953; 17:496-501.
[137]Kono H, On the Ferromagnetic Phase in Manganese-Aluminum System[J]. J. Phys. Soc. Jpn.,1958; 13:1444-1451.
[138]Koch A J J, Hokkeling P, Vandersteeg M G, et al., New Material for Permanent Magnets on a Base of Mn and Al[J]. J. Appl. Phys.,1960; 31:S75-S77.
[139]Koster W, Wachtel E, Aufbau Und Magnetische Eigenschaften Der Aluminium-Mangan-Legierungen Mit Mehr Als 25-at-Percent Mn[J]. Z. Metallkd.,1960; 51:271-280.
[140]Kubaschewski O, Heymer G, Heats of formation of transition-metal aluminides[J]. Trans. Faraday Soc.,1960; 56:473-478.
[141]Drits M E, Kadaner E S, Padezhnova E M, et al., Opredelenie Granits Sovmestnoi Rastvorimosti Margantsa I Kadmiya V Tverdom Alyuminii[J]. Zhurnal Neorganicheskoi Khimii,1964; 9:1397-1400.
[142]Batalin G I, Beloboro.Ea, Chekhovs.Aa, et al., Thermodynamical properties of liquid alloys of Aluminum with Manganese[J]. Ukrainskii Khimicheskii Zhurnal,1972; 38:825-827.
[143]Esin Y O, Bobrov N P, Petrushe.Ms, et al., Concentration-Dependence of Enthalpies of Formation of Mn, Al-Melts at 1626 K[J]. Zh. Fiz. Khim.,1973; 47:1959-1962.
[144]Kematick R J, Myers C E, Thermodynamics and Phase-Equilibria in the Al-Mn System[J]. J. Alloy. Compd.,1992; 178:343-349.
[145]Liu X J, Kainuma R, Ohtani H, et al., Phase equilibria in the Mn-rich portion of the binary system Mn-Al[J]. J. Alloy. Compd.,1996; 235:256-261.
[146]Beerwald A, On the solubility of iron and manganese in magnesium and magnesium-aluminum alloys[J]. Metallwirtschaft,1944; 23:404-407.
[147]Ageev N V, Kornilov I I, Khlapova A N, Magnesium-rich alloys of the system magnesium-aluminum-manganese [J]. Izv. Sekt. Fiz.-Khim. Anal., Inst. Obshch. Neorg. Khim.,Akad.Nauk SSSR,1948; 16:130-143.
[148]Nelson B J, Equilibrium Relations in Magnesium-Aluminum-Manganese Alloys[J]. Journal of Metals,1951; 3:797-799.
[149]Mirgalovskaya M S, Matkova L N, Komova E M, System magnesium-aluminum-manganese [J]. Tr. Inst. Metall., Akad. Nauk SSSR,1957; 139-148.
[150]Oberlander B C, Simensen C J, Svalestuen J, Conf. Magnesium Technology, Inst. of Metals[J].1986; 139-148.
[151]Simensen C J, Oberlander B C, Svalestuen J, et al., Determination of the Equilibrium Phases in Molten Mg-4 Wt-Percent Al-Mn Alloys[J]. Z. Metallkd., 1988; 79:537-540.
[152]Simensen C J, Oberlander B C, Svalestuen J, et al., The Phase-Diagram for Magnesium-Aluminum-Manganese above 650-Degrees-C[J]. Z. Metallkd., 1988; 79:696-699.
[153]Thorvaldsen A, Aliravci C A, In:Can. Inst. Min. Metall. Pet.; 1992, pp. 277-288.
[154]Leemann W G, Hanemann H, The system aluminum-magnesium-manganese[J]. Aluminium-Arch.,1938; 9:6-17.
[155]Hofmann W, X-Ray methods on investigation of aluminium alloys[J]. Aluminium,1938; 20:865-872.
[156]Butchers E, Raynor G V, Hume-Rothery W, The constitution of magnesium-manganese-zinc-aluminium alloys in range 0-5%magnesium, 0-2% manganese,0-8% zinc. I. The liquidus[J]. J Inst. Met.,1943; 69:209-228.
[157]Little A T, Raynor G V, Hume-Rothery W, The constitution of magnesium-manganese-zinc-aluminium alloys in the range 0-5% magnesium, 0-2% manganese,0-8% zinc. Ⅲ. The 500℃ and 400 ℃ isothermals[J]. J Inst. Met.,1943;69:423-440.
[158]Mondolfo L F, Metallography of aluminum alloys[M], J. Wiley & sons, inc.; 1943.
[159]Butchers E, Humerothery W, On the constitution of aluminium magnesium manganese zinc alloys-the solidus[J]. J Inst. Met.,1945; 71:291-311.
[160]Wakeman D W, Raynor G V, The Constitution of Aluminium Manganese Magnesium and Aluminium Manganese Silver Alloys, with Special Reference to Ternary-Compound Formation[J]. J Inst. Met.,1948; 75:131-150.
[161]Ohnishi T, Nakatani Y, Shimizu K, Phase diagrams and ternary compounds of aluminum-magnesium-chromium and aluminum-magnesium-manganese systems in the aluminum-rich corner[J]. Keikinzoku,1973; 23:202-209.
[162]Ohnishi T, Nakatani Y, Shimizu K, Phase diagram in the aluminum- rich side of the aluminum-magnesium-manganese-chromium quaternary system[J]. Keikinzoku,1973; 23:437-443.
[163]Fun H K, Lin H C, Lee T J, et al., T-Phase Al18Mg3Mn2[J]. Acta Crystallogr. C, 1994; 50:661-663.
[164]Barlock J G, Mondolfo L F, Structure of Some Aluminium-Iron-Magnesium-Manganese-Silicon Alloys[J]. Z. Metallkd.,1975; 66:605-611.
[165]Taylor M A, Space group of MnAl3[J]. Acta Crystallographica,1961; 14:84-84.
[166]Abrikosov N K, Ivanova L D, Danil'chenko V A, Phase transition of Mn4A11 into MnA13[J].Izv.Akad.Nauk SSSR,Neorg. Mater.,1971; 7:1053-1055.
[167]Andersson J O, Guillermet A F, Hillert M, et al., A Compound-Energy Model of Ordering in a Phase with Sites of Different Coordination Numbers[J]. Acta Metallurgica 1986; 34:437-445.
[168]Hobbs D, Hafner J, Spisak D, Understanding the complex metallic element Mn. I. Crystalline and noncollinear magnetic structure of alpha-Mn[J]. Phys. Rev. B, 2003; 68:014407.
[169]Sundman B, Jansson B, Andersson J O, The Thermo-Calc Databank System[J]. CALPHAD,1985; 9:153-190.
[170]Du Y, SchmidFetzer R, Ohtani H, Thermodynamic assessment of the V-N system[J]. Z. Metallkd.,1997; 88:545-556.
[171]Liu Z K, First-Principles Calculations and CALPHAD Modeling of Thermodynamics [J]. J. Phase. Equilib. Diffus.,2009; 30:517-534.
[172]Shang S, Zhang H, Ganeshan S, et al., The development and application of a thermodynamic database for magnesium alloys[J]. JOM,2008; 60:45-47.
[173]Chen H L, Du Y, Xu H H, et al., Experimental investigation and thermodynamic modeling of the ternary Al-Cu-Fe system[J]. J. Mater. Res.,2009; 24: 3154-3164.
[174]Du Y, Schuster J C, Liu Z K, et al., A thermodynamic description of the Al-Fe-Si system over the whole composition and temperature ranges via a hybrid approach of CALPHAD and key experiments [J]. Intermetallics.,2008; 16:554-570.
[175]Du Y, Schuster J C, Weitzer F, et al., A thermodynamic description of the Al-Mn-Si system over the entire composition and temperature ranges[J]. Metall. Mater. Trans. A,2004; 35A:1613-1628.
[176]He C Y, Du Y, Chen H L, et al., Experimental investigation and thermodynamic modeling of the Al-Cu-Si system[J]. CALPHAD,2009; 33:200-210.
[177]Xiong W, Du Y, Hu R X, et al., Construction of the AlNiSi phase diagram over the whole composition and temperature ranges:thermodynamic modeling supported by key experiments and first-principles calculations [J]. Int. J. Mater. Res.,2008; 99:598-612.
[178]Zhao J R, Zhang L J, Du Y, et al., Experimental Investigation and Thermodynamic Reassessment of the Cu-Fe-Si System[J]. Metall. Mater. Trans. A,2009;40A:1811-1825.
[179]Yan X, Chang Y A, A Thermodynamic analysis of the Cu-Si system[J]. J. Alloy. Compd.,2000; 308:221-229.
[180]Shin D, Saal J E, Liu Z K, Thermodynamic modeling of the Cu-Si system[J]. CALPHAD,2008; 32:520-526.
[181]Jacobs M H G, Spencer P J, A critical thermodynamic evaluation of the systems Si-Zn and Al-Si-Zn[J]. CALPHAD,1996; 20:307-320.
[182]Spencer P J, A thermodynamic evaluation of the copper-zinc system [J]. CALPHAD,1986; 10:175-185.
[183]Kowalski M, Spencer P J, Thermodynamic reevaluation of the copper-zinc system[J]. J. Phase Equilib.,1993; 14:432-438.
[184]Kowalski M, Spencer P J, In:I Ansara editor Thermochemical database for light metal alloys[M], EUR; 1998, pp.186-191.
[185]David N, Fiorani J M, Vilasi M, et al., Thermodynamic reevaluation of the Cu-Zn system by electromotive force measurements in the zinc-rich part[J]. J. Phase Equilib.,2003; 24:240-248.
[186]Gierlotka W, Chen S W, Thermodynamic descriptions of the Cu-Zn system[J]. J. Mater. Res.,2008; 23:258-263.
[187]Liang H, Chang Y A, A thermodynamic description for the Al-Cu-Zn system[J]. J. Phase Equilib.,1998; 19:25-37.
[188]Saunders N, In:I Ansara editor Thermochemical database for light metal alloys[M], EUR; 1998, pp.28-33.
[189]Bochvar N, Dobatkina T, In:Landolt-Bornstein New Series [M]:MSIT; 2007, pp.393-408.
[190]Miettinen J, Thermodynamic description of the Cu-Si-Zn system in the copper-rich corner[J]. CALPHAD,2007; 31:422-427.
[191]Borggren U, Selleby M, A Thermodynamic Database for Special Brass[J]. J. Phase Equilib.,2003; 24:110-121.
[192]Pops H, The Constitution of Copper-Rich Copper-Silicon-Zinc Alloys[J]. Trans. Met. Soc. AIME,1964; 230:813-820.
[193]熊伟,Ni合金相图、相平衡及相变的热力学研究[D].博士学位论文,中南大学,中国.2010.
[194]Mima G, Hasegawa M, The Diagram of Cu-Si-Zn Alloy-Ⅱ[J]. Technol. Repts. Osaka Univ.,1957; 7:385-397.
[195]Raynor G V, Equilibrium diagram of the system Cu-Zn[J]. Inst. Met. (London), Annotated Equil. Diagram Ser.,1944; No.3:5 pp.
[196]Hansen M, Anderko K, In:Constitution of Binary Alloys[M], New York: McGraw-Hill; 1958, pp.649-655.
[197]Massalski T B, Murray J L, H B L, et al., American Society for Metals, Metal Park, Ohio; 1986.
[198]Bauer O, Hansen M, Structure of copper-zinc alloys[J]. Z. Metallkd.,1927; 19: 423-434.
[199]Ruer R, Kremers K, The system:copper-zinc [J]. Z. Anorg. Allg. Chem.,1929; 184:193-231.
[200]Schramm J, The copper-zinc diagram[J]. Metallwirtsch,1935; 14:995-1001.
[201]v. Samson-Himmelstjerna H O, Heat content and heat of formation of molten alloys[J]. Z. Metallkd.,1936; 28:197-202.
[202]Parameswaran K, Healy G, A calorimetric investigation of the copper-zinc system[J]. Metall. Trans., B,1978; 9B:657-664.
[203]Schneider A, Schmid H, Metal vapor pressures. III. The vapor pressures of Zn and Cd over their binary alloys with Cu, Ag and Au[J]. Z. Elektrochem. Angew. Phys. Chem.,1942; 48:627-639.
[204]Everett L H, Jacobs P W M, Kitchener J A, Activity of zinc in liquid copper-zinc alloys[J]. Acta Met.,1957; 5:281-284.
[205]Downie D B, Thermodynamic and structural properties of liquid zinc/copper alloys[J]. Acta Met.,1964; 12:875-882.
[206]Azakami T, Yazawa A, Thermodynamic studies of liquid copper alloys. III. Activities of zinc and cadmium in liquid copper-base alloys [J]. Nippon Kogyo Kaishi,1968; 84:1663-1668.
[207]Solov'ev S L, Knyazev M V, Ivanov Y I, et al., Mass-spectrometric study of partial characteristics of zinc in the copper-zinc system[J]. Zavod. Lab.,1979; 45:841-844.
[208]Sugino S, Hagiwara H, Activity of zinc in molten copper and copper-gold alloys[J]. Nippon Kinzoku Gakkaishi 1986; 50:186-192.
[209]Leitgebel W, The boiling of certain metals and alloys at atmospheric pressure[J]. Z. Anorg. Allg. Chem.,1931; 202:305-324.
[210]Baker E H, Vapor pressures and thermodynamic behavior of liquid zinc-copper alloys at 1150.deg[J]. T. I. Min. Metall. C,1970; 79:C1-C5.
[211]Kleppa O J, Thalmayer C E, An e.m.f. investigation of binary liquid alloys rich in zinc[J]. J. Phys. Chem.,1959; 63:1953-1958.
[212]Gerling U, Predel B, Thermodynamic properties of liquid copper-zinc-alloys[J]. Z. Metallkd.,1980; 71:158-164.
[213]Blair G R, Downie D B, Calorimetric study of silver-zinc and copper-zinc alloys[J]. Metal Sci. J.,1970; 4:1-5.
[214]Kleppa O J, King R C, Heats of formation of the solid solutions of zinc, gallium, and germanium in copper[J].Acta Met.,1962; 10:1183-1186.
[215]Orr R L, Argent B B, Heats of formation of the alpha -brasses[J]. Trans. Faraday Soc.,1965; 61:2126-2131.
[216]Korber F, Oelsen W, Thermochemistry of alloys. III. The heats of formation of the binary alloys iron-antimony, cobalt-antimony, nickel-antimony, cobalt-tin, nickel-tin, copper-tin and copper-zinc for the cast state [J]. Mitt. Kaiser-Wilhelm-Inst. Eisenforsch. Duesseldorf,1937; 19:209-219.
[217]Weibke F, The systematic study of affinity. LXXI. The heats of formation in the system copper-zinc [J]. Z. Anorg. Allgem. Chem.,1937; 232:289-296.
[218]Hargreaves R, The vapor pressure of zinc in brasses[J]. J. Inst. Met.,1939; 64: 10 pp.
[219]Seith W, Krauss W, Diffusion and vapor pressure of the zinc in brass[J]. Z. Elektrochem. Angew. Phys. Chem.,1938; 44:98-102.
[220]Argent B B, Wakeman D W, Thermodynamic properties of solid solutions. I. Copper+zinc solid solution[J]. Trans. Faraday Soc.,1958; 54:799-806.
[221]Masson D B, Sheu J-L, Variations in the composition dependence of the activity coefficient in terminal solid solutions of silver-zinc, silver-cadmium, and copper-zinc[J]. Metall. Trans.,1970; 1:3005-3009.
[222]Pemsler J P, Rapperport E J, Thermodynamic activity measurements using atomic absorption:copper-zinc [J]. Trans. AIME,1969; 245:1395-1400.
[223]Olander A, An electrochemical investigation of brass. (Fused electrolytes)[J]. Z. Physik. Chem.,1933; A164:428-438.
[224]Herbenar A W, Siebert C A, Duffendack O S, The vapor pressure and thermodynamic activities of zinc in solid alpha brasses[J]. J. Met.,1950; 188: 323-326.
[225]Guertler W, Guertler M, Anastasiadias E,14-29-30[J]. A Comp. of Const. Ternary Diagr. Met. System, Isr. Pro. Sci. Tr., Jerusalem,1969; 19:555-561.
[226]Drits M E, Bochvar N R, Guzei L S, et al., In:Binary and Multicomponent Copper-Base Systems [M], Moscow:Nauka; 1979, pp.158-159.
[227]Chang Y A, Neumann J P, Mikula A, et al., Cu-Si-Zn[J]. INCRA Monograph Series. Phase Diagrams and Thermodynamic Properties of Ternary Copper-Metall Systems, NSRD, Washington,1979; 6:669-675.
[228]Gould H W, Ray K W, Effects of silicon on the properties of brass. I. Constitution[J]. Metals and Alloys,1930; 1:455-457.
[229]Vaders E, A New Silicon-Zinc-Copper Alloy[J]. J. Inst. Met.,1930; 44: 363-383.
[230]Smiryagin A P, In:VA Nemilov editor Spesial Bronzes and Brasses[M], Moscow:Metallurgiya; 1945, pp.5-20.
[231]Smiryagin A P, Smiryagina N A, Belova A V, In:Industrial Non-Ferrous Metals and Alloys[M], Moscow:Metallurgiya; 1974, pp.106-109.
[232]Pops H, The Contributuon of the Primary Solid Solubility Isothermal Limit and Some Intermediate Phase in Cu-Rich Cu-Si-Zn Alloys[D].1962.
[233]Mima G, Hasegawa M, The Diagram of Cu-Si-Zn Alloy-Ⅰ[J]. Technol. Repts. Osaka Univ.,1956; 6:313-321.
[234]Mima G, Hasegawa M, Phase Diagram of the System Cu-Si-Zn in the h Phase Region[J]. Nippon Kinzoku Gakkai-Shi (J. Jpn. Inst. Met.),1959; 23:585-587.
[235]Mima G, Hasegawa M, The Diagram of Cu-Si-Zn Alloy-III[J]. Technol. Repts. Osaka Univ.,1960; 10:157-168
[236]Mima G, Hasegawa M, Study of the Diagram of Cu-Si-Zn Alloy in the Range Near g Solid Solution[J]. Nippon Kinzoku Gakkai-Shi (J. Jpn. Inst. Met.),1963; 27:370-376.
[237]Mima G, Hasegawa M, The Diagram of Cu-Si-Zn Alloy-Ⅳ[J]. Technol. Repts. Osaka Univ.,1964; 14:623-633.
[238]Jacobs M H G, Spencer P J, A critical thermodynamic evaluation of the systems Si-Zn and Al-Si-Zn[J]. CALPHAD,1996; 20:307-320.
[239]He C Y, Du Y, Chen H L, et al., Experimental investigation and thermodynamic modeling of the Al-Cu-Si system[J]. CALPHAD,2009; 33:200-210.
[240]Xiong W, Ph.D thesis, Central South University, China[J]. Ph.D thesis, Central South University, China,2010.
[241]Hu R X, Nash P, Review:Experimental enthalpies of formation of compounds in Al-Ni-X systems[J]. J. Mater. Sci.,2006; 41:631-641.
[242]Curtarolo S, Morgan D, Ceder G, Accuracy of ab initio methods in predicting the crystal structures of metals:A review of 80 binary alloys[J]. CALPHAD, 2005; 29:163-211.
[243]Wang Y, Curtarolo S, Jiang C, et al., Ab initio lattice stability in comparison with CALPHAD lattice stability[J]. CALPHAD,2004; 28:79-90.
[244]Wolverton C, Ozolins V, First-principles aluminum database:Energetics of binary Al alloys and compounds[J]. Phys. Rev. B,2006; 73:144104.
[245]Zunger A, Wei S H, Ferreira L G, et al., Special Quasirandom Structures[J]. Phys. Rev. Lett.,1990; 65:353-356.
[246]Zhang H, Shang S L, Saal J E, et al., Enthalpies of formation of magnesium compounds from first-principles calculations[J]. Intermetallics.,2009; 17: 878-885.
[247]Born M, Huang K, Dynamical Theory of Crystal Lattices[M], Oxford University Press; 1988.
[248]Nye J F, Physical Properties of Crystals:Their Representation by Tensors and Matrices[M], New York:Oxford University Press; 1985.
[249]Cowley R A, Acoustic Phonon Instabilities and Structural Phase-Tansitions[J]. Phys. Rev. B,1976; 13:4877-4885.
[250]Chen L Q, Phase-field models for microstructure evolution[J]. Ann. Rev. Mater. Res.,2002; 32:113-140.
[251]Pugh S F, Relations Between the Elastic Moduli and the Plastic Properties of Polycrystalline Pure Metals[J]. Philosophical Magazine,1954; 45:823-843.
[252]Clerc D G, Ledbetter H M, Mechanical hardness:A semiempirical theory based on screened electrostatics and elastic smear[J]. J. Phys. Chem. Solids,1998; 59: 1071-1095.
[253]Kim D, Shang S L, Liu Z K, Effects of alloying elements on elastic properties of Ni by first-principles calculations[J]. Comp. Mater. Sci.,2009; 47:254-260.
[254]Zhang H, Shang S L, Wang Y, et al., First-principles calculations of the elastic, phonon and thermodynamic properties of Al12Mg17[J]. Acta Mater.,2010; 58: 4012-4018.
[255]Ganeshan S, Shang S L, Zhang H, et al., Elastic constants of binary Mg compounds from first-principles calculations[J]. Intermetallics.,2009; 17: 313-318.
[256]Shang S L, Wang Y, Kim D, et al., First-principles thermodynamics from phonon and Debye model:Application to Ni and Ni3Al[J]. Comp. Mater. Sci., 2010; 47:1040-1048.
[257]Shang S L, Wang Y, Liu Z K, First-principles elastic constants of alpha- and theta-Al2O3[J]. Appl. Phys. Lett.,2007; 90:101909.
[258]Simmons G, Wang H, Single Crystal Elastic Constants and Calculated Aggregate Properties:A Handbook[M], M.I.T Press, Cambridge; 1971.
[259]Villars P, Calvert L D, Pearson's handbook:crystallographic data for intermetallic phases.[M], ASM International, Materials Park, Ohio; 1991.
[260]Shang S L, Wang Y, Liu Z K, First-principles calculations of phonon and thermodynamic properties in the boron-alkaline earth metal binary systems: B-Ca, B-Sr, and B-Ba[J]. Phys. Rev. B,2007; 75:024302.
[261]Ghosh G, Asta M, First-principles calculation of structural energetics of Al-TM (TM=Ti, Zr, Hf) intermetallics[J]. Acta Mater.,2005; 53:3225-3252.
[262]Tao X A M, Ouyang Y F, Liu H S, et al., Ab initio calculations of mechanical and thermodynamic properties for the B2-based AIRE[J]. Comp. Mater. Sci., 2007; 40:226-233.
[263]Chen X Q, Podloucky R, Miedema's model revisited:The parameter phi* for Ti, Zr, and Hf[J]. CALPHAD,2006; 30:266-269.
[264]Olesen W, Thermochemistry of alloys (Ⅰ) detn. of the heats of formation of the alloys series Co-Si, Fe-Al, Co-Al, Ni-Al, Cu-Al and Sb-Zn for the case state[J]. Mitt. Kaiser-Wilhelm-Inse. Eisenforsch Dusseldorf,1937; 19:2.
[265]Dupin N, Ansara I, Thermodynamic assessment of the system Al-Co[J]. Rev. Metall-paris.,1998; 95:1121-1129.
[266]Biltz W, On the heat of formation of intermetallic compounds V Cobalt-aluminium alloys, copper alloys[J]. Z. Anorg. Allg. Chem.,1924; 134: 25-36.
[267]Henig E T, Lukas H L, Petzow G, Enthalpy of Formation and Description of the Deffect Structure of the Ordered Beta-Phase in Co-Al[J]. Z. Metallkd.,1980; 71: 398-402.
[268]Sandakov V M, Geld P V, Esin Y O, Heats of Formation and Thermodynamics of Nickel and Cobalt Mono-Aluminides[J]. Zh. Fiz. Khim.,1972; 46:1567.
[269]Murray J L. Int. Met. Rev.,1985; 30:211-218.
[270]Ansara I, Dinsdale A T, Rand M H, COST507:Thermodynamic database for light metal alloys[M], rue de la loi 200 (SDME 1/44), B-1049 Brussels: European Commission; 1998.
[271]Wang T, Jin Z P, Zhao J C, Thermodynamic assessment of the AI-Hf binary system[J]. J. Phase. Equilib.,2002; 23:416-423.
[272]Meschel S V, Kleppa O J, Standard Enthalpies of Formation of Some Rare-Earth Carbides by Direct Synthesis Calorimetry[J]. J. Alloy. Compd., 1993; 191:111-116.
[273]Balducci G, Ciccioli A, Gigli G, et al., Thermodynamic Study of Intermetallic Phases in the Hf-Al System[J]. J. Alloy. Compd.,1995; 220:117-121.
[274]Kaufman L, Nesor H, Calculation of Ni-Al-W, Ni-Al-Hf and Ni-Cr-Hf System[J]. Can. Metall. Quart.,1975; 14:221-232.
[275]Zhong Y, Yang M, Liu Z K, Contribution of first-principles energetics to Al-Mg thermodynamic modeling[J]. CALPHAD,2005; 29:303-311.
[276]Brown J A, Pratt J N, Thermodynamic Properties of Solid Al-Mg Alloys[J]. Metall. Trans.,1970; 1:2743-2750.
[277]Predel B, Hulse K, Some Thermodynamic Properties of Aluminium-Magnesium Alloys[J]. Z. Metallkd.,1978; 69:661-666.
[278]Kubaschewski O, Heymer G, Heats of Formation of Transtion-Metal Aluminides[J]. Trans. Faraday Soc.,1960; 56:473-478.
[279]Kubaschewski O, The heats of formation in the system in the system aluminium +nickel+titanium[J]. Trans. Faraday Soc.,1958; 54:814-820.
[280]Dupin N, Ansara I, Sundman B, Thermodynamic re-assessment of the ternary system Al-Cr-Ni[J]. CALPHAD,2001; 25:279-298.
[281]Rzyman K, Moser Z, Calorimetric studies of the enthalpies of formation of Al(3)Ni(2), AlNi and AlNi3[J]. Prog. Mater. Sci.,2004; 49:581-606.
[282]Rzyman K, Moser Z, Watson R E, et al., Enthalpies of formation of AlNi: Experiment versus theory[J]. J. Phase. Equilib.,1998; 19:106-111.
[283]Hu R X, Nash P, The enthalpy of formation of NiAl[J]. J. Mater. Sci.,2005;40: 1067-1069.
[284]Rzyman K, Moser Z, Watson R E, et al., Enthalpies of formation of Ni3Al: Experiment versus theory[J].J. Phase. Equilib.,1996; 17:173-178.
[285]Wang C, Jin Z P, Du Y, Thermodynamic modeling of the Al-Sr system[J]. J. Alloy. Compd.,2003; 358:288-293.
[286]Zhong Y, Wolverton C, Chang Y A, et al., A combined CALPHAD/first-principles remodeling of the thermodynamics of Al-Sr: unsuspected ground state energies by "rounding up the (un)usual suspects"[J]. Acta Mater.,2004; 52:2739-2754.
[287]Kubaschewski O, Dench W A, The Heats of Formation in the Systems Titanium-Aluminium and Titanium-Iron[J]. Acta Metallurgica,1955; 3: 339-346.
[288]Nassik M, Chrifi-Alaoui F Z, Mahdouk K, et al., Calorimetric study of the aluminium-titanium system[J]. J. Alloy. Compd.,2003; 350:151-154.
[289]Gong W P, Du Y, Huang B Y, et al., Thermodynamic reassessment of the Al-V system[J]. Z. Metallkd.,2004; 95:978-986.
[290]Neckel A, Howotny H, In:Fifth International Conference on Light Metals, Leoben;1968, p.72.
[291]Timofeev V S, Turchanin A A, Zubkov A A, et al., Enthalpies of formation for the Al-Y and Al-Y-Ni intermetallic compounds[J]. Thermochim. Acta,1997; 299:37-41.
[292]Liu S H, Du Y, Chen H L, A thermodynamic reassessment of the Al-Y system[J]. CALPHAD,2006; 30:334-340.
[293]Snyder R L.1960.
[294]Jung W G, Kleppa O J, Topor L, Standard Molar Enthalpies of Formation of PdAl, PtAl, ScAl1.78, YA12 and LaAl2[J]. J. Alloy. Compd.,1991; 176:309-318.
[295]Wang T, Jin Z P, Zhao J C, Thermodynamic assessment of the Al-Zr binary system[J]. J. Phase. Equilib.,2001; 22:544-551.
[296]Alcock C B, Jacob K T, In:O Kubaschewski editor Zirconium: physico-chemical properties of its compounds.[M], Vienna:IAEA:Atomic energy review; 1976.
[297]Kematick R J, Franzen H F, Thermodynamic Study of the Zirconium Aluminum System[J]. J. Solid State Chem.,1984; 54:226-234.
[298]Klein R, Jacob I, Ohare P A G, et al., Solution-Calorimetri Determination of the Standard Molar Enthalpies of Formation of the Pseudobinary Compounds Zr(AlxFe(1-x))2 at the Temperature 298.15 K[J]. J. Chem. Thermodyn.,1994; 26:599-608.
[299]Saunders N, Calculated Stable and Metastable Phase-Equilibria in Al-Li-Zr Alloys[J]. Z. Metallkd.,1989; 80:894-903.
[300]Ouyang Y, Zhong X, Du Y, et al., Formation enthalpies of Fe-Al-RE ternary alloys calculated with a geometric model and Miedema's theory [J]. J. Alloy. Compd.,2006; 416:148-154.
[301]刘树红,铝合金有序-无序相变、相图拓扑关系及其在凝固过程的应用[D].博士学位论文,中南大学,中国.2010.
[302]Guo Q T, Kleppa O J, The standard enthalpies of formation of the compounds of early transition metals with late transition metals and with noble metals as determined by Kleppa and co-workers at the University of Chicago-A review[J]. J. Alloy. Compd.,2001; 321:169-182.
[303]Murray J, Peruzzi A, Abriata J, The Al-Zr (aluminum-zirconium) system[J]. J. Phase. Equilib.,1992; 13:277-291.
[304]Kleppa O, Systematic aspects of the high-temperature thermochemistry of binary alloys and related compounds[J]. J. Phase. Equilib.,1994; 15:240-263.
[305]Zhou W, Liu L J, Li B L, et al., Structural, Elastic, and Electronic Properties of Al-Cu Intermetallics from First-Principles Calculations [J]. J. Electron. Mater., 2009; 38:356-364.
[306]Jahnatek M, Krajci M, Hafner J, Interatomic bonding, elastic properties, and ideal strength of transition metal aluminides:A case study for Al-3(V,Ti)[J]. Phys. Rev. B,2005; 71:024101.
[307]Fu C L, Yoo M H, Elastic-Constant, Fault Energies, and Dislocation Reactions in TiAl:A 1 st-Principles Total-Energy Investigation[J]. Phil. Mag. Lett.,1990; 62:159-165.
[308]Eshelman F R, Smith J F, Single-Crysta Elastic-Constants of Al2Cu[J]. J. Appl. Phys.,1978; 49:3284-3288.
[309]Wang N, Yu W Y, Tang B Y, et al., Structural and mechanical properties of Mg17A112 and Mg24Y5 from first-principles calculations [J]. J. Phys. D. Appl. Phys.,2008; 41:195408.
[310]Shi D M, Wen B, Melnik R, et al., First-principles studies of Al-Ni intermetallic compounds[J]. J. Solid State Chem.,2009; 182:2664-2669.
[311]Rusovic N, Warlimont H, Elastic Behavior of Beta-2-NiAl Alloys[J]. Phys. Status. Solidi. A,1977; 44:609-619.
[312]Mishin Y, Mehl M J, Papaconstantopoulos D A, Embedded-atom potential for B2-NiAl[J]. Phys. Rev. B,2002; 65:224114.
[313]Kayser F X, Stassis C, The Elastic-Constants of Ni3Al at 0 and 23.5℃[J]. Phys. Status. Solidi. A,1981; 64:335-342.
[314]Prikhodko S V, Carnes J D, Isaak D G, et al., Temperature and composition dependence of the elastic constants of Ni3Al[J]. Metall. Mater. Trans. A,1999; 30:2403-2408.
[315]Kim D E, Shang S L, Liu Z K, Effects of alloying elements on elastic properties of Ni3Al by first-principles calculations[J]. Intermetallics,2010; 18: 1163-1171.
[316]Nakamura M, Kimura K, Elastic-Constants of TiAl3 and ZrAl3 Single-Crystals[J]. J. Mater. Sci.,1991; 26:2208-2214.
[317]He Y, Schwarz R B, Migliori A, et al., Elastic-constants of single-crystal gamma-TiAl[J]. J. Mater. Res.,1995; 10:1187-1195.
[318]Tanaka K, Koiwa M, Single-crystal elastic constants of intermetallic compounds[J]. Intermetallics.,1996; 4:S29-S39.
[319]Ranganathan S I, Ostoja-Starzewski M, Universal elastic anisotropy index[J]. Phys. Rev. Lett.,2008; 101:055504.
[320]Hill R, The Elastic Behaviour of A Crystalline Aggregate[J]. Proceedings of the Physical Society of London Section A,1952; 65:349-355.
[321]Shang S L, Wang Y, Kim D E, et al., First-principles thermodynamics from phonon and Debye model:Application to Ni and Ni3A1[J]. Comp. Mater. Sci., 2010; 47:1040-1048.
[322]Liu J Z, Ghosh G, van de Walle A, et al., Transferable force-constant modeling of vibrational thermodynamic properties in fcc-based Al-TM (TM=Ti, Zr, Hf) alloys[J]. Phys. Rev. B,2007; 75:104117.
[323]Mei Z G, Shang S L, Wang Y, et al., Density-functional study of the thermodynamic properties and the pressure-temperature phase diagram of Ti[J]. Phys. Rev. B,2009; 80:104116
[324]Saal J E, Wang Y, Shang S L, et al., Thermodynamic Properties of Co3O4 and Sr6Co5O15 from First-Principles[J]. Inorg. Chem.,2010; 49:10291-10298.
[325]Wang Y, Ahuja R, Johansson B, Mean-field potential approach to the quasiharmonic theory of solids[J]. Int. J. Quantum. Chem.,2004; 96:501-506.
[326]Moruzzi V L, Janak J F, Schwarz K, Calculated thermal-properties of metals[J]. Phys. Rev. B,1988; 37:790-799.
[327]项金钟,吴兴惠译,Kittel C原著固体物理导论[M],化学工业出版社；2005.
[328]固体物理学[M],北京大学出版社；2009.
[329]Methfessel M, Paxton A T, High-precision sampling for Brillouin-zone integration in metals[J]. Phys. Rev. B,1989; 40:3616-3621.
[330]van de Walle A, Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the Alloy Theoretic Automated Toolkit[J]. CALPHAD,2009; 33:266-278.
[331]van de Walle A, Ceder G, The effect of lattice vibrations on substitutional alloy thermodynamics[J]. Rev. Mod. Phys.,2002; 74:11-45.
[332]Shang S L, Wang J, Wang Y, et al., Phonon and thermodynamic properties of Al-Mn compounds:A first-principles study[J]. to be submitted,2010.
[333]Shang S L, Wang Y, Arroyave R, et al., Phase stability in alpha- and beta-rhombohedral boron[J]. Phys. Rev. B,2007; 75:092101.
[334]Shang S L, Wang Y, Zhang H, et al., Lattice dynamics and anomalous bonding in rhombohedral As:First-principles supercell method[J]. Phys. Rev. B,2007; 76:052301.
[335]Luo W, Ahuja R, Ding Y, et al., Unusual lattice dynamics of vanadium under high pressure[J]. Proceedings of the National Academy of Sciences of the United States of America,2007;104:16428-16431.
[336]Phonon States of Alloys; Electron States and Fermi Surfaces of Strained Elements[M], Springer-Verlag GmbH; 1983.
[337]Saunders N, Miodownik A P, CALPHAD (Calculation of Phase Diagrams):A Comprehensive Guide[M], New York:Pergamon; 1998.
[338]Shang S L, Wang Y, Liu Z K, Thermodynamic fluctuations between magnetic states from first-principles phonon calculations:The case of bcc Fe[J]. Phys. Rev. B,2010; 82:014425.
[339]Saal J E, Shang S, Wang Y, et al., Magnetic phase transformations of face-centered cubic and hexagonal close-packed Co at zero Kelvin[J]. J. Phys-condens. Mat.,2010; 22.
[340]Shang S-L, Saal J E, Mei Z-G, et al., Magnetic thermodynamics of fcc Ni from first-principles partition function approach[J]. J. Appl. Phys.,2010; 108.
[341]Villars P, Calvert L D, Pearson's handbook of crystallographic data for intermetallic phases[M],2nd ed., Newbury, OH:ASTM International; 1991.
[342]Simmons G, Wang H, Single Crystal Elastic Constants and Calculated Aggregate Properties[M], Cambridge (Mass.):MIT press; 1971.
[343]Gerward L, The bulk modulus and its pressure derivative for 18 metals [J]. J. Phys. Chem. Solids,1985; 46:925-927.
[344]Phonon states of elements. Electron states and Fermi surfaces of alloys [M], Berlin:Springer; 1981.
[345]Takemura K, Shimomura O, Hase K, et al., The high-pressure equation of state of alpha-Mn to 42 GPa[J]. J. Phys. F. Met. Phys.,1988; 18:197-204.
[346]Fujihisa H, Takemura K, Stability and the equation of state of alpha-Manganese under ultrahigh pressure [J]. Phys. Rev. B,1995; 52:13257-13260.
[347]Tarumi R, Kawasaki Y, Tabe Y, et al., Magnetic phase transition and elastic properties of alpha-Mn at low temperature [J]. Jpn. J. Appl. Phys.,2006; 45: 4497-4499.
[348]Kittel C, Introduction to solid state physics[M], New York:Wiley; 1976.
[349]Mori N, Takahashi M, Oomi G, Magnetic contribution to the bulk modulus of 3d-transition metal-alloys[J]. J. Magn. Magn. Mater.,1983; 31-4:135-136.
[350]Rosen M, Elastic moduli and ultrasonic attenuation of polycrystalline alpha-Mn from 4.2-300 K[J]. Phys. Rev.,1968;165:357-359.
[351]de Laissardiere G T, Manh D N, Magaud L, et al., Electronic structure and hybridization effects in Hume-Rothery alloys containing transition elements [J]. Phys. Rev. B,1995;52:7920.
[352]Solyom J, Fundamentals of the physics of solids:Structure and dynamics[M], Berlin:Springer-Verlag; 2008.
[353]de Laissardiere G T, Nguyen-Manh D, Mayou D, Electronic structure of complex Hume-Rothery phases and quasicrystals in transition metal aluminides[J]. Prog. Mater. Sci.,2005; 50:679-788.
[354]Perdew J P, Chevary J A, Vosko S H, et al., Atoms, molecules, solids, and surfaces:Applications of the generalized gradient approximation for exchange and correlation[J]. Phys. Rev. B,1992;46:6671-6687.
[355]Shang S, Bottger A J, Steenvoorden M P, et al., Hyperfine interactions in hexagonal epsilon-Fe6Ny phase investigated by Mossbauer spectroscopy and ab initio calculations [J]. Acta Mater.,2006;54:2407-2417.
[356]Shang S L, Bottger A J, Liu Z K, The influence of interstitial distribution on phase stability and properties of hexagonal epsilon-Fe6Cx, epsilon-Fe6Ny and epsilon-Fe6CxNy phases:A first-principles calculation [J]. Acta Mater.,2008; 56:719-725.
[357]Shang S L, Mei Z G, Saengdeejing A, et al., First-principles calculations of pure elements:Equations of state and elastic constants[J]. Comp. Mater. Sci.,2010; 48:813-826.
[358]El-Moneim A A, Bond compression bulk modulus and Poisson's ratio of the polycomponent silicate glasses[J]. Mater. Chem. Phys.,2001; 70:340-343.
[359]Shukla A, Pelton A, Thermodynamic Assessment of the Al-Mn and Mg-Al-Mn Systems[J]. J. Phase. Equilib. Diffus.,2009; 30:28-39.
[360]Kopp H, Investigations of the Specific Heat of Solid Bodies[J]. Philos. T. Roy. Soc.,1865; 155:71-202.
[361]Shang S, Wang T, Liu Z-K, Thermodynamic modelling of the B-Ca, B-Sr and B-Ba systems[J]. CALPHAD,2007; 31:286-291.
[362]Shang S L, Wang Y, Liu Z K, In:SR Agnew, NR Neelameggham, EA Nyberg, WH Sillekens editors Magnesium Technology 2010; 2010, pp.617-622.
[363]Wolverton C, Yan X Y, Vijayaraghavan R, et al., Incorporating first-principles energetics in computational thermodynamics approaches[J]. Acta Mater.,2002; 50:2187-2197.
[364]Barin I, Thermochemical Data of Pure Substances[M], Weinheim, New York; 1995.
[365]Davis J R, Joseph R, Aluminum and aluminum alloys[M], ASM International; 1993.
[366]Wang J, Shang S L, Wang Y, et al., First-principles calculations of binary Al compounds:enthalpies of formation and elastic properties[J]. CALPHAD,2011; 35:562-573.
[367]Clerc D G, Ledbetter H M, Mechanical hardness:A semiempirical theory based on screened electrostatics and elastic smear[J]. J. Phys. Chem. Solids,1998; 59: 1071.
[368]Music D, Schneider J M, Effect of transition metal additives on electronic structure and elastic properties of TiAl and Ti3Al[J]. Phys. Rev. B,2006; 74.
[369]Zhang C L, Han P D, Li J M, et al., First-principles study of the mechanical properties of NiAl microalloyed by M (Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd)[J]. J. Phys. D. Appl. Phys.,2008; 41:095410.
[370]Ganeshan S, Shang S L, Wang Y, et al., Effect of alloying elements on the elastic properties of Mg from first-principles calculations [J]. Acta Mater.,2009; 57:3876-3884.
[371]Tonejc A, Bonefaci A, Enhanced solubility of Iron in Aluminum obtained by rapid quenching technique[J]. J. Appl. Phys.,1969; 40:419-420.
[372]Bendijk A, Delhez R, Katgerman L, et al., Characterization of Al-Si-alloys rapidly quenched from the melt[J]. J. Mater. Sci.,1980; 15:2803-2810.
[373]Tonejc A, Bonefaci A, Al-rich metastable Al-Ti solid solutions[J]. Scripta Metallurgica 1969; 3:145-148.
[374]Wang T, Chen L Q, Liu Z K, Lattice parameters and local lattice distortions in fcc-Ni solutions[J]. Metall. Mater. Trans. AMetall. Mater. Trans. A-Phys. Metall. Mater. Sci.,2007; 38A:562-569.
[375]Scheuer U, Lengeler B, Lattice distortion of solute atoms in metals studied by X-ray-absorption fine-structure [J]. Phys. Rev. B,1991; 44:9883-9894.
[376]Shang S L, Saengdeejing A, Mei Z G, et al., First-principles calculations of pure elements:Equations of state and elastic stiffness constants[J]. Comp. Mater. Sci.,2010; 48:813-826.
[377]Gault C, Dauger A, Boch P, Variations of elastic constants of Aluminum-Magnesium single-crystals with guinier-preston zones[J]. Phys. Status. Solidi. A,1977; 43:625-632.
[378]Hearmon R F S, The elastic constants of anisotropic materials[J]. Rev. Mod. Phys.,1946; 18:409-440.
[379]Ledbetter H, Relationship between bulk-modulus temperature-dependence and thermal expansivity [J]. Phys. Status. Solidi. B,1994; 181:81-85.
[380]Miedema A R, Deboer F R, Dechatel P F, Empirical description of role of electronegativity in alloy formation[J]. J. Phys. F. Met. Phys.,1973; 3: 1558-1576.
[381]Wolverton C, Ozolins V, Entropically favored ordering:The metallurgy of A12Cu revisited[J]. Phys. Rev. Lett.,2001; 86:5518-5521.
[382]Rose J H, Shore H B, Elastic-constants of the transition-metals from a uniform electron-gas[J]. Phys. Rev. B,1994; 49:11588-11601.
[383]Rose J H, Shore H B, Uniform electron-gas for transition-metals-input parameters[J]. Phys. Rev. B,1993; 48:18254-18256.
[384]Rose J H, Shore H B, Bonding energetics of metals-explanation of trends[J]. Phys. Rev. B,1991; 43:11605-11611.
[2]Zolotorevsky V S, Belov N A, Glazoff M V, Casting Aluminum Alloys[M], Amsterdam:Elsevier; 2007.
[3]潘复生,张丁非,铝合金及应用[M],化学工业出版社；2006.
[4]王祝堂,新的变形铝合金的成分与简明性能[J].轻合金加工技术,2001；29：1-4.
[5]张君尧,铝合金材料的新进展[J].轻合金加工技术,1998；26：1-10.
[6]http://market.cnal.com/statistics/2012/02-21/1329785236266980.shtml
[7]http://market.cnal.com/statistics/2012/02-21/1329784946266975.shtml
[8]Integrated Computational Materials Engineering:A Transformational Discipline for Improved Competitivies and National Security[M], Washinton, D.C.:The National Academies Press; 2008.
[9]http://www.whitehouse.gov/blog/2011/06/24/materials-genome-initiative-renaissa nce-american-manufacturing
[10]Kaufman L, Bernstein H, Computer Calculations of Phase Diagrams[M], New York:Academic Press; 1970.
[11]Andersson J O, Helander T, Hoeglund L, et al., THERMO-CALC and DICTRA, Computational Tools for Materials Science[J]. CALPHAD,2002; 26(2): 273-312.
[12]Du Y, Wang J, Ouyang Y F, et al., An Approach to Determine Enthalpies of Formation for Ternary Compounds[J]. J. Min. Metall. Sect. B-Metall.,2010; 46: 1-9.
[13]Du Y, Liu S H, Zhang L J, et al., An overview on phase equilibria and thermodynamic modeling in multicomponent Al alloys:Focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system[J]. CALPHAD,2011; 35:427-445.
[14]Kohn W, Sham L J, Self-Consistent Equations Including Exchange and Correlation Effects[J]. Phys. Rev. A,1965; 140(2):1133-1138.
[15]Wang Y, Liu Z K, Chen L Q, Thermodynamic properties of Al, Ni, NiAl, and Ni3Al from first-principles calculations [J]. Acta Mater.,2004; 52:2665-2671.
[16]乔芝郁,郝士明,相图计算研究的进展[J].材料与冶金学报,2005；4(2)83-89.
[17]徐祖耀,材料热力学[M],北京：高等教育出版社；2009.
[18]张圣弼,李道子,相图-原理、计算及在冶金中的应用[M],北京：冶金工业出版社：1986.
[19]Kodentsov A A, Bastin G F, van Loo F J J, The diffusion couple technique in phase diagram determination [J]. J. Alloys Compd.,2001; 320:207-217.
[20]Girchner G, Larbo G, Uhrenius B, Distribution of chromium and manganese between ferrite and austenite using experimental measurements and thermodynamic calculations[J]. Prakt. Metall.,1971; 8:641-654.
[21]Hasebe M, Nishizawa T, Applications of phase diagrams in metallurgy and ceramics[M], Washington:National Bureau of Standards SP-496; 1978.
[22]Jin Z P, A study of the range of stability of sigma phase in some ternary system [J]. Scand. J. Metall.,1981; 10:178-187.
[23]Xu H H, Du Y, Huang B Y, et al., Phase diagram of the Co-Cu-Ti system at 850 ℃[J]. Z. Metallkd.,2006; 97:140-144.
[24]Zhao J C, The diffusion-multiple approach to designing alloys[J]. Ann. Rev. Mater. Res.,2005; 35:51-73.
[25]Zhao J C, Combinatorial approaches as effective tools in the study of phase diagrams and composition-structure-property relationships [J]. Prog. Mater. Sci., 2006; 51:557-631.
[26]王培铭,许乾慰,材料研究方法[M],北京：科学出版社；2005.
[27]Du Y, Schuster J C, An effective approach to describe growths of binary intermediate phases with narrow ranges of homogeneity [J]. Metall. Mater. Trans. A,2001; 32(9):2396-2400.
[28]http://www.calphad.org/
[29]Turchi P E A, Abrikosov I A, Burton B, et al., Interface between quantum-mechanical-based approaches, experiments, and CALPHAD methodology [J]. CALPHAD,2007; 31:4-27.
[30]冯端,师昌绪,刘治国,材料科学导论[M],北京：化学工业出版社；2002.
[31]http://www.thermocalc.com
[32]Hillert M, Phase Equilibria, Phase Diagrams and Phase Transformations:Their Thermodynamic Basis[M], UK:Cambridge University Press; 1998.
[33]郝士明,材料热力学[M],北京：化学工业出版社；2003.
[34]Curtarolo S, Kolmogorov A N, Cocks F H, High-throughput ab initio analysis of the Bi-In, Bi-Mg, Bi-Sb, In-Mg, In-Sb and Mg-Sb systems[J]. CALPHAD,2005; 29:155-161.
[35]Gonzales-Ormeno P G, Petrilli H M, Schon C G, Ab initio calculation of the bcc Mo-Al (Molybdenum-aluminium) phase diagram:Implications for the nature of the z2-MoAl phase[J]. Scripta Mater.,2005; 53:751-756.
[36]Lechermann F, Faehnle M, Sanchez J M, First-Principles Investigation of the Ni-Fe-Al System[J]. Intermetallics,2005; 13(10):1096-1109.
[37]Kaufman L, Fahnle M, Turchi P E A, et al., Thermodynamics of the Cr-Ta-W system by combing the ab initio and CALPHAD methods[J]. CALPHAD,2002; 25:419-433.
[38]Chvatalova K, Fahnle M, Houserova J, et al., First-principles calculations of energetics of sigma phase formation and thermodynamic modeling in Fe-Ni-Cr system[J]. J. Alloys Compd.,2004; 378:71-74.
[39]Ohtani H, Fahnle M, Yamano M, et al., Thermodynamic analysis of the Co-Al-C and Ni-Al-C systems by incorporating ab initio energetic calculations into the CALPHAD approach[J]. CALPHAD,2004; 28:177-190.
[40]Jiang C, Gleeson B, A Combined First-Principles/CALPHAD Modeling of the Al-Ir System[J]. Acta Mater.,2006; 54(15):4101-4110.
[41]Du Y, Wang J, Zhao J R, et al., Reassessment of the Al-Mn system and a thermodynamic description of the Al-Mg-Mn system[J]. Int. J. Mater. Res.,2007; 98:855-871.
[42]Zhang L J, Wang J, Du Y, et al., Thermodynamic properties of the Al-Fe-Ni system acquired via a hybrid approach combining calorimetry, first-principles and CALPHAD[J]. Acta Mater.,2009; 57:5324-5341.
[43]Dinsdale A T, SGTE Data for Pure Elements[J]. CALPHAD,1991; 15:317-425.
[44]Wang Y, Curtarolo S, Jiang C, et al., Ab initio lattice stability in comparison with CALPHAD lattice stability[J]. CALPHAD,2004; 28:79-90.
[45]Sluiter M H F, Ab initio lattice stabilities of some elemental complex structures[J]. CALPHAD,2006; 30:357-366.
[46]Redlich O, Kister A T, Algebraic Representation of Thermodynamic Properties and the Classification of Solutions[J]. Ind. Eng. Chem.,1948; 40:345-348.
[47]Hillert M, Staffans.Li, Regular Solution Model for Stoichiometric Phases and Ionic Melts[J]. Acta Chem. Scand.,1970; 24:3618-3626.
[48]Bragg W L, Williams E J, The Effect of Thermal Agitation on Atomic Arrangement in Alloys[J]. Proc. Roy. Soc. Lond. A,1934; 145:699-730.
[49]Bragg W L, Williams E J, The Effect of Thermal Agitation on Atomic Arrangement in Alloys. Ⅱ[J]. Proc. Roy. Soc. Lond. A,1935; 151:540-566.
[50]Pelton A, Blander M, Thermodynamic analysis of ordered liquid solutions by a modified quasichemical approach-Application to silicate slags[J]. Metall. Mater. Trans. B,1986; 17:805-815.
[51]Hildebrand J H, Eastman E D, The Vapor Pressure of Thallium Amalgams[J]. J. Am. Chem. Soc.,1915; 37:2452-2459.
[52]Yuan X, Sun W, Du Y, et al., Thermodynamic modeling of the Mg-Si system with the Kaptay equation for the excess Gibbs energy of the liquid phase [J]. CALPHAD,2009; 33:673-678.
[53]Kaptay G, A new equation for the temperature dependence of the excess Gibbs energy of solution phases [J]. CALPHAD,2004; 28:115-124.
[54]Hillert M, Jarl M, A model for alloying in ferromagnetic metals[J]. CALPHAD, 1978; 2:227-238.
[55]Ansara I, Sundman B, Willemin P, Thermodynamic modeling of ordered phases in the Ni-Al system[J]. Acta Metallurgica,1988; 36:977-982.
[56]Ansara I, Dupin N, Lukas H L, et al., Thermodynamic assessment of the Al-Ni system[J]. J. Alloy. Compd.,1997; 247:20-30.
[57]http://cst-www.nrl.navy.mil/lattice/
[58]Massalski T B, Okamoto H, Subramanian P R, et al., Binary Alloy Phase Diagrams[M], ASM International; 1990.
[59]罗伯编著D,项金钟,吴兴惠译,计算材料学[M],北京：化学工业出版社；2002.
[60]Frenkel, Smit,汪文川等译,分子模拟-从算法到应用[M],北京：化学工业出版社;2002.
[61]Born M, Oppenheimer J R, Concerning the Quantum Theory of Molecules[J]. Ann. Phys-new. York.,1927; 84:457-484.
[62]Hartree D R, The wave mechanics of an atom with a non-Coulomb central field[J]. Proc. Cambridge. Philos. Soc.,1928; 24:89-110.
[63]黄昆原著,韩汝琦改编,固体物理学[M],北京：高等教育出版社；1988.
[64]Fock V, Naherungsmethode zur Losung des quanten-mechanischen Mehrkorper-probleme[J]. Z. Phys.,1930; 61:126-148.
[65]谢希德,陆栋,固体能带理论[M],上海：复旦大学出版社；1998.
[66]Thomas L H, The calculation of atomic fields[J]. Proc. Cambridge. Philos. Soc., 1927; 23:542-548.
[67]Fermi E, A statistical method for the determination of some properties of atoms. II. Application to the periodic system of the elements[J]. Z. Phys.,1928,48. 73-79.
[68]Dirac P A M, Note on exchange phenomena in the Thomas atom[J]. Proc. Cambridge. Philos. Soc.,1930; 26:376-385.
[69]Hohenberg P, Kohn W, Inhomogeneous Electron Gas[J]. Phys. Rev. B,1964; 136: B864-B871.
[70]Kohn W, Sham L J, Self-Consistent Equations Including Exchange and Correlatioin Effects[J]. Physical Review,1965; 140:A1133-A1138.
[71]Perdew J P, Wang Y, Accurate and Simple Analytic Representation of the Electron-Gas Correlation-Energy [J]. Phys. Rev. B,1992; 45:13244-13249.
[72]Slater J C, A simplification of the Hartree-Fock method[J]. Phys. Rev.,1951; 81: 385-390.
[73]Mahan G D, Many particle physics[M], New York:Plenum Publishing; 1990.
[74]Slater J C, Wilson T M, Wood J H, Comparison of several exchange potentials for electrons in the Cu+ ion[J]. Phys. Rev.,1969; 179:28-38.
[75]Hedin L, Lundqvis.Bi, Explicit local exchange correlaiton potentials[J]. J Phys C Solid State Phys,1971; 4:2064-2083.
[76]Vosko S H, Wilk L, Nusair M, Accurate spin-dependent electron liquid correlation energies for local spin density calculations:a critical analysis[J]. Can. J. Phys.,1980; 58:1200-1211.
[77]Perdew J P, Zunger A, Self-interaction correction to density-functional approximations for many-electron systems[J]. Phys. Rev. B,1981; 23: 5048-5079.
[78]Ceperley D M, Alder B J, Ground-state of the Electron Gas by a Stochastic Method[J]. Phys. Rev. Lett.,1980; 45:566-569.
[79]Becke A D, Density-functional exchange-energy approximation with correct asymptotic behavior[J]. Physical Review A,1988; 38:3098-3100.
[80]Becke A D, Density functional calculations of molecular bond energies[J]. J. Chem. Phys.,1986; 84:4524-4529.
[81]Lee C T, Yang W T, Parr R G, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density [J]. Physical Review B,1988; 37:785-789.
[82]Perdew J P, Burke K, Ernzerhof M, Generalized gradient approximation made simple[J]. Physical Review Letters,1996; 77:3865-3868.
[83]Kohn W, Nobel Lecture:Electronic structure of matter-wave functions and density functionals[J]. Rev. Mod. Phys.,1999; 71:1253-1266.
[84]Monkhorst H J, Pack J D, Special Points for Brillouin-Zone Integrations [J]. Phys. Rev. B,1976; 13:5188-5192.
[85]Pack J D, Monkhorst H J, Special points for Brillouin-zone integrations-a reply[J]. Phys. Rev. B,1977; 16:1748-1749.
[86]Payne M C, Teter M P, Allan D C, et al., Iterative minimization techniques for ab initio total-energy calculations-molecular-dynamics and conjugate gradients[J]. Rev. Mod. Phys.,1992; 64:1045-1097.
[87]Fermi E. Nuovo Cimento,1934; 11:157.
[88]Hellmann H. Acta Physiochimica URSS,1935; 1:913.
[89]Hamann D R, Schluter M, Chiang C, Norm-Conserving Pseudopotentials[J]. Phys. Rev. Lett.,1979; 43:1494-1497.
[90]Vanderbilt D, Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism[J]. Phys. Rev. B,1990; 41:7892-7895.
[91]Blochl P E, Projector Augmented-Wave Method[J]. Phys. Rev. B,1994; 50: 17953-17979.
[92]Hellmann H, Einfuhrung in die Quantumchemie[M], Leipzig:Deuticke; 1937.
[93]Feynman R P, Forces in molecules[J]. Phys. Rev.,1939; 56:340-343.
[94]Press W H, Teukolsky S A, Vetterling W T, et al., Numerical recipes:the art of scientific computing[M], Cambridge:Cambridge University Press; 1986.
[95]Kresse G, Hafner J, Abinitio Molecular-Dynamics for Liquid-Metals.[J]. Phys. Rev. B,1993; 47:558-561.
[96]Kresse G, Furthmuller J, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[J]. Comp. Mater. Sci., 1996; 6:15-50.
[97]Kresse G, Furthmuller J, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J]. Phys. Rev. B,1996; 54: 11169-11186.
[98]Kresse G, Joubert D, From ultrasoft pseudopotentials to the projector augmented-wave method[J]. Phys. Rev. B,1999; 59:1758-1775.
[99]Kresse G, Hafner J, Norm-Conserving and Ultrasoft Pseudopotentials for First-Row and Transition-Elements[J]. J. Phys-condens. Mat.,1994; 6: 8245-8257.
[100]Davidson E R, Methods in computational molecular physics, Vol 113 of NATO Advanced Study Institute, Series C:Mathematical and Physical Sciences[M], New York:Plenum Press.
[101]Pulay P, Convergence acceleration of iterative sequences-the case of scf iteration[J]. Chem. Phys. Lett.,1980; 73:393-398.
[102]Jepsen O, Andersen O K, The electronic-structure of hcp ytterbium[J]. Solid State Commun.,1993; 88:871-875.
[103]Blochl P E, Jepsen O, Andersen O K, Improved Tetrahedron Method for Brillouin-Zone Integrations[J]. Phys. Rev. B,1994; 49:16223-16233.
[104]Fu C L, Ho K M, First-principles calculation of the equilibrium ground-state properties of transition metals:Applications to Nb and Mo[J]. Phys. Rev. B, 1983; 28:5480-5486.
[105]Methfessel M, Paxton A T, High-Pricision Sampling for Brillouin-Zone Integration in Metals[J]. Phys. Rev. B,1989; 40:3616-3621.
[106]Liang P, Su H L, Donnadieu P, et al., Experimental investigation and thermodynamic calculation of the central part of the Mg-Al phase diagram[J]. Z. Metallkd.,1998; 89:536-540.
[107]Grobner J, Mirkovic D, Ohno M, et al., Experimental investigation and thermodynamic calculation of binary Mg-Mn phase equilibria[J]. J. Phase. Equilib. Diffus.,2005; 26:234-239.
[108]Villars P, Calvert L D, Pearson's Handbook of Crystallographic Data for Intermetallic Phases,2nd Edition[M], Materials Park, Ohio, USA:ASM International; 1991.
[109]Ellner M, The Structure of the High-Temperature Phase Mnal(H) and the Displacive Transformation from Mnal(H) into Mn5Al8[J]. Metall. Mater. Trans. A,1990; 21:1669-1672.
[110]Kreiner G, Franzen H F, The crystal structure of lambda-Al4Mn[J]. J. Alloy. Compd.,1997; 261:83-104.
[111]Ohno M, Schmid-Fetzer R, Thermodynamic assessment of Mg-Al-Mn phase equilibria, focusing on Mg-rich alloys[J]. Z. Metallkd.,2005; 96:857-869.
[112]Liu X J, Ohnuma I, Kainuma R, et al., Thermodynamic assessment of the aluminum-manganese (Al-Mn) binary phase diagram[J]. J. Phase. Equilib., 1999; 20:45-56.
[113]Jansson A, A Thermodynamic Evaluation of the Al-Mn System[J]. Metall. Mater. Trans. A,1992; 23:2953-2962.
[114]Dix E H, Fink W L, Willey L A, Equilibrium Relations in Aluminum-Manganese Alloys of High Purity, II[J]. Trans. AIME,1933; 104: 335-352.
[115]Godecke T, Koster W, Supplement to constitution of Aluminium-Manganese system[J]. Z. Metallkd.,1971; 62:727-732.
[116]Thornton M C. Unpublished research work, Alcan International Ltd, Banbury Laboratory, USA,1996.
[117]Weitzer F, Rogl P, Hayes F H, et al., In:F Aldinger, H Mughrabi editors Werkstoff Woche'96, Materialwissenschaftliche Grundlagen, Deutsche Gesellschaft fur Materialkunde, Germany [M]; 1996, pp.185-190.
[118]Taylor M A, Intermetallic Phases in the Aluminium-Manganese Binary System[J]. Acta Metallurgica,1960; 8:256-262.
[119]Murray J L, McAlister A J, Schaefer R J, et al., Stable and Metastable Phase-Equilibria in the Al-Mn System[J]. Metall. Mater. Trans. A,1987; 18: 385-392.
[120]Robinson J A J, Hayes F H, Serneels A, et al., In:COST 507:Definition of thermochemical and thermophysical properties to provide a database for the development of new light alloys, Vol.1, COST Secretariat[M], Brussels, Belgium; 1998, p.230.
[121]Hanawalt J D, Nelson C E, Peloubet J A, Corrosion studies of magnesium and its alloys[J]. Trans. AIME,1942; 147:273-298.
[122]Nelson C E, Transactions of the American Foundrymen's Society[M], American Foundrymen's Society; 1948.
[123]Ran Q S, In:G Effenberg, F Aldinger, L Rokhlin editors Graphischer Betrieb Konrad Triltsch, D-07070 Wurzburg[M]; 1999.
[124]Ansara I, Dinsdale A T, Rand M H, COST 507:Thermochemical database for light metal alloys[M], Office for Official Publications of the European Communities; 1998.
[125]McAlister A, Murray J, The (Al-Mn) Aluminum-Manganese system[J]. J. Phase. Equilib.,1987; 8:438-447.
[126]Kuznetsov G M, Barsukov A D, Abas M I,Study of manganese, chromium, titanium, and zirconium solubility in solid aluminum[J]. Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall.,1983; 96-100.
[127]Minamino Y, Yamane T, Araki H, et al., Solid Solubilities of Manganese and Titanium in Aluminum at 0.1-Mpa and 2.1-Gpa[J]. Metall. Mater. Trans. A, 1991; 22:783-786.
[128]Chastel R, Saito M, Bergman C, Thermodynamic Investigation on All-Xmnx Melts by Knudsen Cell Mass-Spectrometry[J]. J. Alloy. Compd.,1994; 205: 39-43.
[129]Meschel S V, Kleppa O J, The standard enthalpies of formation of some 3d transition metal aluminides by high-temperature direct synthesis calorimetry[J]. NATO ASI SER., SER. E,1994; 256:103-113.
[130]Sigli C, In:CALPHAD XXIV, Kyoto, Japan; 1995.
[131]Matuo M, Muramatsu T, Asanuma A, et al., Estimation of solute Fe and Mn concentration in aluminum alloys by phenol filtrate analysis[J]. Keikinzoku, 1997; 47:15-20.
[132]Dix E H, Jr., Keith W D, Equilibrium Relations in Aluminum-Manganese Alloys of High Purity[J]. Trans. AIME,1927; No.1633-E:315-335.
[133]Fahrenhorst E, Hofmann W, The solubility of manganese in aluminum containing up to 2% magnesium[J]. Metallwirtsch,1940; 19:891-893.
[134]Phillips H W L, The constitution of alloys of Aluminium with Manganese, Silicon, and Iron. I. The binary system:Aluminium-Manganese. Ⅱ. The ternary systems:Aluminium-Manganese-Silicon and Aluminium-Manganese-iron[J]. J Inst. Met.,1943; 69:275-316.
[135]Butchers E, Humerothery W, The solubility of manganese in aluminium[J]. J Inst. Met.,1945; 71:87-91.
[136]Obinata I, Yamaji K, Hata E, Subcooled aluminum-manganese alloys. I[J]. Nippon Kinzoku Gakkaishi,1953; 17:496-501.
[137]Kono H, On the Ferromagnetic Phase in Manganese-Aluminum System[J]. J. Phys. Soc. Jpn.,1958; 13:1444-1451.
[138]Koch A J J, Hokkeling P, Vandersteeg M G, et al., New Material for Permanent Magnets on a Base of Mn and Al[J]. J. Appl. Phys.,1960; 31:S75-S77.
[139]Koster W, Wachtel E, Aufbau Und Magnetische Eigenschaften Der Aluminium-Mangan-Legierungen Mit Mehr Als 25-at-Percent Mn[J]. Z. Metallkd.,1960; 51:271-280.
[140]Kubaschewski O, Heymer G, Heats of formation of transition-metal aluminides[J]. Trans. Faraday Soc.,1960; 56:473-478.
[141]Drits M E, Kadaner E S, Padezhnova E M, et al., Opredelenie Granits Sovmestnoi Rastvorimosti Margantsa I Kadmiya V Tverdom Alyuminii[J]. Zhurnal Neorganicheskoi Khimii,1964; 9:1397-1400.
[142]Batalin G I, Beloboro.Ea, Chekhovs.Aa, et al., Thermodynamical properties of liquid alloys of Aluminum with Manganese[J]. Ukrainskii Khimicheskii Zhurnal,1972; 38:825-827.
[143]Esin Y O, Bobrov N P, Petrushe.Ms, et al., Concentration-Dependence of Enthalpies of Formation of Mn, Al-Melts at 1626 K[J]. Zh. Fiz. Khim.,1973; 47:1959-1962.
[144]Kematick R J, Myers C E, Thermodynamics and Phase-Equilibria in the Al-Mn System[J]. J. Alloy. Compd.,1992; 178:343-349.
[145]Liu X J, Kainuma R, Ohtani H, et al., Phase equilibria in the Mn-rich portion of the binary system Mn-Al[J]. J. Alloy. Compd.,1996; 235:256-261.
[146]Beerwald A, On the solubility of iron and manganese in magnesium and magnesium-aluminum alloys[J]. Metallwirtschaft,1944; 23:404-407.
[147]Ageev N V, Kornilov I I, Khlapova A N, Magnesium-rich alloys of the system magnesium-aluminum-manganese [J]. Izv. Sekt. Fiz.-Khim. Anal., Inst. Obshch. Neorg. Khim.,Akad.Nauk SSSR,1948; 16:130-143.
[148]Nelson B J, Equilibrium Relations in Magnesium-Aluminum-Manganese Alloys[J]. Journal of Metals,1951; 3:797-799.
[149]Mirgalovskaya M S, Matkova L N, Komova E M, System magnesium-aluminum-manganese [J]. Tr. Inst. Metall., Akad. Nauk SSSR,1957; 139-148.
[150]Oberlander B C, Simensen C J, Svalestuen J, Conf. Magnesium Technology, Inst. of Metals[J].1986; 139-148.
[151]Simensen C J, Oberlander B C, Svalestuen J, et al., Determination of the Equilibrium Phases in Molten Mg-4 Wt-Percent Al-Mn Alloys[J]. Z. Metallkd., 1988; 79:537-540.
[152]Simensen C J, Oberlander B C, Svalestuen J, et al., The Phase-Diagram for Magnesium-Aluminum-Manganese above 650-Degrees-C[J]. Z. Metallkd., 1988; 79:696-699.
[153]Thorvaldsen A, Aliravci C A, In:Can. Inst. Min. Metall. Pet.; 1992, pp. 277-288.
[154]Leemann W G, Hanemann H, The system aluminum-magnesium-manganese[J]. Aluminium-Arch.,1938; 9:6-17.
[155]Hofmann W, X-Ray methods on investigation of aluminium alloys[J]. Aluminium,1938; 20:865-872.
[156]Butchers E, Raynor G V, Hume-Rothery W, The constitution of magnesium-manganese-zinc-aluminium alloys in range 0-5%magnesium, 0-2% manganese,0-8% zinc. I. The liquidus[J]. J Inst. Met.,1943; 69:209-228.
[157]Little A T, Raynor G V, Hume-Rothery W, The constitution of magnesium-manganese-zinc-aluminium alloys in the range 0-5% magnesium, 0-2% manganese,0-8% zinc. Ⅲ. The 500℃ and 400 ℃ isothermals[J]. J Inst. Met.,1943;69:423-440.
[158]Mondolfo L F, Metallography of aluminum alloys[M], J. Wiley & sons, inc.; 1943.
[159]Butchers E, Humerothery W, On the constitution of aluminium magnesium manganese zinc alloys-the solidus[J]. J Inst. Met.,1945; 71:291-311.
[160]Wakeman D W, Raynor G V, The Constitution of Aluminium Manganese Magnesium and Aluminium Manganese Silver Alloys, with Special Reference to Ternary-Compound Formation[J]. J Inst. Met.,1948; 75:131-150.
[161]Ohnishi T, Nakatani Y, Shimizu K, Phase diagrams and ternary compounds of aluminum-magnesium-chromium and aluminum-magnesium-manganese systems in the aluminum-rich corner[J]. Keikinzoku,1973; 23:202-209.
[162]Ohnishi T, Nakatani Y, Shimizu K, Phase diagram in the aluminum- rich side of the aluminum-magnesium-manganese-chromium quaternary system[J]. Keikinzoku,1973; 23:437-443.
[163]Fun H K, Lin H C, Lee T J, et al., T-Phase Al18Mg3Mn2[J]. Acta Crystallogr. C, 1994; 50:661-663.
[164]Barlock J G, Mondolfo L F, Structure of Some Aluminium-Iron-Magnesium-Manganese-Silicon Alloys[J]. Z. Metallkd.,1975; 66:605-611.
[165]Taylor M A, Space group of MnAl3[J]. Acta Crystallographica,1961; 14:84-84.
[166]Abrikosov N K, Ivanova L D, Danil'chenko V A, Phase transition of Mn4A11 into MnA13[J].Izv.Akad.Nauk SSSR,Neorg. Mater.,1971; 7:1053-1055.
[167]Andersson J O, Guillermet A F, Hillert M, et al., A Compound-Energy Model of Ordering in a Phase with Sites of Different Coordination Numbers[J]. Acta Metallurgica 1986; 34:437-445.
[168]Hobbs D, Hafner J, Spisak D, Understanding the complex metallic element Mn. I. Crystalline and noncollinear magnetic structure of alpha-Mn[J]. Phys. Rev. B, 2003; 68:014407.
[169]Sundman B, Jansson B, Andersson J O, The Thermo-Calc Databank System[J]. CALPHAD,1985; 9:153-190.
[170]Du Y, SchmidFetzer R, Ohtani H, Thermodynamic assessment of the V-N system[J]. Z. Metallkd.,1997; 88:545-556.
[171]Liu Z K, First-Principles Calculations and CALPHAD Modeling of Thermodynamics [J]. J. Phase. Equilib. Diffus.,2009; 30:517-534.
[172]Shang S, Zhang H, Ganeshan S, et al., The development and application of a thermodynamic database for magnesium alloys[J]. JOM,2008; 60:45-47.
[173]Chen H L, Du Y, Xu H H, et al., Experimental investigation and thermodynamic modeling of the ternary Al-Cu-Fe system[J]. J. Mater. Res.,2009; 24: 3154-3164.
[174]Du Y, Schuster J C, Liu Z K, et al., A thermodynamic description of the Al-Fe-Si system over the whole composition and temperature ranges via a hybrid approach of CALPHAD and key experiments [J]. Intermetallics.,2008; 16:554-570.
[175]Du Y, Schuster J C, Weitzer F, et al., A thermodynamic description of the Al-Mn-Si system over the entire composition and temperature ranges[J]. Metall. Mater. Trans. A,2004; 35A:1613-1628.
[176]He C Y, Du Y, Chen H L, et al., Experimental investigation and thermodynamic modeling of the Al-Cu-Si system[J]. CALPHAD,2009; 33:200-210.
[177]Xiong W, Du Y, Hu R X, et al., Construction of the AlNiSi phase diagram over the whole composition and temperature ranges:thermodynamic modeling supported by key experiments and first-principles calculations [J]. Int. J. Mater. Res.,2008; 99:598-612.
[178]Zhao J R, Zhang L J, Du Y, et al., Experimental Investigation and Thermodynamic Reassessment of the Cu-Fe-Si System[J]. Metall. Mater. Trans. A,2009;40A:1811-1825.
[179]Yan X, Chang Y A, A Thermodynamic analysis of the Cu-Si system[J]. J. Alloy. Compd.,2000; 308:221-229.
[180]Shin D, Saal J E, Liu Z K, Thermodynamic modeling of the Cu-Si system[J]. CALPHAD,2008; 32:520-526.
[181]Jacobs M H G, Spencer P J, A critical thermodynamic evaluation of the systems Si-Zn and Al-Si-Zn[J]. CALPHAD,1996; 20:307-320.
[182]Spencer P J, A thermodynamic evaluation of the copper-zinc system [J]. CALPHAD,1986; 10:175-185.
[183]Kowalski M, Spencer P J, Thermodynamic reevaluation of the copper-zinc system[J]. J. Phase Equilib.,1993; 14:432-438.
[184]Kowalski M, Spencer P J, In:I Ansara editor Thermochemical database for light metal alloys[M], EUR; 1998, pp.186-191.
[185]David N, Fiorani J M, Vilasi M, et al., Thermodynamic reevaluation of the Cu-Zn system by electromotive force measurements in the zinc-rich part[J]. J. Phase Equilib.,2003; 24:240-248.
[186]Gierlotka W, Chen S W, Thermodynamic descriptions of the Cu-Zn system[J]. J. Mater. Res.,2008; 23:258-263.
[187]Liang H, Chang Y A, A thermodynamic description for the Al-Cu-Zn system[J]. J. Phase Equilib.,1998; 19:25-37.
[188]Saunders N, In:I Ansara editor Thermochemical database for light metal alloys[M], EUR; 1998, pp.28-33.
[189]Bochvar N, Dobatkina T, In:Landolt-Bornstein New Series [M]:MSIT; 2007, pp.393-408.
[190]Miettinen J, Thermodynamic description of the Cu-Si-Zn system in the copper-rich corner[J]. CALPHAD,2007; 31:422-427.
[191]Borggren U, Selleby M, A Thermodynamic Database for Special Brass[J]. J. Phase Equilib.,2003; 24:110-121.
[192]Pops H, The Constitution of Copper-Rich Copper-Silicon-Zinc Alloys[J]. Trans. Met. Soc. AIME,1964; 230:813-820.
[193]熊伟,Ni合金相图、相平衡及相变的热力学研究[D].博士学位论文,中南大学,中国.2010.
[194]Mima G, Hasegawa M, The Diagram of Cu-Si-Zn Alloy-Ⅱ[J]. Technol. Repts. Osaka Univ.,1957; 7:385-397.
[195]Raynor G V, Equilibrium diagram of the system Cu-Zn[J]. Inst. Met. (London), Annotated Equil. Diagram Ser.,1944; No.3:5 pp.
[196]Hansen M, Anderko K, In:Constitution of Binary Alloys[M], New York: McGraw-Hill; 1958, pp.649-655.
[197]Massalski T B, Murray J L, H B L, et al., American Society for Metals, Metal Park, Ohio; 1986.
[198]Bauer O, Hansen M, Structure of copper-zinc alloys[J]. Z. Metallkd.,1927; 19: 423-434.
[199]Ruer R, Kremers K, The system:copper-zinc [J]. Z. Anorg. Allg. Chem.,1929; 184:193-231.
[200]Schramm J, The copper-zinc diagram[J]. Metallwirtsch,1935; 14:995-1001.
[201]v. Samson-Himmelstjerna H O, Heat content and heat of formation of molten alloys[J]. Z. Metallkd.,1936; 28:197-202.
[202]Parameswaran K, Healy G, A calorimetric investigation of the copper-zinc system[J]. Metall. Trans., B,1978; 9B:657-664.
[203]Schneider A, Schmid H, Metal vapor pressures. III. The vapor pressures of Zn and Cd over their binary alloys with Cu, Ag and Au[J]. Z. Elektrochem. Angew. Phys. Chem.,1942; 48:627-639.
[204]Everett L H, Jacobs P W M, Kitchener J A, Activity of zinc in liquid copper-zinc alloys[J]. Acta Met.,1957; 5:281-284.
[205]Downie D B, Thermodynamic and structural properties of liquid zinc/copper alloys[J]. Acta Met.,1964; 12:875-882.
[206]Azakami T, Yazawa A, Thermodynamic studies of liquid copper alloys. III. Activities of zinc and cadmium in liquid copper-base alloys [J]. Nippon Kogyo Kaishi,1968; 84:1663-1668.
[207]Solov'ev S L, Knyazev M V, Ivanov Y I, et al., Mass-spectrometric study of partial characteristics of zinc in the copper-zinc system[J]. Zavod. Lab.,1979; 45:841-844.
[208]Sugino S, Hagiwara H, Activity of zinc in molten copper and copper-gold alloys[J]. Nippon Kinzoku Gakkaishi 1986; 50:186-192.
[209]Leitgebel W, The boiling of certain metals and alloys at atmospheric pressure[J]. Z. Anorg. Allg. Chem.,1931; 202:305-324.
[210]Baker E H, Vapor pressures and thermodynamic behavior of liquid zinc-copper alloys at 1150.deg[J]. T. I. Min. Metall. C,1970; 79:C1-C5.
[211]Kleppa O J, Thalmayer C E, An e.m.f. investigation of binary liquid alloys rich in zinc[J]. J. Phys. Chem.,1959; 63:1953-1958.
[212]Gerling U, Predel B, Thermodynamic properties of liquid copper-zinc-alloys[J]. Z. Metallkd.,1980; 71:158-164.
[213]Blair G R, Downie D B, Calorimetric study of silver-zinc and copper-zinc alloys[J]. Metal Sci. J.,1970; 4:1-5.
[214]Kleppa O J, King R C, Heats of formation of the solid solutions of zinc, gallium, and germanium in copper[J].Acta Met.,1962; 10:1183-1186.
[215]Orr R L, Argent B B, Heats of formation of the alpha -brasses[J]. Trans. Faraday Soc.,1965; 61:2126-2131.
[216]Korber F, Oelsen W, Thermochemistry of alloys. III. The heats of formation of the binary alloys iron-antimony, cobalt-antimony, nickel-antimony, cobalt-tin, nickel-tin, copper-tin and copper-zinc for the cast state [J]. Mitt. Kaiser-Wilhelm-Inst. Eisenforsch. Duesseldorf,1937; 19:209-219.
[217]Weibke F, The systematic study of affinity. LXXI. The heats of formation in the system copper-zinc [J]. Z. Anorg. Allgem. Chem.,1937; 232:289-296.
[218]Hargreaves R, The vapor pressure of zinc in brasses[J]. J. Inst. Met.,1939; 64: 10 pp.
[219]Seith W, Krauss W, Diffusion and vapor pressure of the zinc in brass[J]. Z. Elektrochem. Angew. Phys. Chem.,1938; 44:98-102.
[220]Argent B B, Wakeman D W, Thermodynamic properties of solid solutions. I. Copper+zinc solid solution[J]. Trans. Faraday Soc.,1958; 54:799-806.
[221]Masson D B, Sheu J-L, Variations in the composition dependence of the activity coefficient in terminal solid solutions of silver-zinc, silver-cadmium, and copper-zinc[J]. Metall. Trans.,1970; 1:3005-3009.
[222]Pemsler J P, Rapperport E J, Thermodynamic activity measurements using atomic absorption:copper-zinc [J]. Trans. AIME,1969; 245:1395-1400.
[223]Olander A, An electrochemical investigation of brass. (Fused electrolytes)[J]. Z. Physik. Chem.,1933; A164:428-438.
[224]Herbenar A W, Siebert C A, Duffendack O S, The vapor pressure and thermodynamic activities of zinc in solid alpha brasses[J]. J. Met.,1950; 188: 323-326.
[225]Guertler W, Guertler M, Anastasiadias E,14-29-30[J]. A Comp. of Const. Ternary Diagr. Met. System, Isr. Pro. Sci. Tr., Jerusalem,1969; 19:555-561.
[226]Drits M E, Bochvar N R, Guzei L S, et al., In:Binary and Multicomponent Copper-Base Systems [M], Moscow:Nauka; 1979, pp.158-159.
[227]Chang Y A, Neumann J P, Mikula A, et al., Cu-Si-Zn[J]. INCRA Monograph Series. Phase Diagrams and Thermodynamic Properties of Ternary Copper-Metall Systems, NSRD, Washington,1979; 6:669-675.
[228]Gould H W, Ray K W, Effects of silicon on the properties of brass. I. Constitution[J]. Metals and Alloys,1930; 1:455-457.
[229]Vaders E, A New Silicon-Zinc-Copper Alloy[J]. J. Inst. Met.,1930; 44: 363-383.
[230]Smiryagin A P, In:VA Nemilov editor Spesial Bronzes and Brasses[M], Moscow:Metallurgiya; 1945, pp.5-20.
[231]Smiryagin A P, Smiryagina N A, Belova A V, In:Industrial Non-Ferrous Metals and Alloys[M], Moscow:Metallurgiya; 1974, pp.106-109.
[232]Pops H, The Contributuon of the Primary Solid Solubility Isothermal Limit and Some Intermediate Phase in Cu-Rich Cu-Si-Zn Alloys[D].1962.
[233]Mima G, Hasegawa M, The Diagram of Cu-Si-Zn Alloy-Ⅰ[J]. Technol. Repts. Osaka Univ.,1956; 6:313-321.
[234]Mima G, Hasegawa M, Phase Diagram of the System Cu-Si-Zn in the h Phase Region[J]. Nippon Kinzoku Gakkai-Shi (J. Jpn. Inst. Met.),1959; 23:585-587.
[235]Mima G, Hasegawa M, The Diagram of Cu-Si-Zn Alloy-III[J]. Technol. Repts. Osaka Univ.,1960; 10:157-168
[236]Mima G, Hasegawa M, Study of the Diagram of Cu-Si-Zn Alloy in the Range Near g Solid Solution[J]. Nippon Kinzoku Gakkai-Shi (J. Jpn. Inst. Met.),1963; 27:370-376.
[237]Mima G, Hasegawa M, The Diagram of Cu-Si-Zn Alloy-Ⅳ[J]. Technol. Repts. Osaka Univ.,1964; 14:623-633.
[238]Jacobs M H G, Spencer P J, A critical thermodynamic evaluation of the systems Si-Zn and Al-Si-Zn[J]. CALPHAD,1996; 20:307-320.
[239]He C Y, Du Y, Chen H L, et al., Experimental investigation and thermodynamic modeling of the Al-Cu-Si system[J]. CALPHAD,2009; 33:200-210.
[240]Xiong W, Ph.D thesis, Central South University, China[J]. Ph.D thesis, Central South University, China,2010.
[241]Hu R X, Nash P, Review:Experimental enthalpies of formation of compounds in Al-Ni-X systems[J]. J. Mater. Sci.,2006; 41:631-641.
[242]Curtarolo S, Morgan D, Ceder G, Accuracy of ab initio methods in predicting the crystal structures of metals:A review of 80 binary alloys[J]. CALPHAD, 2005; 29:163-211.
[243]Wang Y, Curtarolo S, Jiang C, et al., Ab initio lattice stability in comparison with CALPHAD lattice stability[J]. CALPHAD,2004; 28:79-90.
[244]Wolverton C, Ozolins V, First-principles aluminum database:Energetics of binary Al alloys and compounds[J]. Phys. Rev. B,2006; 73:144104.
[245]Zunger A, Wei S H, Ferreira L G, et al., Special Quasirandom Structures[J]. Phys. Rev. Lett.,1990; 65:353-356.
[246]Zhang H, Shang S L, Saal J E, et al., Enthalpies of formation of magnesium compounds from first-principles calculations[J]. Intermetallics.,2009; 17: 878-885.
[247]Born M, Huang K, Dynamical Theory of Crystal Lattices[M], Oxford University Press; 1988.
[248]Nye J F, Physical Properties of Crystals:Their Representation by Tensors and Matrices[M], New York:Oxford University Press; 1985.
[249]Cowley R A, Acoustic Phonon Instabilities and Structural Phase-Tansitions[J]. Phys. Rev. B,1976; 13:4877-4885.
[250]Chen L Q, Phase-field models for microstructure evolution[J]. Ann. Rev. Mater. Res.,2002; 32:113-140.
[251]Pugh S F, Relations Between the Elastic Moduli and the Plastic Properties of Polycrystalline Pure Metals[J]. Philosophical Magazine,1954; 45:823-843.
[252]Clerc D G, Ledbetter H M, Mechanical hardness:A semiempirical theory based on screened electrostatics and elastic smear[J]. J. Phys. Chem. Solids,1998; 59: 1071-1095.
[253]Kim D, Shang S L, Liu Z K, Effects of alloying elements on elastic properties of Ni by first-principles calculations[J]. Comp. Mater. Sci.,2009; 47:254-260.
[254]Zhang H, Shang S L, Wang Y, et al., First-principles calculations of the elastic, phonon and thermodynamic properties of Al12Mg17[J]. Acta Mater.,2010; 58: 4012-4018.
[255]Ganeshan S, Shang S L, Zhang H, et al., Elastic constants of binary Mg compounds from first-principles calculations[J]. Intermetallics.,2009; 17: 313-318.
[256]Shang S L, Wang Y, Kim D, et al., First-principles thermodynamics from phonon and Debye model:Application to Ni and Ni3Al[J]. Comp. Mater. Sci., 2010; 47:1040-1048.
[257]Shang S L, Wang Y, Liu Z K, First-principles elastic constants of alpha- and theta-Al2O3[J]. Appl. Phys. Lett.,2007; 90:101909.
[258]Simmons G, Wang H, Single Crystal Elastic Constants and Calculated Aggregate Properties:A Handbook[M], M.I.T Press, Cambridge; 1971.
[259]Villars P, Calvert L D, Pearson's handbook:crystallographic data for intermetallic phases.[M], ASM International, Materials Park, Ohio; 1991.
[260]Shang S L, Wang Y, Liu Z K, First-principles calculations of phonon and thermodynamic properties in the boron-alkaline earth metal binary systems: B-Ca, B-Sr, and B-Ba[J]. Phys. Rev. B,2007; 75:024302.
[261]Ghosh G, Asta M, First-principles calculation of structural energetics of Al-TM (TM=Ti, Zr, Hf) intermetallics[J]. Acta Mater.,2005; 53:3225-3252.
[262]Tao X A M, Ouyang Y F, Liu H S, et al., Ab initio calculations of mechanical and thermodynamic properties for the B2-based AIRE[J]. Comp. Mater. Sci., 2007; 40:226-233.
[263]Chen X Q, Podloucky R, Miedema's model revisited:The parameter phi* for Ti, Zr, and Hf[J]. CALPHAD,2006; 30:266-269.
[264]Olesen W, Thermochemistry of alloys (Ⅰ) detn. of the heats of formation of the alloys series Co-Si, Fe-Al, Co-Al, Ni-Al, Cu-Al and Sb-Zn for the case state[J]. Mitt. Kaiser-Wilhelm-Inse. Eisenforsch Dusseldorf,1937; 19:2.
[265]Dupin N, Ansara I, Thermodynamic assessment of the system Al-Co[J]. Rev. Metall-paris.,1998; 95:1121-1129.
[266]Biltz W, On the heat of formation of intermetallic compounds V Cobalt-aluminium alloys, copper alloys[J]. Z. Anorg. Allg. Chem.,1924; 134: 25-36.
[267]Henig E T, Lukas H L, Petzow G, Enthalpy of Formation and Description of the Deffect Structure of the Ordered Beta-Phase in Co-Al[J]. Z. Metallkd.,1980; 71: 398-402.
[268]Sandakov V M, Geld P V, Esin Y O, Heats of Formation and Thermodynamics of Nickel and Cobalt Mono-Aluminides[J]. Zh. Fiz. Khim.,1972; 46:1567.
[269]Murray J L. Int. Met. Rev.,1985; 30:211-218.
[270]Ansara I, Dinsdale A T, Rand M H, COST507:Thermodynamic database for light metal alloys[M], rue de la loi 200 (SDME 1/44), B-1049 Brussels: European Commission; 1998.
[271]Wang T, Jin Z P, Zhao J C, Thermodynamic assessment of the AI-Hf binary system[J]. J. Phase. Equilib.,2002; 23:416-423.
[272]Meschel S V, Kleppa O J, Standard Enthalpies of Formation of Some Rare-Earth Carbides by Direct Synthesis Calorimetry[J]. J. Alloy. Compd., 1993; 191:111-116.
[273]Balducci G, Ciccioli A, Gigli G, et al., Thermodynamic Study of Intermetallic Phases in the Hf-Al System[J]. J. Alloy. Compd.,1995; 220:117-121.
[274]Kaufman L, Nesor H, Calculation of Ni-Al-W, Ni-Al-Hf and Ni-Cr-Hf System[J]. Can. Metall. Quart.,1975; 14:221-232.
[275]Zhong Y, Yang M, Liu Z K, Contribution of first-principles energetics to Al-Mg thermodynamic modeling[J]. CALPHAD,2005; 29:303-311.
[276]Brown J A, Pratt J N, Thermodynamic Properties of Solid Al-Mg Alloys[J]. Metall. Trans.,1970; 1:2743-2750.
[277]Predel B, Hulse K, Some Thermodynamic Properties of Aluminium-Magnesium Alloys[J]. Z. Metallkd.,1978; 69:661-666.
[278]Kubaschewski O, Heymer G, Heats of Formation of Transtion-Metal Aluminides[J]. Trans. Faraday Soc.,1960; 56:473-478.
[279]Kubaschewski O, The heats of formation in the system in the system aluminium +nickel+titanium[J]. Trans. Faraday Soc.,1958; 54:814-820.
[280]Dupin N, Ansara I, Sundman B, Thermodynamic re-assessment of the ternary system Al-Cr-Ni[J]. CALPHAD,2001; 25:279-298.
[281]Rzyman K, Moser Z, Calorimetric studies of the enthalpies of formation of Al(3)Ni(2), AlNi and AlNi3[J]. Prog. Mater. Sci.,2004; 49:581-606.
[282]Rzyman K, Moser Z, Watson R E, et al., Enthalpies of formation of AlNi: Experiment versus theory[J]. J. Phase. Equilib.,1998; 19:106-111.
[283]Hu R X, Nash P, The enthalpy of formation of NiAl[J]. J. Mater. Sci.,2005;40: 1067-1069.
[284]Rzyman K, Moser Z, Watson R E, et al., Enthalpies of formation of Ni3Al: Experiment versus theory[J].J. Phase. Equilib.,1996; 17:173-178.
[285]Wang C, Jin Z P, Du Y, Thermodynamic modeling of the Al-Sr system[J]. J. Alloy. Compd.,2003; 358:288-293.
[286]Zhong Y, Wolverton C, Chang Y A, et al., A combined CALPHAD/first-principles remodeling of the thermodynamics of Al-Sr: unsuspected ground state energies by "rounding up the (un)usual suspects"[J]. Acta Mater.,2004; 52:2739-2754.
[287]Kubaschewski O, Dench W A, The Heats of Formation in the Systems Titanium-Aluminium and Titanium-Iron[J]. Acta Metallurgica,1955; 3: 339-346.
[288]Nassik M, Chrifi-Alaoui F Z, Mahdouk K, et al., Calorimetric study of the aluminium-titanium system[J]. J. Alloy. Compd.,2003; 350:151-154.
[289]Gong W P, Du Y, Huang B Y, et al., Thermodynamic reassessment of the Al-V system[J]. Z. Metallkd.,2004; 95:978-986.
[290]Neckel A, Howotny H, In:Fifth International Conference on Light Metals, Leoben;1968, p.72.
[291]Timofeev V S, Turchanin A A, Zubkov A A, et al., Enthalpies of formation for the Al-Y and Al-Y-Ni intermetallic compounds[J]. Thermochim. Acta,1997; 299:37-41.
[292]Liu S H, Du Y, Chen H L, A thermodynamic reassessment of the Al-Y system[J]. CALPHAD,2006; 30:334-340.
[293]Snyder R L.1960.
[294]Jung W G, Kleppa O J, Topor L, Standard Molar Enthalpies of Formation of PdAl, PtAl, ScAl1.78, YA12 and LaAl2[J]. J. Alloy. Compd.,1991; 176:309-318.
[295]Wang T, Jin Z P, Zhao J C, Thermodynamic assessment of the Al-Zr binary system[J]. J. Phase. Equilib.,2001; 22:544-551.
[296]Alcock C B, Jacob K T, In:O Kubaschewski editor Zirconium: physico-chemical properties of its compounds.[M], Vienna:IAEA:Atomic energy review; 1976.
[297]Kematick R J, Franzen H F, Thermodynamic Study of the Zirconium Aluminum System[J]. J. Solid State Chem.,1984; 54:226-234.
[298]Klein R, Jacob I, Ohare P A G, et al., Solution-Calorimetri Determination of the Standard Molar Enthalpies of Formation of the Pseudobinary Compounds Zr(AlxFe(1-x))2 at the Temperature 298.15 K[J]. J. Chem. Thermodyn.,1994; 26:599-608.
[299]Saunders N, Calculated Stable and Metastable Phase-Equilibria in Al-Li-Zr Alloys[J]. Z. Metallkd.,1989; 80:894-903.
[300]Ouyang Y, Zhong X, Du Y, et al., Formation enthalpies of Fe-Al-RE ternary alloys calculated with a geometric model and Miedema's theory [J]. J. Alloy. Compd.,2006; 416:148-154.
[301]刘树红,铝合金有序-无序相变、相图拓扑关系及其在凝固过程的应用[D].博士学位论文,中南大学,中国.2010.
[302]Guo Q T, Kleppa O J, The standard enthalpies of formation of the compounds of early transition metals with late transition metals and with noble metals as determined by Kleppa and co-workers at the University of Chicago-A review[J]. J. Alloy. Compd.,2001; 321:169-182.
[303]Murray J, Peruzzi A, Abriata J, The Al-Zr (aluminum-zirconium) system[J]. J. Phase. Equilib.,1992; 13:277-291.
[304]Kleppa O, Systematic aspects of the high-temperature thermochemistry of binary alloys and related compounds[J]. J. Phase. Equilib.,1994; 15:240-263.
[305]Zhou W, Liu L J, Li B L, et al., Structural, Elastic, and Electronic Properties of Al-Cu Intermetallics from First-Principles Calculations [J]. J. Electron. Mater., 2009; 38:356-364.
[306]Jahnatek M, Krajci M, Hafner J, Interatomic bonding, elastic properties, and ideal strength of transition metal aluminides:A case study for Al-3(V,Ti)[J]. Phys. Rev. B,2005; 71:024101.
[307]Fu C L, Yoo M H, Elastic-Constant, Fault Energies, and Dislocation Reactions in TiAl:A 1 st-Principles Total-Energy Investigation[J]. Phil. Mag. Lett.,1990; 62:159-165.
[308]Eshelman F R, Smith J F, Single-Crysta Elastic-Constants of Al2Cu[J]. J. Appl. Phys.,1978; 49:3284-3288.
[309]Wang N, Yu W Y, Tang B Y, et al., Structural and mechanical properties of Mg17A112 and Mg24Y5 from first-principles calculations [J]. J. Phys. D. Appl. Phys.,2008; 41:195408.
[310]Shi D M, Wen B, Melnik R, et al., First-principles studies of Al-Ni intermetallic compounds[J]. J. Solid State Chem.,2009; 182:2664-2669.
[311]Rusovic N, Warlimont H, Elastic Behavior of Beta-2-NiAl Alloys[J]. Phys. Status. Solidi. A,1977; 44:609-619.
[312]Mishin Y, Mehl M J, Papaconstantopoulos D A, Embedded-atom potential for B2-NiAl[J]. Phys. Rev. B,2002; 65:224114.
[313]Kayser F X, Stassis C, The Elastic-Constants of Ni3Al at 0 and 23.5℃[J]. Phys. Status. Solidi. A,1981; 64:335-342.
[314]Prikhodko S V, Carnes J D, Isaak D G, et al., Temperature and composition dependence of the elastic constants of Ni3Al[J]. Metall. Mater. Trans. A,1999; 30:2403-2408.
[315]Kim D E, Shang S L, Liu Z K, Effects of alloying elements on elastic properties of Ni3Al by first-principles calculations[J]. Intermetallics,2010; 18: 1163-1171.
[316]Nakamura M, Kimura K, Elastic-Constants of TiAl3 and ZrAl3 Single-Crystals[J]. J. Mater. Sci.,1991; 26:2208-2214.
[317]He Y, Schwarz R B, Migliori A, et al., Elastic-constants of single-crystal gamma-TiAl[J]. J. Mater. Res.,1995; 10:1187-1195.
[318]Tanaka K, Koiwa M, Single-crystal elastic constants of intermetallic compounds[J]. Intermetallics.,1996; 4:S29-S39.
[319]Ranganathan S I, Ostoja-Starzewski M, Universal elastic anisotropy index[J]. Phys. Rev. Lett.,2008; 101:055504.
[320]Hill R, The Elastic Behaviour of A Crystalline Aggregate[J]. Proceedings of the Physical Society of London Section A,1952; 65:349-355.
[321]Shang S L, Wang Y, Kim D E, et al., First-principles thermodynamics from phonon and Debye model:Application to Ni and Ni3A1[J]. Comp. Mater. Sci., 2010; 47:1040-1048.
[322]Liu J Z, Ghosh G, van de Walle A, et al., Transferable force-constant modeling of vibrational thermodynamic properties in fcc-based Al-TM (TM=Ti, Zr, Hf) alloys[J]. Phys. Rev. B,2007; 75:104117.
[323]Mei Z G, Shang S L, Wang Y, et al., Density-functional study of the thermodynamic properties and the pressure-temperature phase diagram of Ti[J]. Phys. Rev. B,2009; 80:104116
[324]Saal J E, Wang Y, Shang S L, et al., Thermodynamic Properties of Co3O4 and Sr6Co5O15 from First-Principles[J]. Inorg. Chem.,2010; 49:10291-10298.
[325]Wang Y, Ahuja R, Johansson B, Mean-field potential approach to the quasiharmonic theory of solids[J]. Int. J. Quantum. Chem.,2004; 96:501-506.
[326]Moruzzi V L, Janak J F, Schwarz K, Calculated thermal-properties of metals[J]. Phys. Rev. B,1988; 37:790-799.
[327]项金钟,吴兴惠译,Kittel C原著固体物理导论[M],化学工业出版社；2005.
[328]固体物理学[M],北京大学出版社；2009.
[329]Methfessel M, Paxton A T, High-precision sampling for Brillouin-zone integration in metals[J]. Phys. Rev. B,1989; 40:3616-3621.
[330]van de Walle A, Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the Alloy Theoretic Automated Toolkit[J]. CALPHAD,2009; 33:266-278.
[331]van de Walle A, Ceder G, The effect of lattice vibrations on substitutional alloy thermodynamics[J]. Rev. Mod. Phys.,2002; 74:11-45.
[332]Shang S L, Wang J, Wang Y, et al., Phonon and thermodynamic properties of Al-Mn compounds:A first-principles study[J]. to be submitted,2010.
[333]Shang S L, Wang Y, Arroyave R, et al., Phase stability in alpha- and beta-rhombohedral boron[J]. Phys. Rev. B,2007; 75:092101.
[334]Shang S L, Wang Y, Zhang H, et al., Lattice dynamics and anomalous bonding in rhombohedral As:First-principles supercell method[J]. Phys. Rev. B,2007; 76:052301.
[335]Luo W, Ahuja R, Ding Y, et al., Unusual lattice dynamics of vanadium under high pressure[J]. Proceedings of the National Academy of Sciences of the United States of America,2007;104:16428-16431.
[336]Phonon States of Alloys; Electron States and Fermi Surfaces of Strained Elements[M], Springer-Verlag GmbH; 1983.
[337]Saunders N, Miodownik A P, CALPHAD (Calculation of Phase Diagrams):A Comprehensive Guide[M], New York:Pergamon; 1998.
[338]Shang S L, Wang Y, Liu Z K, Thermodynamic fluctuations between magnetic states from first-principles phonon calculations:The case of bcc Fe[J]. Phys. Rev. B,2010; 82:014425.
[339]Saal J E, Shang S, Wang Y, et al., Magnetic phase transformations of face-centered cubic and hexagonal close-packed Co at zero Kelvin[J]. J. Phys-condens. Mat.,2010; 22.
[340]Shang S-L, Saal J E, Mei Z-G, et al., Magnetic thermodynamics of fcc Ni from first-principles partition function approach[J]. J. Appl. Phys.,2010; 108.
[341]Villars P, Calvert L D, Pearson's handbook of crystallographic data for intermetallic phases[M],2nd ed., Newbury, OH:ASTM International; 1991.
[342]Simmons G, Wang H, Single Crystal Elastic Constants and Calculated Aggregate Properties[M], Cambridge (Mass.):MIT press; 1971.
[343]Gerward L, The bulk modulus and its pressure derivative for 18 metals [J]. J. Phys. Chem. Solids,1985; 46:925-927.
[344]Phonon states of elements. Electron states and Fermi surfaces of alloys [M], Berlin:Springer; 1981.
[345]Takemura K, Shimomura O, Hase K, et al., The high-pressure equation of state of alpha-Mn to 42 GPa[J]. J. Phys. F. Met. Phys.,1988; 18:197-204.
[346]Fujihisa H, Takemura K, Stability and the equation of state of alpha-Manganese under ultrahigh pressure [J]. Phys. Rev. B,1995; 52:13257-13260.
[347]Tarumi R, Kawasaki Y, Tabe Y, et al., Magnetic phase transition and elastic properties of alpha-Mn at low temperature [J]. Jpn. J. Appl. Phys.,2006; 45: 4497-4499.
[348]Kittel C, Introduction to solid state physics[M], New York:Wiley; 1976.
[349]Mori N, Takahashi M, Oomi G, Magnetic contribution to the bulk modulus of 3d-transition metal-alloys[J]. J. Magn. Magn. Mater.,1983; 31-4:135-136.
[350]Rosen M, Elastic moduli and ultrasonic attenuation of polycrystalline alpha-Mn from 4.2-300 K[J]. Phys. Rev.,1968;165:357-359.
[351]de Laissardiere G T, Manh D N, Magaud L, et al., Electronic structure and hybridization effects in Hume-Rothery alloys containing transition elements [J]. Phys. Rev. B,1995;52:7920.
[352]Solyom J, Fundamentals of the physics of solids:Structure and dynamics[M], Berlin:Springer-Verlag; 2008.
[353]de Laissardiere G T, Nguyen-Manh D, Mayou D, Electronic structure of complex Hume-Rothery phases and quasicrystals in transition metal aluminides[J]. Prog. Mater. Sci.,2005; 50:679-788.
[354]Perdew J P, Chevary J A, Vosko S H, et al., Atoms, molecules, solids, and surfaces:Applications of the generalized gradient approximation for exchange and correlation[J]. Phys. Rev. B,1992;46:6671-6687.
[355]Shang S, Bottger A J, Steenvoorden M P, et al., Hyperfine interactions in hexagonal epsilon-Fe6Ny phase investigated by Mossbauer spectroscopy and ab initio calculations [J]. Acta Mater.,2006;54:2407-2417.
[356]Shang S L, Bottger A J, Liu Z K, The influence of interstitial distribution on phase stability and properties of hexagonal epsilon-Fe6Cx, epsilon-Fe6Ny and epsilon-Fe6CxNy phases:A first-principles calculation [J]. Acta Mater.,2008; 56:719-725.
[357]Shang S L, Mei Z G, Saengdeejing A, et al., First-principles calculations of pure elements:Equations of state and elastic constants[J]. Comp. Mater. Sci.,2010; 48:813-826.
[358]El-Moneim A A, Bond compression bulk modulus and Poisson's ratio of the polycomponent silicate glasses[J]. Mater. Chem. Phys.,2001; 70:340-343.
[359]Shukla A, Pelton A, Thermodynamic Assessment of the Al-Mn and Mg-Al-Mn Systems[J]. J. Phase. Equilib. Diffus.,2009; 30:28-39.
[360]Kopp H, Investigations of the Specific Heat of Solid Bodies[J]. Philos. T. Roy. Soc.,1865; 155:71-202.
[361]Shang S, Wang T, Liu Z-K, Thermodynamic modelling of the B-Ca, B-Sr and B-Ba systems[J]. CALPHAD,2007; 31:286-291.
[362]Shang S L, Wang Y, Liu Z K, In:SR Agnew, NR Neelameggham, EA Nyberg, WH Sillekens editors Magnesium Technology 2010; 2010, pp.617-622.
[363]Wolverton C, Yan X Y, Vijayaraghavan R, et al., Incorporating first-principles energetics in computational thermodynamics approaches[J]. Acta Mater.,2002; 50:2187-2197.
[364]Barin I, Thermochemical Data of Pure Substances[M], Weinheim, New York; 1995.
[365]Davis J R, Joseph R, Aluminum and aluminum alloys[M], ASM International; 1993.
[366]Wang J, Shang S L, Wang Y, et al., First-principles calculations of binary Al compounds:enthalpies of formation and elastic properties[J]. CALPHAD,2011; 35:562-573.
[367]Clerc D G, Ledbetter H M, Mechanical hardness:A semiempirical theory based on screened electrostatics and elastic smear[J]. J. Phys. Chem. Solids,1998; 59: 1071.
[368]Music D, Schneider J M, Effect of transition metal additives on electronic structure and elastic properties of TiAl and Ti3Al[J]. Phys. Rev. B,2006; 74.
[369]Zhang C L, Han P D, Li J M, et al., First-principles study of the mechanical properties of NiAl microalloyed by M (Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd)[J]. J. Phys. D. Appl. Phys.,2008; 41:095410.
[370]Ganeshan S, Shang S L, Wang Y, et al., Effect of alloying elements on the elastic properties of Mg from first-principles calculations [J]. Acta Mater.,2009; 57:3876-3884.
[371]Tonejc A, Bonefaci A, Enhanced solubility of Iron in Aluminum obtained by rapid quenching technique[J]. J. Appl. Phys.,1969; 40:419-420.
[372]Bendijk A, Delhez R, Katgerman L, et al., Characterization of Al-Si-alloys rapidly quenched from the melt[J]. J. Mater. Sci.,1980; 15:2803-2810.
[373]Tonejc A, Bonefaci A, Al-rich metastable Al-Ti solid solutions[J]. Scripta Metallurgica 1969; 3:145-148.
[374]Wang T, Chen L Q, Liu Z K, Lattice parameters and local lattice distortions in fcc-Ni solutions[J]. Metall. Mater. Trans. AMetall. Mater. Trans. A-Phys. Metall. Mater. Sci.,2007; 38A:562-569.
[375]Scheuer U, Lengeler B, Lattice distortion of solute atoms in metals studied by X-ray-absorption fine-structure [J]. Phys. Rev. B,1991; 44:9883-9894.
[376]Shang S L, Saengdeejing A, Mei Z G, et al., First-principles calculations of pure elements:Equations of state and elastic stiffness constants[J]. Comp. Mater. Sci.,2010; 48:813-826.
[377]Gault C, Dauger A, Boch P, Variations of elastic constants of Aluminum-Magnesium single-crystals with guinier-preston zones[J]. Phys. Status. Solidi. A,1977; 43:625-632.
[378]Hearmon R F S, The elastic constants of anisotropic materials[J]. Rev. Mod. Phys.,1946; 18:409-440.
[379]Ledbetter H, Relationship between bulk-modulus temperature-dependence and thermal expansivity [J]. Phys. Status. Solidi. B,1994; 181:81-85.
[380]Miedema A R, Deboer F R, Dechatel P F, Empirical description of role of electronegativity in alloy formation[J]. J. Phys. F. Met. Phys.,1973; 3: 1558-1576.
[381]Wolverton C, Ozolins V, Entropically favored ordering:The metallurgy of A12Cu revisited[J]. Phys. Rev. Lett.,2001; 86:5518-5521.
[382]Rose J H, Shore H B, Elastic-constants of the transition-metals from a uniform electron-gas[J]. Phys. Rev. B,1994; 49:11588-11601.
[383]Rose J H, Shore H B, Uniform electron-gas for transition-metals-input parameters[J]. Phys. Rev. B,1993; 48:18254-18256.
[384]Rose J H, Shore H B, Bonding energetics of metals-explanation of trends[J]. Phys. Rev. B,1991; 43:11605-11611.