基于固溶体短程序结构的团簇式合金成分设计方法

姜贝贝; 王清; 董闯

doi:10.7498/aps.66.026102

摘要

合金成分设计对于研发高性能复杂合金材料至关重要，是实现新材料研发由经验指导实验的传统模式向理论预测、实验验证的新模式转变的关键环节.总结了合金研发中常用设计方法的应用领域及存在的局限性，包括Hume-Rothery规则、电子理论、当量法、计算机模拟等.详细介绍了我们提出的基于固溶体局域短程序结构的团簇成分式设计方法.该方法建立在团簇加连接原子稳定固溶体结构模型基础上，其在不同复杂合金体系中的成功应用表明了该方法的普适性，为多元复杂合金成分设计提供了一种简单、精确的途径.

关键词:

Abstract

The composition design is of importance for developing high-performance complex alloys and is also the primary step to realize a new mode for material development via theoretical prediction and experimental verification, in comparison with the traditional experience-oriented experiments. Traditional alloy design approaches, including Hume-Rothery rule, electron theories, equivalent method, computer simulation, etc., are first reviewed from the viewpoints of their theoretical basis and applicability to limitations. Almost all the traditional alloys are based on solid solution structures, in which the typical characteristic is the chemical short-range order (CSRO) of the solute distribution. We propose a cluster-plus-glue-atom model for stable solid solutions in light of CSRO. A cluster-formula composition design approach is presented for developing the multi-component high-performance alloys. The cluster-plus-glue-atom model classifies the solid solution structure into two parts, i.e., the cluster part and the glue atom part, where the clusters are centered by solute atoms, showing the strong interactions of clusters with the solvent base and the weak interactions of clusters with solute atoms. The clusters are the nearest-neighbor polyhedrons, being cuboctahedron with a coordination number of 12 (CN12) in FCC structure and rhombic dodecahedron with a CN14 in BCC structure, respectively. Then a uniform cluster-formula of[CN12/14 cluster](glue atom)x is achieved from the cluster model. Its wide applications in different multi-component alloy systems confirm its universality as a simple and accurate tool for multiple-component complex alloy composition design. Such alloy systems include corrosion-resistant Cu alloys, high-performance Ni-base superalloys, high-strength maraging stainless steels, Ti/Zr alloys with low Young's modulus, high-entropy alloys, amorphous metallic glasses, quasicrystals, etc.. The specific alloy design steps are incarnated in the up-Ti alloys with low Young's modulus. Firstly, the necessary alloying elements are chosen according to the service requirements (BCC stability and low Young's modulus). Secondly, the local cluster unit to present CSRO and the corresponding cluster formula of[(Mo, Sn)-(Ti, Zr)14](Nb, Ta)x are built, in which the occupations of the alloying elements in the cluster formula are determined by the enthalpy of mixing H between them with the base Ti. Thirdly, these designed alloys are verified experimentally, and the lowest Young's modulus appears at the up-[(Mo0.5Sn0.5)-(Ti13Zr1)]Nb1. Finally, a new Mo equivalent formula under the guidance of phase diagram features is proposed to characterize the structural stability of Ti alloy. Thus all the Ti alloy compositions with different structural types can be expressed with a uniform cluster formula, in which the structural types of alloys are determined by the Mo equivalent.

Keywords:

作者及机构信息

1.
大连理工大学材料科学与工程学院, 三束材料改性教育部重点实验室, 大连 116024

通信作者: 王清, wangq@dlut.edu.cn

基金项目: 国家自然科学基金（批准号：51131002）、辽宁省自然科学基金（批准号：2015020202）、国际科技合作计划（批准号：2015DFR60370）、中央高校基本科研业务费专项资金（批准号：DUT16ZD212）和国家重点研发计划（批准号：2016YFB0701200）资助的课题.

Authors and contacts

1.
Key Laboratory of Materials Modification by Laser, Ion and Electron Beams of the Ministry of Education, School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China

Corresponding author: Wang Qing, wangq@dlut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51131002), the Natural Science Foundation of Liaoning Province of China (Grant No. 2015020202), the International Science Technology Cooperation Program of China (Grant No. 2015DFR60370), the Fundamental Research Funds for the Central Universities (Grant No. DUT16ZD212), and the National Key Research and Development Plan (Grant No. 2016YFB0701200).

参考文献

[1]	Hume-Rothery W, Raynor G V 1940 Proc. R. Soc. London, Ser. A Math. Phys. Sci. 174 471
[2]	Bania P J 1994 Jom. 46 16
[3]	Bagariatskii I A, Nosova G I 1958 Sov. Phys. Dokl. 3 1014
[4]	Morinaga M, Yukawa N, Adachi H 1985 J. Phys. F 15 1071
[5]	Ghosh G, Asta M 2005 Acta Mater. 53 3225
[6]	Xu W, Rivera-Díaz-del-Castillo P E J, Yan W, Yang K, San Martín D, Kestens L A I, van der Zwaag S 2010 Acta Mater. 58 4067
[7]	Malinov S, Sha W 2004 Mater. Sci. Eng. A 365 202
[8]	Dong C, Wang Q, Qiang J B, Wang Y M, Jiang N, Han G, Li Y H, Wu J, Xia J H 2007 J. Phys. D:Appl. Phys. 40 R273
[9]	Hong H L, Wang Q, Dong C, Liaw P K 2014 Sci. Rep. 4 7065
[10]	Pang C, Jiang B, Shi Y, Wang Q, Dong C 2015 J. Alloys Compd. 652 63
[11]	Darken L S, Gurry R W 1953 Physical Chemistry of Metals (New York:McGraw-Hill Co) pp258-266
[12]	Gschneidner K A 1964 Solid State Phys. 16 275
[13]	Chelikowsky J R 1979 Phys. Rev. B 19 686
[14]	Alonso J A, Simozar S 1980 Phys. Rev. B 22 5583
[15]	Zhang B W, Liao S Z 1996 Z. Phys. B 99 235
[16]	Inoue A 2000 Acta Mater. 48 279
[17]	Zhang Y, Zuo T T, Tang Z, Gao M C, Dahmen K A, Liaw P K, Lu Z P 2014 Prog. Mater. Sci. 61 1
[18]	Hume-Rothery W 1966 Acta Metall. 14 17
[19]	Hao Y L, Li S J, Sun S Y, Zheng C Y, Yang R 2007 Acta Biomater. 3 277
[20]	Guo S, Ng C, Lu J, Liu C T 2011 J. Appl. Phys. 109 103505
[21]	Hall E O, Algie S H 1966 Metall. Rev. 11 61
[22]	Zhang J S, Cui H, Hu Z L, Murata Y, Morinaga M, Yukawa N 1993 Acta Metall. Sin. 29 289 (in Chinese)[张济山, 崔华, 胡壮麟, 村田纯教, 森永正彦, 汤川夏夫1993金属学报29 289]
[23]	Abdel-Hady M, Hinoshita K, Morinaga M 2006 Scripta Mater. 55 477
[24]	Chen H, Ding T S, Wang T, Xiao X S, Zhao J L, Jiang L Z 2010 Rare Metal. Mat. Eng. 39 386 (in Chinese)[陈宏, 丁铁锁, 王涛, 肖学山, 赵钧良, 江来珠2010稀有金属材料与工程39 386]
[25]	Saito T, Furuta T, Hwang J H, Kuramoto S, Nishino K, Suzuki N, Chen R, Yamada A, Ito K, Seno Y, Nonaka T, Ikehata H, Nagasako N, Iwamoto C, Ikuhara C, Sakuma T 2003 Science 300 464
[26]	Kuroda D, Niinomi M, Morinaga M, Kato Y, Yashiro T 1998 Mater. Sci. Eng. A 243 244
[27]	Yu R H 1978 Chin. Sci. Bull. 13 217 (in Chinese)[余瑞璜1978科学通报13 217]
[28]	Liu Z L, Lin C 2006 Prog. Nat. Sci. 16 78
[29]	Cai J Y, Peng J Z, Yang X Z, Gray M F 2008 Mater. Lett. 62 3957
[30]	Pang X M, Zheng Y, Wang S G, Wang Q H 2009 Int. J. Refract. Met. Hard Mater. 27 777
[31]	Okazaki Y, Gotoh E 2005 Biomaterials 26 11
[32]	Rosenberg H W, Jaffee R I 1970 The Science, Technology and Application of Titanium (Oxford:Pergamon Press) p851
[33]	Schaeffler A L 1949 Met. Prog. 56 680
[34]	Morachevskii A G 2001 Russ. J. Appl. Chem. 74 1610
[35]	Ferjutz K, Davis J R 1993 ASM Handbook, Volume 6:Welding, Brazing and Soldering (The USA:ASM International) p1009
[36]	Morishita K, Sugano R, Wirth B D, Diaz de la Rubia T 2003 Nucl. Instrum. Methods Phys. Res. Sect. B 202 76
[37]	Lee N T S, Tan V B C, Lim K M 2006 Appl. Phys. Lett. 88 031913
[38]	Holland J H 1992 Sci. Am. 267 66
[39]	Ikeda Y 1997 Mater. Trans. JIM 38 771
[40]	Zeng W D, Shu Y, Zhou Y G 2004 Rare Metal. Mat. Eng. 33 1041 (in Chinese)[曾卫东, 舒滢, 周义刚2004稀有金属材料与工程33 1041]
[41]	Reddy N S, Lee Y H, Park C H, Lee C S 2008 Mater. Sci. Eng. A 492 276
[42]	Damask A C 1956 J. Appl. Phys. 27 610
[43]	Butt M Z, Ghauri I M 1988 Phys. Stat. Sol. 107 187
[44]	Reinhard L, Schönfeld B, Kostorz G, Bhrer W 1990 Phys. Rev. B 41 1727
[45]	Cowley J M 1960 Phys. Rev. B 120 1648
[46]	Häussler P 1992 Phys. Rep. 222 65
[47]	Takeuchi A, Inoue A 2005 Mater. Trans. 46 2817
[48]	Zhang J, Wang Q, Wang Y M, Li C Y, Wen L S, Dong C 2010 J. Mater. Res. 25 328
[49]	Zhang J, Wang Q, Wang Y M, Wen L S, Dong C 2010 J. Alloys Compd. 505 179
[50]	Zhang X Y, Li X N, Nie L F, Chu J P, Wang Q, Lin C H, Dong C 2011 Appl. Surf. Sci. 257 3636
[51]	Li B Z, Gu J J, Wang Q, Ji C J, Wang Y M, Qaing J B, Dong C 2012 Mater. Charact. 68 94
[52]	Wang Q, Zha Q F, Liu E X, Dong C, Wang X J, Tan C X, Ji C J 2012 Acta Metall. Sin. 48 1201 (in Chinese)[王清, 查钱锋, 刘恩雪, 董闯, 王学军, 谭朝鑫, 冀春俊2012金属学报48 1201]
[53]	Wang Q, Ji C J, Wang Y M, Qiang J B, Dong C 2013 Metall. Mater. Trans. A 44 1872
[54]	Wang Q, Dong C, Liaw P K 2015 Metall. Mater. Trans. A 46 3440
[55]	Murray J L 1992 ASM Handbook, Volume 3:Alloy Phase Diagrams (The USA:ASM International) p1156
[56]	Welsch G, Boyer R, Collings E W 1993 Materials Properties Handbook:Titanium Alloys (The USA:ASM International) pp439-921
[57]	Che J D, Jiang B B, Wang Q, Dong C, Chen G Q, Zhang R Q, Tang R 2016 Rare Metal. Mat. Eng. (in press) (in Chinese)[车晋达, 姜贝贝, 王清, 董闯, 陈国清, 张瑞谦, 唐睿2016稀有金属材料与工程(已接收)]
[58]	Pang C, Wang Q, Zhang R Q, Li Q, Dai X, Dong C, Liaw P K 2015 Mater. Sci. Eng., A 626 369
[59]	Yamamoto Y, Pint B A, Terrani K A, Field K G, Yang Y, Snead L L 2015 J. Nucl. Mater. 467 703
[60]	Kondo R, Nomura N, Tsutsumi Y, Doi H, Hanawa T 2011 Acta Biomater. 7 4278
[61]	Zhao W J, Miao Z, Jiang H M, Yu X W, Li W J, Li C, Zhou B X 2002 J. Chin. Soc. Corros. Rrot. 2 61 (in Chinese)[赵文金, 苗志, 蒋宏曼, 于晓卫, 李卫军, 李聪, 周邦新2002中国腐蚀与防护学报2 61]
[62]	Jeong Y H, Lee K O, Kim H G 2002 J. Nucl. Mater. 302 9
[63]	Park J Y, Choi B K, Yoo S J, Jeong Y H 2006 J. Nucl. Mater. 3 59
[64]	Park J Y, Choi B K, Jeong Y H, Jung Y H 2005 J. Nucl. Mater. 340 237
[65]	Jeong Y H, Kim H G, Kim T H 2003 J. Nucl. Mater. 37 1
[66]	Smith D L, Chung H M, Loomis B A, Matsui H, Votinov S, Van Witzenburg W 1995 Fusion. Eng. Des. 29 399
[67]	Senkov O N, Miller J D, Miracle D B, Woodward C 2015 Nature Comm. 6 7529
[68]	Gludovatz B, Hohenwarter A, Catoor D, Chang E H, George E P, Ritchie R O 2014 Science 345 1153
[69]	Wang Q, Ma Y, Jiang B B, Li X N, Shi Y, Dong C, Liaw P K 2016 Scripta Mater. 120 85
[70]	Zhi T, Yuan T, Tsai C W, Yeh J W, Lundin C D, Liaw P K 2015 Acta Mater. 99 247
[71]	Klement W, Willens R H, Duwez P O L 1960 Nature 187 869
[72]	Luo L J, Chen H., Wang Y M, Qiang J B, Wang Q, Dong C, Häussler P 2014 Philos. Mag. 94 2520
[73]	Han G, Qiang J, Li F, Yuan L, Quan S G, Wang Q, Wang Y M, Dong C, Häussler P 2011 Acta Mater. 59 5917
[74]	Geng Y X, Wang Y M, Qiang J B, Zhang G F, Dong C, Haussler P 2016 J. Non-Cryst. Solids. 432 453
[75]	Wang Z R, Qiang J B, Wang Y M, Wang Q, Dong D D, Dong C 2016 Acta Mater. 111 366
[76]	Chen H, Qiang J B, Wang Y M, Dong C 2014 Acta Phys. Pol. A 126 446

施引文献

[1]	Hume-Rothery W, Raynor G V 1940 Proc. R. Soc. London, Ser. A Math. Phys. Sci. 174 471
[2]	Bania P J 1994 Jom. 46 16
[3]	Bagariatskii I A, Nosova G I 1958 Sov. Phys. Dokl. 3 1014
[4]	Morinaga M, Yukawa N, Adachi H 1985 J. Phys. F 15 1071
[5]	Ghosh G, Asta M 2005 Acta Mater. 53 3225
[6]	Xu W, Rivera-Díaz-del-Castillo P E J, Yan W, Yang K, San Martín D, Kestens L A I, van der Zwaag S 2010 Acta Mater. 58 4067
[7]	Malinov S, Sha W 2004 Mater. Sci. Eng. A 365 202
[8]	Dong C, Wang Q, Qiang J B, Wang Y M, Jiang N, Han G, Li Y H, Wu J, Xia J H 2007 J. Phys. D:Appl. Phys. 40 R273
[9]	Hong H L, Wang Q, Dong C, Liaw P K 2014 Sci. Rep. 4 7065
[10]	Pang C, Jiang B, Shi Y, Wang Q, Dong C 2015 J. Alloys Compd. 652 63
[11]	Darken L S, Gurry R W 1953 Physical Chemistry of Metals (New York:McGraw-Hill Co) pp258-266
[12]	Gschneidner K A 1964 Solid State Phys. 16 275
[13]	Chelikowsky J R 1979 Phys. Rev. B 19 686
[14]	Alonso J A, Simozar S 1980 Phys. Rev. B 22 5583
[15]	Zhang B W, Liao S Z 1996 Z. Phys. B 99 235
[16]	Inoue A 2000 Acta Mater. 48 279
[17]	Zhang Y, Zuo T T, Tang Z, Gao M C, Dahmen K A, Liaw P K, Lu Z P 2014 Prog. Mater. Sci. 61 1
[18]	Hume-Rothery W 1966 Acta Metall. 14 17
[19]	Hao Y L, Li S J, Sun S Y, Zheng C Y, Yang R 2007 Acta Biomater. 3 277
[20]	Guo S, Ng C, Lu J, Liu C T 2011 J. Appl. Phys. 109 103505
[21]	Hall E O, Algie S H 1966 Metall. Rev. 11 61
[22]	Zhang J S, Cui H, Hu Z L, Murata Y, Morinaga M, Yukawa N 1993 Acta Metall. Sin. 29 289 (in Chinese)[张济山, 崔华, 胡壮麟, 村田纯教, 森永正彦, 汤川夏夫1993金属学报29 289]
[23]	Abdel-Hady M, Hinoshita K, Morinaga M 2006 Scripta Mater. 55 477
[24]	Chen H, Ding T S, Wang T, Xiao X S, Zhao J L, Jiang L Z 2010 Rare Metal. Mat. Eng. 39 386 (in Chinese)[陈宏, 丁铁锁, 王涛, 肖学山, 赵钧良, 江来珠2010稀有金属材料与工程39 386]
[25]	Saito T, Furuta T, Hwang J H, Kuramoto S, Nishino K, Suzuki N, Chen R, Yamada A, Ito K, Seno Y, Nonaka T, Ikehata H, Nagasako N, Iwamoto C, Ikuhara C, Sakuma T 2003 Science 300 464
[26]	Kuroda D, Niinomi M, Morinaga M, Kato Y, Yashiro T 1998 Mater. Sci. Eng. A 243 244
[27]	Yu R H 1978 Chin. Sci. Bull. 13 217 (in Chinese)[余瑞璜1978科学通报13 217]
[28]	Liu Z L, Lin C 2006 Prog. Nat. Sci. 16 78
[29]	Cai J Y, Peng J Z, Yang X Z, Gray M F 2008 Mater. Lett. 62 3957
[30]	Pang X M, Zheng Y, Wang S G, Wang Q H 2009 Int. J. Refract. Met. Hard Mater. 27 777
[31]	Okazaki Y, Gotoh E 2005 Biomaterials 26 11
[32]	Rosenberg H W, Jaffee R I 1970 The Science, Technology and Application of Titanium (Oxford:Pergamon Press) p851
[33]	Schaeffler A L 1949 Met. Prog. 56 680
[34]	Morachevskii A G 2001 Russ. J. Appl. Chem. 74 1610
[35]	Ferjutz K, Davis J R 1993 ASM Handbook, Volume 6:Welding, Brazing and Soldering (The USA:ASM International) p1009
[36]	Morishita K, Sugano R, Wirth B D, Diaz de la Rubia T 2003 Nucl. Instrum. Methods Phys. Res. Sect. B 202 76
[37]	Lee N T S, Tan V B C, Lim K M 2006 Appl. Phys. Lett. 88 031913
[38]	Holland J H 1992 Sci. Am. 267 66
[39]	Ikeda Y 1997 Mater. Trans. JIM 38 771
[40]	Zeng W D, Shu Y, Zhou Y G 2004 Rare Metal. Mat. Eng. 33 1041 (in Chinese)[曾卫东, 舒滢, 周义刚2004稀有金属材料与工程33 1041]
[41]	Reddy N S, Lee Y H, Park C H, Lee C S 2008 Mater. Sci. Eng. A 492 276
[42]	Damask A C 1956 J. Appl. Phys. 27 610
[43]	Butt M Z, Ghauri I M 1988 Phys. Stat. Sol. 107 187
[44]	Reinhard L, Schönfeld B, Kostorz G, Bhrer W 1990 Phys. Rev. B 41 1727
[45]	Cowley J M 1960 Phys. Rev. B 120 1648
[46]	Häussler P 1992 Phys. Rep. 222 65
[47]	Takeuchi A, Inoue A 2005 Mater. Trans. 46 2817
[48]	Zhang J, Wang Q, Wang Y M, Li C Y, Wen L S, Dong C 2010 J. Mater. Res. 25 328
[49]	Zhang J, Wang Q, Wang Y M, Wen L S, Dong C 2010 J. Alloys Compd. 505 179
[50]	Zhang X Y, Li X N, Nie L F, Chu J P, Wang Q, Lin C H, Dong C 2011 Appl. Surf. Sci. 257 3636
[51]	Li B Z, Gu J J, Wang Q, Ji C J, Wang Y M, Qaing J B, Dong C 2012 Mater. Charact. 68 94
[52]	Wang Q, Zha Q F, Liu E X, Dong C, Wang X J, Tan C X, Ji C J 2012 Acta Metall. Sin. 48 1201 (in Chinese)[王清, 查钱锋, 刘恩雪, 董闯, 王学军, 谭朝鑫, 冀春俊2012金属学报48 1201]
[53]	Wang Q, Ji C J, Wang Y M, Qiang J B, Dong C 2013 Metall. Mater. Trans. A 44 1872
[54]	Wang Q, Dong C, Liaw P K 2015 Metall. Mater. Trans. A 46 3440
[55]	Murray J L 1992 ASM Handbook, Volume 3:Alloy Phase Diagrams (The USA:ASM International) p1156
[56]	Welsch G, Boyer R, Collings E W 1993 Materials Properties Handbook:Titanium Alloys (The USA:ASM International) pp439-921
[57]	Che J D, Jiang B B, Wang Q, Dong C, Chen G Q, Zhang R Q, Tang R 2016 Rare Metal. Mat. Eng. (in press) (in Chinese)[车晋达, 姜贝贝, 王清, 董闯, 陈国清, 张瑞谦, 唐睿2016稀有金属材料与工程(已接收)]
[58]	Pang C, Wang Q, Zhang R Q, Li Q, Dai X, Dong C, Liaw P K 2015 Mater. Sci. Eng., A 626 369
[59]	Yamamoto Y, Pint B A, Terrani K A, Field K G, Yang Y, Snead L L 2015 J. Nucl. Mater. 467 703
[60]	Kondo R, Nomura N, Tsutsumi Y, Doi H, Hanawa T 2011 Acta Biomater. 7 4278
[61]	Zhao W J, Miao Z, Jiang H M, Yu X W, Li W J, Li C, Zhou B X 2002 J. Chin. Soc. Corros. Rrot. 2 61 (in Chinese)[赵文金, 苗志, 蒋宏曼, 于晓卫, 李卫军, 李聪, 周邦新2002中国腐蚀与防护学报2 61]
[62]	Jeong Y H, Lee K O, Kim H G 2002 J. Nucl. Mater. 302 9
[63]	Park J Y, Choi B K, Yoo S J, Jeong Y H 2006 J. Nucl. Mater. 3 59
[64]	Park J Y, Choi B K, Jeong Y H, Jung Y H 2005 J. Nucl. Mater. 340 237
[65]	Jeong Y H, Kim H G, Kim T H 2003 J. Nucl. Mater. 37 1
[66]	Smith D L, Chung H M, Loomis B A, Matsui H, Votinov S, Van Witzenburg W 1995 Fusion. Eng. Des. 29 399
[67]	Senkov O N, Miller J D, Miracle D B, Woodward C 2015 Nature Comm. 6 7529
[68]	Gludovatz B, Hohenwarter A, Catoor D, Chang E H, George E P, Ritchie R O 2014 Science 345 1153
[69]	Wang Q, Ma Y, Jiang B B, Li X N, Shi Y, Dong C, Liaw P K 2016 Scripta Mater. 120 85
[70]	Zhi T, Yuan T, Tsai C W, Yeh J W, Lundin C D, Liaw P K 2015 Acta Mater. 99 247
[71]	Klement W, Willens R H, Duwez P O L 1960 Nature 187 869
[72]	Luo L J, Chen H., Wang Y M, Qiang J B, Wang Q, Dong C, Häussler P 2014 Philos. Mag. 94 2520
[73]	Han G, Qiang J, Li F, Yuan L, Quan S G, Wang Q, Wang Y M, Dong C, Häussler P 2011 Acta Mater. 59 5917
[74]	Geng Y X, Wang Y M, Qiang J B, Zhang G F, Dong C, Haussler P 2016 J. Non-Cryst. Solids. 432 453
[75]	Wang Z R, Qiang J B, Wang Y M, Wang Q, Dong D D, Dong C 2016 Acta Mater. 111 366
[76]	Chen H, Qiang J B, Wang Y M, Dong C 2014 Acta Phys. Pol. A 126 446

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[13]	倪军, 王世范. 面心立方结构填隙固溶体有序结构的确定. , 1993, 42(2): 290-296. doi: 10.7498/aps.42.290
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[15]	唐棣生, 车广灿, 田静华. 碱金属碘酸盐赝二元系固溶体的研究. , 1980, 29(8): 1068-1074. doi: 10.7498/aps.29.1068
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[17]	王其闵, 何广兴. 镁-钇稀固溶体的应变时效. , 1965, 21(6): 1316-1320. doi: 10.7498/aps.21.1316
[18]	张宗燧. 固溶体的位形配分函数. , 1959, 15(1): 42-54. doi: 10.7498/aps.15.42
[19]	张宗燧. 多元多原子分子的固溶体. , 1959, 15(12): 652-663. doi: 10.7498/aps.15.652
[20]	王德懋, 许永焕, 张宗燧. 二元固溶体的配分函数. , 1957, 13(6): 525-542. doi: 10.7498/aps.13.525

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