Effects of point defect concentrations on elastic properties of off-stoichiometric L12-type A13Sc

Zhang Chao-Min; Jiang Yong; Yin Deng-Feng; Tao Hui-Jin; Sun Shun-Ping; Yao Jian-Gang

doi:10.7498/aps.65.076101

Abstract

Elastic properties and phase stabilities of L12-A13Sc precipitate phase in Al-Sc alloys have been topics of experimental and theoretical research over the past years. However, these properties of off-stoichiometric L12-A13Sc have not been investigated. Firstly, in combination with Wagner-Schottky model, the first-principles total energy calculations based on density functional theory are performed to study point defect concentrations of intermetallic L12-A13Sc each as a function of temperature and alloy composition. We calculate the point defect formation enthalpies and plot the point defect density curves of stoichiometric and off-stoichiometric L12-A13Sc at 1000 K. The results show that within the whole temperature range (300-1200 K), Al and Sc vacancies dominate on stoichiometric L12-A13Sc but with low concentrations (~10-6 even at 1200 K); on the Al-rich side of off-stoichiometric L12-A13Sc, the Al anti-site and the Sc vacancy concentrations dominate, and their concentrations are comparable, however, on Sc-rich side of off-stoichiometric L12-A13Sc, the Sc anti-site defect dominates. Furthermore, the lattice constants and the elastic constants of stoichiometric and off-stoichiometric L12-A13Sc are calculated, and it is worth noting that 222 supercell models with a point defect are used for off-stoichiometric L12-A13Sc in the calculation. Then employing calculated elastic constants, the values of Youngs modulus, shear modulus, bulk modulus, anisotropic index, G/B ratio, Cauchy pressure, and Poisson ratio of stoichiometric and off-stoichiometric L12-A13Sc are computed. And lastly, combining these data with point defect concentrations of off-stoichiometric L12-A13Sc at 1000 K, the comprehensive effects of four point defects on elastic properties of L12-A13Sc are evaluated. The four point defects coexist in L12-A13Sc as we know from the calculations of equilibrium point defect density. The conclusions are as follows. 1) The point defects can cause off-stoichiometric L12-A13Sc lattice distortion. On the Sc-rich side, lattice constant appears to be an increasing tendency, from 4.105 to the biggest value of ~4.13 (~0.5% growth), while on the Al-rich side, it shows an opposite trend, from 4.105 to the smallest value of ~4.10 (~0.24% fall). Although there is the lattice distortion in off-stoichiometric L12-A13Sc, off-stoichiometric L12-A13Sc can still keep stable crystal structure for the value of xAl in a range of 0.72-0.78. 2) The point defects also affect elastic constants of off-stoichiometric L12-A13Sc. Specifically, on the Sc-rich side, elastic constant c11 decreases with the increase of deviation degree of stoichiometric ratio, and the maximal reduction is ~9% at xAl = 0.72, while elastic constants c12 and c44 show the opposite variation trends, and the maximal increase is ~8% at xAl = 0.72. On the Al-rich side, there are little changes for elastic constants c11, c12 and c44. 3) The point defects obviously increase the elastic anisotropy of off-stoichiometric L12-A13Sc, and especially on the Sc-rich side, the notable increase is found, which jumps from 1.610-6 to 0.04. 4) The values of Youngs modulus, shear modulus, and bulk modulus of off-stoichiometric L12-A13Sc decrease due to point defects, with the maximal reduction being 3%-4%. These elastic modules fall first rapidly and then slowly on the Sc-rich side, while they present approximately a linear downward trend on the Al-rich side. In addition, weak influences are exerted on brittleness and toughness of off-stoichiometric L12-A13Sc by the point defects, compared with the other elastic effects mentioned above. In summary, in the scope of xAl = 0.72-0.78, the point defects can not only reduce Youngs modulus, shear modulus, and bulk modulus of off-stoichiometric L12-A13Sc, but also increase the anisotropies of the elastic properties of off-stoichiometric L12-A13Sc. However, the point defects have weak influences on the brittleness and toughness of off-stoichiometric L12-A13Sc.

Keywords:

Authors and contacts

1.
Mathematics and Physics Department, College of Engineering, Yantai Nanshan University, Longkou 265713, China;
2.
School of Materials Science and Engineering, Central South University, Changsha 410083, China;
3.
Key Lab for Nonferrous Materials of Ministry of Education, Central South University, Changsha 410083, China;
4.
School of Materials Engineering, Jiangsu University of Technology, Changzhou 213001, China

Corresponding author: Jiang Yong, yjiang@csu.edu.cn;ydfchh@mail.csu.edu.cn ; Yin Deng-Feng, yjiang@csu.edu.cn;ydfchh@mail.csu.edu.cn ;

Funds: Project supported by the Science and Technology Development Plan of Shandong Province, China (Grant No. 2014GGX102006) and the Higher Educational Science and Technology Program of Shandong Province, China (Grant No. J14LJ51).

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[29]	Hu Q M, Yang R, Hao Y L, Xu D S, Li D 2004 Phys. Rev. Lett. 92 185505
[30]	Jiang C, Chen L Q, Liu Z K 2006 Intermetallics 14 248
[31]	Jiang C, Sordelet D J, Gleeson B 2006 Acta Mater. 54 1147
[32]	Jiang C 2007 Acta Mater. 55 1599
[33]	Jiang C 2008 Acta Mater. 56 6224
[34]	Foata-Prestavoine M, Robert G, Nadal M H, Bernard S 2007 Phys. Rev. B 76 104104
[35]	Hyland R W, Stiffler J R C 1991 Scripta. Metall. Mater. 25 473
[36]	Mao Z, Chen W, Seidman D N, Wolverton C 2011 Acta Mater. 59 3012
[37]	Hill R 1952 Proc. Phys. Soc. A 65 349
[38]	Jhi S H, Ihm J, Louie G S 1999 Nature 399 132
[39]	Ranganathan S I, Ostoja-Starzewski M 2008 Phys. Rev. Lett. 101 055504
[40]	Pugh S F 1954 Philos. Mag. 45 823
[41]	Pettifor D G 1992 Mater. Sci. Technol. 8 345
[42]	Wang R N, Tang B Y, Peng L M, Ding W J 2012 Comput. Mater. Sci. 59 87

Cited By

[1]	Karnesky R A, Dunand D C, Seidmand N 2009 Acta Mater. 57 4022
[2]	Krug M E, Dunand D C, Seidman D N 2011 Acta Mater. 59 1700
[3]	Chen Q, Pan Q L, Wang Y, Peng H, Zhang Z Y, Yin Z M 2012 Trans. Nonferrous Met. Soc. China 22 1555 (in Chinese) [陈琴, 潘清林, 王迎, 彭虹, 张志野, 尹志民 2012 中国有色金属学报 22 1555]
[4]	Dai X Y, Xia C Q, Long C G, Kou L L 2011 Rare Metal Mat. Eng. 40 265 (in Chinese) [戴晓元, 夏长清, 龙春光, 寇莉莉 2011 稀有金属材料与工程 40 265]
[5]	Røyset J, Ryum N 2005 Int. Mater. Rev. 50 19
[6]	Li X P, Sun S P, Yu Y, Wang H J, Jiang Y, Yi D Q 2015 Chin. Phys. B 24 120502
[7]	Peng J H, Zeng Q F, Xie C W, Zhu K J, Tan J H 2015 Acta Phys. Sin. 64 236102 (in Chinese) [彭军辉, 曾庆丰, 谢聪伟, 朱开金, 谭俊华 2015 64 236102]
[8]	Fu C L 1990 J. Mater. Res. 5 971
[9]	Tao X M 2008 Ph. D. Dissertation (Changsha: Central South University) (in Chinese) [陶小马 2008 博士学位论文 (长沙: 中南大学)]
[10]	Wang N, Tang B Y 2009 Acta Phys. Sin. 58 S230 (in Chinese) [王娜, 唐壁玉 2009 58 S230]
[11]	Zhang X D, Wang S Q 2013 Acta Metall. Sin. 49 501 (in Chinese) [张旭东, 王绍青 2013 金属学报 49 501]
[12]	Hu W C, Liu Y, Li D J, Zeng X Q, Xu C S 2013 Physica B 427 85
[13]	Duan Y H, Sun Y, Peng M J, Zhou S G 2014 J. Alloys Compd. 585 587
[14]	Chen D, Chen Z, Wu Y, Wang M L, Ma N H, Wang H W 2014 Comput. Mater. Sci. 91 165
[15]	Woodward C, Asta M, Kresse G, Hafner J 2001 Phys. Rev. B 63 094103
[16]	Sun S P, Li X P, Lei W N, Wang H J, Wang X C, Jiang H F, Li R X, Jiang Y, Yi D Q 2013 Trans. Nonferrous Met. Soc. China 23 2147 (in Chinese) [孙顺平, 李小平, 雷卫宁, 王洪金, 汪贤才, 江海锋, 李仁兴, 江勇, 易丹青 2013 中国有色金属学报 23 2147]
[17]	Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169
[18]	Perdew J P, Burke K M, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[19]	Kresse G, Joubert J 1999 Phys. Rev. B 59 1758
[20]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[21]	Wagner C, Schottky W 1930 Z. Phys. Chem. B 11 163
[22]	Sun S P, Li X P, Yu Y, Lu Y L, Zang B, Yi D Q, Jiang Y 2013 Trans. Nonferrous Met. Soc. China 23 370 (in Chinese) [孙顺平, 李小平, 于赟, 卢雅琳, 臧冰, 易丹青, 江勇 2013 中国有色金属学报 23 370]
[23]	Asta M, Ozolins V 2001 Phys. Rev. B 64 094104
[24]	Asia M, Foiles S M, Quong A A 1998 Phys. Rev. B 57 11265
[25]	Sun S P, Li X P, Lu Y L, Li Y, Huang D Y, Yi D Q 2013 Rare Metal Mat. Eng. 42 1478 (in Chinese) [孙顺平, 李小平, 卢雅琳, 李勇, 黄道远, 易丹青 2013 稀有金属材料与工程 42 1478]
[26]	Cacciamani G, Riani P, Borzone G, Parodi N, Saccone A, Ferro R, Pisch A, Schmid-Fetzer R 1999 Intermetallics 7 101
[27]	Meyer B, Fähnle M 1999 Phys. Rev. B 59 6072
[28]	Korzhavyi P A, Ruban A V, Lozovoi A Y, Vekilov Y K, Abrikosov I A, Johansson B 2000 Phys. Rev. B 61 6003
[29]	Hu Q M, Yang R, Hao Y L, Xu D S, Li D 2004 Phys. Rev. Lett. 92 185505
[30]	Jiang C, Chen L Q, Liu Z K 2006 Intermetallics 14 248
[31]	Jiang C, Sordelet D J, Gleeson B 2006 Acta Mater. 54 1147
[32]	Jiang C 2007 Acta Mater. 55 1599
[33]	Jiang C 2008 Acta Mater. 56 6224
[34]	Foata-Prestavoine M, Robert G, Nadal M H, Bernard S 2007 Phys. Rev. B 76 104104
[35]	Hyland R W, Stiffler J R C 1991 Scripta. Metall. Mater. 25 473
[36]	Mao Z, Chen W, Seidman D N, Wolverton C 2011 Acta Mater. 59 3012
[37]	Hill R 1952 Proc. Phys. Soc. A 65 349
[38]	Jhi S H, Ihm J, Louie G S 1999 Nature 399 132
[39]	Ranganathan S I, Ostoja-Starzewski M 2008 Phys. Rev. Lett. 101 055504
[40]	Pugh S F 1954 Philos. Mag. 45 823
[41]	Pettifor D G 1992 Mater. Sci. Technol. 8 345
[42]	Wang R N, Tang B Y, Peng L M, Ding W J 2012 Comput. Mater. Sci. 59 87

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