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采用密度泛函理论与Wagner-Schottky热力学模型计算了金属间化合物L12-A13Sc中点缺陷浓度与温度、成分间的关系. 结果表明: 在考察的温度区间(T=300-1200 K), 理想化学计量比L12-A13Sc中的点缺陷主要为Al空位和Sc空位, 且缺陷浓度较低(在1200 K时仅约为10-6). 当L12-A13Sc偏离化学计量比成分时, 富Al成分端的点缺陷主要为Al反位与Sc空位, 且两种缺陷的浓度相当; 富Sc成分端的点缺陷则主要为Sc反位. 利用超胞模型进一步计算了含点缺陷L12-A13Sc晶体的弹性常数, 并计算预测了点缺陷形式和浓度对其弹性性能的影响. 结果表明: 在理想化学计量比成分附近, 点缺陷的引入均会降低非化学计量比L12-Al3Sc晶体的杨氏、剪切和体积弹性模量, 增加非化学计量比L12-Al3Sc弹性性能的各向异性, 但是对其脆-韧性的影响不大.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.
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Keywords:
- L12-Al3Sc /
- point defect densities /
- elastic modulus /
- first-principles
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[2] Krug M E, Dunand D C, Seidman D N 2011 Acta Mater. 59 1700
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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
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[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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