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点缺陷浓度对非化学计量比L12型结构的A13Sc弹性性能的影响

张朝民 江勇 尹登峰 陶辉锦 孙顺平 姚建刚

引用本文:
Citation:

点缺陷浓度对非化学计量比L12型结构的A13Sc弹性性能的影响

张朝民, 江勇, 尹登峰, 陶辉锦, 孙顺平, 姚建刚

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
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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.
      通信作者: 江勇, yjiang@csu.edu.cn;ydfchh@mail.csu.edu.cn ; 尹登峰, yjiang@csu.edu.cn;ydfchh@mail.csu.edu.cn
    • 基金项目: 山东省科技发展计划(批准号: 2014GGX102006)和山东省高等学校科技计划(批准号: J14LJ51)资助的课题.
      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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    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)]

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    Wang N, Tang B Y 2009 Acta Phys. Sin. 58 S230 (in Chinese) [王娜, 唐壁玉 2009 物理学报 58 S230]

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    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]

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    Hu W C, Liu Y, Li D J, Zeng X Q, Xu C S 2013 Physica B 427 85

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    Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169

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    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188

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    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]

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    Asia M, Foiles S M, Quong A A 1998 Phys. Rev. B 57 11265

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    Korzhavyi P A, Ruban A V, Lozovoi A Y, Vekilov Y K, Abrikosov I A, Johansson B 2000 Phys. Rev. B 61 6003

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    Mao Z, Chen W, Seidman D N, Wolverton C 2011 Acta Mater. 59 3012

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    Hill R 1952 Proc. Phys. Soc. A 65 349

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    Jhi S H, Ihm J, Louie G S 1999 Nature 399 132

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    Ranganathan S I, Ostoja-Starzewski M 2008 Phys. Rev. Lett. 101 055504

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    Pugh S F 1954 Philos. Mag. 45 823

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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 物理学报 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 物理学报 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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出版历程
  • 收稿日期:  2015-06-25
  • 修回日期:  2016-01-22
  • 刊出日期:  2016-04-05

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