固溶合金第一性原理计算方法初探

doi:10.12288/szjs.s2020-0705

数值计算与计算机应用 ›› 2021, Vol. 42 ›› Issue (1): 18-32.DOI: 10.12288/szjs.s2020-0705

• 论文 • 上一篇

固溶合金第一性原理计算方法初探

徐黎闽¹, 杨真², 方俊³, 高兴誉³, 宋海峰³

1. 清华大学数学科学系, 北京 100084;
2. 北京科技大学应用物理研究所, 北京 100083;
3. 计算物理重点实验室, 北京应用物理与计算数学研究所, 北京 100088

收稿日期:2020-10-10 发布日期:2021-03-18
通讯作者: 高兴誉,gao_xingyu@iapcm.ac.cn.
基金资助:
国防基础科研核科学挑战专题（TZ2018002）、计算物理重点实验室基金和自然科学基金（11701037、11871297）资助.

PDF ( 46 ) 引用

徐黎闽, 杨真, 方俊, 高兴誉, 宋海峰. 固溶合金第一性原理计算方法初探[J]. 数值计算与计算机应用, 2021, 42(1): 18-32.

Xu Limin, Yang Zhen, Fang Jun, Gao Xingyu, Song Haifeng. A PRIMARY STUDY ON THE FIRST-PRINCIPLES CALCULATION METHOD FOR SOLID SOLUTION ALLOY[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(1): 18-32.

A PRIMARY STUDY ON THE FIRST-PRINCIPLES CALCULATION METHOD FOR SOLID SOLUTION ALLOY

Xu Limin¹, Yang Zhen², Fang Jun³, Gao Xingyu³, Song Haifeng³

1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
2. Institute for Applied Physics, University of Science and Technology Beijing, Beijing 100083, China;
3. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2020-10-10 Published:2021-03-18

固溶合金第一性原理计算在新型合金物性研究与合金组分优化设计中扮演着重要角色.固溶合金具有化学无序结构，晶格平移对称性破缺，难以直接应用标准的第一性原理计算方法.本文介绍了确定组分固溶合金第一性原理计算的主要两类方法.第一类方法是相干势近似方法，我们推导了相干势近似的自洽方程，基于多重散射理论梳理了单格点杂质系统Green函数的计算方法.第二类方法是超胞结构建模方法，我们介绍了相似原子环境的数学模型，推导了整体化学无序与短程化学有序的统一描述方法，证明了两种超胞结构建模方法最优解之间的关系.结合第一性原理计算与热力学模型，我们应用这两类方法预测了变组分铀铌合金的晶格参数与典型镁铝合金的热力学物性，获得了实验验证.

关键词： 固溶合金, 第一性原理, 多重散射理论, 相似原子环境, 相干势近似

First-principles calculations of solid solution alloy play an important role in property study and optimal design of new alloys. The solid solution alloy is in chemical disorder with translation symmetry broken, which raises difficulty in using directly conventional firstprinciples approaches. In this paper, we discuss two first-principles methods for the solid solution alloy with given concentration. The first is the coherent potential approximation (CPA). We derive the self-consistent equation of CPA, and revisit the computational scheme for the Green function of the single impurity system. The second method is based on the supercell modeling. We introduce the mathematical model of the similar atomic environment (SAE) and the unified description of chemical disorder with short-range order. And we prove the relationship between the optimal solutions of two modeling methods. Combined with first-principles calculations and thermodynamic models, we apply the two methods to predict the lattice structures of U-Nb alloys with varying concentration and thermodynamic properties of one typical Mg-Al alloy, which is verified by comparing with the experiment results.

Key words: solid solution alloy, first-principles, multiple scattering theory, similar atomic environment, coherent potential approximation

MR(2010)主题分类:

65Z05

分享此文:

[1] Lifshits I M, Gredeskul S A, Pastur L A, Lifshits I M, Pastur L A. Introduction to the theory of disordered systems[M]. Wiley, 1988.
[2] Sanchez J M, Ducastelle F, Gratias D. Generalized cluster description of multicomponent systems[J]. Physica A, 1984, 128(1-2):334-350.
[3] Sanchez J M. Cluster expansions and the configurational energy of alloys[J]. Phys. Rev. B, Nov 1993, 48:14013-14015.
[4] Zunger A, Wei S H, Ferreira L G, Bernard J E. Special quasirandom structures[J]. Phys. Rev. Lett., Jul 1990, 65:353-356.
[5] Wei S H, Ferreira L G, Bernard J E, Zunger A. Electronic properties of random alloys:Special quasirandom structures[J]. Phys. Rev. B, Nov 1990, 42:9622-9649.
[6] van de Walle A, Ceder G. First-principles computation of the vibrational entropy of ordered and disordered Pd₃V[J]. Phys. Rev. B, Mar 2000, 61:5972-5978.
[7] Wu E J, Ceder G, van de Walle A. Using bond-length-dependent transferable force constants to predict vibrational entropies in Au-Cu, Au-Pd, and Cu-Pd alloys[J]. Phys. Rev. B, Apr 2003, 67:134103.
[8] Ruban A V, Skriver H L. Screened Coulomb interactions in metallic alloys. I. Universal screening in the atomic-sphere approximation[J]. Phys. Rev. B, Jun 2002, 66:024201.
[9] Ruban A V, Simak S I, Korzhavyi P A, Skriver H L. Screened Coulomb interactions in metallic alloys. II. Screening beyond the single-site and atomic-sphere approximations[J]. Phys. Rev. B, Jun 2002, 66:024202.
[10] Jiang C. First-principles study of ternary bcc alloys using special quasi-random structures[J]. Acta Materialia, 2009, 57(16):4716-4726.
[11] Soven P. Coherent-Potential Model of Substitutional Disordered Alloys[J]. Phys. Rev., Apr 1967, 156:809-813.
[12] Taylor D W. Vibrational Properties of Imperfect Crystals with Large Defect Concentrations[J]. Phys. Rev., Apr 1967, 156:1017-1029.
[13] Gyorffy B L. Coherent-Potential Approximation for a Nonoverlapping-Muffin-Tin-Potential Model of Random Substitutional Alloys[J]. Phys. Rev. B, Mar 1972, 5:2382-2384.
[14] Faulkner J. The modern theory of alloys[J]. Progress in Materials Science, 1982, 27(1):1-187.
[15] Abrikosov I A, Johansson B. Applicability of the coherent-potential approximation in the theory of random alloys[J]. Phys. Rev. B, Jun 1998, 57:14164-14173.
[16] Ruban A V, Abrikosov I A. Configurational thermodynamics of alloys from first principles:effective cluster interactions[J]. Reports on Progress in Physics, 2008, 71(4):46501-0.
[17] Faulkner J S, Stocks G M, Wang Y. Multiple Scattering Theory[M]. 2053-2563. IOP Publishing, 2018.
[18] Faulkner J. The modern theory of alloys[M]. Pergamon, 1982.
[19] Crampin S. Electronic Structure of Disordered Alloys, Surfaces and Interfaces, I. Turek, V. Drchal, J. Kudrnovsky, M. ob, P. Weinberger. Kluwer Academic Press, Singapore (1997), ISBN:0-7923-9798-3[J]. Computer Physics Communications, 1998, 111.
[20] Faulkner J, Stocks G. Calculating properties with the coherent-potential approximation[J]. Physical Review B, 1980, 21(8):3222.
[21] Gonis A, Butler W H. Multiple Scattering in Solids[J]. 2000.
[22] Sébilleau, Didier. Basis-independent multiple-scattering theory for electron spectroscopies:General formalism[J]. Physical Review B, 2000, 61(20):14167-14178.
[23] Zabloudil J, Weinberger P, Szunyogh L, Hammerling R. Electron Scattering in Solid Matter[J]. Springer Series in Solid-State Sciences, 2005, 147.
[24] Zhang F X, Zhao S, Jin K, Xue H, Velisa G, Bei H, Huang R, Ko J Y P, Pagan D C, Neuefeind J C, Weber W J, Zhang Y. Local Structure and Short-Range Order in a NiCoCr Solid Solution Alloy[J]. Phys. Rev. Lett., May 2017, 118:205501.
[25] Sanchez J M. Foundations and Practical Implementations of the Cluster Expansion[J]. Journal of Phase Equilibria and Diffusion, 2017, 38(3):238-251.
[26] Tian F, Lin D Y, Gao X, Zhao Y F, Song H F. A structural modeling approach to solid solutions based on the similar atomic environment[J]. The Journal of Chemical Physics, 2020, 153(3):034101.
[27] Tian F, Lin D Y, Gao X, Zhao Y F, Song H F. Erratum:"A structural modeling approach to solid solutions based on the similar atomic environment"[J. Chem. Phys. 153, 034101(2020)] [J]. The Journal of Chemical Physics, 2020, 153(8):089901.
[28] Anagnostidis M, Colombié M, Monti H. Phases metastables dans les alliages uranium-niobium[J]. Journal of Nuclear Materials, 1964, 11(1):67-76.
[29] Tangri K, Chaudhuri D K. Metastable phases in uranium alloys with high solute solubility in the BCC gamma phase. Part I the system U-Nb[J]. Journal of Nuclear Materials, 1965, 15(4):278-287.
[30] Kresse G, Furthmüller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[J]. Computational Materials Science, 1996, 6:15-50.
[31] Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J]. Physical Review B, Oct, pages 11169-11186.
[32] Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method[J]. Physical Review B, Jan, pages 1758-1775.
[33] Brown D W, Bourke M A M, Clarke A J, Field R D, Thoma D J. The effect of low-temperature aging on the microstructure and deformation of uranium 6wtstudy[J]. Journal of Nuclear Materials, 2016, 481:164-175.
[34] Vitos L. Total-energy method based on the exact muffin-tin orbitals theory[J]. Phys. Rev. B, Jun 2001, 64:014107.
[35] Vitos L, Abrikosov I A, Johansson B. Anisotropic Lattice Distortions in Random Alloys from First-Principles Theory[J]. Phys. Rev. Lett., Sep 2001, 87:156401.
[36] Vitos L. Computational Quantum Mechanics for Materials Engineers[M]. Springer London, 2007.
[37] Otero-De-La-Roza A, Víctor Luaña. Gibbs2:A new version of the quasi-harmonic model code. I. Robust treatment of the static data[J]. Computer Physics Communications, 2011, 182(8):1708-1720.
[38] Wang Y, Li L. Mean-field potential approach to thermodynamic properties of metal:Al as a prototype[J]. Phys.rev.b, 2000, 62(1):196-202.
[39] Song H F, Liu H F. Modified mean-field potential approach to thermodynamic properties of a low-symmetry crystal:Beryllium as a prototype[J]. Physical Review B Condensed Matter, 2007, 75(24):2288-2288.
[40] McQueen R, Marsh S, Taylor J, Fritz J, Carter W. The equation of state of solids from shock wave studies[J]. High velocity impact phenomena, 1970, 293-417.

[1]	施意. 不同密度与粘性的多相流移动接触线问题的自适应有限元方法[J]. 数值计算与计算机应用, 2015, 36(4): 297-309.
[2]	蔡耀雄, 任全伟, 庄清渠. 一类四阶微积分方程的四阶差分格式[J]. 数值计算与计算机应用, 2014, 35(1): 59-68.

阅读次数

全文

摘要

固溶合金第一性原理计算方法初探

A PRIMARY STUDY ON THE FIRST-PRINCIPLES CALCULATION METHOD FOR SOLID SOLUTION ALLOY

扫码分享