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α-B晶体的Lennard-Jones对势和对势型多体势构建

于智清 王逊 刘艳侠 王梅 杨合 薛向欣

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α-B晶体的Lennard-Jones对势和对势型多体势构建

于智清, 王逊, 刘艳侠, 王梅, 杨合, 薛向欣

Construction of Lennard-Jones pair potential and pairwise many-body potential for crystal α-boron

Yu Zhi-Qing, Wang Xun, Liu Yan-Xia, Wang Mei, Yang He, Xue Xiang-Xin
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  • 精确原子间相互作用势函数的建立是分子动力学模拟的核心. 针对α-B晶体(R3m群), 分别构建Lennard-Jones (L-J)型对势和对势型多体势, 这两类势函数的构建仅需考虑晶体的原子平均结合能和几何构型参数. 前者取最近邻原子间距的势函数为最小值; 后者采用负指数(L-J型)函数和分段插值多项式形式来分别构造势函数, 在近邻处为势能极小值, 相邻极小值位置的中点引入势垒. 针对完整的α-B 晶体和偏离完整α-B晶体结构, 首先利用第一性原理计算结果来确定势函数的参数, 然后借助分子动力学的能量最小化方法优化结构, 并对这两类势函数以及Tersoff 势函数进行比较. 结果表明: L-J对势和Tersoff势的结果与α-B晶体构型有较大偏离; 而对势型多体势, 无论初始晶体构型完整与否, 其结果与完整α-B晶体构型比较一致.
    For α-boron, R3m group, Lennard-Jones (L-J) pair potential function is fitted, and a pairwise many-body potential is constructed. For constructing both interatomic potentials, only the atomic average cohesive energy and geometric information are needed. And the cohesive energy and geometry of α-boron crystal are calculated by first-principles code Castep. The fitting procedure for the potentials is as follows. For L-J potential, the minimum of the function is set to be located at the nearest neighbors. For the pairwise many-body potential, L-J potential is minimal, and the form of the function is chosen as a piecewise function, which consists of the L-J function and polynomial function. The minima of L-J potential are located at the distances between the different neighbors of atoms, and the potential barriers are at the midpoints of the distances of the two neighbor minima. L-J potential, L-J pair potential, and Tersoff potential for boron are tested and compared with each other, by energy minimization method in molecular dynamics (MD) simulation. The radial distribution function is used to analyze the structure obtained from the simulation results obtained by using different potentials. The results show that the structure after minimization deviates significantly from the initial crystal of α-boron by L-J potential, and final structure is consistent well with the initial ideal crystal, with L-J potential used. The NVT ensemble is used in MD simulation, where the temperature is set to be 2000 K, and the α-boron crystal experiences the thermodynamic evolutions for 10 fs and 100 fs, to obtain the deviated initial structures. Then the minimization by MD simulation is made to test the three potentials, which also shows that the L-J potential can give the much better result than the other two potentials.
    • 基金项目: 国家自然科学基金(批准号: 51474056, U1261120)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51474056, U1261120).
    [1]

    Yang J S, Huang D H, Cao Q L, Li Q, Wang L Z, Wang F H 2013 Chin. Phys. B 22 098101

    [2]

    Yu T, Xie H X, Wang C Y 2012 Chin. Phys. B 21 026104

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    Zhang B L, Wang J, Hou Q 2011 Chin. Phys. B 20 036105

    [4]

    Wang X, Liu Y X, Wang Y H, Ma Z N, Shan Y N, Wang J Y 2009 Acta Phys. Sin. 58 s035 (in Chinese) [王迅, 刘艳侠, 王悦华, 马振宁, 单亚拿, 王景禹 2009 物理学报 58 s035]

    [5]

    Wang C Y, Wang Z Q, Meng Q Y 2010 Acta Phys. Sin. 59 3370 (in Chinese) [王超营, 王振清, 孟庆元 2010 物理学报 59 3370]

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    Oganov A R, Chen J H, Gatti C, Ma Y Z, Ma Y M, Glass C W, Liu Z X, Yu T, Kurakevych O O, Solozhenko V L 2009 Nature 457 863

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    Segall M D, Lindan P J D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys.: Condens. Matter 14 2717

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    Plimpton S J 1995 J. Comp. Phys. 117 1

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    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865

    [10]

    Lennard-Jones J E 1924 Proc. R. Soc. Lond. A 106 463

    [11]

    Wang X, Yu Z Q, Liu Y X, Sun H 2015 Empirical Pair-wise Many-body Potentials for C60 Cluster and Diamond Crystal (submitted to Nature)

    [12]

    Tersoff J 1988 Phys. Rev. B 37 6991

  • [1]

    Yang J S, Huang D H, Cao Q L, Li Q, Wang L Z, Wang F H 2013 Chin. Phys. B 22 098101

    [2]

    Yu T, Xie H X, Wang C Y 2012 Chin. Phys. B 21 026104

    [3]

    Zhang B L, Wang J, Hou Q 2011 Chin. Phys. B 20 036105

    [4]

    Wang X, Liu Y X, Wang Y H, Ma Z N, Shan Y N, Wang J Y 2009 Acta Phys. Sin. 58 s035 (in Chinese) [王迅, 刘艳侠, 王悦华, 马振宁, 单亚拿, 王景禹 2009 物理学报 58 s035]

    [5]

    Wang C Y, Wang Z Q, Meng Q Y 2010 Acta Phys. Sin. 59 3370 (in Chinese) [王超营, 王振清, 孟庆元 2010 物理学报 59 3370]

    [6]

    Oganov A R, Chen J H, Gatti C, Ma Y Z, Ma Y M, Glass C W, Liu Z X, Yu T, Kurakevych O O, Solozhenko V L 2009 Nature 457 863

    [7]

    Segall M D, Lindan P J D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys.: Condens. Matter 14 2717

    [8]

    Plimpton S J 1995 J. Comp. Phys. 117 1

    [9]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865

    [10]

    Lennard-Jones J E 1924 Proc. R. Soc. Lond. A 106 463

    [11]

    Wang X, Yu Z Q, Liu Y X, Sun H 2015 Empirical Pair-wise Many-body Potentials for C60 Cluster and Diamond Crystal (submitted to Nature)

    [12]

    Tersoff J 1988 Phys. Rev. B 37 6991

计量
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  • PDF下载量:  320
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-11-14
  • 修回日期:  2014-12-26
  • 刊出日期:  2015-05-05

α-B晶体的Lennard-Jones对势和对势型多体势构建

  • 1. 东北大学材料与冶金学院, 沈阳 110819;
  • 2. 沈阳建筑大学理学院, 沈阳 110168;
  • 3. 辽宁大学物理学院, 沈阳 110036;
  • 4. 中国科学院金属研究所钛合金研究部, 沈阳 110016
    基金项目: 国家自然科学基金(批准号: 51474056, U1261120)资助的课题.

摘要: 精确原子间相互作用势函数的建立是分子动力学模拟的核心. 针对α-B晶体(R3m群), 分别构建Lennard-Jones (L-J)型对势和对势型多体势, 这两类势函数的构建仅需考虑晶体的原子平均结合能和几何构型参数. 前者取最近邻原子间距的势函数为最小值; 后者采用负指数(L-J型)函数和分段插值多项式形式来分别构造势函数, 在近邻处为势能极小值, 相邻极小值位置的中点引入势垒. 针对完整的α-B 晶体和偏离完整α-B晶体结构, 首先利用第一性原理计算结果来确定势函数的参数, 然后借助分子动力学的能量最小化方法优化结构, 并对这两类势函数以及Tersoff 势函数进行比较. 结果表明: L-J对势和Tersoff势的结果与α-B晶体构型有较大偏离; 而对势型多体势, 无论初始晶体构型完整与否, 其结果与完整α-B晶体构型比较一致.

English Abstract

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