First principles lattice dynamics of NaCoO$_2$

第一性原理发展简史（2）——霍恩贝格-科恩定理与里兹变分法•关于第一性原理这个词语在1900前哲学与数学中使用的问题很多人追问文中一段话出处，其实严格意义上逐字逐句的表述应该算作者原创，并不是直接引用，但是这样论述并非是毫无根据的。

这段内容最初是作者学生时代一门课程老师所述，写文章时已经默认这是本领域中学界的一个共识。

今天的文字资料中第一性原理(first principle)一般已经默认就是指计算材料学中的第一性原理计算，个别国家特别是德国、奥地利等德语区为了学术严谨起见则更愿意使用ab-initia（又译为从头算），美国、澳大利亚、英国等英语区国家则是二者并用，中文环境下由于历史原因主要是源自外文翻译与编辑，因此主流说法认为汉语环境“第一性原理”仅指代计算材料学。

上期之所以说1900年前第一性原理主要用于哲学、数学、理论物理，根据与逻辑如下：亚里士多德时代已经诞生了第一性原理(firstprinciple)的定义，而计算材料学的源头——量子力学诞生于1900年之后。

1900年以前的哲学、数学著作中时常可以见到first principle 这一术语的使用，当然这些著作今天流通的修订本或者是再编版已不再使用第一性原理的表述：哲学中往往用priori-principle替代之前的第一性原理表述；数学中今天已经统一使用规范术语“公理”（axioms）表述，因此今天再说第一性原理涵盖哲学、数学已经有些不合时宜。

另外第一性原理这个词语本身的使用一定程度上也体现了欧洲16世纪以来，人文主义的兴起初期理论、知识是以人为本、以人为核心的，它的出发点是希望不依赖（那时认为是上帝或神创造的）物质实验、测量建立起一个完全由人的意识引出的（与神学足以抗衡的）理论体系。

这一点上与中华神话《夸父逐日》的精髓类似，反映出人类在探索自然时不屈、奋进的精神。

•关于分子动力学是否属于第一性原理此处的分子动力学特指molecule dynamics，简称MD，中文环境中由于各种原因“分子动力学”可一词可能涵盖其他意义，如作者接触过的物理化学中的分子马达领域将相关的内容称为分子动力学。

第50卷第3期2021年5月内蒙古师范大学学报(自然科学版)Journal of Inner Mongolia Normal University(Natural Science Edition)Vol.50No.3May2021六硼化钇纳米粒子超导及光吸收性能研究王军】，包黎红】，潮洛蒙2（1.内蒙古师范大学物理与电子信息学院，内蒙古呼和浩特010022；2.内蒙古科技大学理学院，内蒙古包头014010）摘要：采用固相烧结法成功制备出了六硼化钇（YB&）纳米粒子，首次系统研究了该纳米粉末超导及光吸收性能.结果表明，当超导转变温度T=2.75K时由正常态转变为超导态，其临界磁场为H c2=0.18T.为进一步研究YB6纳米粒子电-声子相互作用机理，采用拉曼光谱对声子振动频率进行了测量，结合McMillan公式计算出YB6纳米粒子电-声子作用常数为A=0.63,该值远小于单晶块体YB6的1.01.为进一步解释其原因，采用高分辨透射电镜对晶体缺陷进行了详细表征.结果发现，晶体缺陷导致其声子振动频率的改变，从而降低了纳米YB6电-声子相互作用常数.光吸收结果表明YB6纳米粒子吸收谷波长为785nm,对可见光具有很强的穿透性.关键词：超导性；光吸收；YB6中图分类号：O511+.3文献标志码：A文章编号：1001—8735（2021）03—0204—06doi：10.3969/j.issn.1001—8735.2021.03.003众所周知，材料的宏观物理化学性能与微观结构密切相关[12].特别是当材料晶粒尺寸减小到纳米尺度后，纳米晶材料不仅具有亚稳态的特点，而且相比于粗晶材料展现出许多新奇的物理化学性能.与此同时,材料的纳米化会改变材料电子态密度及电-声子相互等物理量，从而会对超导及光学性能有很大的影响[34].因此，如何将纳米材料微观结构与宏观性能之间进行有效关联，将对材料新性能的发现和研究具有重要作用.在众多金属硼化物中，由于六硼化钇YB6具有第二高超导转变温度T c=&4K,故其超导性能受到广泛关注.目前关于这方面的研究主要集中于单晶YB6块体材料上[8],而对于YB6纳米离子超导性能研究未见报道.研究者们为了解释单晶块体超导机理及提高临界转变温度，系统研究了压强对YB6单晶块体晶体结构和声子振动的影响[912].结果发现，当压强从0增加至40GPa时，电子-声子相互作用常数从1.44减小到0.44.与此同时，相对应的超导转变温度也从&9K减小到1.4K,表明压强对电-声子作用具有很大影响.这项研究工作的一个重要提示是,YB6的纳米化是否会改变费米能级周围的电子态密度及电子-声子相互作用，从而展现出一些新的超导性能，这是本文的重要研究内容之一.此外，虽然YB6与LaB6具有相同立方晶体结构[13],但它是否同样具有对可见光的高穿透特性，是本论文另一个重要研究内容.目前国内外对纳米YB6超导性能及光吸收实验方面的系统研究未见报道.本文首次系统研究了YB6纳米粒子超导及光吸收性能.为进一步揭示材料微观结构与宏观性能之间的内在关联，采用高分辨透射电镜和拉曼光谱等测量手段对微观结构进行了有效表征，并对超导及光吸收机理进行探讨.收稿日期：2020-11-30基金项目：国家自然科学基金资助项目（51662034）；内蒙古自治区自然科学基金资助项目（2019LH05001）；内蒙古自治区留学人员创新创业启动基金资助项目.作者简介：王军（1992-），男，内蒙古阿拉善左旗人，在读硕士研究生，主要从事纳米稀土六硼化物光吸收及热发射性能研究.通讯作者：包黎红（1983—）,男，内蒙古兴安盟人，教授，博士，主要从事纳米金属硼化物物理性能研究,E-mail:baolihong@.第3期王军等：六硼化钇纳米粒子超导及光吸收性能研究-205-1材料与方法将无水氯化钇(YCl,纯度99.95%)和硼氢化钠(NaBH4,纯度98%)粉末在空气中按摩尔比为1：&8混合研磨10〜15min.将混合均匀的粉末放入压机中，在压强为10GPa下预压成块，将其装入石英管中进行真空烧结.反应温度为1100C,保温2h.由于固相反应后产物中有YBO s的杂相，故对烧结后产物分别使用稀盐酸，蒸馏水，无水乙醇等溶液进行多次清洗.采用场发射扫描电子显微镜(日立SU-8010)和X射线衍射仪(飞利浦PW1830,CuKa)对YB6纳米粒子的物相及形貌进行表征.采用PPMS测量仪对纳米YB6交流磁化率和临界磁场进行了测量，最低温度为1.8K.采用透射电子显微镜(FEITecnai F20S-Twin200kv)观察微观结构.拉曼散射由拉曼光谱仪(LabRamHR,波长：514.5nm,激光源:Ar+)进行测量.采用分光光度计(UH4150)在光源波长350〜2500nm范围内测量其光吸收。

量子力学第一性原理：仅需五个物理基本常数——电子质量、电子电量、普郎克常数、光速和玻耳兹曼常数，通过求薛定谔方程得到材料的电子结构，而不依赖于任何经验常数即可以预测微观体系的状态和性质，预测材料的组分、结构、性能之间的关系，进一步设计具有特定性能的新材料。

作为评价事物的依据，第一性原理和经验参数是两个极端。

第一性原理是某些硬性规定或推演得出的结论，而经验参数则是通过大量实例得出的规律性的数据，这些数据可以来自第一性原理(称为理论统计数据)，也可以来自实验(称为实验统计数据)。

如果某些原理或数据来源于第一性原理，但推演过程中加入了一些假设(这些假设当然是很有说服力的)，那么这些原理或数据就称为“半经验的”。

量子化学的第一性原理是指多电子体系的Schrödinger方程，但是光有这个方程是无法解决任何问题的，量子力学能够准确的解决的问题很少很少，绝大多数都是有各种各样的近似，为此计算量子力学提出一个称为“从头计算”的原理作为第一性原理，除了Schrödinger方程外还允许使用下列参数和原理：(1) 物理常数，包括光速c、Planck常数h、电子电量e、电子质量me以及原子的各种同位素的质量，尽管这些常数也是通过实验获得的。

(在国际单位值中，光速是定义值，Planck 常数是测量值，在原子单位制中则相反。

)(2) 各种数学和物理的近似，最基本的近似是“非相对论近似”(Schrödinger方程本来就是非相对论的原理)、“绝热近似”(由于原子核质量比电子大得多，而把原子核当成静止的点处理)和“轨道近似”(用一个独立函数来描述一个独立电子的运动)。

量子化学的从头计算方法就是在各种近似上作的研究。

如果只考虑一个电子，而把其他电子对它的作用近似的处理成某种形式的势场，这样就可以把多电子问题简化成单电子问题，这种近似称为单电子近似，也称为平均场近似，例如最基本的从头计算方法哈特里－富克（Hartree-Fock）方法，是平均场近似的一种，它把所有讨论的电子视为在离子势场和其他电子的平均势场中的运动。

第一性原理根据原子核和电子互相作用的原理及其基本运动规律，运用量子力学原理，从具体要求出发，经过一些近似处理后直接求解薛定谔方程的算法，习惯上称为第一原理第一性原理通常是跟计算联系在一起的，是指在进行计算的时候除了告诉程序你所使用的原子和他们的位置外，没有其他的实验的，经验的或者半经验的参量，且具有很好的移植性。

作为评价事物的依据，第一性原理和经验参数是两个极端。

第一性原理是某些硬性规定或推演得出的结论，而经验参数则是通过大量实例得出的规律性的数据，这些数据可以来自第一性原理(称为理论统计数据)，也可以来自实验(称为实验统计数据)。

但是就某个特定的问题，第一性原理和经验参数没有明显的界限，必须特别界定。

如果某些原理或数据来源于第一性原理，但推演过程中加入了一些假设(这些假设当然是很有说服力的)，那么这些原理或数据就称为“半经验的”。

第一性原理，英文First Principle，是一个计算物理或计算化学专业名词，广义的第一性原理计算指的是一切基于量子力学原理的计算。

我们知道物质由分子组成，分子由原子组成，原子由原子核和电子组成。

量子力学计算就是根据原子核和电子的相互作用原理去计算分子结构和分子能量（或离子），然后就能计算物质的各种性质。

从头算（ab initio）是狭义的第一性原理计算，它是指不使用经验参数，只用电子质量，光速，质子中子质量等少数实验数据去做量子计算。

但是这个计算很慢，所以就加入一些经验参数，可以大大加快计算速度，当然也会不可避免的牺牲计算结果精度。

那为什么使用“第一性原理”这个字眼呢？据说这是来源于“第一推动力”这个宗教词汇。

第一推动力是牛顿创立的，因为牛顿第一定律说明了物质在不受外力的作用下保持静止或匀速直线运动。

如果宇宙诞生之初万事万物应该是静止的，后来却都在运动，是怎么动起来的呢？牛顿相信这是由于上帝推了一把，并且牛顿晚年致力于神学研究。

现代科学认为宇宙起源于大爆炸，那么大爆炸也是有原因的吧。

Nb2N3的力学和电子性质的第一性原理祝颖;徐丹;李全军;陈洪斌【摘要】The crystal structure, dynamics, lattice dynamics, and electronic properties of Nb2 N3 were studied by means of first-principles method of the density functional theory. The results show that Nb2N3 has orthogonal 7;-Ta2N3 structure at normal pressure, the elastic constants of this structure meet the Bonn-Huangkun criterion, and its lattice is dynamics stable. Nb2N3 has large bulk modulus (304 Gpa) and hardness (19. 3 Gpa). Because of the hybridization of 4d orbital of Nb and 2p orbital of N forming three-dimensional Nb-N covalent bonds, Nb2N3 is ionic semiconductor materials.%采用基于密度泛函理论的第一性原理方法研究Nb2N3的晶体结构、力学、晶格动力学和电子性质.结果表明:Nb2N3常压下具有正交η-Ta2N3结构,其弹性常数满足波恩-黄昆判据,且晶格动力学稳定；Nb2N3具有较大的体弹性模量(304 GPa)和硬度(19.3 GPa),由于Nb 4d轨道与N2p轨道杂化形成三维Nb-N共价键,因此Nb2N3为离子性较强的半导体材料.【期刊名称】《吉林大学学报（理学版）》【年(卷),期】2012(050)001【总页数】4页(P118-121)【关键词】氮化铌;硬质材料;高压物理【作者】祝颖;徐丹;李全军;陈洪斌【作者单位】吉林医药学院公共卫生院,吉林吉林132013;吉林大学超硬材料国家重点实验室,长春130012;吉林大学超硬材料国家重点实验室,长春130012;吉林医药学院公共卫生院,吉林吉林132013【正文语种】中文【中图分类】O521.2过渡族金属氮化物应用广泛[1-3], 其中TiN,VN,NbN等主要应用于硬质涂层材料[4], NbN的超导转变温度高达17.3 K[5]. Zerr等[2]在高温(>2 500 K)、高压(>16 GPa)条件下合成了Zr3N4和Hf3N4, Zr3N4薄膜的耐磨性比TiN提高约一个数量级[6]. Gregoryanz等[7]在高温(>2 000 K)、高压(>45 GPa)条件下合成了第一个过渡金属二氮化物PtN2, 理论预测其维氏硬度大于46 GPa[8]. Young等[9]合成了IrN2和OsN2, 其中IrN2的体弹性模量为428 GPa, 略低于金刚石的体弹性模量(440 GPa).Zerr等[10]在高温(>1 700 K)、高压(>11 GPa)条件下制备了含有少量O杂质且具有正交对称性的η-Ta2N3, η-Ta2N3是第一个氮离子与金属离子化学计量比为3∶2的过渡金属氮化物, 晶体的针状外形表明其具有高断裂韧度. 第一性原理研究表明, 常压下η-Ta2N3的弹性常数不满足波恩-黄昆判据, O杂质对η-Ta2N3的弹性稳定具有重要作用[11]. 本文采用第一性原理方法研究Nb2N3的晶体结构、力学、晶格动力学和电子性质.1 理论方法本文所有结构优化和电子性质计算均在密度泛函理论框架下采用“维也纳从头算模拟包”(简称VASP)[12]. 原子核与电子间的相互作用采用投影缀加波“冷冻核”全势[13]; 电子间的交换关联作用采用广义梯度近似[14]; Nb和N的价电子组态分别采用4p65s24d3和2s22p3. 平面波截断能为600 eV, 当布里渊区K点MP采样间距小于0.025 时, 计算中体系的焓(H=E+pV)收敛到每原子1 meV量级; 当局域优化时, 作用在原子上的力收敛到每纳米10 meV量级, 总的残余应力收敛到0.01 GPa量级. 弹性常数计算采用“应变-应力”方法[15]: 先对晶胞实施大小分别为±0.7%和±1.3%的应变, 再固定晶格基矢优化原子位置求得应力, 并根据胡克定律由奇异值分解方法求得晶体弹性常数的最小二乘解.2 结果与分析图1 Nb2N3的物态方程Fig.1 Equations of states of Nb2N3实验表明, η-Ta2N3具有正交结构, 空间群为Pnma, 当压力低于7.7 GPa时, 其相变到空间群为P-4m2的四方结构(以下简称为t-Ta2N3)[11], 常压和高压下t-Ta2N3的弹性常数均满足波恩-黄昆判据, 表明其力学稳定. 为考察Nb2N3是否存在类似相变, 本文将Nb2N3在-8～20 GPa压力下以4 GPa为间隔进行定压局域优化, 所得物态方程如图1所示. Pnma相的平衡晶胞参数分别为a=0.813 46 nm, b=0.301 72 nm, c=0.819 86 nm, 平衡体积为每个分子式0.051 39 nm3, 晶格中所有原子均占据Wyckoff的4c(x,1/4,z)位置, 各原子的晶体坐标列于表1. P-4m2相的平衡晶胞参数分别为a=0.300 12 nm, c=0.586 68 nm, 平衡体积为每个分子式0.052 84 nm3. 晶格Nb占据Wyckoff的2g(0,1/2,0.243 8)位置; N分别占据Wyckoff的2g(0,1/2,0.859 4)和1c(1/2,1/2,1/2)位置. 与Ta2N3不同, Nb2N3为Pnma结构(以下简称为η-Nb2N3), 其常压下的能量和平衡体积均明显低于P-4m2结构(以下简称为t-Nb2N3), 表明η-Nb2N3在常压和高压(<20 GPa)下均为Nb2N3能量稳定的结构, 而t-Nb2N3为能量亚稳相.表1 η-Nb2N3中Nb和N原子的晶体坐标Table 1 Crystal coordinates of Nb and N atoms of η-Nb2N3原子x轴y轴z轴Nb1 0.694 70.250.4958Nb20.022 20.250.686 9N10.778 80.250.798 2N20.121 30.250.4519N30.954 20.250.125 9本文拟合了η-Nb2N3和t-Nb2N3的三阶Birch-Murnaghan物态方程, 并将它们在压力作用下的体积变化趋势与η-Ta2N3,t-Ta2N3,NbN进行对比, 结果如图1所示. 由图1可见, Nb2N3和Ta2N3在高压下的四方相抵抗外力压缩性能明显优于正交相. 与t-Ta2N3体弹性模量(B0=331 GPa)略高于η-Ta2N3体弹性模量(B0=323 GPa)的结果相符[11]. 此外, Nb2N3比Ta2N3和NbN更易于压缩,Ta2N3在压力作用下的体积变化趋势更接近于NbN. 由三阶Birch-Murnaghan 物态方程得到η-Nb2N3和t-Nb2N3的体弹性模量分别为307 GPa和311 GPa, 小于NbN,η-Ta2N3,t-Ta2N3的体弹性模量.本文采用基于密度泛函理论的第一性原理计算应力. 在笛卡尔坐标系中, 材料的晶格基矢可表示为其中a1, b1, c1分别为晶格基矢a, b,c的第一个笛卡尔坐标, 其余类推. 先对R施加一组应变s=(s1 s2 s3 s4 s5 s6), 其中: s1,s2,s3为常规应变;s4,s5,s6为剪切应变. 所得畸变晶格可表示为每个畸变晶格可由第一性原理求得一个应力t=(t1 t2 t3 t4 t5 t6), 与s满足胡克定律: t=sC, 其中C是6×6维的弹性常数矩阵, 矩阵元cij服从沃伊特标记. 若存在n个应变S, 则可求得n个应力T, 进而获得n×6维的非满秩弹性常数矩阵C, 满足C=S-1T, 其中“-1”表示求逆. 采用奇异值分解方法求解该方程可得弹性常数的最小二乘解. 根据晶体不同的对称性, 计算弹性常数所需最小线性不相关应变数分别为: 立方晶系2个; 六方和三方晶系3个; 四方晶系4个; 正交、单斜和三斜晶系6个.采用应变-应力方法求得η-Nb2N3的弹性常数cij为由于η-Nb2N3的c66为正数, 且η-Nb2N3的所有弹性常数均满足波恩-黄昆弹性稳定性判据, 因此常压下η-Nb2N3可稳定存在. 由弹性常数可得正交结构的剪切各向异性因子分别为A1=4c44/(c11+c33-2c13)=1.02, A2=4c55/(c22+c33-2c23)=0.86, A3=4c66/(c11+c22-2c12)=0.81. A1,A2,A3分别对应(100),(010),(001)剪切平面, 因此(010)和(001)剪切平面存在较强的各向异性. Voigt-Reuss-Hill平均形式的多晶体弹性模量(B=304 GPa)[16], 略低于含有少量O杂质的η-Ta2N3(323 GPa), 但大于单质Nb[3]的弹性模量(172 GPa), 接近于NbC的弹性模量(301 GPa)和NbN的弹性模量(309 GPa), 表明η-Nb2N3具有较强的抗压缩能力[4]; 由η-Nb2N3的剪切模量G、杨氏模量Y、泊松比υ分别为146 GPa, 377 GPa, 0.29可知, η-Nb2N3具有较强的抗剪切能力. 由B/G≈2.1可推测η-Nb2N3为脆性材料[17]. 晶体材料微观硬度理论可预测材料的硬度[18-22]. 本文利用文献[21]的理论模型求得η-Nb2N3和η-Ta2N3的维氏硬度分别为19.3 GPa和19.7 GPa. Zerr等[10]预测致密的η-Ta2N3硬度为30 GPa, 因此可推测η-Nb2N3的硬度较大. η-Nb2N3原子轨道角动量投影的电子能态密度(分立态密度)如图2所示, 其中竖线表示Fermi能级. 由图2可见, η-Nb2N3是带隙约为0.4 eV的半导体材料. 在-14.5～0 eV能量范围内, Nb的4d轨道和N的2p轨道间存在较强的杂化, 表明Nb-N键具有较强的共价性. η-Nb2N3在(001)平面上的电荷密度如图3所示. 由图3可见, Nb-N键的电子局域行为表明了其共价性, 与η-Nb2N3的半导体特性相符. 此外, 基于AIM理论的Bader分析[23]表明, η-Nb2N3中平均每个Nb离子向N离子转移2.17个电荷, 即Nb和N之间的化学键具有强离子性.图2 η-Nb2N3的分立态密度Fig.2 Discrete density of sta te of η-Nb2N3 图3 η-Nb2N3在(001)平面上的电荷密度Fig.3 Charge density of η-Nb2N3 on the (001) plane本文以Nb和Ta体心立方相及N的α相为参照相, 计算了η-Nb2N3和η-Ta2N3的形成焓: Δ H=H(η-M2N3)-2H(M)-(3/2)H(N2), 其中M表示Nb或Ta 原子. 由式(1)可知, 零压下η-Nb2N3和η-Ta2N3的形成焓分别为-4.2 eV和-5.2eV. 表明两个相在常压下能量稳定, 未分解为金属单质和氮气. 对于η-Ta2N3, 本文的理论结果与实验相符[10]. 由于η-Nb2N3与η-Ta2N3形成焓相近, 因此η-Nb2N3可在与η-Ta2N3相似的压力(11 GPa)和温度(>1 700 K)条件下合成.综上, 本文采用基于密度泛函理论的第一性原理方法研究了Nb2N3的性质. 结果表明: η-Nb2N3为具有较强离子性的半导体材料, 其带隙约为0.4 eV; η-Nb2N3在常压下的弹性稳定, 具有较强的抗压缩性、剪切各向异性和脆性, 其硬度与η-Ta2N3的硬度相似; η-Nb2N3在常压下能量稳定, 可在高温、高压条件下合成. 参考文献【相关文献】[1] Jhi S H, Louie S G, Cohen M L, et al. Vacancy Hardening and Softening in Transition Metal Carbides and Nitrides [J]. Phys Rev Lett, 2001, 86(15): 3348-3351.[2] Zerr A, Miehe G, Riedel R. Synthesis of Cubic Zirconium and Hafnium Nitride Having Th3P4 Structure [J]. Nat Mater, 2003, 2(3): 185-189.[3] Isaev E I, Simak S I, Abrikosov I A, et al. Phonon Related Properties of Transition Metals, Their Carbides, and Nitrides: A First-Principles Study [J]. J Appl Phys, 2007, 101(12): 123519.[4] Brazhkin V V, Lyapin A G, Hemley R J. Harder Than Diamond: Dreams and Reality [J]. Philos Mag A, 2002, 82(2): 231-253.[5] Alén P, Ritala M, Arstila K, et al. The Growth and Diffusion Barrier Properties of Atomic Layer Deposited NbNx Thin Films [J]. Thin Solid Films, 2005, 491(1/2): 235-241.[6] Chhowalla M, Unalan H E. Thin Films of Hard Cubic Zr3N4 Stabilized by Stress [J]. Nat Mater, 2005, 4: 317-322.[7] Gregoryanz E, Sanloup C, Somayazulu M, et al. Synthesis and Characterization of a Binary Noble Metal Nitride [J]. Nat Mater, 2004, 3: 294-297.[8] GUO Xiao-ju, LI Lei, LIU Zhong-yuan, et al. Hardness of Covalent Compounds: Roles of Metallic Component and d Valence Electrons [J]. J Appl Phys, 2008, 104(2): 023503. [9] Young A F, Sanloup C, Gregoryanz E, et al. Synthesis of Novel Transition Metal Nitrides IrN2 and OsN2 [J]. Phys Rev Lett, 2006, 96(15): 155501.[10] Zerr A, Miehe G, LI Jing-wang, et al. High-Pressure Synthesis of Tantalum Nitride Having Orthorhombic U2S3 Structure [J]. Adv Funct Mater, 2009, 19(14): 2282-2288. [11] JIANG Chao, LIN Zhi-jun, ZHAO Yu-sheng. Thermodynamic and Mechanical Stabilities of Tantalum Nitride [J]. Phys Rev Lett, 2009, 103(18): 185501.[12] Kresse G, Furthmüller J. Efficient Iterative Schemes for ab initio Total-Energy Calculations Using a Plane-Wave Basis Set [J]. Phys Rev B, 1996, 54(16): 11169-11186. [13] Blöchl P E. Projector Augmented-Wave Method [J]. Phys Rev B, 1994, 50(24): 17953-17979.[14] Perdew J P, Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple [J]. Phys Rev Lett, 1996, 77(18): 3865-3868.[15] Shang S, Wang Y, Liu Z K. First-Principles Elastic Constants of α- and θ-Al2O3[J]. Appl Phys Lett, 2007, 90: 101909.[16] Hill R. The Elastic Behaviour of a Crystalline Aggregate [J]. Proc Phys Soc A, 1952,65(5): 349-356.[17] Ravindran P, Fast L, Korzhavyi P A, et al. Density Functional Theory for Calculation of Elastic Properties of Orthorhombic Crystals: Application to TiSi2 [J]. J Appl Phys, 1998,84(9): 4891.[18] GAO Fa-ming, HE Ju-long, WU Er-dong, et al. Hardness of Covalent Crystals [J]. Phys Rev Lett, 2003, 91(1): 015502.[19] Simunek A, Vackar J. Hardness of Covalent and Ionic Crystals: First-Principle Calculations [J]. Phys Rev Lett, 2006, 96(8): 085501.[20] GAO Fa-ming. Theoretical Model of Intrinsic Hardness [J]. Phys Rev B, 2006, 73(13): 132104.[21] Simunek A. How to Estimate Hardness of Crystals on a Pocket Calculator [J]. Phys Rev B, 2007, 75(17): 172108.[22] LI Ke-yan, WANG Xing-tao, ZHANG Fang-fang, et al. Electronegativity Identification of Novel Superhard Materials [J]. Phys Rev Lett, 2008, 100(23): 235504.[23] Henkelman G, Arnaldsson A, Jónsson H. A Fast and Robust Algorithm for Bader Decomposition of Charge Density [J]. Comput Mater Sci, 2006, 36(3): 354-360.。

a rXiv:mtrl -th/9522v14Fe b1995First-principle study of excitonic self-trapping in diamond Francesco Mauri ∗and Roberto Car Institut Romand de Recherche Num´e rique en Physique des Mat´e riaux (IRRMA)IN-Ecublens 1015Lausanne,Switzerland Abstract We present a first-principles study of excitonic self-trapping in diamond.Our calculation provides evidence for self-trapping of the 1s core exciton and gives a coherent interpretation of recent experimental X-ray absorption and emission data.Self-trapping does not occur in the case of a single valence exciton.We predict,however,that self-trapping should occur in the case of a valence biexciton.This process is accompanied by a large local relaxation of the lattice which could be observed experimentally.PACS numbers:61.80.−x,71.38.+i,71.35+z,71.55.−iTypeset using REVT E XDiamond presents an unusually favorable combination of characteristics that,in connection with the recent development of techniques for the deposition of thin diamondfilms,make this material a good candidate for many technological applications.Particularly appealing is the use of diamond in electronic or in opto-electronic devices,as e.g.UV-light emitting devices.Moreover,diamond is an ideal material for the construction of windows that operate under high power laser radiation or/and in adverse environments.It is therefore interesting to study radiation induced defects with deep electronic levels in the gap,since these can have important implications in many of these applications.Excitonic self-trapping is a possible mechanism for the formation of deep levels in the gap.The study of such processes in a purely covalent material,like diamond,is interesting also from a fundamental point of view.Indeed,excitonic self-trapping has been studied so far mostly in the context of ionic compounds,where it is always associated with,and often driven by,charge transfer effects.In a covalent material the driving mechanism for self-trapping is instead related to the difference in the bonding character between the valence and the conduction band states.Both experimental data and theoretical arguments suggest the occurrence of self-trapping processes in diamond.In particular,a nitrogen(N)substitutional impurity induces a strong local deformation of the lattice[1–3]that can be interpreted as a self-trapping of the donor electron.The structure of a1s core exciton is more controversial[4–9].Indeed the similarity between an excited core of carbon and a ground-state core of nitrogen suggests that the core exciton should behave like a N impurity.However,the position of the core exciton peak in the diamond K-edge absorption spectra is only0.2eV lower than the conduction band minimum[4,7,8],while a N impurity originates a deep level1.7eV below the conduction band edge[10].On the other hand,emission spectra[8]suggest that a1s core exciton should self-trap like a N impurity.Finally,we consider valence excitations.In this case experimental evidence indicates that a single valence exciton is of the Wannier type,i.e.there is no self-trapping.To our knowledge,neither experimental nor theoretical investigations on the behavior of a valence biexciton in diamond have been performed,although simple scalingarguments suggest that the tendency to self-trap should be stronger for biexcitons than for single excitons.In this letter,we present a detailed theoretical study of excitonic self-trapping effects in diamond.In particular,we have investigated the Born-Oppenheimer(BO)potential energy surfaces corresponding to a core exciton,a valence exciton and a valence biexciton in the context of density functional theory(DFT),within the local density approximation(LDA) for exchange and correlation.Our calculation indicates that the1s core exciton is on a different BO surface in absorption and in emission experiments.Indeed X-ray absorption creates excitons in a p-like state as required by dipole selection rules.Subsequently the system makes a transition to an s-like state associated to a self-trapping distortion of the atomic lattice,similar to that found in the N impurity case.These results provide a coherent interpretation of the experimental data.In addition,our calculation suggests that self-trapping should also occur for a valence biexciton.This is a prediction that could be verified experimentally.Let us start by discussing a simple model[11,12].In diamond,the occupied valence and the lower conduction band states derive from superpositions of atomic sp3hybrids having bonding and antibonding character,respectively.Thus,when an electron,or a hole,or an electron-hole pair is added to the system,this can gain in deformation energy by relaxing the atomic lattice.Scaling arguments suggest that the deformation energy gain E def∝−1/N b, where N b is the number of bonds over which the perturbation is localized.This localization,due to quantum confinement.The in turn,has a kinetic energy cost E kin∝+1/N2/3bbehavior of the system is then governed by the value of N b that minimizes the total energy E sum=E def+E kin.Since the only stationary point of E sum is a maximum,E sum attains its minimum value at either one of the two extrema N b=1or N b=∞.If the minimum occurs for N b=1,the perturbation is self-trapped on a single bond which is therefore stretched.If the minimum occurs for N b=∞,there is no self-trapping and the perturbation is delocalized.When N p particles(quasi-particles)are added to the system,one can showthat,for a given N b,E def scales as N2p,while E kin scales as N p.As a consequence,the probability of self-trapping is enhanced when N p is larger.This suggests that biexcitons should have a stronger tendency to self-trap than single excitons[12,13].In order to get a more quantitative understanding of self-trapping phenomena in dia-mond,we performed self-consistent electronic structure calculations,using norm-conserving pseudopotentials[14]to describe core-valence interactions.The wave-functions and the electronic density were expanded in plane-waves with a cutoffof35and of140Ry,respec-tively.We used a periodically repeated simple cubic supercell containing64atoms at the experimental equilibrium lattice constant.Only the wave-functions at theΓpoint were con-sidered.Since the self-trapped states are almost completely localized on one bond,they are only weakly affected by the boundary conditions in a64atom supercell.The effect of the k-point sampling was analysed in Ref.[3]where similar calculations for a N impurity were performed using the same supercell.It was found that a more accurate k-point sampling does not change the qualitative physics of the distortion but only increases the self-trapping energy by20%compared to calculations based on theΓ-point only[3].In order to describe a core exciton we adopted the method of Ref.[15],i.e.we generated a norm conserving pseudopotential for an excited carbon atom with one electron in the1s core level andfive electrons in the valence2s-2p levels.In our calculations for a valence exciton or biexciton we promoted one or two electrons,respectively,from the highest valence band state to the lowest conduction band state.Clearly,our single-particle approach cannot account for the(small)binding energy of delocalized Wannier excitons.However our approach should account for the most important contribution to the binding energy in the case of localized excitations.Structural relaxation studies were based on the Car-Parrinello(CP) approach[16].We used a standard CP scheme for both the core and the valence exciton, while a modified CP dynamics,in which the electrons are forced to stay in an arbitrary excited eigenstate[12,17],was necessary to study the BO surfaces corresponding to a valence biexciton.All the calculations were made more efficient by the acceleration methods of Ref.[18].Wefirst computed the electronic structure of the core exciton with the atoms in the ideal lattice positions.In this case the excited-core atom induces two defect states in the gap:a non-degenerate level belonging to the A1representation of the T d point group,0.4eV below the conduction band edge,and a3-fold degenerate level with T2character,0.2eV below the conduction band edge.By letting the atomic coordinates free to relax,we found that the absolute minimum of the A1potential energy surface correponds to an asymmetric self-trapping distortion of the lattice similar to that found for the N impurity[3].In particular, the excited-core atom and its nearest-neighbor,labeled a and b,respectively,in Fig.1, move away from each other on the(111)direction.The corresponding displacements from the ideal sites are equal to10.4%and to11.5%of the bond length,respectively,so that the (a,b)-bond is stretched by21.9%.The other atoms move very little:for instance the nearest-neighbor atoms labeled c move by2.4%of the bond length only.This strong localization of the distortion is consistent with the simple scaling arguments discussed above.As a consequence of the atomic relaxation,the non-degenerate level ends up in the gap at1.5eV below the conduction band edge,while the corresponding wavefunction localizes on the stretched bond.The3-fold degenerate level remains close to the conduction band edge,but since the distortion lowers the symmetry from T d to C3v,the3-fold degenerate level splits into a2-fold degenerate E level and a non-degenerate A1level.In Fig.2we report the behavior of the potential energy surfaces corresponding to the ground-state,the A1and the T2core exciton states as a function of the self-trapping dis-tortion.Notice that the distortion gives a total energy gain of0.43eV on the A1potential energy surface.The same distortion causes an increase of the ground-state energy of1.29 eV.Our calculation indicates that the core-exciton behaves like the N impurity[3],support-ing,at least qualitatively,the validity of the equivalent core approximation.The similar behavior of the A1level in the core exciton and in the N impurity case was also pointed out recently in the context of semi-empirical CNDO calculations[9].The differences between the core exciton and the impurity[3]are only quantitative:in particular,the relaxationenergy and especially the distance of the A1level from the conduction band edge are smaller for the core exciton than for the N impurity.Our results suggest the following interpretation of the experimental data of Refs.[4,8]: (i)During X-ray absorption the atoms are in the ideal lattice positions.Dipole transitions from a1s core level to a A1valence level are forbidden,but transitions to the T2level are allowed.In our calculation the T2level is0.2eV lower than the conduction band edge,in good agreement with the core exciton peak observed in X-ray absorption spectra[4,8].(ii) On the T2BO potential energy surface the lattice undergoes a Jahn-Teller distortion which lowers its energy(see Fig.2).(iii)Since the LO phonon energy in diamond(0.16eV)is comparable to the energy spacing between the A1and the T2surfaces,which is less than 0.2eV after the Jahn-Teller distortion,the probability of a non-adiabatic transition from the T2to the A1surface is large.(iv)On the A1level the system undergoes a strong lattice relaxation resulting in a localization of the exciton on a single bond.(v)The self-trapping distortion induces a Stokes shift in the emitted photon energy.If the atomic relaxation were complete the Stokes shift would be equal to1.9eV,which correponds(see Fig.2) to the energy dissipated in the T2-A1transition(0.2eV),plus the energy gained by self trapping on the A1surface(0.43eV),plus the energy cost of the self-trapping distortion on the ground-state energy surface(1.29eV).The data reported in Ref.[8]show a shift of about1eV in the positions of the peaks associated to the1s core exciton in X-ray absorption and emission spectra.The emission peak is very broad,with a large sideband that corresponds to Stokes shifts of up to5eV.As pointed out in Ref.[8],this large sideband is likely to be the effect of incomplete relaxation. This is to be expected since the core exciton lifetime should be comparable to the phonon period[8].As a consequence,the atomic lattice would be able to perform only a few damped oscillations around the distorted minimum structure during the lifetime of the core exciton.We now present our results for the valence excitations.While in the case of a single exciton the energy is minimum for the undistorted crystalline lattice,in the case of a biex-citon wefind that the energy is minimized in correspondence of a localized distortion of theatomic lattice.This is characterized by a large outward symmetric displacement along the (111)direction of the atoms a and b in Fig.1.As a result the(a,b)-bond is broken since the distance between the atoms a and b is increased by51.2%compared to the crystalline bondlength.This distortion can be viewed as a kind of local graphitization in which the atoms a and b change from fourfold to threefold coordination and the corresponding hy-bridized orbitals change from sp3to sp2character.Again,in agreement with the model based on simple scaling arguments,the distortion is strongly localized on a single bond.As a matter of fact and with reference to the Fig.1,the atoms c and d move by1.2%of the bondlength,the atoms e and f move by2.3%,and the atoms not shown in thefigure by less than0.9%.The self-trapping distortion of the biexciton gives rise to two deep levels in the gap: a doubly occupied antibonding level,at1.7eV below the conduction band edge,and an empty bonding level,at1.6eV above the valence band edge.Both states are localized on the broken bond.In Fig.3we show how different BO potential energy surfaces behave as a function of the self-trapping distortion of the valence biexciton.In particular,from thisfigure we see that,while for the biexciton there is an energy gain of1.74eV in correspondence with the self-trapping distortion,the same distortion has an energy cost of1.49eV for the single exciton,and of4.85eV for the unexcited crystal.We notice that,while DFT-LDA predicts self-trapping for the valence biexciton,it does not do so for the single exciton,in agreement with experiment.Similarly to the case of the core exciton the major experimental consequence of the self-trapping of the valence biexciton is a large Stokes shift in the stimulated-absorption spontaneous-emission cycle between the exciton and the biexciton BO surfaces.As it can be seen from Fig.3,this Stokes shift should be equal to3.23eV,i.e.to the sum of the energy gain of the biexciton(1.74eV)and of the energy cost of the exciton(1.49eV) for the self-trapping relaxation.The fundamental gap of diamond is indirect.Thus the spontaneous decay of a Wannier exciton in an ideal diamond crystal is phonon assistedand the radiative lifetime of the exciton is much longer than in direct gap semiconductors. However,after self-trapping of the biexciton,the translational symmetry is broken and direct spontaneous emission becomes allowed.As a consequence the radiative life time of the self-trapped biexciton is much smaller than that of the Wannier ing the DFT-LDA wavefunctions,we obtained a value of∼7ns for the radiative lifetime of the biexciton within the dipole approximation.This is several orders of magnitude larger than the typical phonon period.Therefore the self-trapping relaxation of the valence biexciton should be completed before the radiative decay.A self-trapped biexciton is a bound state of two excitons strongly localized on a single bond.Thus the formation of self-trapped biexcitons requires a high excitonic density.To realize this condition it is possible either to excite directly bound states of Wannier excitons, or to create a high density electron-hole plasma,e.g.by strong laser irradiation.In the second case many self-trapped biexcitons could be produced.This raises some interesting implications.If many self-trapped biexcitons are created,they could cluster producing a macroscopic graphitization.Moreover,since the process of self-trapping is associated with a relevant energy transfer from the electronic to the ionic degrees of freedom,in a high density electron hole plasma biexcitonic self-trapping could heat the crystal up to the melting point in fractions of a ps,i.e in the characteristic time of ionic relaxation.Interestingly,melting ofa GaAs crystal under high laser irradiation has been observed to occur in fractions of a ps[19].In Ref.[19]this phenomenon has been ascribed to the change in the binding properties due to the electronic excitations.Our study on diamond leads one to speculate that in a sub-picosecond melting experiment self-trapping phenomena could play an important role.In conclusion,we have studied excited-state BO potential energy surfaces of crystalline diamond within DFT-LDA.Our calculation predicts self-trapping of the core exciton and provides a coherent description of the X-ray absorption and emission processes,which com-pares well with the experimental data.Moreover,we also predict self-trapping of the valence biexciton,a process characterized by a large local lattice relaxation.This implies a strong Stokes shift in the stimulated absorption-spontaneous emission cycle of about3eV,whichcould be observed experimentally.It is a pleasure to thank F.Tassone for many useful discussions.We acknowledge support from the Swiss National Science Foundation under grant No.20-39528.93REFERENCES∗Present address:Departement of Physics,University of California,Berkeley CA94720, USA.[1]C.A.J.Ammerlaan,Inst.Phys.Conf.Ser.59,81(1981).[2]R.J.Cook and D.H.Whiffen,Proc.Roy.Soc.London A295,99(1966).[3]S.A.Kajihara et al,Phys.Rev.Lett.66,2010(1991).[4]J.F.Morar et al,Phys.Rev.Lett.54,1960(1985).[5]K.A.Jackson and M.R.Pederson,Phys.Rev.Lett.67,2521(1991).[6]J.Nithianandam,Phys.Rev.Lett.69,3108(1992).[7]P.E.Batson,Phys.Rev.Lett.70,1822(1993).[8]Y.Ma et al,Phys.Rev.Lett.71,3725(1993).[9]A.Mainwood and A.M.Stoneham,J.Phys.:Condens.Matter6,4917(1994).[10]R.G.Farrer,Solid State Commun.7,685(1969).[11]W.Hayes and A.M.Stoneham,Defects and defect processes in nonmetallic solids,(Wiley&Sons,New York,1985)pags.29-38.[12]F.Mauri,R.Car,(to be published).[13]The number of equal particles that can be accommodated on one bond of the crystal inthe same quantum state is limited by the Pauli principle.Thus no more than two holes or/and two electrons with opposite spins can be localized on one bond of a sp3bonded semiconductor.[14]G.Bachelet,D.Hamann,and M.Schl¨u ter,Phys.Rev.B26,4199(1982).[15]E.Pehlke and M.Scheffler,Phys.Rev.B47,3588(1993).[16]R.Car and M.Parrinello,Phys.Rev.Lett.55,2471(1985).[17]F.Mauri,R.Car and E.Tosatti,Europhys.Lett.24,431(1993).[18]F.Tassone,F.Mauri,and R.Car,Phys.Rev.B50,10561(1994).[19]orkov,I.L.Shumay,W.Rudolph,and T.Schroder,Opt.Lett.16,1013(1991);P.Saeta,J.-K.Wang,Y.Siegal,N.Bloembergen,and E.Mazur,Phys.Rev.Lett.67, 1023(1991);K.Sokolowski-Tinten,H.Schulz,J.Bialkowski,and D.von der Linde, Applied Phys.A53,227(1991).FIGURESFIG.1.Atoms and bonds in the ideal diamond crystal(left panel).Atoms and bonds after the self-trapping distortion associated with the valence biexciton(right panel).In this case the distance between the atoms a and b increases by51.2%.A similar but smaller distortion is associated with the core exciton:in this case the(a,b)distance is increased by21.9%.FIG.2.Total energy vs self-trapping distortion of the core-exciton.Thefigure displays the BO potential energy surfaces correponding to the ground-state,the A1,and the T2core exciton states.FIG.3.Total energy as a function of the self-trapping distortion of the biexciton.The BO energy surfaces correponding to the ground state,the valence exciton,and the valence biexciton are shown in thefigure.a b ce df(111)ground stateA 1−core excitonT 2−core excitonconduction ideal lattice distorted latticeground statebi−excitonexcitondistorted lattice ideal lattice。

CASTEP Scientific References - 20121.Jian Sun, Miguel Martinez-Canales, Dennis D. Klug, Chris J. Pickard, and Richard J.Needs,Persistence and Eventual Demise of Oxygen Molecules at Terapascal Pressures,Physical Review Letters108 (2012) 045503 ( abstract )2.Miguel Martinez-Canales, Chris J. Pickard, Richard J. Needs,Thermodynamically Stable Phases of Carbon at Multiterapascal Pressures,Physical Review Letters108 (2012) 045704 ( abstract )3. A. Chroneos and A. Dimoulas,Defect configurations of high-k cations in germanium,Journal of Applied Physics111 (2012) 023714 ( abstract )4.Roland Gillen and John Robertson,Hybrid functional calculations of the Al impurity in α quartz: Hole localization andelectron paramagnetic resonance parameters,Physical Review B85 (2012) 014117 ( abstract )5. A. Bhattacharya, S. Bhattacharya, and G. P. Das,Band gap engineering by functionalization of BN sheet,Physical Review B85 (2012) 035415 ( abstract )6.L. Fishwick, M. Walker, M. K. Bradley, D. P. Woodruff, and C. F. McConville,Surface structure of GaP(110): Ion scattering and density functional theory study,Physical Review B85 (2012) 045322 ( abstract )7.Takatsugu Endo, Scarlett Widgeon, Ping Yu, Sabyasachi Sen, and Keiko Nishikawa,Cation and anion dynamics in supercooled and glassy states of the ionic liquid1-butyl-3-methylimidazolium hexafluorophosphate: Results from 13C, 31P, and 19F NMRspectroscopy,Physical Review B85 (2012) 054307 ( abstract )8.James D. Aldous et al.,Cubic MnSb: Epitaxial growth of a predicted room temperature half-metal,Physical Review B85 (2012) 060403 ( abstract )9.N. D. Drummond, V. Zolyomi, and V. I. Fal'ko,Electrically tunable band gap in silicene,Physical Review B85 (2012) 075423 ( abstract )10.Philip W. Avraam, Nicholas D. M. Hine, Paul Tangney, and Peter D. Haynes,Fermi-level pinning can determine polarity in semiconductor nanorods,Physical Review B85 (2012) 115404 ( abstract )11.Naoki Imamura, Hiroshi Mizoguchi, and Hideo Hosono,Superconductivity in LaT M BN and La3T M2B2N3 (T M = Transition Metal) Synthesizedunder High Pressure,J. Am. Chem. Soc.134 (2012) 2516–2519 ( abstract )12.Jakub S. Jirkovsky, Itai Panas, Simon Romani, Elisabet Ahlberg, and David J. Schiffrin,Potential-Dependent Structural Memory Effects in Au-Pd Nanoalloys,J. Phys. Chem. Lett.3 (2012) 315–321 ( abstract )13.Martin Dracinsky, Milos Budesinsky, Beata Warzajtis, and Urszula Rychlewska,Solution and Solid-State Effects on NMR Chemical Shifts in Sesquiterpene Lactones: NMR, X-ray, and Theoretical Methods,J. Phys. Chem. A116 (2012) 680–688 ( abstract )14.Luke A. O'Dell, Christopher I. Ratcliffe, Xianqi Kong, and Gang Wu,Multinuclear Solid-State Nuclear Magnetic Resonance and Density Functional Theory Characterization of Interaction Tensors in Taurine,J. Phys. Chem. A116 (2012) 1008–1014 ( abstract )15.Yutaka Natsume et al.,Chemical-State Analysis of Organic Semiconductors Using Soft X-ray AbsorptionSpectroscopy Combined with First-Principles Calculation,J. Phys. Chem. A116 (2012) 1527–1531 ( abstract )16.Tingting Lin, Xiang-Yang Liu, and Chaobin He,Calculation of Infrared/Raman Spectra and Dielectric Properties of Various Crystalline Poly(lactic acid)s by Density Functional Perturbation Theory (DFPT) Method,J. Phys. Chem. B116 (2012) 1524–1535 ( abstract )17.Marco Delgado et al.,Evolution of Structure and of Grafting Properties of γ-Alumina with PretreatmentTemperature,J. Phys. Chem. C116 (2012) 834–843 ( abstract )ardo Cuervo Reyes, Adam Slabon-Turski, Christian Mensing, and Reinhard Nesper,Spin-Glass Behavior and Electronic Structure of LiEu2Si3,J. Phys. Chem. C116 (2012) 1158–1164 ( abstract )19.Daejin Kim et al.,Pillared Covalent Organic Frameworks with Balanced V olumetric and GravimetricHydrogen Uptake,J. Phys. Chem. C116 (2012) 1479–1484 ( abstract )ardo Cuervo Reyes and Reinhard Nesper,Electronic Structure and Properties of the Alkaline Earth Monosilicides,J. Phys. Chem. C116 (2012) 2536–2542 ( abstract )21.Jung-Il Hong et al.,Magnetism in Dopant-Free ZnO Nanoplates,Nano Letters12 (2012) 576–581 ( abstract )22.Nan Gao, Wei Tao Zheng and Qing Jiang,Density functional theory calculations for two-dimensional silicene with halogenfunctionalization,Physical Chemistry Chemical Physics14 (2012) 257–261 ( abstract )23.Marco Sacchi, Martin C. E. Galbraith and Stephen J. Jenkins,The interaction of iron pyrite with oxygen, nitrogen and nitrogen oxides: a first-principles study,Physical Chemistry Chemical Physics14 (2012) 3627–3633 ( abstract )24.Zhi Yang et al.,Density functional theory studies of Nb-benzene and Nb-borazine sandwich clusters andmolecular wires,Journal of Physics B45 (2012) 025102 ( abstract )25.P Pluengphon, T Bovornratanaraks, S V annarat and U Pinsook,The effects of Na on high pressure phases of CuIn0.5Ga0.5Se2 from ab initio calculation, Journal of Physics: Condensed Matter24 (2012) 095802 ( abstract )26.Ran He, Z S Lin, Tao Zheng, He Huang and C T Chen,Energy band gap engineering in borate ultraviolet nonlinear optical crystals: ab initiostudies,Journal of Physics: Condensed Matter24 (2012) 145503 ( abstract )27.M. G. Brik,First-principles calculations of electronic, optical and elastic properties of Ba2MgWO6 double perovskite,Journal of Physics and Chemistry of Solids73 (2012) 252–256 ( abstract )28.Y. H. Liu et al.,Study on the transformation from NaCl-type Na2TiO3 to layered titanate,Journal of Physics and Chemistry of Solids73 (2012) 402–406 ( abstract )29.Elena Bichoutskaia et al.,High-precision imaging of an encapsulated Lindqvist ion and correlation of its structure and symmetry with quantum chemical calculations,Nanoscale4 (2012) 1190–1199 ( abstract )30.Pan Li et al.,Effects of surface chemistry on the morphology transformation of ZnWO4 nanocrystals: investigated from experiment and theoretical calculations,CrystEngComm14 (2012) 920–928 ( abstract )31.Zhonghua Li et al.,Single crystal titanate-zirconate nanoleaf: Synthesis, growth mechanism and enhanced photocatalytic hydrogen evolution properties,CrystEngComm14 (2012) 1874–1880 ( abstract )32.Yonggang Wang et al.,Hydrothermal growths, optical features and first-principles calculations of sillenite-type crystals comprising discrete MO4 tetrahedra,CrystEngComm14 (2012) 1063–1068 ( abstract )33.Dajiang Mei et al.,LiGaGe2Se6: A New IR Nonlinear Optical Material with Low Melting Point,Inorganic Chemistry51 (2012) 1035–1040 ( abstract )34.Kai Feng et al.,NaGe3P3: a new ternary germanium phosphide featuring an unusual [Ge3P7] ring,Dalton Transactions41 (2012) 484–489 ( abstract )35.Su-Yun Zhang, Chun-Li Hu and Jiang-Gao Mao,New mixed metal selenites and tellurites containing Pd2+ ions in a square planar geometry, Dalton Transactions41 (2012) 2011–2017 ( abstract )36.Caixia Xu, Qian Li, Yunqing Liu, Jinping Wang, and Haoran Geng,Hierarchical Nanoporous PtFe Alloy with Multimodal Size Distributions and Its CatalyticPerformance toward Methanol Electrooxidation,Langmuir28 (2012) 1886–1892 ( abstract )37.Linjuan Zhang et al.,Lattice distortion and its role in the magnetic behavior of the Mn-doped ZnO system, New Journal of Physics14 (2012) 013033 ( abstract )38.Itziar Goikoetxea et al.,Non-adiabatic effects during the dissociative adsorption of O2 at Ag(111)? Afirst-principles divide and conquer study,New Journal of Physics14 (2012) 013050 ( abstract )39.Yongjun Zhou et al.,First-principles study on the catalytic role of Ag in the oxygen adsorption of LaMnO3(0 01) surface,Applied Surface Science258 (2012) 2602–2606 ( abstract )40.Jun Zhou et al.,Density functional theory study on oxygen adsorption in LaSrCoO4: An extended cathode material for solid oxide fuel cells,Applied Surface Science258 (2012) 3133–3138 ( abstract )41.Hui Zhao, Na Qin,The stability boundary of group-III transition metal diboride ScB2 (0 0 0 1) surfaces,Applied Surface Science258 (2012) 3328–3330 ( abstract )42.Qi-Jun Liu et al.,Structural and electronic properties of cubic SrHfO3 surface: First-principles calculations, Applied Surface Science258 (2012) 3455–3461 ( abstract )43.Baojun Wang, Luzhi Song, Riguang Zhang,The dehydrogenation of CH4 on Rh(1 1 1), Rh(1 1 0) and Rh(1 0 0) surfaces: A density functional theory study,Applied Surface Science258 (2012) 3714–3722 ( abstract )44.Li-Ming Yang, Ponniah Ravindran, Ponniah V ajeeston and Mats Tilset,Ab initio investigations on the crystal structure, formation enthalpy, electronic structure, chemical bonding, and optical properties of experimentally synthesized isoreticularmetal-organic framework-10 and its analogues: M-IRMOF-10 (M = Zn, Cd, Be, Mg, Ca, Sr and Ba),RSC Advances2 (2012) 1618–1631 ( abstract )45.Jiri Czernek, Tomasz Pawlak, Marek J. Potrzebowski,Benchmarks for the 13C NMR chemical shielding tensors in peptides in the solid state, Chemical Physics Letters527 (2012) 31–35 ( abstract )46.Min Li, Junying Zhang, Yue Zhang,First-principles calculation of compensated (2N, W) codoping impacts on band gapengineering in anatase TiO2,Chemical Physics Letters528 (2012) 63–66 ( abstract )47.X. P. Yang et al.,Preparation and XRD analyses of Na-doped ZnO nanorod arrays based on experiment and theory,Chemical Physics Letters528 (2012) 16–20 ( abstract )48.Feng Yuan et al.,Structure and hydrogen storage properties of the first rare-earth metal borohydrideammoniate: Y(BH4)3.4NH3,Journal of Materials Chemistry22 (2012) 1061–1068 ( abstract )49.Jiang Xu, Daohui Lai, ZongHan Xie, Paul Munroe and Zhong-Tao Jiang,A critical role for Al in regulating the corrosion resistance of nanocrystallineMo(Si1-x Al x)2 films,Journal of Materials Chemistry22 (2012) 2596–2606 ( abstract )50.Tae Hoon Noh et al.,Photophysical and Photocatalytic Properties of Zn3M2O8 (M = Nb, Ta),Journal of the American Ceramic Society95 (2012) 227–231 ( abstract )51.Y. H. Duan et al.,Elastic constants of AlB2-type compounds from first-principles calculations,Computational Materials Science51 (2012) 112–116 ( abstract )52.Bengt E. Tegner, Graeme J. Ackland,Pseudopotential errors in titanium,Computational Materials Science52 (2012) 2 6 ( abstract )53.D. Sen, R. Thapa, K. Bhattacharjee, K.K. Chattopadhyay,Site dependent metal adsorption on (3 ×3) h-BN monolayer: Stability, magnetic and optical properties,Computational Materials Science51 (2012) 165–171 ( abstract )54.M. G. Brik, C.-G. Ma,First-principles studies of the electronic and elastic properties of metal nitrides XN (X = Sc, Ti, V, Cr, Zr, Nb),Computational Materials Science51 (2012) 380–388 ( abstract )55.Mingjun Pang et al.,First-principles calculations on the crystal, electronic structures and elastic properties of Ag-rich γ' phase approximates in Al-Ag alloys,Computational Materials Science51 (2012) 415–421 ( abstract )56.Souraya Goumri-Said, Nawel Kanoun-Bouayed, Ali H. Reshak, Mohammed BenaliKanoun,On the electronic nature of silicon and germanium based oxynitrides and their related mechanical, optical and vibrational properties as obtained from DFT and DFPT,Computational Materials Science53 (2012) 158–168 ( abstract )57.K. Haddadi, A. Bouhemadou, S. Bin-Omran,Structural, elastic, electronic, chemical bonding and thermodynamic properties ofCaMg2N2 and SrMg2N2: First-principles calculations,Computational Materials Science53 (2012) 204–213 ( abstract )58.Huiyang Gou et al.,Origin of the rigidity in tetragonal MB (M = Cr, Mo and W) and softening of defective WB: First-principles investigations,Computational Materials Science53 (2012) 460–463 ( abstract )59.Haizhou Wang, Yongzhong Zhan, Mingjun Pang,The structure, elastic, electronic properties and Debye temperature of M2AlC (M=V, Nband Ta) under pressure from first-principles,Computational Materials Science54 (2012) 16–22 ( abstract )60.Hai-You Huang, Ming Wu,First principles calculations of hydrogen-induced decrease in the cohesive strength of α-Al2O3 single crystals,Computational Materials Science54 (2012) 81–83 ( abstract )61.Xinrui Cao, Yunsong Li, Xuan Cheng, Ying Zhang,First-principles studies of structural, electronic and optical properties of AB2 (A = Si, Ge and B = O, S) nanotubes,Computational Materials Science54 (2012) 84–90 ( abstract )62.Wei Zhou, Lijuan Liu, Mengying Yuan, Qinggong Song, Ping Wu,Electronic and optical properties of W-doped SnO2 from first-principles calculations,Computational Materials Science54 (2012) 109–114 ( abstract )63.A. Bouhemadou et al.,Theory study of structural parameters, elastic stiffness, electronic structures and lattice dynamics of RBRh3 (R = Sc, Y, La and Lu),Computational Materials Science54 (2012) 336–344 ( abstract )64.M. Romero, R. Escamilla,First-principles calculations of structural, elastic and electronic properties of Nb2SnC under pressure,Computational Materials Science55 (2012) 142–146 ( abstract )65.Benhua Luo, Xueye Wang, Y u Zhang, Yong Xia,First principle calculations for pressure induced structural phase transitions of Fe doped in SrMnO3,Computational Materials Science55 (2012) 199–204 ( abstract )66.Fanjie Kong, Yanhua Liu, Baolin Wang, Yanzong Wang, Lili Wang,Lattice dynamics of PbTe polymorphs from first principles,Computational Materials Science56 (2012) 18–24 ( abstract )67.Yong-Hui Zhang et al.,Tuning the magnetic and transport property of graphene with Ti atom and cluster,Computational Materials Science56 (2012) 95–99 ( abstract )68.Ch. Bheema Lingam, K. Ramesh Babu, Surya P. Tewari, G. Vaitheeswaran,Density functional study of electronic,bonding, and vibrational properties ofCa(NH2BH3)2,Journal of Computational Chemistry33 (2012) 987–997 ( abstract )69.Zhiwei Cui, Feng Gao, Zhihua Cui and Jianmin Qu,Developing a second nearest-neighbor modified embedded atom method interatomicpotential for lithium,Modelling and Simulation in Materials Science and Engineering20 (2012) 015014( abstract )70.Alexei Bosak et al.,New insights into the lattice dynamics of α-quartz,Zeitschrift fur Kristallographie227 (2012) 84–91 ( abstract )71.Zuocai Huang, Jing Feng, Wei Pan,Theoretical investigations of the physical properties of zircon-type YVO4,Journal of Solid State Chemistry185 (2012) 42–48 ( abstract )72.Dajiang Mei et al.,Synthesis, structure, and electronic structure of CsAgGa2Se4,Journal of Solid State Chemistry186 (2012) 54–57 ( abstract )73.Haimin Ding, Jinfeng Wang, Chunyan Li, Jinfeng Nie, Xiangfa Liu,Study of the surface segregation of carbon vacancies in TiC x,Solid State Communications152 (2012) 185–188 ( abstract )74.Mei Xia Xiao, Yong Fu Zhu, Qing Jiang,Improved electromigration reliability of Cu films by doping and interface engineering, Solid State Communications152 (2012) 210–214 ( abstract )75.R. Escamilla, M. Romero, F. Morales,Elastic properties, Debye temperature, density of states and electron-phonon coupling of ZrB12 under pressure,Solid State Communications152 (2012) 249–252 ( abstract )76.Yan Wang, Xi Zhang, Yanguang Nie, Chang Q. Sun,Under-coordinated atoms induced local strain, quantum trap depression and valencecharge polarization at W stepped surfaces,Physica B: Condensed Matter407 (2012) 49–53 ( abstract )77.Yingce Yan et al.,First-principle calculations of dilute nitride GaP1-x N x alloy in zinc-blende structures, Physica B: Condensed Matter407 (2012) 112–115 ( abstract )78.Jie Liu et al.,Influence of Ni and N on generalized stacking-fault energies in Fe-Cr-Ni alloy: A first principle study,Physica B: Condensed Matter407 (2012) 891–895 ( abstract )79.T. Chihi, M. Fatmi, B. Ghebouli,First-principles prediction of metastable niobium and tantalium nitrides M4N5 and M5N6 stoichiometry,Solid State Sciences14 (2012) 80–83 ( abstract )80.Lizhao Liu et al.,Amorphous structural models for graphene oxides,Carbon50 (2012) 1690–1698 ( abstract )81.Jingying Lu, Shang-Peng Gao, Jun Yuan,ELNES for boron, carbon, and nitrogen K-edges with different chemical environments in layered materials studied by density functional theory,ultramicroscopy112 (2012) 61–68 ( abstract )82.Tian Meng-kui, Shangguan Wen-feng,Photocatalytical water decomposition on visible light-driven solid-solution compounds K4Ce2Ta10-x Nb x O30 (x = 0-10),Materials Chemistry and Physics131 (2012) 569–574 ( abstract )83.M.G. Brik, A.M. Srivastava,First-principles calculations of structural, electronic, and elastic properties of MgZrSi2O7, Materials Chemistry and Physics132 (2012) 6–9 ( abstract )84.Maochang Liu, Yuanchang Du, Lijng Ma, Dengwei Jing, Liejin Guo,Manganese doped cadmium sulfide nanocrystal for hydrogen production from waterunder visible light,International Journal of Hydrogen Energy37 (2012) 730–736 ( abstract )85.Ying Lv, Zhian Zhang, Yanqing Lai, and Yexiang Liu,Electrodeposition of Porous Mg(OH)2 Thin Films Composed of Single-CrystalNanosheets,Journal of The Electrochemical Society159 (2012) D187–D189 ( abstract )86.Lu Peng-Fei et al.,Electronic Structure and Optical Properties of Antimony-Doped SnO2 from First-Principle Study,Communications in Theoretical Physics57 (2012) 145–150 ( abstract )87.Chuan-Hui Zhang, Qiong Ran, Jiang Shen,Structural stability of silicene-like nanotubes,Computer Physics Communications183 (2012) 30–33 ( abstract )88.A. Gray et al.,Mapping application performance to HPC architecture,Computer Physics Communications183 (2012) 520–529 ( abstract )89.Wei Li Cheah and Michael W. Finnis,Structure of multilayer ZrO2/SrTiO3,Journal of Materials Science47 (2012) 1631–1640 ( abstract )90.Qi-Jun Liu, Zheng-Tang Liu, Qian-Qian Gao, Li-Ping Feng and Hao Tian,The doping effect of N substituting for different atoms in orthorhombic SrHfO3,Journal of Materials Science47 (2012) 3046–3051 ( abstract )91.A. Yangthaisong,Electronic and Lattice Vibrational Properties of Cubic SrHfO3 from First-PrinciplesCalculations,Journal of Electronic Materials41 (2012) 535–539 ( abstract )92.M. J. Phasha, P. E. Ngoepe,An alternative DFT-based model for calculating structural and elastic properties ofrandom binary HCP, FCC and BCC alloys: Mg-Li system as test case,Intermetallics21 (2012) 88–96 ( abstract )93.Teruyasu Mizoguchi, Katsuyuki Matsunaga, Eita Tochigi, Yuichi Ikuhara,First principles pseudopotential calculation of electron energy loss near edge structures of lattice imperfections,Micron43 (2012) 37–42 ( abstract )94.D.G. McCulloch, D.W.M. Lau, R.J. Nicholls, J.M. Perkins,The near edge structure of cubic boron nitride,Micron43 (2012) 43–48 ( abstract )95.Masataka Hakamada, Fumi Hirashima, Kota Kajikawa and Mamoru Mabuchi,Magnetism of fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt,Applied Physics A106 (2012) 237–244 ( abstract )96.Xing Ming et al.,First-principles study of pressure-induced magnetic transition in siderite FeCO3,Journal of Alloys and Compounds510 (2012) L1–L4 ( abstract )97.Tingting Tan, Zhengtang Liu, Yanyan Li,First-principles calculations of electronic and optical properties of Ti-doped monoclinic HfO2,Journal of Alloys and Compounds510 (2012) 78–82 ( abstract )98.Yongzhong Zhan, Mingjun Pang, Haizhou Wang, Yong Du,The structural, electronic, elastic and optical properties of AlCu(Se1-x Te x)2 compounds from first-principle calculations,Current Applied Physics12 (2012) 373–379 ( abstract )99.Mingjun Pang, Yongzhong Zhan, Haizhou Wang,Ab initio investigation into the structural, electronic and elastic properties of AlCu2TM (TM = Ti, Zr and Hf) ternary compounds,Current Applied Physics12 (2012) 957–962 ( abstract )100.N. Mazumder, A. Bharati, S. Saha, D. Sen, K.K. Chattopadhyay,Effect of Mg doping on the electrical properties of SnO2 nanoparticles,Current Applied Physics12 (2012) 975–982 ( abstract )101.Hongchen Du, Guixiang Wang, Xuedong Gong, Heming Xiao,Theoretical study on the adduct of chlorine trifluoride oxide and borontrifluoride-molecular and crystal structures, vibrational spectrum, and thermodynamic properties,International Journal of Quantum Chemistry112 (2012) 1291–1298 ( abstract )102.Wenlin Zhang, Xiaoqing Wang, Guangqiu Shen, Dezhong Shen,Top-seeded growth, optical properties and theoretical studies of noncentrosymmetricTe2V2O9,Crystal Research and Technology47 (2012) 163–168 ( abstract )103.Baodan Liu et al.,Microstructure and cathodoluminescence study of GaN nanowires without/with P-doping, Crystal Research and Technology47 (2012) 207–212 ( abstract )104.Peter A. Tanner, Guohua Jia, Bing-Ming Cheng, Mikhail G. Brik,Analysis of spectra of neat and lanthanide ion-doped KPb2Cl5 excited by synchrotron radiation,physica status solidi (b)249 (2012) 581–5872 ( abstract )105.A. Trejo, A. Miranda, L. Nino de Rivera, A. Daaz-Mendez, M. Cruz-Irisson, Phonon optical modes and electronic properties in diamond nanowires,Microelectronic Engineering90 (2012) 92–95 ( abstract )106.A. Trejo, J.L. Cuevas, R. Vazquez-Medina, M. Cruz-Irisson,Phonon band structure of porous Ge from ab initio supercell calculation,Microelectronic Engineering90 (2012) 141–144 ( abstract )107.Minoru Osada and Takayoshi Sasaki,A- and B-Site Modified Perovskite Nanosheets and Their Integrations into High-kDielectric Thin Films,International Journal of Applied Ceramic Technology9 (2012) 29–36 ( abstract ) 108.D.L. Geatches, S.J. Clark, H.C. Greenwell,Iron reduction in nontronite-type clay minerals: Modelling a complex system,Geochimica et Cosmochimica Acta81 (2012) 13–27 ( abstract )109.Ting-Feng Yi et al.,Stabilities and electronic properties of lithium titanium oxide anode material for lithium ion battery,Journal of Power Sources198 (2012) 318–321 ( abstract )110.Wenjing Tang, Dechun Li, Shengzhi Zhao, Guiqiu Li and Kejian Yang, First principle study of the elastic properties of InGaAs with different dopingconcentrations of indium,Molecular Simulation38 (2012) 84–89 ( abstract )111.C. L. Zhang et al.,First principles study on mechanical properties of Mg-MgCd interface micro-zone,Molecular Simulation38 (2012) 200–203 ( abstract )112.Mengkui Tian, Wenfeng Shangguan, Wenliang Tao,The photocatalytical activities for water decomposition of K4R2M10O30 (R = Y, La, Ce, Nd, Sm; M = Ta, Nb) and their photophysical properties based on the first principlecalculation,Journal of Molecular Catalysis A: Chemical352 (2012) 95–101 ( abstract )113.Manuel Ramos, Gilles Berhault, Domingo A. Ferrer, Brenda Torres and Russell R.Chianelli,HRTEM and molecular modeling of the MoS2-Co9S8 interface: understanding thepromotion effect in bulk HDS catalysts,Catalysis Science & Technology2 (2012) 164–178 ( abstract )114.Wei Huang, Lulu Sun, Peide Han, Jinzhen Zhao,CH4 dissociation on Co(0001): A density functional theory study,Journal of Natural Gas Chemistry21 (2012) 98–103 ( abstract )115.Lu Yong-Fang, Shi Li-Qun, Ding Wei and Long Xing-Gui,First-Principles Study of Hydrogen Impact on the Formation and Migration of Helium Interstitial Defects in hcp Titanium,Chinese Physics Letters29 (2012) 013102 ( abstract )116.Sun Hong-Guo, Zhou Zhong-Xiang, Yuan Cheng-Xun, Yang Wen-Long and Wang He, Structural, Electronic and Optical Properties of KTa0.5Nb0.5O3 Surface: A First-Principles Study,Chinese Physics Letters29 (2012) 017303 ( abstract )117.Yang Ping et al.,Uniaxial stress influence on lattice, band gap and optical properties of n-type ZnO:first-principles calculations,Chinese Physics B21 (2012) 016803 ( abstract )118.Niu Wen-Xia and Zhang Hong,Ar adsorptions on Al (111) and Ir (111) surfaces: a first-principles study,Chinese Physics B21 (2012) 026802 ( abstract )119.Ye-Yu Li et al.,Synthesis, Crystal and Electronic Structures of Ba3ZnSb2O9 with the 6H-perovskite-type Structure,Chinese Journal of Structural Chemistry31 (2012) 73–78 ( abstract )120.Wang Li, Fang Li-hong, Gong Jian-hong,First-principles study of TiC(110) surface,Transactions of Nonferrous Metals Society of China22 (2012) 170–174 ( abstract )。

你用得着的五个功能强大的（论文写作以及专业英语）翻译网站新年第一帖，我把自己搜集的几个功能非常强大的学术翻译网站分享给大家：1）句库网址：/翻译的非常好，基本上都能找到自己所需的，同时也可以发音，这有利于提高自己的专业英语听力！举例：翻译f irst principles/s ... st+principles在第4个清楚的给出了”第一原理“的解释！2）词博网址：/翻译的很杂，可以供多种选择；而且可以发音，这一点感觉很好！举例：翻译f irst principles/sea ... st+principles没有找到确切的”第一原理“的翻译，但是其他词汇的翻译还好！3）句译网址：/v iewPage.php翻译的很好，基本你都可以在他的翻译中找到合适的！举例：翻译f irst principles/v iewPage.php（这个要自己输入f irt principle)翻译结果非常好！它给出10个例句，结果又8个符合我们的要求，而且给出的例句非常有用，完全是文献里摘出来的！！！我特意放在下面：~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1. 第一过渡金属酞菁分子的电子结构的第一性原理计算A f irst-principles study on the electronic structure of the first transition metal phthalocy anines2. 首要原则First Principles3. 首要教学原理First principles of Instruction4. NiTi合金的第一性原理研究A f irst principles inv estigation on NiTi alloy5. KTa_(0.5)Nb_(0.5)O_3电子结构的第一性原理研究First Principles on KTa_0.5Nb_0.506. NiTi合金的第一原理研究First-Principles Inv estigation of NiTi Alloy7. In-N共掺杂ZnO第一性原理计算First principles study of In-N codoped ZnO8. 碳纳米管的第一性原理研究First-Principles Study of Carbon Nanotubes9. Cu掺杂ZnS的第一性原理计算First-principles Calculation of Cu-doped ZnS10. 分子电子器件第一性原理设计First Principles Design of Molecular Electric Dev ices~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4)词都/查词也还算不错，并且给出很多来自文献的例句，非常不错！举例：翻译f irst principles给出了“第一原理”的翻译，而且给出了很多直接来自文献的例句，有些都是长句。