LiNbO3和LiTaO3晶体电子结构、平面声波和光折射特性

doi:10.15541/jim20150338

摘要/Abstract

摘要：

本研究基于密度泛函理论的第一性原理超软赝势平面方法计算了LiNbO₃和LiTaO₃的晶格参数、电子结构和弹性常数, 并利用Christoffel方程研究了二者平面声波特征。结果表明: 两者的理论计算晶格参数和弹性常数与实验值接近, 禁带宽度分别为3.78和3.98 eV, 导带底和价带顶主要由O-2p和Nb-4d(Ta-5d)态电子贡献。化学键理论揭示Li和Nb(Ta)与O原子之间有两种成键类型。电荷布局分析结果显示有两种相应的重叠布居数, Nb(Ta)-O键呈现强共价键作用, 并且Nb-O(Ta-O)键长小于Li-O键长。LiNbO₃和LiTaO₃晶体平面声波有两支横波和一支纵波, 纵波速度大于横波速度, 在xy平面呈现六重对称性, 在xz和yz平面各向异性程度强于xy平面, 沿[001]、晶向上两支横波振动速度相等。最后利用模守恒赝势(Norm-conserving)计算了介电常数和静态折射率, 计算表明LiNbO₃晶体的折射性能和非寻常光(e光)离散程度均强于LiTaO₃晶体。

关键词: 第一性原理, 电子结构, 弹性常数, 平面声波, LiNbO3, LiTaO3

Abstract:

Lattice parameters, electronic structures and elastic constants of lithium niobate and lithium tantalate were calculated with the plane wave pseudopotential method based on the first-principles density functional theory. The results show that calculated lattice parameters and elastic constants are in consistent with the corresponding experimental values. It was found that the bottom of the valence band and the top of the conductive band are mainly determined by electron orbits of O-2p and Nb-4d (Ta-5d). The chemical bonds theory indicate that Li, Nb (Ta) and O atoms have two types of bonds, and the Mulliken population analysis exhibits that there are two corresponding bond populations. The Nb-O (Ta-O) covalence is stronger than that of Li-O, and band length shorter than that of Li-O. Moreover, the planar acoustic velocities, studied by Christoffel equation, shows that the three-dimensional images of the planar acoustic wave consisting of a longitudinal wave and two transverse waves, indicating the anisotropic feature. The velocity of the longitudinal wave is larger than those of the two transverse waves. In xz and yz planes, not only the plane projections of the planar acoustic waves show the stronger anisotropy than those in xy plane which have a six-fold symmetry, but also the velocities of the two transverse waves are equal in [001] and directions. The calculated static dielectric constants and optical permittivity indicate the refractive index of LiNbO₃is stronger than that of LiTaO₃.

Key words: first-principles, electronic structure, elastic constants, planar acoustic velocity

中图分类号:

O735

邵栋元, 程南璞, 陈晶晶, 李孝, 陈志谦, 李春梅, 惠群. LiNbO₃和LiTaO₃晶体电子结构、平面声波和光折射特性[J]. 无机材料学报, 2016, 31(2): 171-179.

SHAO Dong-Yuan, CHENG Nan-Pu, CHEN Jing-Jing, LI Xiao, CHEN Zhi-Qian, LI Chun-Mei, HUI Qun. Electronic Structure, Plane Acoustic Velocity and Refractive Property of LiNbO₃and LiTaO₃[J]. Journal of Inorganic Materials, 2016, 31(2): 171-179.

图/表 13

图1 LiNbO3、LiTaO3晶体结构

Fig. 1 The crystal structure of LiNbO3 or LiTaO3

表1 晶格参数(a, c)、密度ρ和体积V

Table 1 Lattice constants (a, c), density ρ and volume V

Material	Method	(a=b)/nm	c/nm	ρ/(g·cm^-3)	V/nm³
LiNbO₃	Exp	0.51483	1.3863		0.131821^[24]
	LDA	0.52332	1.4131	4.395	0.33514
	GGA	0.52447	1.4222	4.251	0.33999
	PBEsol	0.51531	1.3837	4.630	0.31821^[7]
LiTaO₃	Exp	0.5147	1.3766		0.31585^[24]
	GGA	0.5104	1.3546	7.434	0.32610
	LDA	5.050	13.386	7.433	0.29578
	LDA	5.129	13.938	7.400	0.31763^[7]

图2 LiNbO3和LiTaO3晶体分波态密度

Fig. 2 Partial density of states of LiNbO3 and LiTaO3

图3 LiNbO3(a)和LiTaO3(b)能带结构

Fig. 3 Energy band structures of LiNbO3(a) and LiTaO3(b)

图4 LiNbO3和LiTaO3 和电荷密度

Fig. 4 The contour charge densities of LiNbO3 and LiTaO3 in and planes

表2 LiNbO3和LiTaO3原子轨道电子占据数、各原子静电荷、键长(L1, L2)和电子云重叠布居(P1, P2)

Table 2 Atomic orbital populations, atomic charges, bond lengths (L1, L2), and band populations (P1, P2) of LiNbO3 and LiTaO3

Material	Atom	s	p	d	Total	Charge	Bond	L₁/nm	P₁	L₂/nm	P₂
LiNbO₃	Li	-0.17	0	0	-0.17	1.17	O—Nb	0.1971	0.79	0.2184	0.37
	O	1.87	4.87	0	6.75	-0.75	O—Li	0.2084	-0.06	0.2289	0.01
	Nb	0.36	0.38	3.20	3.93	1.07	O—O	0.2869
LiTaO₃	Li	0.22	0	0	-0.22	1.22	O—Ta	0.1852	0.82	0.2047	0.45
	O	1.84	4.99	0	6.83	-0.83	O—Li	0.2093	-0.08	0.2230	0.01
	Ta	0.38	0.41	2.94	3.73	1.27	O—O	0.2669

表3 LiNbO3和LiTaO3晶体弹性常数Cij

Table 3 Elastic constants Cij of LiNbO3 and LiTaO3

Material	Method	C₁₁/GPa	C₁₂/GPa	C₁₃/GPa	C₁₄/GPa	C₃₃/GPa	C₄₄/GPa	C₆₆/GPa
LiNbO₃	LDA	191.7	61.8	71.7	4.6	205.1	57.7	64.9
	GGA	160.11	9.37	19.36	-12.04	161.77	63.50	75.37
	Other work	203.0	53.0	75.0	9	245.0	60	75^[4]
	Other work	196.9	54.8	66.4	0	225.4	58.8^[7]
LiTaO₃	GGA	193.6	44.1	58.9	21.7	292.1	39.3	74.7
	LDA	235.7	64.1	97.6	11.6	256.1	60.7	85.8
	Other work	233.3	47.0	80.0	-11.0	275.0	94.0^[4]
	Other work	235.2	63.8	87.7	0	264.1	102.1^[7]

图5 LiNbO3晶体平面声波三维图(a, b横波模型, c纵波模型)与平面投影图(d~f) (红线和蓝线表示横波, 绿线表示纵波)(LDA)

Fig. 5 The 3-D planar acoustic velocities, in which a and b are transverse wave models, and c longitudinal model, and the plane projected pictures of LiNbO3 with red and blue lines indicating transverse wave velocities, and the green line indicating longitudinal wave velocity (LDA)

图6 LiTaO3晶体平面声波三维图(a, b横波模型, c纵波模型)与平面投影图(d~f) (红线和蓝线表示横波, 绿线表示纵波) (LDA)

Fig. 6 The 3-D plane acoustic velocities, in which a and b are transverse wave models, and c longitudinal model, and the planar projected picture of LiTaO3 crystal with red and blue lines indicating transverse wave velocities, and the green line indicating longitudinal wave velocity (LDA)

表4 不同晶向平面声波速度v1, v2, v3

Table 4 The planar acoustic velocities v1, v2, v3 in different crystal orientations

表5 静态介电常数ε (0)、静态折射率n和光学介电常数ε(∞)

Table 5 Calculated static dielectric constants ε (0), static refractive indices n and optical permittivity ε (∞)

Materal	Method	Index	ε(0)	n	ε(∞)
LiNbO₃	GGA	11	43.6779	2.5401	6.4557
	GGA	33	30.6094	2.4925	6.2126
	LDA	11	43.6779	2.5587	6.5467
	LDA	33	30.6094	2.5408	6.4980
	Other Work^[7]	11	50.42	2.58	6.68
		33	34.16	2.57	6.58
		11	41.50	2.29	5.00
		33	26.00	2.20	4.60
LiTaO₃	GGA	11	47.0227	2.1751	4.7311
	GGA	33	31.9626	2.2199	4.8637
	LDA	11	34.1709	2.2054	4.9278
	LDA	33	34.8047	2.2236	4.9446

图7 折射率no和ne随入射角的变化

Fig. 7 Incidence angle-dependent refractive index no and ne of LiNbO3 (a) and LiTaO3 (b)

图8 LiNbO3和LiTaO3晶体非寻常光离散角

Fig. 8 The discrete angles of extraordinary wave for LiNbO3 and LiTaO3 crystals

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LiNbO₃和LiTaO₃晶体电子结构、平面声波和光折射特性

Electronic Structure, Plane Acoustic Velocity and Refractive Property of LiNbO₃and LiTaO₃

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