氮化锗多形体的四方、 单斜和正交畸变的理论研究

doi:10.7503/cjcu20150921

摘要/Abstract

摘要：

采用量子化学从头算方法, 对Ge₃N₄的四方、单斜和正交结构同质异相体的微结构、态密度和声子谱进行了研究. 形成焓为负值、弹性常数满足Born稳定性准则和声子谱无虚频等结果证实在0~20 GPa范围内3种相都能保持结构稳定. 温度变化影响到晶胞体积, 从而使体模量发生改变. 3种Ge₃N₄都属于半导体, Ge原子和N原子之间存在明显的s-p杂化现象. 当压强增大时诱发了离域电子, 从而使体系的带隙减小. 本文还采用准谐近似对Ge₃N₄的热力学性质进行了研究, 结果表明, 温度和压强对热膨胀系数、熵、热容、德拜温度和格林爱森参数产生了明显影响. m-Ge₃N₄和t-Ge₃N₄的热膨胀系数分别为o-Ge₃N₄的3倍和2倍. t-Ge₃N₄和o-Ge₃N₄的晶格谐振频率基本不受温度的影响.

关键词: 从头算, 氮化锗, 电子结构, 稳定性

Abstract:

Applying the ab initio pseudo-potential technique, we had predicted the lattice structures, density of states, phonon dispersion curves of the recently-discovered tetragonal, monoclinic and orthorhombic phases of Ge₃N₄. The negative formation enthalpy, the satisfactory of Born’s stability criteria and no imaginary frequency can be seen in the phonon dispersion curves proof that the three Ge₃N₄ polymorphs can retain their stabilities in the pressure range of 0―20 GPa. The temperature affects the cell volume, thereby decreasing the bulk modulus. The band gaps show that Ge₃N₄ are semiconductors, while obvious s-p hybridizations can be seen in the density of states. The band gaps decrease with applied pressure, which is due mainly to the generation of non-local electrons. Then, the quasi-harmonic approximation is used to study the thermodynamic properties of Ge₃N₄. The results show that the thermal expansion coefficient, entropy, heat capacity, Debye temperature and Grüneisen parameter are significantly affected by both temperature and pressure. The thermal expansions of m-Ge₃N₄ and t-Ge₃N₄ are three and two times greater than that of o-Ge₃N₄, respectively. The lattice vibration frequency of o-Ge₃N₄ keeps unchanged at different temperatures. Our results are concordant with the experimental data and the previous results. Therefore, the present results indicate that the combination of ab initio calculations and quasi-harmonic approximation is an efficient method to simulate the high-temperature behaviors of different Ge₃N₄ polymorphs. Generally speaking, the results listed in this work are all predictions, which need to be verified by experiments in the near future.

Key words: Ab initio, Germanium nitride, Electronic structure, Stability

中图分类号:

O641

TrendMD:

仓玉萍, 陈东, 杨帆, 杨慧明. 氮化锗多形体的四方、单斜和正交畸变的理论研究. 高等学校化学学报, 2016, 37(4): 674.

CANG Yuping, CHEN Dong, YANG Fan, YANG Huiming. Theoretical Studies on Tetragonal, Monoclinic and Orthorhombic Distortions of Germanium Nitride Polymorphs^†. Chem. J. Chinese Universities, 2016, 37(4): 674.

图/表 9

Fig.1 Crystal structures of tetragonal(A), monoclinic(B) and orthorhombic(C) Ge3N4 phases ^The small and big balls represent the N and Ge atoms, respectively.

Fig.2 Total energy as a function of volume for t-Ge3N4(A), m-Ge3N4(B) and o-Ge3N4(C)

Table 1 Lattice constants a, b, c (nm), formation enthalpy ΔH (eV), bulk modulus B, shear modulus G and elastic constants Cij(GPa) of Ge3N4

Species	t-Ge₃N₄		m-Ge₃N₄		o-Ge₃N₄		c-Ge₃N₄
Species	0 GPa	20 GPa	0 GPa	20 GPa	0 GPa	20 GPa	Calcd.	Expt.
a	0.4410	0.4240	1.0215	0.9735	0.5256	0.5104	a=0.8212	a=0.8173^[34]
b			0.3103	0.2987	1.0074	0.9901	B=221.8	B=242.0^[36]
c	0.8835	0.8524	0.7928	0.7789	0.5319	0.5119	G=170.9	G=176.2^[36]
ΔH	-24.16	-14.06	-24.34	-13.77	-23.09	-14.68	C₁₁=378.8	C₁₁=395.1^[36]
B	146.8	206.8	124.1	189.1	203.4	122.1	C₁₂=147.9	C₁₂=165.4^[36]
G	86.8	85.4	72.8	65.1	296.1	132.5	C₄₄=223.7	C₄₄=234.5^[36]
C₁₁	200.4	249.6	175.2	236.8	300.1	411.6		a=0.8210^[12]
C₁₂	125.5	200.5	31.3	80.3	170.8	268.5		B=296^[22]
C₁₃	109.6	167.7	106.5	169.7	139.7	238.4		B=268.6^[20]
C₂₂			337.9	459.8	418.2	520.7		a=0.8168^[16]
C₂₃			41.1	79.9	99.0	171.9		a=0.8211^[20]
C₂₅			9.8	8.9				a=0.8120^[25]
C₃₃	232.2	286.4	276.7	400.3	311.5	399.1
C₃₅			19.9	35.2		151.8
C₄₄	124.8	140.5	54.6	46.0	140.8
C₄₆			22.4	22.2
C₅₅			90.4	104.2	143.9	164.5
C₆₆	147.6	169.9	62.6	30.8	141.1	161.8

Fig.3 Phonon dispersions and phonon density of states for t-Ge3N4(A), m-Ge3N4(B) and o-Ge3N4(C)^ The blue and red lines are the DOS of N and Ge, respectively.

Fig.4 Total(A) and partial density of states for Ge(B), N(C) atoms of t-Ge3N4

Fig.5 Total(A) and partial density of states for Ge(B), N(C) atoms of m-Ge3N4

Fig.6 Total(A) and partial density of states for Ge(B), N(C) atoms of o-Ge3N4

Fig.7 Temperature dependences of the normalized bulk moduli B/B0(A) and pressure dependences of the bulk moduli B(B) for the new Ge3N4 phases^a. t-Ge3N4; b. m-Ge3N4; c. o-Ge3N4.

Fig.8 Variations of the volume thermal expansion α(V)(A), entropy S(B), heat capacity Cv(C), normalized Debye temperature θD and heat capacity Cv (D) and Grüneisen parameter γ(E) for the three Ge3N4 compounds

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