高压下P42/mnm和Pnnm晶体结构SnO2密度泛函研究

刘克伟; 于杰; 周晓龙; 胡明钰; 占建翔

doi:10.11858/gywlxb.2017.01.012

高压下P42/mnm和Pnnm晶体结构SnO₂密度泛函研究

doi: 10.11858/gywlxb.2017.01.012

昆明理工大学稀贵及有色金属先进材料教育部重点实验室, 云南省新材料制备与加工重点实验室, 云南昆明 650093

基金项目:

国家自然科学联合基金 u0837601

云南省创新团队 2009CI003

稀贵金属综合利用新技术国家重点实验开放课题 SKL-SPM-201510

详细信息

作者简介:
刘克伟(1990—)，男，硕士研究生，主要从事稀贵金属的第一性原理模拟研究.E-mail:634173000@qq.com

通讯作者:
于杰(1976—)，男，博士，副教授，主要从事金属材料及复合材料制备与基础理论研究.E-mail:yujieone@163.com

中图分类号: O641.12
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出版历程
- 收稿日期: 2015-09-15
- 修回日期: 2015-12-09

Rutile and CaCl₂ Structure of SnO₂ Phase Transition under High-Pressure Studied by First-Principles Method

Key Laboratory of Advance Material of Rare Precious and Nonferrous Metals, Education Ministry of China; Key Laboratory of Advanced Materials of Yunnan Province, Kunming University of Science and Technology, Kunming 650093, China

摘要

摘要: 采用基于密度泛函理论(DFT)的平面波超软赝势法，用广义梯度近似(GGA)PBE交换相关泛函，对P42/mnm和Pnnm晶体结构SnO₂的力学性质进行第一性原理计算。计算表明，两种结构SnO₂的晶体结构参数与实验和理论值符合较好。随着压强的增大，P42/mnm型SnO₂的生成焓呈抛物线状缓慢增大，Pnnm型SnO₂的生成焓为一直线迅速上升。P42/mnm结构弹性常数随压强增加规律增大，Pnnm结构弹性常数无规律性变化，外界压强为11.06 GPa时发生相变。两结构中低指数面中Pnnm结构的{100}晶面族之间滑移的可能性最大、最不稳定，{001}晶面族间结合最牢固。金红石型SnO₂维氏硬度计算理论值为10.49 GPa，Pnnm结构为11.42 GPa。德拜温度计算表明，结构对称性高低的差异，造成P42/mnm结构德拜温度在一个小范围内波动，而Pnnm结构德拜温度在8~10 GPa内有突变，呈缓慢下降的趋势。
- 氧化锡 /
- 压强 /
- 第一性原理 /
- 相变 /
- 弹性系数 /
- 德拜温度
Abstract: In the present work we performed the first principles calculations based on the density functional theory and investigated the P42/mnm-Pnnm phase transition and the mechanical properties of SnO₂.For the exchange-correction energy we employed the generalized gradient approximation (GGA) in the Perdew, Burke and Ernzerhof (PBE) form.The elastic stiffness coefficients, c_ij, bulk modulus, shear modulus, Young modulus, Reuss modulus, Voigt modulus and anisotropy factor were calculated for two polymorphs of SnO₂:rutile and CaCl₂ structure.Our results for the structural parameters and elastic constants at the equilibrium phase are in good agreement with the available theoretical and experimental values.Using the enthalpy-pressure data, we observed the rutile to CaCl₂ structural phase transition under 11.06 GPa pressure.In the low index plane of two polymorphs' SnO₂, the most unstable and the possibility of slippage crystal planes was the {100} crystal planes of Pnnm structure, and the {001} crystal planes has the strongest binding force.The Vickers hardness calculated for the P42/mnm of SnO₂ was 10.49 GPa, and the Pnnm structure was 11.42 GPa.Because of the differences in the level of the structure symmetry, results from calculation show that the Debye temperature waverd in a small range for the utile structure but it had mutations in 8-10 GPa and showed a downward trend for the CaCl₂ structure.
- tin oxide /
- pressure /
- first principles /
- phase transition /
- elastic stiffness coefficients /
- Debye temperature

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图 1 金红石型SnO₂晶体结构

Figure 1. Rutile-type and CaCl₂-type crystal structures of SnO₂

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图 2 体积与晶格常数随外界压强变化曲线

Figure 2. Volumeand lattice constant difference corresponding to stable intermediate structural parameters as function of pressure

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图 3 生成焓与外界压强变化曲线

Figure 3. Enthalpy difference corresponding to stable intermediate structural parameters as function of pressure

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图 4 两种结构弹性常数、体模量、剪切模量及杨氏模量随压强的变化关系

Figure 4. Elastic constants c_ij, bulk modulus B, shear modulus and Young modulus of SnO₂ for P42/mnm and Pnnm structures as function of pressure

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表 1 几何优化后不同SnO₂晶体结构的晶胞参数

Table 1. Lattice constants of different SnO₂ crystal structures

Space	p/(GPa)	Unit-cell parameter/(nm)			Volume/(nm³)	Space	p/(GPa)	Unit-cell parameter/(nm)			Volume/(nm³)
Space	p/(GPa)	a	b	c	Volume/(nm³)	Space	p/(GPa)	a'	b'	c'	Volume/(nm³)
P42/mnm	0	0.468 64	0.468 64	0.315 57	0.069 31	Pnnm	6	0.467 76	0.460 02	0.314 02	0.067 57
	2	0.467 02	0.467 02	0.315 06	0.068 72		8	0.467 29	0.457 97	0.313 46	0.067 08
	4	0.465 44	0.465 44	0.314 61	0.068 16		10	0.466 32	0.454 84	0.312 63	0.066 31
	6	0.464 09	0.464 09	0.313 97	0.067 62		12	0.465 49	0.452 87	0.312 27	0.065 83
	8	0.462 55	0.462 55	0.313 69	0.066 99		14	0.464 10	0.451 71	0.311 85	0.065 38
	10	0.461 42	0.461 42	0.313 09	0.066 66		16	0.463 70	0.450 06	0.311 27	0.064 96
	12	0.460 14	0.460 14	0.312 72	0.066 21		18	0.461 92	0.449 14	0.311 06	0.064 53
	14	0.458 66	0.458 66	0.312 58	0.065 76		20	0.462 17	0.446 45	0.310 48	0.064 06

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表 2 各向异性系数及各向异性压缩因子理论计算值

Table 2. Calculated shear anisotropic factors A₁, A₂, A₃, and A_B, A_G for SnO₂

Species	A₁	A₂	A₃	A_B/(%)	A_G/(%)
P42/mnm	1.030 1	1.030 1	5.969 3	1.42	16.33
Pnnm	0.955 1	1.038 6	8.227 6	7.29	25.84

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表 3 两不同结构维氏硬度

Table 3. Calculated Vickers hardness of SnO₂ type of P42/mnm and Pnnm

Species	Coordination	Z_Sn	Z_O	n_Sn	n_O	d/(nm)	N_e/(nm^-3)	H_V^x/(GPa)	H_V/(GPa)
P42/mnm	Pol(1)	5	6	4	2	0.199 0	478	11.83	10.49
P42/mnm	Pol(2)	4	6	4	2	0.201 0	418	10.08	13.80^[16]
Pnnm	Pol(1)	5	6	4	2	0.197 8	310	12.73	11.42
Pnnm	Pol(2)	4	6	4	2	0.198 5	400	11.02	11.42

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表 4 两不同结构的横波、纵波、总晶格振动波矢和德拜温度

Table 4. Transverse, longitudinal, average elastic wave velocities and Debye temperature for P42/mnm and Pnnm structures

Space	p/(GPa)	ν_P	ν_S	ν_m	Θ_D/(K)
P42/mnm	0	3.95	7.29	5.19	492
	2	4.02	7.42	5.29	508
	4	4.03	7.50	5.30	507
	6	3.91	7.52	5.19	494
	8	4.03	7.68	5.34	509
	10	3.92	7.67	5.21	495
	12	3.96	7.78	5.29	501
	14	3.89	7.78	5.21	492
Pnnm	6	3.02	7.68	5.12	488
	8	3.00	7.04	5.23	497
	10	2.96	6.31	4.12	390
	12	2.94	7.11	4.06	384
	14	2.92	7.14	4.04	381
	16	2.90	7.54	4.03	378
	18	2.89	7.27	4.02	375
	20	2.86	6.99	3.97	371

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