外压下ZrN结构相变的第一性原理研究

谭心; 贾亦超; 刘学杰

doi:10.11858/gywlxb.2014.02.006

外压下ZrN结构相变的第一性原理研究

doi: 10.11858/gywlxb.2014.02.006

谭心^{1, 2,},
贾亦超²,
刘学杰²

1.
东北大学机械工程与自动化学院，辽宁沈阳 110000
2.
内蒙古科技大学机械工程学院，内蒙古包头 014010

基金项目: 国家自然科学基金(50845065)；内蒙古自然科学基金(2009MS0812)；内蒙古自治区高等学校科学研究项目(NJ10103)；内蒙古科技大学创新基金(2009NC028)

详细信息

作者简介:
谭心(1974—), 女, 副教授, 主要从事纳米材料数字仿真研究.E-mail:heart_tan@126.com

中图分类号: O521.2
计量
- 文章访问数: 7023
- HTML全文浏览量: 2496
- PDF下载量: 329
出版历程
- 收稿日期: 2012-10-22
- 修回日期: 2013-01-16

First-Principles Investigations on Phase Transition of ZrN under External Pressure

1.
School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China
2.
School of Mechanical Engineering, Inner Mongolia University of Science & Technology, Baotou 014010, China

摘要

摘要: 利用基于密度泛函理论的赝势平面波方法，研究了面心立方(fcc)和体心立方(bcc)结构ZrN的平衡态性质以及不同压力下的弹性性质, 计算了fcc和bcc结构ZrN的焓-压关系，讨论了其相对稳定性。通过对总能、焓-压关系、弹性性质以及声子色散关系的分析，推测fcc结构到bcc结构的相变发生在205~235 GPa之间。
- 外压 /
- 第一性原理 /
- ZrN /
- 弹性常数 /
- 声子
Abstract: Using a plane-wave pseudo-potential density functional theory method, the equilibrium and elastic properties of fcc and bcc ZrN structures under different pressures were studied.The relationship between enthalpy and pressure of fcc and bcc structures was also investigated, and their relative stability was discussed.From the analysis of the relationship between the total energy, enthalpy with pressure, elastic properties and the phonon spectra, conclusion is found that transformation from the fcc structural phase to bcc structural phase occurs at 205-235 GPa.
- external pressure /
- ab-initio /
- ZrN /
- elastic constant /
- phonon

HTML全文

图 1 fcc和bcc结构ZrN焓与压力关系曲线

Figure 1. Enthalpy as functions of pressure of fcc and bcc structures of ZrN

下载: 全尺寸图片幻灯片

图 2 fcc-ZrN随压力变化的弹性常数

Figure 2. Elastic constants as a function of pressure of fcc-ZrN structure

下载: 全尺寸图片幻灯片

图 3 零压下ZrN声子谱

Figure 3. Phonon spectrum of ZrN at zero pressure

下载: 全尺寸图片幻灯片

图 4 100 GPa下ZrN声子谱

Figure 4. Phonon spectrum of ZrN at 100 GPa

下载: 全尺寸图片幻灯片

图 5 200 GPa下ZrN声子谱

Figure 5. Phonon spectrum of ZrN at 200 GPa

下载: 全尺寸图片幻灯片

图 6 235 GPa下ZrN声子谱

Figure 6. Phonon spectrum of ZrN at 235 GPa

下载: 全尺寸图片幻灯片

表 1 零压下ZrN平衡态的晶格常数

Table 1. Lattice constant of the equilibrium state of ZrN at zero pressure

Compond	a₀/(nm)
Compond	This study	Ref.[16](Cal.)	Ref.[17](Cal.)	Ref.[14](Exp.)
fcc-ZrN	0.459	0.459 1	0.458 3	0.457
bcc-ZrN	0.228	0.283 6	0.25

下载: 导出CSV

表 2 零压下fcc-ZrN的弹性常数(C₁₁、C₁₂、C₄₄)，剪切模量(G)，体弹模量(B)和杨氏模量(E)

Table 2. The elastic constants (C₁₁, C₁₂, C₄₄), the shear modulus (G), the bulk modulus (B) and the Young's modulus (E) of fcc-ZrN at zero pressure

Data sources	C₁₁/(GPa)	C₁₂/(GPa)	C₄₄/(GPa)	G/(GPa)	B/(GPa)	E/(GPa)
This study	683.41	104.87	162.37	231.57	259.25	535.32
Ref.[16] (Cal.)	512	73	128	219.5	219.33	493.78
Ref.[18] (Exp.)	470	100	160	185	223.33	434.91

下载: 导出CSV

表 3 压力下fcc-ZrN的力学常数

Table 3. Mechanical constants of fcc-ZrN at external pressures

Pressure/(GPa)	C₁₁/(GPa)	C₁₂/(GPa)	C₄₄/(GPa)	G/(GPa)	B/(GPa)
0	683.41	104.87	162.83	231.57	259.25
10	772.24	139.42	187.63	316.41	350.36
20	866.51	146.07	192.17	360.22	386.22
30	956.66	151.64	198.51	402.51	419.98
40	1 043.79	156.83	203.74	443.48	452.48
50	1 127.87	161.05	208.65	483.41	483.32
100	1 519.18	175.22	220.73	671.98	623.21
150	1 871.94	179.96	222.39	845.99	743.95
200	2 153.34	201.60	213.63	975.87	852.18
210	2 279.34	168.52	214.42	1 055.41	872.13
220	2 316.33	179.85	216.26	1 068.24	892.01

下载: 导出CSV

表 4 压力下bcc-ZrN的力学常数

Table 4. Mechanical constants of bcc-ZrN at external pressures

Pressure/(GPa)	C₁₁/(GPa)	C₁₂/(GPa)	C₄₄/(GPa)	G/(GPa)	B/(GPa)
0	583.22	156.40	54.49	213.41	298.67
50	830.78	300.76	175.28	265.01	477.43
100	1 021.35	425.79	290.81	297.78	624.31
150	1 180.43	538.95	411.40	320.74	752.78
200	1 315.92	643.98	528.94	335.97	867.96
250	1 434.26	741.30	645.66	346.48	972.29
300	1 539.82	830.98	758.66	354.42	1 067.26
350	1 633.78	913.92	874.67	359.93	1 153.87

下载: 导出CSV

参考文献(23)

[1]	刘永杰. ZrN薄膜的制备与特性研究[D].阜新: 辽宁工程技术大学, 2002: 12. Liu Y J. The preparation and properties of ZrN films[D]. Fuxing: Liaoning Engineering Technology University, 2002: 12. (in Chinese)
[2]	徐晓明. TiN/ZrN纳米多层膜的制备及其力学性能的研究[D].大连: 大连理工大学, 2006, 12. Xu X M. Fabrication and mechanical properties of TiN/ZrN nano-multilayers[D]. Dalian: Dalian University of Technology, 2006: 12. (in Chinese)
[3]	李广泽. TiN/ZrN纳米多层膜的微结构与力学性能[D].上海: 上海交通大学, 2010: 1. Li G Z. Microstructure and mechanical properties of TiN/ZrN nano-multilayers[D]. Shanghai: Shanghai Jiaotong University, 2010: 1. (in Chinese)
[4]	李成明, 孙晓军, 张增毅, 等. ZrN及其多层膜的性质和耐腐蚀性能[J].材料热处理学报, 2003, 24(4): 55-58, 84. Li C M, Sun X J, Zhang Z Y, et al. Properties and corrosion-resistant of ZrN and ZrN/TiN multilayer films[J]. Transactions of Materials and Heat Treatment, 2003, 24(4): 55-58, 84. (in Chinese)
[5]	Kresse G, Hafner J. Ab initio Hellmann-Feynman molecular dynamics for liquid metals[J]. Journal of Non-Crystalline Solids, 1993, 156-158(2): 956-960.
[6]	Kresse G, Hafner J. Ab initio molecular-dynamics simulation of the liquid-metal-Amorphous-semiconductor transition in germanium[J]. Phys Rev B, 1994, 49: 14251. doi: 10.1103/PhysRevB.49.14251
[7]	Kresse G, Furthmüller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[J]. Comput Mater Sci, 1996, 6: 15-50. doi: 10.1016/0927-0256(96)00008-0
[8]	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: 11169. doi: 10.1103/PhysRevB.54.11169
[9]	Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method[J]. Phys Rev B, 1999, 59: 1758.
[10]	Baroni S, Giannozzi P, Testa A. Green's-function approach to linear response in solids[J]. Phys Rev Lett, 1987, 58(18): 1861-1864. doi: 10.1103/PhysRevLett.58.1861
[11]	Baroni S, Corso A D, Gironcoli S D, et al. First-principles codes for computational crystallography in the Quantum-ESPRESSO package[J]. Z Kristallogr, 2005, 220: 574-579.
[12]	Perdew J P, Chevary J A, Vosko S H, et al. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation[J]. Phys Rev B, 1992, 46: 6671. doi: 10.1103/PhysRevB.46.6671
[13]	Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism[J]. Phys Rev B, 1990, 41: 7892. doi: 10.1103/PhysRevB.41.7892
[14]	Saha B, Acharya J, Sands T D, et al. Electronic structure, phonons, and thermal properties of ScN, ZrN, and HfN: A first-principles study[J]. J Appl Phys, 2010, 107(3): 033715. doi: 10.1063/1.3291117
[15]	Parlinski K, Li Z Q, Kawazoe Y. First-principles determination of the soft mode in cubic ZrO₂[J]. Phys Rev Lett, 1978, 78: 4063.
[16]	Hao A M, Zhou T J, Zhu Yan, et al. First-principles investigations on electronic, elastic and thermodynamic properties of ZrC and ZrN under high pressure[J]. Mater Chem Phys, 2011, 129(1/2): 99-104.
[17]	Liu A Y, Cohen M L. Prediction of new low compressibility solids[J]. Science, 1989, 245(4920): 841-842. doi: 10.1126/science.245.4920.841
[18]	Kim J O, Achenbach J D, Mirkarimi P B, et al. Elastic constants of single-crystal transition-metal nitride films measured by line-focus acoustic microscopy[J]. J Appl Phys, 1992, 72: 1805. doi: 10.1063/1.351651
[19]	Marlo M, Milman V. Density-functional study of bulk and surface properties of titanium nitride using different exchange-correlation functionals[J]. Phys Rev B, 2002, 62: 2899.
[20]	Sinko G V, Smirnow N A. Ab initio calculations of elastic constants and thermodynamic properties of bcc, fcc, and hcp Al crystals under pressure[J]. J Phys: Condens Matter, 2002, 14: 6989. doi: 10.1088/0953-8984/14/29/301
[21]	李宇恒, 胡社军, 曾鹏, 等. ZrN系列薄膜的研究进展[J].工具技术, 2007, 41: 7-12. Li Y H, Hu S J, Zeng P, et al. Development of research in ZrN series film[J]. Tool technology, 2007, 41: 7-12. (in Chinese)
[22]	Isaev E I, Simak S I, Abrikosov I, et al. Phonon related properties of transition metals, their carbides, and nitrides: A first-principles study[J]. J Appl Phys, 2007, 101: 123519. doi: 10.1063/1.2747230
[23]	Chen X J, Struzhkin V V, Kung S, et al. Pressure-induced phonon frequency shifts in transition-metal nitrides[J]. Phys Rev B, 2004, 70: 014501.