压力作用下Mg<sub>2</sub>X(X=Si, Ge)相热力学性质的第一性原理研究

张乐婷; 赵宇宏; 孙远洋; 邓世杰; 吉如意; 韩培德

doi:10.11858/gywlxb.20170630

压力作用下Mg₂X(X=Si, Ge)相热力学性质的第一性原理研究

doi: 10.11858/gywlxb.20170630

1.
中北大学材料科学与工程学院, 山西太原 030051
2.
太原理工大学材料科学与工程学院, 山西太原 030024

基金项目:

国家自然科学基金 51774254

国家自然科学基金 51774253

国家自然科学基金 51701187

国家自然科学基金 U1610123

国家自然科学基金 51674226

国家自然科学基金 51574207

国家自然科学基金 51574206

山西省科技重大专项 MC2016-06

详细信息

作者简介:
张乐婷(1992-), 女, 硕士研究生, 主要从事材料的模拟计算研究.E-mail:1092720809@qq.com

通讯作者:
赵宇宏(1974-), 女, 博士, 教授, 主要从事计算机多尺度模拟研究.E-mail:zhaoyuhong@nuc.edu.cn

中图分类号: O521.2;TG146.2
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出版历程
- 收稿日期: 2017-08-14
- 修回日期: 2017-10-25

Thermodynamic Properties of Mg₂X (X=Si, Ge) Phases under Pressure by First-Principles Calculations

1.
College of Materials Science and Engineering, North University of China, Taiyuan 030051, China
2.
College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China

摘要

摘要: 采用基于密度泛函理论的第一性原理方法，研究了压力作用下Mg₂Si和Mg₂Ge的结构、弹性和热力学性质。计算结果表明：0 GPa压力作用下两者的晶格参数与实验值以及其他理论值吻合较好，且相对晶格常数a/a₀和晶胞体积V/V₀均随压力的增大而减小；在0~25 GPa压力作用下，Mg₂Si和Mg₂Ge相体模量B、剪切模量G、杨氏模量E均随压力的增大而增大，材料的刚度和塑性均增强，当压力达到15 GPa时，材料由脆性转变为延性。最后借助准谐德拜模型和Gibbs软件，研究了温度与压力对Mg₂Si和Mg₂Ge的德拜温度、体模量、热容和热膨胀系数的影响。
- 第一性原理 /
- Mg₂Si /
- Mg₂Ge /
- 结构性质 /
- 弹性性质 /
- 热力学性质
Abstract: The structural, elastic and thermodynamic properties of Mg₂Si and Mg₂Ge phases under pressure were calculated using the first-principles based on the density functional.The calculated results indicated that the lattice parameters under 0 GPa are fairly consistent with the experimental value and other theoretical data.The ratio of a/a₀ and V/V₀ decreased as the external pressure increases.An appropriate pressure (0-25 GPa) can improve their stiffness and plasticity because the bulk modulus B, shear modulus G, and Young's modulus E almost linearly increase with pressure.The brittleness of the material turns to ductility at 15 GPa.Finally, the effect of temperature and pressure on the Debye temperature, bulk modulus, heat capacity and linear thermal expansion coefficient was studied using the quasi-harmonic Debye model and Gibbs software.
- first-principles /
- Mg₂Si /
- Mg₂Ge /
- structural property /
- elastic property /
- thermodynamic property

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图 1 Mg₂X(X=Si，Ge)的晶胞结构

Figure 1. Crystal structure of Mg₂X (X=Si, Ge)

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图 2 Mg₂Si和Mg₂Ge的相对晶格参数(a/a₀)和相对体积(V/V₀)随外压力的变化

Figure 2. Variations of relative lattice parameters (a/a₀) and relative unit cell volume (V/V₀) of Mg₂Si and Mg₂Ge with pressure

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图 3 Mg₂X(X=Si，Ge)体积比V/V₀随压力变化关系

Figure 3. Relative unit cell volume V/V₀ of Mg₂Si and Mg₂Ge with pressure

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图 4 Mg₂Si和Mg₂Ge的体积模量B、剪切模量G和杨氏模量E随压力的变化情况

Figure 4. Variation of bulk modulus B, shear modulus G, Young's modulus E of Mg₂Si and Mg₂Ge with pressure

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图 5 Mg₂Si与Mg₂Ge德拜温度随温度与压强变化关系

Figure 5. Debye temperature of Mg₂Si and Mg₂Ge at various pressures and temperatures

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图 6 Mg₂Si和Mg₂Ge体模量随温度和压力的变化

Figure 6. Bulk modulus of Mg₂Si and Mg₂Ge at various pressures and temperatures

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图 7 Mg₂Si和Mg₂Ge热容随温度和压力的变化

Figure 7. Heat capacity of Mg₂Si and Mg₂Ge at various pressures and temperatures

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图 8 Mg₂Si和Mg₂Ge热膨胀系数随温度和压力的变化

Figure 8. Linear thermal expansion coefficient of Mg₂Si and Mg₂Ge at various pressures and temperatures

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表 1 Mg₂Si和Mg₂Ge的晶格常数

Table 1. Equilibrium crystal parameters (a, c) of Mg₂Si and Mg₂Ge

Phase	This work		Calc.		Exp.
Phase	a/nm	c/nm	a/nm	c/nm	a/nm	c/nm
Mg₂Si	0.635 1	0.635 1	0.638 7^[4]	0.638 7^[4]	0.633 8^[15]	0.633 8^[15]
Mg₂Ge	0.455 3	0.455 3	0.631 8^[15]	0.631 8^[15]	0.639 3^[15]	0.639 3^[15]

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表 2 Mg₂Si和Mg₂Ge的弹性常数

Table 2. Moduli of Mg₂Si and Mg₂Ge

Phase	p/GPa	C₁₁	C₁₂	C₄₄	B/GPa	G/GPa	E/GPa	G/B	υ
	0	110.48	22.04	44.72	51.52	44.52	103.69	0.86	0.160
	Calc.^[18]	115.21	22.14	43.11	53.163	44.48	104.34	0.84	0.173
	5	143.03	42.46	52.29	75.99	51.49	126.00	0.68	0.22
Mg₂Si	10	158.67	52.89	61.20	88.15	57.87	142.45	0.66	0.23
	15	180.72	68.97	61.32	106.22	59.14	149.65	0.56	0.27
	20	200.49	85.12	64.56	123.58	61.81	158.93	0.50	0.27
	25	218.17	102.33	66.19	140.94	62.88	164.22	0.45	0.31
	0	105.80	21.18	41.90	49.39	42.07	98.29	0.85	0.17
	Calc.^[19]	113.56	20.56	45.70	51.56	46.02	106.40	0.85	0.16
	5	140.74	45.52	55.27	77.26	52.21	127.83	0.68	0.22
Mg₂Ge	10	154.03	50.75	54.12	85.17	53.13	131.95	0.62	0.24
	15	175.03	68.13	59.79	103.76	57.25	145.07	0.55	0.27
	20	191.53	83.03	61.82	119.19	58.79	151.48	0.49	0.29
	25	209.82	101.41	63.24	137.54	59.62	156.29	0.43	0.31

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参考文献(20)

[1]	陈茜, 谢泉, 杨创华, 等.掺杂Mg₂Si电子结构及光学性质的第一性原理计算[J].光学学报, 2009, 29(1):229-235. http://cqvip.com/QK/95626X/200901/29234382.html CHEN Q, XIE Q, YANG C H, et al.First-principles calculation of electronic structure and optical properties of Mg₂Si with doping[J].Acta Optica Sinica, 2009, 29(1):229-235. http://cqvip.com/QK/95626X/200901/29234382.html
[2]	傅利, 赵宇宏, 杨晓敏, 等.Mg-Al-Si-Ca合金系金属间化合物的电子结构和力学性能的第一性原理计算[J].稀有金属材料与工程, 2014, 43(11):2733-2738. http://www.cnki.com.cn/Article/CJFDTotal-COSE201411035.htm FU L, ZHAO Y H, YANG X M, et al.First-principle calculation for electronic structure and mechanical properties of intermetallics in Mg-Al-Si-Ca Alloy[J].Rare Metal Materials and Engineering, 2014, 43(11):2733-2738. http://www.cnki.com.cn/Article/CJFDTotal-COSE201411035.htm
[3]	ZHANG J, FAN Z, WANG Y Q, et al.Microstructural development of Al-15 wt.% Mg₂Si in situ composite with mischmetal addition[J].Materials Science and Engineering A, 2000, 281(1/2):104-112. https://www.researchgate.net/publication/271916998_Application_Prospects_and_Microstructural_Features_in_Laser-Induced_Rapidly_Solidified_High-Entropy_Alloys
[4]	余本海, 刘墨林, 陈东.第一性原理研究Mg₂Si同质异相体的结构、电子结构和弹性性质[J].物理学报, 2011, 60(8):584-594. http://wuxizazhi.cnki.net/Sub/jcwl/a/WLXB201107076.html YU B H, LIU M L, CHEN D.First principles study of structural, electronic and elastic properties of Mg₂Si polymorphs[J].Acta Physica Sinica, 2011, 60(8):584-594. http://wuxizazhi.cnki.net/Sub/jcwl/a/WLXB201107076.html
[5]	TANI J, KIDO H.First-principles and experimental studies of impurity doping into Mg₂Si[J].Intermetallics, 2008, 16(3):418-423. doi: 10.1016/j.intermet.2007.12.001
[6]	JUND P, VIENNOIS R, COLINET C, et al.Lattice stability and formation energies of intrinsic defects in Mg₂Si and Mg₂Ge via first principles simulations[J].Journal of Physics:Condensed Matter, 2013, 25(3):4469-4487.
[7]	GANESHAN S, SHANG S L, WANG Y, et al.Temperature dependent elastic coefficients of Mg₂X (X=Si, Ge, Sn, Pb) compounds from first-principles calculations[J].Journal of Alloys and Compounds, 2010, 498(2):191-198. doi: 10.1016/j.jallcom.2010.03.153
[8]	WANG H, JIN H, CHU W, et al.Thermodynamic properties of Mg₂Si and Mg₂Ge investigated by first principles method[J].Journal of Alloys and Compounds, 2010, 499(1):68-74. doi: 10.1016/j.jallcom.2010.01.134
[9]	张建新, 高爱华, 郭学锋, 等.Mg-Sn-Si合金中Mg₂(Si, Sn)复合相的结构与性能研究[J].物理学报, 2013, 62(17):483-488. ZHANG J X, GAO A H, GUO X F, et al.Study on microstructure and poperties of Mg₂(Si, Sn) compound phase in Mg-Sn-Si magnesium alloy[J].Acta Physica Sinica, 2013, 62(17):483-488.
[10]	SHI D M, WEN B, MELNIK R.First-principles studies of Al-Ni intermetallic compounds[J].Journal of Solid State Chemistry, 2009, 182(10):2664-2669. doi: 10.1016/j.jssc.2009.07.026
[11]	WANG F, SUN S J, YU B, et al.First principles investigation of binary intermetallics in Mg-Al-Ca-Sn alloy:stability, electronic structures, elastic properties and thermodynamic properties[J].Transactions of Nonferrous Metals Society of China, 2016, 26(1):203-212. doi: 10.1016/S1003-6326(16)64107-9
[12]	FAGAN S B, MOTA R, BAIERLE R J.Stability investigation and thermal behavior of a hypothetical silicon nanotube[J].Journal of Molecular Structure, 2001, 539(1/2/3):101-106. https://www.sciencedirect.com/science/article/pii/S0166128000007776
[13]	CHADI D J.Special points for Brillouin-zone integrations[J].Physical Review B, 1977, 16(4):5188-5192.
[14]	FISCHER T H, ALMLOF J.General methods for geometry and wave function optimization[J].Journal of Physical Chemistry, 1992, 96(24):9768-9774. doi: 10.1021/j100203a036
[15]	TANI J, KIDO H.Lattice dynamics of Mg₂Si and Mg₂Ge compounds from first-principles calculations[J].Computational Materials Science, 2008, 42(3):531-536. doi: 10.1016/j.commatsci.2007.08.018
[16]	CAO Y, ZHU J C, NONG Z S, et al.First-principles studies of the structural, elastic, electronic and thermal properties of Ni₃Nb[J].Computational Materials Science, 2013, 77(3):208-213.
[17]	PUGH S F.Relations between the elastic moduli and the plastic properties of polycrystalline pure metals[J].Philosophical Magazine, 1954, 45(367):823-843.
[18]	任玉艳, 刘桐宇, 李英民.Mg₂Si金属间化合物的结构稳定性, 热力学和力学性能的第一性原理计算[J].中国科学:物理学力学天文学, 2016, 46(8):26-33. http://wuxizazhi.cnki.net/Sub/jcwl/a/WLXB201107076.html REN Y Y, LIU T Y, LI Y M.First-principles calculation on structure stability, thermodynamic and mechanical properties of Mg₂Si intermetallics[J].Scientia Sinica physica, Mechanica and Astronomica, 2016, 46(8):26-33. http://wuxizazhi.cnki.net/Sub/jcwl/a/WLXB201107076.html
[19]	常少梅.压力作用下Mg₂X(X=Sn, Ge, Si)晶体结构与弹性性质[J].兰州理工大学学报, 2012, 38(5):168-171. CHANG S M.Structural and elastic properties of Mg₂X (X=Sn, Gn, Si) under pressure[J].Journal of Lanzhou University of Technology, 2012, 38(5):168-171.
[20]	GUO S D.First-principles calculations of Mg₂X (X=Si, Ge, Sn) semiconductors with the calcium fluorite structure[J].Journal of Semiconductors, 2015, 36(5):8-13.