高压下新型MAX相M<sub>2</sub>SeC（M=Zr, Hf）的密度泛函理论研究

何鑫; 田辉; 王健; 陈万蕾; 魏兆旋; 刘金程; 齐东丽; 沈龙海

doi:10.11858/gywlxb.20230644

高压下新型MAX相M₂SeC（M=Zr, Hf）的密度泛函理论研究

doi: 10.11858/gywlxb.20230644

何鑫^1,,
田辉^2,*, ,,
王健²,
陈万蕾²,
魏兆旋¹,
刘金程²,
齐东丽²,
沈龙海^2,*, ,

1.
沈阳理工大学材料科学与工程学院, 辽宁沈阳　110159
2.
沈阳理工大学理学院, 辽宁沈阳　110159

基金项目: 国家自然科学基金（12274304）；沈阳理工大学2022年引进高层次人才科研支持经费（1010147001132，1010147001137）

详细信息

作者简介:
何　鑫（1999－），男，硕士研究生，主要从事MAX材料的高压研究. E-mail：1447712537@qq.com

通讯作者:
田　辉（1989－），男，博士，讲师，主要从事MAX材料的高压研究. E-mail：tianhui18@mails.jlu.edu.cn

沈龙海（1977－），男，博士，教授，主要从事纳米材料制备与物性研究. E-mail：shenlonghai@sylu.edu.cn

中图分类号: O521.2; O469
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出版历程
- 收稿日期: 2023-04-20
- 修回日期: 2023-05-11
- 录用日期: 2023-06-07
- 网络出版日期: 2023-09-13
- 刊出日期: 2023-09-01

Density Generalized Function Theory Study on New MAX Phase M₂SeC (M=Zr, Hf) under High Pressure

HE Xin^1
,,
TIAN Hui^{2,*
, ,},
WANG Jian²,
CHEN Wanlei²,
WEI Zhaoxuan¹,
LIU Jincheng²,
QI Dongli²,
SHEN Longhai^{2,*
, ,}

1.
School of Materials Science and Engineering, Shenyang Ligong University, Shenyang 110159, Liaoning, China
2.
School of Science, Shenyang Ligong University, Shenyang 110159, Liaoning, China

摘要

摘要: 基于密度泛函理论的第一性原理，研究了压力对新型MAX相Zr₂SeC和Hf₂SeC晶体结构、弹性、电子和热力学性质的影响。弹性常数和声子计算表明，两种化合物在0～40 GPa压力范围内具有稳定结构。与大多数MAX相不同，Zr₂SeC和Hf₂SeC沿a轴方向比沿c轴方向更容易被压缩，外部压力对Zr₂SeC晶体结构的影响比Hf₂SeC更显著。电子结构计算表明，Zr₂SeC和Hf₂SeC具有金属性质，压力的升高降低了Zr₂SeC和Hf₂SeC在费米能级处的电子态密度，因此提高了Zr₂SeC和Hf₂SeC的稳定性。此外，弹性模量、泊松比和各向异性指数等均随着压力的升高而增大。在0～40 GPa压力范围内，相同压力下Hf₂SeC的弹性模量大于Zr₂SeC，表明高压下Hf₂Se具有比Zr₂SeC更强的抗断裂和抗变形能力。热力学性质计算表明，Zr₂SeC和Hf₂SeC在0～40 GPa压力范围内具有较高的熔化温度。
- M₂SeC /
- 高压 /
- 第一性原理 /
- 晶体结构 /
- 电子结构
Abstract: The effects of pressure on the crystal structure, elasticity, electronic and thermodynamic properties of the new MAX phases Zr₂SeC and Hf₂SeC were investigated by employing the first principle of density generalized function theory. Elastic constants and phonon calculations show that both compounds have stable structure in the pressure range of 0–40 GPa. Unlike most MAX phases, Zr₂SeC and Hf₂SeC are more easily compressed along the a-axis than along the c-axis, and the effect of external pressure on the crystal structure of Zr₂SeC is more significant than Hf₂SeC. Electronic structure calculations show that Zr₂SeC and Hf₂SeC have metallic properties, and the electronic density of states at the Fermi energy level decrease gradually with increasing pressure, thus improving the stability of Zr₂SeC and Hf₂SeC. In addition, the elastic modulus, the Poisson’s ratio and the anisotropy index show an enhancement with increasing pressure. In the pressure range of 0–40 GPa, the elastic modulus of Hf₂SeC is greater than that of Zr₂SeC at the same pressure, indicating that Hf₂SeC has stronger resistance to fracture and deformation than Zr₂SeC at high pressure. Thermodynamic property calculations show that Zr₂SeC and Hf₂SeC have higher melting temperatures in the pressure range of 0–40 GPa.
- M₂SeC /
- high pressure /
- first principles /
- crystal structure /
- electronic structure

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图 1 M₂SeC的晶体结构

Figure 1. Crystal structures of M₂SeC

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图 2 M₂SeC的相对晶格参数和相对体积随压力的变化

Figure 2. Pressure dependence of relative lattice parameters and relative unit cell volume for M₂SeC

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图 3 M₂SeC中M—Se和M—C的相对键长变化

Figure 3. Variations of relative bond lengths between M—Se and M—C atoms of M₂SeC

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图 4 不同压力下M₂SeC的声子色散曲线

Figure 4. Phonon dispersion curves for M₂SeC at different pressures

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图 5 M₂SeC（M=Zr, Hf）的弹性常数随压力的变化

Figure 5. Elastic constants for M₂SeC (M=Zr, Hf) in the dependence of pressure

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图 6 M₂SeC（M=Zr, Hf）的弹性模量随压力的变化

Figure 6. Variations of elastic modulus of M₂SeC (M=Zr, Hf) with pressure

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图 7 M₂SeC（M = Zr，Hf）的泊松比和各向异性指数（A）随压力的变化

Figure 7. Variations of Poisson’s ratio and anisotropic index (A) for the M₂SeC (M = Zr, Hf) in the dependence of pressure

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图 8 不同压力下Zr₂SeC和Hf₂SeC的三维杨氏模量

Figure 8. 3D plot of Young’s modulus (E) surface of Zr₂SeC and Hf₂SeC at various pressures

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图 9 费米能级设置为0 eV时M₂SeC在0、20和40 GPa下的能带结构

Figure 9. Band structure for M₂SeC at pressure 0, 20, and 40 GPa for Fermi level set to 0 eV

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图 10 费米能级设置为0 eV时M₂SeC在0、20和40 GPa下的总态密度和部分态密度

Figure 10. Total and partial density of states for M₂SeC at pressure 0, 20 and 40 GPa for Fermi level set to 0 eV

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表 1 Zr₂SeC和Hf₂SeC的结构参数

Table 1. Structural parameters of Zr₂SeC and Hf₂SeC

Material	Method	a₀/Å	c₀/Å	c₀/a₀	z
Zr₂SeC	This work Exp.^[39] Calc.^[39]	3.476 3.462 3.487	12.633 12.518 12.631	3.634 3.615 3.622	0.095 7 0.096 5
Hf₂SeC	This work Exp.^[40] Calc.^[40]	3.435 3.422 3.436	12.479 12.391 12.452	3.621 3.621 3.624	0.094 6 0.094 5

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表 2 M₂SeC的弹性常数和弹性模量随压力的变化

Table 2. Elastic constant and elastic moduli change of M₂SeC with pressure

M₂AX	Pressure/GPa	C₁₁/GPa	C₁₂/GPa	C₁₃/GPa	C₃₃/GPa	C₄₄/GPa	B/GPa	G/GPa	E/GPa
Zr₂SeC	0 4 8 12 16 20 24 28 32 36 40	272 290 305 320 337 354 366 378 393 404 417	84 91 99 106 113 121 128 135 144 152 161	94 106 118 130 144 157 165 176 187 197 207	293 313 331 349 368 386 397 416 430 446 462	128 140 153 165 178 191 200 212 222 232 243	153 166 179 191 204 217 227 238 249 259 270	106 113 120 126 132 139 143 148 153 157 162	259 277 294 309 326 343 354 368 381 392 404
Hf₂SeC	0 4 8 12 16 20 24 28 32 36 40	288 307 325 341 358 374 391 406 422 437 451	85 93 100 107 115 123 132 141 150 159 167	101 114 127 140 150 161 171 181 192 202 212	307 327 347 366 383 401 418 435 454 470 487	129 144 159 172 185 198 211 223 234 246 257	161 176 189 202 214 226 238 250 262 274 285	111 119 126 133 140 147 153 159 165 170 176	271 291 310 328 345 362 378 393 409 423 437

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表 3 0～40 GPa压力下M₂SeC的横向声速、纵向声速、平均声速和德拜温度

Table 3. Transverse, longitudinal, mean sound velocities, and Debye’s temperaturefor the M₂SeC phase at 0–40 GPa pressure

M₂AX	Pressure/GPa	v_t/(km·s⁻¹)	v_l/(km·s⁻¹)	v_m/(km·s⁻¹)	$\varTheta_{\rm{D}} $/K	T_m/K	Ref.
Zr₂SeC	0 4 8 12 16 20 24 28 32 36 40	3.935 4.013 4.079 4.132 4.200 4.263 4.289 4.335 4.372 4.402 4.437	6.555 6.714 6.859 6.979 7.125 7.260 7.331 7.432 7.527 7.604 7.692	4.353 4.441 4.517 4.578 4.654 4.726 4.756 4.809 4.852 4.886 4.926	508.8 523.4 536.3 547.2 560.0 571.9 578.8 588.3 596.4 603.4 611.1	1 609 1 693 1 767 1 837 1 916 1 995 2 046 2 113 2 178 2 237 2 299
Hf₂SeC	0 4 8 12 16 20 24 28 32 36 40	3.083 3.156 3.218 3.273 3.325 3.374 3.419 3.458 3.498 3.531 3.564	5.149 5.289 5.412 5.523 5.624 5.719 5.811 5.893 5.979 6.056 6.127	3.412 3.493 3.563 3.625 3.683 3.738 3.790 3.833 3.879 3.917 3.954	403.6 416.5 427.8 438.2 447.9 457.1 465.9 473.5 481.4 488.3 495.0	1 678 1 767 1 848 1 927 2 003 2 078 2 154 2 224 2 301 2 371 2 438
Zr₂AlC	0	4.22	6.89	4.66	544		[51]
Hf₂AlC	0	3.38	5.50	3.73	439		[52]

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高压下新型MAX相M2SeC（M=Zr, Hf）的密度泛函理论研究

doi: 10.11858/gywlxb.20230644

作者简介: 何 鑫（1999－），男，硕士研究生，主要从事MAX材料的高压研究. E-mail：1447712537@qq.com

通讯作者: 田 辉（1989－），男，博士，讲师，主要从事MAX材料的高压研究. E-mail：tianhui18@mails.jlu.edu.cn 沈龙海（1977－），男，博士，教授，主要从事纳米材料制备与物性研究. E-mail：shenlonghai@sylu.edu.cn

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Density Generalized Function Theory Study on New MAX Phase M2SeC (M=Zr, Hf) under High Pressure

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高压下新型MAX相M₂SeC（M=Zr, Hf）的密度泛函理论研究

作者简介:
何　鑫（1999－），男，硕士研究生，主要从事MAX材料的高压研究. E-mail：1447712537@qq.com

通讯作者:
田　辉（1989－），男，博士，讲师，主要从事MAX材料的高压研究. E-mail：tianhui18@mails.jlu.edu.cn

沈龙海（1977－），男，博士，教授，主要从事纳米材料制备与物性研究. E-mail：shenlonghai@sylu.edu.cn

Density Generalized Function Theory Study on New MAX Phase M₂SeC (M=Zr, Hf) under High Pressure