高压下新型MAX相Zr3InC2的第一性原理研究

doi:10.15541/jim20250042

无机材料学报 ›› 2025, Vol. 40 ›› Issue (12): 1414-1424.DOI: 10.15541/jim20250042

高压下新型MAX相Zr₃InC₂的第一性原理研究

郭佳芯¹(), 陈美娟¹, 吴浩¹, 郑潇然¹, 闵楠¹, 田辉¹(), 齐东丽¹, 李全军², 都时禹³^,⁴, 沈龙海¹()

1.沈阳理工大学理学院, 沈阳 100159
2.吉林大学超硬材料国家重点实验室, 长春 130012
3.中国科学院宁波材料技术与工程研究所, 宁波 315201
4.中国石油大学(华东) 材料科学与工程学院, 青岛 266580

收稿日期:2025-02-04 修回日期:2025-04-10 出版日期:2025-12-20 网络出版日期:2025-04-15
通讯作者: 沈龙海, 教授. E-mail: shenlonghai@sylu.edu.cn;
田辉, 讲师. E-mail: huitian2022sylu@126.com
作者简介:郭佳芯(2001-), 女, 硕士研究生. E-mail: 463256229@qq.com
基金资助:
国家自然科学基金(12274304);国家自然科学基金(12404060);2024年辽宁省自然科学基金计划(博士科研启动项目)(2024-BS-115);辽宁省教育厅项目(自主选题项目)(LJ212410144038)

First-principles Study of Novel MAX Phase Zr₃InC₂ under High Pressure

GUO Jiaxin¹(), CHEN Meijuan¹, WU Hao¹, ZHENG Xiaoran¹, MIN Nan¹, TIAN Hui¹(), QI Dongli¹, LI Quanjun², DU Shiyu³^,⁴, SHEN Longhai¹()

1. School of Science, Shenyang Ligong University, Shenyang 100159, China
2. State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China
3. Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China
4. School of Materials Science and Engineering, China University of Petroleum (East China), Qingdao 266580, China

Received:2025-02-04 Revised:2025-04-10 Published:2025-12-20 Online:2025-04-15
Contact: SHEN Longhai, professor. E-mail: shenlonghai@sylu.edu.cn;
TIAN Hui, lecturer. E-mail: huitian2022sylu@126.com
About author:GUO Jiaxin (2001-), female, Master candidate. E-mail: 463256229@qq.com
Supported by:
National Natural Science Foundation of China(12274304);National Natural Science Foundation of China(12404060);2024 Liaoning Provincial Natural Science Foundation Program (Doctoral Research Initiation Project)(2024-BS-115);Liaoning Provincial Department of Education Project (Independent Selection Project)(LJ212410144038)

摘要/Abstract

摘要：

新型In基MAX相Zr₃InC₂因其优异的物理性能而受到广泛关注, 但其在高压下的研究仍较为有限。基于密度泛函理论(DFT)的第一性原理, 本工作系统研究了压力对新型MAX相Zr₃InC₂的晶体结构、力学性质、电子结构和热力学性质的影响。通过与Zr₃AlC₂进行对比, 揭示了A位元素由Al替换为In对MAX相材料的晶体结构、物理性质及两者在高压环境下响应的影响。计算得到的Zr₃InC₂和Zr₃AlC₂晶格参数与之前的实验报道相一致。晶格参数随压力的变化结果表明, Zr₃InC₂和Zr₃AlC₂存在明显的各向异性压缩, 即沿c轴方向的压缩率显著高于沿a轴方向。弹性常数和声子色散曲线的结果表明, Zr₃InC₂在0~50 GPa范围内保持力学稳定和动力学稳定。此外, 不同压力下的泊松比结果表明, Zr₃InC₂在常压下为脆性, 随着压力的增加, 其脆性逐渐减弱, 40 GPa时首次呈现韧性, 其中泊松比和柯西压力在50 GPa下存在差异, 表明Zr₃InC₂在高压下可能处于脆韧转变的临界区。经对比发现, Zr₃InC₂的力学性质比Zr₃AlC₂在高压下的响应更为敏感。电子结构的计算结果显示Zr₃InC₂具有金属性。热力学分析显示, Zr₃InC₂在常压下具有相对较低的热膨胀系数, 随着压力的增加, Zr₃InC₂的德拜温度和最小导热系数显著上升, 这表明压力能有效调节Zr₃InC₂的热力学性能, 为其在高温领域中的潜在应用提供了理论支持。

关键词: 高压, 第一性原理, MAX相, 晶体结构, 电子结构

Abstract:

The novel In-based MAX phase Zr₃InC₂ has recently attracted considerable attention for its excellent physical properties, yet investigations into its behaviour under high pressure remain limited. This study systematically investigates effects of pressure on crystal structure, mechanical properties, electronic structure, and thermodynamic behavior of the novel MAX phase Zr₃InC₂ using first-principles calculations based on density functional theory (DFT). Comparative analysis with Zr₃AlC₂ reveals how substituting Al with In at the A-site influences structural and physical properties, as well as responses under high-pressure conditions. Calculated lattice parameters for both Zr₃InC₂ and Zr₃AlC₂ show good agreement with previous experimental reports. Results indicate pronounced anisotropic compression, with significantly higher compressibility along the c-axis than the a-axis. Elastic constants and phonon dispersion curves confirm mechanical and dynamic stability of Zr₃InC₂ up to 50 GPa. Poisson’s ratio analysis suggests brittle behavior at ambient pressure with ductility first appearing at 40 GPa. Discrepancy between the Poisson’s ratio and the Cauchy pressure at 50 GPa suggests that Zr₃InC₂ may be near the critical region of a brittle-to-ductile transition under high pressure. Compared with Zr₃AlC₂, Zr₃InC₂ exhibits greater sensitivity in mechanical properties under high pressure. Electronic structure calculations reveal its metallic nature. Thermodynamic analysis shows a relatively low thermal expansion coefficient at ambient pressure, while increased pressure leads to a significant rise in Debye temperature and minimum thermal conductivity. These findings highlight tunability of Zr₃InC₂’s thermodynamic properties under pressure, offering theoretical support for potential high-temperature applications.

Key words: high pressure, first principles, MAX phase, crystal structure, electronic structure

中图分类号:

O469

郭佳芯, 陈美娟, 吴浩, 郑潇然, 闵楠, 田辉, 齐东丽, 李全军, 都时禹, 沈龙海. 高压下新型MAX相Zr₃InC₂的第一性原理研究[J]. 无机材料学报, 2025, 40(12): 1414-1424.

GUO Jiaxin, CHEN Meijuan, WU Hao, ZHENG Xiaoran, MIN Nan, TIAN Hui, QI Dongli, LI Quanjun, DU Shiyu, SHEN Longhai. First-principles Study of Novel MAX Phase Zr₃InC₂ under High Pressure[J]. Journal of Inorganic Materials, 2025, 40(12): 1414-1424.

图/表 20

图1 (a) Zr3InC2和(b) Zr3AlC2的晶体结构

Fig. 1 Crystal structures of (a) Zr3InC2 and (b) Zr3AlC2

表1 0 GPa压力下Zr3InC2和Zr3AlC2的结构参数[18,41]

Table 1 Structural parameters of Zr3InC2 and Zr3AlC2 at 0 GPa pressure[18,41]

MAX	a/Å	c/Å	V/Å³	c/a	Ref.
Zr₃InC₂	3.332	20.177	200.776	6.055	This work
Zr₃InC₂	3.351	20.251	194.004	6.042	[18]
Zr₃AlC₂	3.337	19.940	192.362	5.975	This work
Zr₃AlC₂	3.328	20.011	192.01	6.011	[41]

图2 (a) Zr3InC2和(b) Zr3AlC2的相对晶格参数和相对体积随压力变化的关系

Fig. 2 Variations of relative lattice parameters and relative volume of (a) Zr3InC2 and (b) Zr3AlC2 with pressure

表2 0~50 GPa压力下Zr3InC2和Zr3AlC2的弹性常数和弹性模量

Table 2 Elastic constants and elastic moduli of Zr3InC2 and Zr3AlC2 under 0-50 GPa pressure

MAX	Pressure/ GPa	C₁₁/ GPa	C₁₂/ GPa	C₁₃/ GPa	C₃₃/ GPa	C₄₄/ GPa	C₆₆/ GPa	B/ GPa	G/ GPa	E/ GPa	Cauchy pressure
Zr₃InC₂	0	300	73	65	243	87	114	138	100	241	-14
	5	308	96	80	277	102	106	156	104	256	-6
	10	343	95	95	302	112	124	173	116	285	-17
	15	360	104	106	326	121	128	186	122	301	-17
	20	376	119	120	352	128	128	202	126	314	-9
	25	401	124	134	376	139	138	218	135	337	-15
	30	416	136	146	399	148	140	232	140	351	-12
	35	435	142	157	418	154	147	244	146	366	-12
	40	438	164	168	436	160	137	257	145	366	4
	45	471	159	184	457	172	156	273	158	396	-13
	50	487	165	194	474	177	161	284	162	408	-12
Zr₃AlC₂	0	310	72	71	253	103	119	144	108	260	-31
	5	331	82	82	272	112	125	158	115	278	-30
	10	353	94	96	286	130	129	173	124	301	-36
	15	373	99	107	316	134	137	187	130	317	-35
	20	390	111	120	337	143	139	202	136	333	-32
	25	402	128	133	355	152	137	216	139	342	-24
	30	422	130	143	370	161	146	227	146	361	-31
	35	432	143	154	384	164	145	239	147	366	-21
	40	442	150	161	398	170	146	247	150	374	-20
	45	444	166	170	401	172	139	255	147	371	-6
	50	449	179	180	408	176	135	265	147	372	3

图3 (a) Zr3InC2和(b) Zr3AlC2的弹性常数随压力变化的关系

Fig. 3 Variations of elastic constants of (a) Zr3InC2 and (b) Zr3AlC2 with pressure

图4 Zr3InC2和Zr3AlC2的键长随压力变化的关系

Fig. 4 Variations of bond lengths of Zr3InC2 and Zr3AlC2 with pressure

图5 (a) Zr3InC2和(b) Zr3AlC2的弹性模量随压力变化的关系

Fig. 5 Variations of elastic modulus of (a) Zr3InC2 and (b) Zr3AlC2 with pressure

图6 Zr3InC2和Zr3AlC2的泊松比随压力变化的关系

Fig. 6 Variations of Poisson's ratio of Zr3InC2 and Zr3AlC2 with pressure

图7 Zr3InC2在0、30、50 GPa压力下的体积模量(a~c)、杨氏模量(d~f)和剪切模量(g~i)的三维曲面图

Fig. 7 3D surface plots of the bulk modulus (a-c), Young’s modulus (d-f), and shear modulus (g-i) of Zr3InC2 at 0, 30 and 50 GPa pressure

图8 (a) 0、(b) 30和(c) 50 GPa压力下Zr3InC2的声子色散曲线

Fig. 8 Phonon dispersion curves of Zr3InC2 at (a) 0, (b) 30 and (c) 50 GPa

图9 (a) 0、(b) 30和(c) 50 GPa压力下Zr3InC2的能带结构

Fig. 9 Energy band structures of Zr3InC2 at (a) 0, (b) 30 and (c) 50 GPa

图10 (a) 0、(b) 30和(c) 50 GPa压力下Zr3InC2的态密度

Fig. 10 Density of states of Zr3InC2 at (a) 0, (b) 30 and (c) 50 GPa

表3

0~50 GPa压力下Zr3InC2和Zr3AlC2的ρ、横向速度(vt)、纵向速度(vl)、平均声速(vm)、ΘD和Kmin Table 3 ρ, transverse velocity (vt), longitudinal velocity (vl), average sound velocity (vm), ΘD, and Kmin of Zr3InC2 and Zr3AlC2 under 0-50 GPa pressure

MAX	Pressure/ GPa	ρ/ (kg·m^-3)	v_t/ (m·s^-1)	v_l/ (m·s^-1)	v_m/ (m·s^-1)	Θ_D/K	K_min/ (W·m^-1·K^-1)
Zr₃InC₂	0	3375.40	6301.53	3820.01	4221.57	491.4	0.89
	5	3486.67	6461.24	3844.83	4256.71	501.2	0.92
	10	3588.36	6715.97	4001.02	4429.14	526.5	0.97
	15	3683.39	6846.77	4051.64	4488.03	538.2	1.01
	20	3769.65	6967.78	4065.94	4509.69	545.0	1.03
	25	3853.06	7143.07	4165.50	4620.38	562.5	1.07
	30	3931.13	7256.43	4200.63	4662.40	571.4	1.09
	35	4005.88	7360.26	4246.22	4714.42	581.2	1.12
	40	4078.30	7385.32	4190.43	4659.11	577.8	1.12
	45	4148.03	7585.61	4334.05	4815.97	600.5	1.17
	50	4215.80	7656.01	4356.83	4842.92	607.0	1.18
Zr₃AlC₂	0	3375.40	7176.31	4397.61	4854.54	573.2	1.05
	5	3486.67	7333.83	4464.07	4931.28	588.6	1.09
	10	3588.36	7543.72	4569.82	5050.55	608.6	1.14
	15	3683.39	7684.20	4616.35	5106.18	620.7	1.17
	20	3769.65	7822.28	4657.67	5156.31	631.7	1.20
	25	3853.06	7914.84	4652.82	5157.13	636.4	1.22
	30	3931.13	8037.75	4727.22	5239.38	650.9	1.25
	35	4005.88	8080.91	4698.41	5212.88	651.7	1.26
	40	4078.30	8123.75	4703.44	5220.42	656.5	1.28
	45	4148.03	8097.81	4625.81	5140.25	650.1	1.28
	50	4215.80	8109.87	4578.04	5092.24	647.5	1.28

图11 Zr3InC2的(a)德拜温度和(b)最小导热系数随压力变化的关系

Fig. 11 Variations of (a) Debye temperature and (b) minimum thermal conductivity of Zr3InC2 with pressure

图12 Zr3InC2的(a)热膨胀系数和(b)热容随温度变化的关系

Fig. 12 Variations of (a) thermal expansion coefficient and (b) heat capacity of Zr3InC2 with pressure

图S1 Zr3AlC2在0、30、50 GPa压力下的体积模量(a~c)、杨氏模量(d~f)和剪切模量(g~i)的三维曲面图

Fig. S1 3D surface plots of the bulk modulus (a-c), Young’s modulus (d-f), and shear modulus (g-i) of Zr3AlC2 at 0, 30 and 50 GPa pressure

图S2 (a) 0、(b) 30和(c) 50 GPa压力下Zr3AlC2的声子色散曲线

Fig. S2 Phonon dispersion curves of Zr3AlC2 at (a) 0, (b) 30 and (c) 50 GPa

图S3 (a) 0、(b) 30和(c) 50 GPa压力下Zr3AlC2的能带结构

Fig. S3 Energy band structures of Zr3AlC2 at (a) 0, (b) 30 and (c) 50 GPa

图S4 (a) 0、(b) 30和(c) 50 GPa压力下Zr3AlC2的态密度

Fig. S4 Density of states of Zr3AlC2 at (a) 0, (b) 30 and (c) 50 GPa

图S5 Zr3AlC2的(a)德拜温度和(b)最小导热系数随压力的变化

Fig. S5 Variations of (a) Debye temperature and (b) minimum thermal conductivity of Zr3AlC2 with pressure

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高压下新型MAX相Zr₃InC₂的第一性原理研究

First-principles Study of Novel MAX Phase Zr₃InC₂ under High Pressure

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