硫族MAX相硼化物的物相稳定性和性能预测

doi:10.15541/jim20230188

无机材料学报 ›› 2024, Vol. 39 ›› Issue (2): 225-232.DOI: 10.15541/jim20230188 CSTR: 32189.14.10.15541/jim20230188

所属专题：【材料计算】计算材料(202409)；【信息功能】MAX层状材料、MXene及其他二维材料(202409)

• 研究论文 • 上一篇

硫族MAX相硼化物的物相稳定性和性能预测

张宇晨¹(), 陆知遥¹, 赫晓东¹, 宋广平¹, 朱春城², 郑永挺¹, 柏跃磊¹()

1.哈尔滨工业大学特种环境复合材料技术国家级重点实验室/复合材料与结构研究所, 哈尔滨 150080
2.哈尔滨师范大学化学与化工学院, 哈尔滨 150025

收稿日期:2023-04-14 修回日期:2023-07-07 出版日期:2023-08-21 网络出版日期:2023-08-21
通讯作者: 柏跃磊，教授. E-mail: baiyl@hit.edu.cn
作者简介:张宇晨(2001-)，男，本科生. E-mail: 1696409105@qq.com
基金资助:
国家自然科学基金面上项目(51972080);特种环境复合材料技术国家级重点实验室基金(JCKYS2022603C028)

Predictions of Phase Stability and Properties of S-group Elements Containing MAX Borides

ZHANG Yuchen¹(), LU Zhiyao¹, HE Xiaodong¹, SONG Guangping¹, ZHU Chuncheng², ZHENG Yongting¹, BAI Yuelei¹()

1. National Key Laboratory of Science and Technology on Advanced Composites in Special Environments/Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China
2. School of Chemistry and Chemical Engineering, Harbin Normal University, Harbin 150025, China

Received:2023-04-14 Revised:2023-07-07 Published:2023-08-21 Online:2023-08-21
Contact: BAI Yuelei, professor. E-mail: baiyl@hit.edu.cn
About author:ZHANG Yuchen(2001-), male, undergraduate student. E-mail: 1696409105@qq.com
Supported by:
National Natural Science Foundation of China(51972080);National Key Laboratory Fund of Special Environmental Composites Technology(JCKYS2022603C028)

摘要/Abstract

摘要：

Zr₂SB、Hf₂SB、Zr₂SeB、Hf₂SeB、Hf₂TeB都是近期发现的硫族MAX相硼化物, 与典型MAX相相比，具有明显不同的性质, 因此备受人们关注。本文采用第一性原理并结合“线性优化法”、键刚度模型和准简谐近似研究了MAX相硼化物(M = Zr, Hf; A = S, Se, Te)的物相稳定性、力学性能和热性能。理论分析结果与目前可用的实验结果一致。经热力学和本征稳定性分析后发现, 只有M₂AB可以稳定存在。较短的M−A键与M−B键长使Hf系化合物的键刚度高于Zr系化合物, 这也同样导致Hf系化合物的硬度高于Zr系。随着A元素由S到Se再到Te, M−B与M−A键长逐渐增加, 键刚度减小导致弹性模量降低。而且, 这些化合物的体积模量取决于其平均化学键刚度。更加重要的是, 最弱键和最强键的刚度比(k_min/k_max)较高，显示这些MAX相硼化物不同于传统MAX相, 均呈本征脆性。考虑晶格振动(声子)和电子激发的贡献后计算得到M₂AB等压热容及热膨胀系数(TEC), 均在300 K以下随温度升高先快速上升后上升速率逐渐降低, 这与其它MAX相类似。较低的键刚度导致Zr系MAX相硼化物的平均线热膨胀系数整体上高于Hf系, 而且在300~1300 K区间与大部分MAX和MAB相一致。

关键词: 第一性原理, MAX相硼化物, 物相稳定性, 力学行为, 热学性能

Abstract:

Zr₂SB, Hf₂SB, Zr₂SeB, Hf₂SeB, and Hf₂TeB are all recently discovered S-group elements containing MAX-phase borides, which attract much attention since the MAX phase borides are significantly unlike the typical MAX phases. Here, the phase stability, mechanical properties and thermal properties of MAX phase borides (M = Zr, Hf, A = S, Se, Te) were studied by using first principles and "linear optimization method", bond stiffness model and quasi-simple harmonic approximation. The results of the theoretical analysis were consistent with the currently available experimental results. Only M₂AB was found to be stable after thermodynamic and intrinsic stability analysis. The shorter M−A bond and M−B bond lengths cause bond stiffness of Hf lineage higher than that of Zr, which also leads to the higher hardness of Hf lineage compound than that of Zr. the A site element goes from S to Se and to Te, the bond lengths of M−B and M−A are gradually increased, which lead to decrease in the elastic modulus. Moreover, the bulk modulus of these compounds is determined by their average chemical bond stiffness. Importantly, the high k_min/k_max(stiffness ratio of the weakest and the strongest bonds) shows that these MAX phases are inherently brittle, different from conventional MAX phase. Including the contribution of lattice vibration (phonon) and electron excitation, the isobaric heat capacity and heat expansion coefficient of M₂AB increase rapidly with increasing the temperature below 300 K and then the rise rate gradually decreases, similar to other MAX phases. Lower bond stiffness results in an overall higher TEC of MAX phase borides in the Zr lineage than in the Hf lineage. The TEC values of these compounds in the 300−1300 K interval are consistent with most of the MAX and MAB phases.

Key words: first-principle, MAX phase boride, phase stability, mechanical property, thermal property

中图分类号:

TQ134

张宇晨, 陆知遥, 赫晓东, 宋广平, 朱春城, 郑永挺, 柏跃磊. 硫族MAX相硼化物的物相稳定性和性能预测[J]. 无机材料学报, 2024, 39(2): 225-232.

ZHANG Yuchen, LU Zhiyao, HE Xiaodong, SONG Guangping, ZHU Chuncheng, ZHENG Yongting, BAI Yuelei. Predictions of Phase Stability and Properties of S-group Elements Containing MAX Borides[J]. Journal of Inorganic Materials, 2024, 39(2): 225-232.

图/表 10

参考文献 43

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Compound	a/Å	c/Å	V/Å³	Most competing phases	ΔH_comp/(eV·atom^-1)
Zr₂SB	3.521	12.302	132.12	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Exp.^[8]	3.500	12.271	130.19	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Hf₂SB	3.484	12.122	127.40	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Exp.^[8]	3.467	12.105	126.01	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Zr₂SeB	3.573	12.733	140.78	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Exp.^[9]	3.644	12.632	145.27	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Hf₂SeB	3.538	12.544	136.01	0.0185Hf₂₃Se₂₅ + 0.5370Hf₂Se + 0.5HfB₂	-0.0838
Exp.^[9]	3.523	12.478	134.11	0.0185Hf₂₃Se₂₅ + 0.5370Hf₂Se + 0.5HfB₂	-0.0838
Hf₂TeB	3.619	13.239	150.14	0.5Hf₃Te₂ + 0.5HfB₂	-0.0100
Exp.^[10]	3.605	13.127	147.72	0.5Hf₃Te₂ + 0.5HfB₂	-0.0100

Compound	a/Å	c/Å	V/Å³	Most competing phases	ΔH_comp/(eV·atom^-1)
Zr₂SB	3.521	12.302	132.12	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Exp.^[8]	3.500	12.271	130.19	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Hf₂SB	3.484	12.122	127.40	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Exp.^[8]	3.467	12.105	126.01	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Zr₂SeB	3.573	12.733	140.78	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Exp.^[9]	3.644	12.632	145.27	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Hf₂SeB	3.538	12.544	136.01	0.0185Hf₂₃Se₂₅ + 0.5370Hf₂Se + 0.5HfB₂	-0.0838
Exp.^[9]	3.523	12.478	134.11	0.0185Hf₂₃Se₂₅ + 0.5370Hf₂Se + 0.5HfB₂	-0.0838
Hf₂TeB	3.619	13.239	150.14	0.5Hf₃Te₂ + 0.5HfB₂	-0.0100
Exp.^[10]	3.605	13.127	147.72	0.5Hf₃Te₂ + 0.5HfB₂	-0.0100

Compound	c₁₁/GPa	c₁₂/GPa	c₁₃/GPa	c₃₃/GPa	c₄₄/GPa	G/GPa	B/GPa	E/GPa	μ	G/B	Ref.
Zr₂SB	264	76	91	298	135	108	148	262	0.206	0.730	This work
Hf₂SB	296	74	97	318	147	122	160	292	0.196	0.763	This work
Zr₂SeB	252	64	83	277	125	105	137	250	0.197	0.766	This work
Hf₂SeB	275	66	90	292	134	113	148	270	0.195	0.764	This work
Zr₂TeB	198	67	78	225	104	79	118	194	0.226	0.669	This work
Hf₂TeB	225	61	88	257	119	93	130	225	0.211	0.715	This work
Ti₃SiC₂	366	94	100	352	153	142	187	339	0.192	0.759	[16]
Ti₃GeC₂	357	94	97	333	143	142	182	340	0.196	0.780	[16]
Hf₂InC	309	81	80	273	98	105	152	256	0.21	0.691	[37]
Hf₂SnC	251	71	107	238	101	87	145	218	0.25	0.600	[37]

Compound	c₁₁/GPa	c₁₂/GPa	c₁₃/GPa	c₃₃/GPa	c₄₄/GPa	G/GPa	B/GPa	E/GPa	μ	G/B	Ref.
Zr₂SB	264	76	91	298	135	108	148	262	0.206	0.730	This work
Hf₂SB	296	74	97	318	147	122	160	292	0.196	0.763	This work
Zr₂SeB	252	64	83	277	125	105	137	250	0.197	0.766	This work
Hf₂SeB	275	66	90	292	134	113	148	270	0.195	0.764	This work
Zr₂TeB	198	67	78	225	104	79	118	194	0.226	0.669	This work
Hf₂TeB	225	61	88	257	119	93	130	225	0.211	0.715	This work
Ti₃SiC₂	366	94	100	352	153	142	187	339	0.192	0.759	[16]
Ti₃GeC₂	357	94	97	333	143	142	182	340	0.196	0.780	[16]
Hf₂InC	309	81	80	273	98	105	152	256	0.21	0.691	[37]
Hf₂SnC	251	71	107	238	101	87	145	218	0.25	0.600	[37]

Compound	M−A bond		M−B bond		k_min/k_max	H_micro/GPa	H_macro/GPa
Compound	d/nm	k/GPa	d/nm	k/GPa	k_min/k_max	H_micro/GPa	H_macro/GPa
Zr₂SB	0.26997	458.93	0.24124	612.75	0.7490	21.29	18.40
Exp.^[8]	0.26844		0.24032			9-12^[12]
Hf₂SB	0.26800	472.37	0.23722	652.32	0.7241	24.74		21.20
Exp.^[8]	0.26643		0.23688
Zr₂SeB	0.28062	442.87	0.24282	560.54	0.7901	21.09		19.30
Exp.^[9]	0.28071		0.24729
Hf₂SeB	0.27869	455.17	0.23899	595.24	0.7647	22.97		20.17
Exp.^[9]	0.27735		0.23789
Zr₂TeB	0.29743	432.53	0.24526	487.09	0.8880	14.45		13.12
Hf₂TeB	0.29604	439.17	0.24156	517.33	0.8489	17.90		16.16

硫族MAX相硼化物的物相稳定性和性能预测

Predictions of Phase Stability and Properties of S-group Elements Containing MAX Borides

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Compound	Included phase	a/Å	c/Å	V/Å³	Most competing phases	ΔH_comp/(eV·atom^-1)
Zr₂SB	Zr, S, B, Zr₂S, Zr₃S₄, Zr₉S₂, ZrS, ZrS₂, ZrS₃, ZrB₂, B₂S₃, BS₂	3.521	12.302	132.12	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Exp.^[8]		3.500	12.271	130.19	0.6Zr₂S + 0.1Zr₃S₄+ 0.5ZrB₂	-0.0749
Zr₃SB₂					0.0833Zr₉S₂+ 0.5833ZrB₂ + 0.8333Zr₂SB	0.0919
Zr₄SB₃					0.1667Zr₉S₂+ 1.1667ZrB₂ + 0.6667Zr₂SB	0.1588
Hf₂SB	Hf, S, B, Hf₂S, HfS, HfS₂, HfS₃, HfB₂, B₂S₃, BS₂	3.484	12.122	127.40	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Exp.^[8]		3.467	12.105	126.01	0.5Hf₂S + 0.5HfS + 0.5HfB₂	-0.0512
Hf₃SB₂					0.5Hf + 0.5HfB₂+ Hf₂SB	0.0807
Hf₄SB₃					Hf + HfB₂+ Hf₂SB	0.1422
Zr₂SeB	Zr, Se, B, Zr₂Se, Zr₂Se₃, ZrSe, ZrSe₂, ZrSe₃, ZrB₂, BSe₂	3.573	12.733	140.78	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Exp.^[9]		3.644	12.632	145.27	0.5Zr₂Se + 0.5ZrSe + 0.5ZrB₂	-0.0259
Zr₃SeB₂					0.5Zr + 0.5ZrB₂+ Zr₂SeB	0.1649
Zr₄SeB₃					Zr + ZrB₂+ Zr₂SeB	0.1559
Hf₂SeB	Hf, Se, B, Hf₂Se, Hf₂Se₃, HfSe₂, HfSe₃, Hf₂₃Se₂₅, HfB₂, BSe₂	3.538	12.544	136.01	0.0185Hf₂₃Se₂₅+ 0.5370Hf₂Se + 0.5HfB₂	-0.0838
Exp.^[9]		3.523	12.478	134.11	0.0185Hf₂₃Se₂₅+ 0.5370Hf₂Se + 0.5HfB₂	-0.0838
Hf₃SeB₂					0.5Hf + 0.5HfB₂+ Hf₂SeB	0.0836
Hf₄SeB₃					Hf + HfB₂+ Hf₂SeB	0.1457
Zr₂TeB	Zr, Te, B, Zr₂Te₃, Zr₃Te, Zr₅Te₄, ZrTe, ZrTe₂, ZrTe₃, ZrTe₅, ZrB₂	3.650	13.415	154.77	0.2143Zr₅Te₄+ 0.1429Zr₃Te + 0.5ZrB₂	0.0305
Zr₃TeB₂					0.1429Zr₅Te₄+ 0.4286Zr₃Te + ZrB₂	0.1321
Zr₄TeB₃					0.0174Zr₅Te₄+ 0.7143Zr₃Te + 1.5ZrB₂	0.1960
Hf₂TeB	Hf, Te, B, Hf₃Te₂,Hf₅Te₄, HfTe₂, HfTe₅, HfB₂	3.619	13.239	150.14	0.5Hf₃Te₂+ 0.5HfB₂	-0.0100
Exp.^[10]		3.605	13.127	147.72	0.5Hf₃Te₂+ 0.5HfB₂	-0.0100
Hf₃TeB₂					0.5Hf + 0.5HfB₂+ Hf₂TeB	0.0994
Hf₄TeB₃					Hf + HfB₂+ Hf₂TeB	0.1613

Compound	Curve fitting equation (300-1300 K)	TEC (300-1300 K)/ K^-1
Zr₂SB	C_P= 0.83×10^-2T + 96.9 - 1.28×10⁶T^-2	10.97×10^-6K^-1
Hf₂SB	C_P = 0.74×10^-2T + 96.6 - 1.25×10⁶T^-2	9.66×10^-6K^-1
Zr₂SeB	C_P = 0.82×10^-2T + 96.7 - 1.06×10⁶T^-2	11.11×10^-6K^-1
Hf₂SeB	C_P = 1.28×10^-2T + 94.4 - 0.89×10⁶T^-2	10.17×10^-6K^-1
Zr₂TeB	C_P = 1.07×10^-2T + 94.7 - 0.84×10⁶T^-2	12.63×10^-6K^-1
Hf₂TeB	C_P = 0.83×10^-2T + 96.1 - 0.87×10⁶T^-2	10.07×10^-6K^-1

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