Formation Mechanism of Vacancies on M2SnC (M=Ti, V, Hf, Zr) and Its Effect on Mechanical Properties

doi:10.16553/j.cnki.issn1000-985x.2026.0036

Abstract

Abstract: To address the unresolved issues regarding the formation of Sn vacancies in M₂SnC （M=Ti，V，Hf，Zr） and its influence on mechanical properties，this study systematically employed the first-principles calculation method based on density functional theory to investigate the formation energies，structural stability of Sn vacancies，and their effects on mechanical properties. The results indicate that the formation energies of Sn vacancies in M₂SnC are lower than those of M and C vacancies，suggesting that Sn vacancies are more readily formed. Among the compounds，V₂SnC exhibits the lowest formation energy for Sn vacancies，while Zr₂SnC shows the highest formation energy for Sn vacancies. The formation enthalpy calculation and elastic constant analysis reveal that the structures remain thermodynamic and mechanical stablility after the introduction of Sn vacancies. Mechanical property analysis demonstrates that the influence of Sn vacancies varies significantly across different M₂SnC phases. After the introduction of Sn vacancies，the bulk modulus，shear modulus and elastic modulus of Ti₂SnC，Hf₂SnC and Zr₂SnC decrease，whereas the shear modulus and elastic modulus of V₂SnC increase，whose enhancement may be attributed to vacancy-induced local bond reconstruction. MAX phases are a family of ternary layered carbide/nitride ceramic materials.The research results provide a theoretical foundation for the construction and modulation of A-site vacancies in MAX phases.

Key words: M₂SnC; Sn vacancy; first-principle; formation energy; mechanical property

CLC Number:

O469

SHEN Yunan, PING Yutong, HUANG Miaoyan, CHEN Yue, LIU Yushuang. Formation Mechanism of Vacancies on M₂SnC (M=Ti, V, Hf, Zr) and Its Effect on Mechanical Properties[J]. Journal of Synthetic Crystals, 2026, 55(6): 949-955.

Figures/Tables 7

References 23

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Phase	C₁₁/GPa	C₁₂/GPa	C₁₃/GPa	C₃₃/GPa	C₄₄/GPa
Ti₂SnC	257.575 50	70.217 00	62.283 93	257.704 40	95.645 25
Ti₂SnC（V_Sn）	259.214 60	66.129 55	62.966 35	222.275 80	77.989 10
V₂SnC	271.001 20	107.306 85	139.287 75	283.238 90	114.747 70
V₂SnC（V_Sn）	288.961 85	98.602 45	118.899 32	258.438 90	101.821 50
Hf₂SnC	268.140 20	54.459 50	80.382 32	257.340 60	92.706 90
Hf₂SnC（V_Sn）	231.234 40	54.404 20	86.183 92	208.161 00	78.019 70
Zr₂SnC	226.567 55	54.509 00	88.838 37	233.370 85	98.133 60
Zr₂SnC（V_Sn）	220.923 80	68.802 75	53.535 88	117.966 35	87.655 30

Phase	C₁₁/GPa	C₁₂/GPa	C₁₃/GPa	C₃₃/GPa	C₄₄/GPa
Ti₂SnC	257.575 50	70.217 00	62.283 93	257.704 40	95.645 25
Ti₂SnC（V_Sn）	259.214 60	66.129 55	62.966 35	222.275 80	77.989 10
V₂SnC	271.001 20	107.306 85	139.287 75	283.238 90	114.747 70
V₂SnC（V_Sn）	288.961 85	98.602 45	118.899 32	258.438 90	101.821 50
Hf₂SnC	268.140 20	54.459 50	80.382 32	257.340 60	92.706 90
Hf₂SnC（V_Sn）	231.234 40	54.404 20	86.183 92	208.161 00	78.019 70
Zr₂SnC	226.567 55	54.509 00	88.838 37	233.370 85	98.133 60
Zr₂SnC（V_Sn）	220.923 80	68.802 75	53.535 88	117.966 35	87.655 30

Phase	B/GPa	G/GPa	E/GPa	ν	H_V/GPa
Ti₂SnC	129.15	95.51	229.87	0.203 4	16.47
Ti₂SnC（V_Sn）	124.64	86.20	211.02	0.217 8	14.33
V₂SnC	176.88	89.30	229.31	0.283 9	10.17
V₂SnC（V_Sn）	167.66	92.29	233.95	0.267 4	11.49
Hf₂SnC	135.96	96.64	234.39	0.212 7	15.88
Hf₂SnC（V_Sn）	124.88	77.67	192.99	0.203 4	11.68
Zr₂SnC	127.40	85.72	210.06	0.225 2	13.70
Zr₂SnC（V_Sn）	96.30	73.41	175.60	0.196 1	14.15

Phase	B/GPa	G/GPa	E/GPa	ν	H_V/GPa
Ti₂SnC	129.15	95.51	229.87	0.203 4	16.47
Ti₂SnC（V_Sn）	124.64	86.20	211.02	0.217 8	14.33
V₂SnC	176.88	89.30	229.31	0.283 9	10.17
V₂SnC（V_Sn）	167.66	92.29	233.95	0.267 4	11.49
Hf₂SnC	135.96	96.64	234.39	0.212 7	15.88
Hf₂SnC（V_Sn）	124.88	77.67	192.99	0.203 4	11.68
Zr₂SnC	127.40	85.72	210.06	0.225 2	13.70
Zr₂SnC（V_Sn）	96.30	73.41	175.60	0.196 1	14.15

Formation Mechanism of Vacancies on M₂SnC (M=Ti, V, Hf, Zr) and Its Effect on Mechanical Properties

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