Phase stability and mechanical properties of senary high entropy transition metal carbides via a first-principles study

Tianmin Li; Lei Chen; Qinchen Liu; Ya Li; Qingyi Kong; Xianfeng Liao; Sijia Huo; Yujin Wang; Yulia Egorova; Podbolotov Kirill

doi:10.1016/j.ceramint.2026.01.335

Phase stability and mechanical properties of senary high entropy transition metal carbides via a first-principles study

Tianmin Li
, Lei Chen^*
, Qinchen Liu
, Ya Li
, Qingyi Kong
, Xianfeng Liao
, Sijia Huo
, Yujin Wang^*
, Yulia Egorova
, Podbolotov Kirill

^*Corresponding author for this work

School of Materials Science and Engineering

Harbin Institute of Technology
Harbin Institute of Technology
Heilongjiang Institute of Technology
Belarus Academy of Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The phase stability and elastic constants of senary high-entropy transition metal carbide ceramics (HECs) have been studied. Forty-three systems exhibit good single-phase stability. The mechanical properties of these systems have been predicted through the calculation of elastic constants. Among them, the (TiZrHfNbTaW)C system is predicted to exhibit excellent combined hardness and fracture toughness, and the (VNbTaCrMoW)C system exhibits intrinsic ductility. The calculated Vickers hardness and fracture toughness of (TiZrHfNbTaW)C are 27.11 GPa and 4.98 MPa (Formula presented) m1/2. Correspondingly, the experimental Vickers hardness and fracture toughness for (TiZrHfNbTaW)C are 24.03 ± 1.02 GPa and 3.76 ± 0.41 MPa m1/2, respectively. The calculation results also indicate that the resistance to fracture of HECs correlates with their valence electron concentration (VEC). The fracture toughness initially increases with VEC and then decreases, reaching optimal value at a VEC of 9.0.

Original language	English
Pages (from-to)	11779-11789
Number of pages	11
Journal	Ceramics International
Volume	52
Issue number	9
DOIs	https://doi.org/10.1016/j.ceramint.2026.01.335
State	Published - Apr 2026

Keywords

First-principles calculation
High-entropy carbide
Mechanical properties
Phase stability

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10.1016/j.ceramint.2026.01.335

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title = "Phase stability and mechanical properties of senary high entropy transition metal carbides via a first-principles study",

abstract = "The phase stability and elastic constants of senary high-entropy transition metal carbide ceramics (HECs) have been studied. Forty-three systems exhibit good single-phase stability. The mechanical properties of these systems have been predicted through the calculation of elastic constants. Among them, the (TiZrHfNbTaW)C system is predicted to exhibit excellent combined hardness and fracture toughness, and the (VNbTaCrMoW)C system exhibits intrinsic ductility. The calculated Vickers hardness and fracture toughness of (TiZrHfNbTaW)C are 27.11 GPa and 4.98 MPa (Formula presented) m1/2. Correspondingly, the experimental Vickers hardness and fracture toughness for (TiZrHfNbTaW)C are 24.03 ± 1.02 GPa and 3.76 ± 0.41 MPa m1/2, respectively. The calculation results also indicate that the resistance to fracture of HECs correlates with their valence electron concentration (VEC). The fracture toughness initially increases with VEC and then decreases, reaching optimal value at a VEC of 9.0.",

keywords = "First-principles calculation, High-entropy carbide, Mechanical properties, Phase stability",

author = "Tianmin Li and Lei Chen and Qinchen Liu and Ya Li and Qingyi Kong and Xianfeng Liao and Sijia Huo and Yujin Wang and Yulia Egorova and Podbolotov Kirill",

note = "Publisher Copyright: {\textcopyright} 2026 Elsevier Ltd and Techna Group S.r.l. All rights are reserved, including those for text and data mining, AI training, and similar technologies.",

year = "2026",

month = apr,

doi = "10.1016/j.ceramint.2026.01.335",

language = "英语",

volume = "52",

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TY - JOUR

T1 - Phase stability and mechanical properties of senary high entropy transition metal carbides via a first-principles study

AU - Li, Tianmin

AU - Chen, Lei

AU - Liu, Qinchen

AU - Li, Ya

AU - Kong, Qingyi

AU - Liao, Xianfeng

AU - Huo, Sijia

AU - Wang, Yujin

AU - Egorova, Yulia

AU - Kirill, Podbolotov

PY - 2026/4

Y1 - 2026/4

N2 - The phase stability and elastic constants of senary high-entropy transition metal carbide ceramics (HECs) have been studied. Forty-three systems exhibit good single-phase stability. The mechanical properties of these systems have been predicted through the calculation of elastic constants. Among them, the (TiZrHfNbTaW)C system is predicted to exhibit excellent combined hardness and fracture toughness, and the (VNbTaCrMoW)C system exhibits intrinsic ductility. The calculated Vickers hardness and fracture toughness of (TiZrHfNbTaW)C are 27.11 GPa and 4.98 MPa (Formula presented) m1/2. Correspondingly, the experimental Vickers hardness and fracture toughness for (TiZrHfNbTaW)C are 24.03 ± 1.02 GPa and 3.76 ± 0.41 MPa m1/2, respectively. The calculation results also indicate that the resistance to fracture of HECs correlates with their valence electron concentration (VEC). The fracture toughness initially increases with VEC and then decreases, reaching optimal value at a VEC of 9.0.

AB - The phase stability and elastic constants of senary high-entropy transition metal carbide ceramics (HECs) have been studied. Forty-three systems exhibit good single-phase stability. The mechanical properties of these systems have been predicted through the calculation of elastic constants. Among them, the (TiZrHfNbTaW)C system is predicted to exhibit excellent combined hardness and fracture toughness, and the (VNbTaCrMoW)C system exhibits intrinsic ductility. The calculated Vickers hardness and fracture toughness of (TiZrHfNbTaW)C are 27.11 GPa and 4.98 MPa (Formula presented) m1/2. Correspondingly, the experimental Vickers hardness and fracture toughness for (TiZrHfNbTaW)C are 24.03 ± 1.02 GPa and 3.76 ± 0.41 MPa m1/2, respectively. The calculation results also indicate that the resistance to fracture of HECs correlates with their valence electron concentration (VEC). The fracture toughness initially increases with VEC and then decreases, reaching optimal value at a VEC of 9.0.

KW - First-principles calculation

KW - High-entropy carbide

KW - Mechanical properties

KW - Phase stability

UR - https://www.scopus.com/pages/publications/105034386850

U2 - 10.1016/j.ceramint.2026.01.335

DO - 10.1016/j.ceramint.2026.01.335

M3 - 文章

AN - SCOPUS:105034386850

SN - 0272-8842

VL - 52

SP - 11779

EP - 11789

JO - Ceramics International

JF - Ceramics International

IS - 9

ER -

Phase stability and mechanical properties of senary high entropy transition metal carbides via a first-principles study

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