Research Progress on Theoretical Calculation in the Field of High-entropy Ceramics

doi:10.15541/jim20250342

Abstract

Abstract:

High-entropy ceramic (HEC) demonstrates exceptional thermal and mechanical properties, along with outstanding chemical stability, which can be attributed to their high entropy, lattice distortion, sluggish diffusion, and cocktail effects. However, the expansive compositional and structural space associated with HEC renders traditional trial-and-error methods time-consuming, costly and inadequate for investigation of complex systems. Thus, theoretical calculation has become an indispensable tool for addressing these challenges. To outline recent advances in theoretical calculation for HEC, this article focuses on prevalent calculation methods, including first-principles calculations, molecular dynamics, machine learning, and calculation of phase diagrams. Additionally, it discusses research paradigms such as high-throughput computing and performance descriptors, providing a comprehensive overview of their key roles and specific applications in HEC. The article first outlines fundamental characteristics and core effects of HEC, then turns to critically examine theoretical basis of these calculation methods, elaborating on their applications through specific examples in composition design, property prediction, microstructural parsing, and phase stability assessment. Finally, this paper summarizes the major challenges encountered in theoretical calculations in the study of multi-component systems, such as the scarcity of high-quality datasets and the ambiguity of structure-property relationships. It concludes with a forward-looking outlook on the development directions in this field, including data-driven design, cross-scale correlation, and extreme environment simulation.

Key words: high-entropy ceramic, theoretical calculation, first principles, multiscale simulation, machine learning, review

CLC Number:

TB321

XIE Chenyi, MIAO Huaming, ZHANG Weiran, LIU Rongjun, WANG Yanfei, LI Duan. Research Progress on Theoretical Calculation in the Field of High-entropy Ceramics[J]. Journal of Inorganic Materials, 2026, 41(5): 545-560.

Figures/Tables 9

Fig. 1 Overview of research in the field of HEC (a) Amount of publications of HEC in Web of Science database from 2017 to 2024; (b) Percentage of publications on various types of HEC in 2024; (c) Schematic diagrams of HEC with different crystal structures[26]; (d) Relationship between entropy and number of components, as well as definition of medium-entropy and high-entropy ceramics

Fig. 2 Four major effects of high-entropy materials

Fig. 3 Development history of relevant theoretical calculation methods

Table 1 Comparison of mechanisms, scale applicability, advantages, limitations, and application scenarios of different theoretical computing methods

Method	Mechanism	Spatial scale	Time scale	Advantage	Limitation	Application
FPC	Quantum mechanics	Atomic/electronic scale (angstrom)	Femtosecond to picosecond level	High accuracy without empirical parameters	High computational cost and limited system size	Electronic structures, interface mechanisms
MDS	Newtonian mechanics and force fields	Nanoscale	Picosecond to microsecond level	Simulation of kinetic processes	Highly dependent on accuracy of the potential function	Mechanical properties, diffusion behavior
MCS	Probability sampling	Atomic to macroscopic scale	Equilibrium state	Exploring equilibrium state processes	Inability to simulate kinetic processes	Phase equilibrium prediction, formation energy calculation
CALPHAD	Gibbs free energy	Macro system	Thermodynamic equilibrium state	Predicting phase diagrams	Calibration dependent on experimental data	Phase diagram calculation, component optimization
ML	Algorithm and data-driven	Multi-scale	Instantaneous prediction	High-throughput screening and resolving complex associations	Weak model interpretability	Performance prediction, component optimization

Fig. 4 Researches on phase structure prediction[66,76,82] (a) EFA of 56 kinds of high-entropy ceramics calculated by FPC[66]; (b) Flowchart of the HEBs formation capability descriptor prediction model[76]; (c) Pseudo-binary phase diagrams for (Ti-Zr-Hf-Nb-Ta-Mo)-C and (Ti-Zr-Hf-Nb-Ta)-C[82]

Fig. 5 Researches on structural characterization and performance correlation of high-entropy ceramics[83,85] (a) “Composition-structure-elastic properties” correlation heatmapping of (TiZrNbTaMo)C[83]; (b) Spatial schematic diagrams of high-entropy ceramic components with different carbon vacancy concentrations[85]

Fig. 6 Researches on simulation and prediction methods of physical properties of high-entropy ceramics driven by machine learning[86,88] (a) Schematic of transferable machine-learning-potential-based MDS for HECs[86]; (b) Performance of five ML models[88]

Fig. 7 Researches on diffusive behavior and atomic scale mechanisms[93,96] (a) Adsorption energy and diffusion barrier of high-entropy diborides and four single-component diborides[93]; (b) Simplified schematic diagrams of oxidation mechanism of (Mo0.2Nb0.2Ta0.2V0.2W0.2)Si2 and MoSi2[96]

Fig. 8 Researches on data-driven assisted material design[61,97 -99] (a) Preprocessing of characterization parameters based on their importance relative to CTE[61]; (b) Ranking of features which have the greatest impact on hardness[97]; (c) ML-assisted design strategy for prediction of mechanical properties and descriptor-property correlation analysis of HENs[98]; (d) Comparison of mechanical properties of high-entropy ceramic coatings[99]

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