Figure/Table detail

Recent advances in high-entropy ceramics: Design principles, structural characteristics, and emerging properties
Yiran Li, Donghui Pan, Jiehui Cao, Wenhui Fang, Yiwang Bao, Bin Liu
Extreme Materials, 2025, 1(2): 42-72.   DOI: 10.1016/j.exm.2025.05.002

Symbol Name Definitional Formula Physical Meaning Ref
$\mathrm{\Delta }{S}_{\text{mix}\text{ }}$ Mixing Entropy $\mathrm{\Delta }{S}_{\text{mix}\text{ }}=-R{\mathrm{\Sigma }}_{i}{c}_{i}\mathrm{l}\mathrm{n}{c}_{i}$ Enthalpy change of a system when different components are mixed to form a homogeneous system. [71]
$\mathrm{\Delta }{H}_{\text{mix}\text{ }}$ Mixing Enthalpy $\mathrm{\Delta }{H}_{\text{mix}\text{ }}={E}_{\text{HEC}\text{ }}-{\sum }_{i} {c}_{i}{E}_{i}$ The sum of the interaction energy differences in the ideal state. [72]
$\mathrm{\Omega }$ Entropy-Enthalpy Balance Factor $\mathrm{\Omega }=\frac{{T}_{\mathrm{m}}\mathrm{\Delta }{S}_{\text{mix}\text{ }}}{\left|\mathrm{\Delta }{H}_{\text{mix}\text{ }}\right|}$ Tm is the isothermal temperature. [73]
$\delta $ Atomic (ion) Radius Difference $\delta ={\left[{\sum }_{i} {c}_{i}\left(1-\frac{{r}_{i}}{\stackrel{‾}{r}}\right)\right]}^{1/2},\stackrel{‾}{r}={\sum }_{i} {c}_{i}{r}_{i}$ Contribution of differences in atomic/ionic radii of components to lattice distortion [74]
$\mathrm{\Delta }\chi $ Electronegativity Difference $\mathrm{\Delta }\chi =\sqrt{{\sum }_{i} {c}_{i}{\left({\chi }_{i}-\stackrel{‾}{\chi }\right)}^{2}},\stackrel{‾}{\chi }={\sum }_{i} {c}_{i}{\chi }_{i}$ $\mathrm{\Delta }\chi $ reflects the difference in electronegativity between different elements. [75]
VEC Valence Electron Concentration $VEC={\sum }_{i} {c}_{i}VE{C}_{i}$ Reflects the degree of electron filling and energy band structure characteristics of the system [74]
DEED Disordered Enthalpy-Entropy Descriptor $DEED=\sqrt{\frac{{\sigma }_{\mathrm{\Omega }}^{-1}\left[{H}_{\mathrm{f}}\right]}{{⟨\mathrm{\Delta }{H}_{\mathrm{h}\mathrm{u}\mathrm{l}\mathrm{l}}⟩}_{\mathrm{\Omega }}}}$ Predicting the possibility of single-phase disordered structures in multicomponent systems, Hf and Hhull  are the DFT formation energies of the partial occupation POCC tiles and the convex hull, respectively. [76]
EFA Entropy Forming Ability $EFA={\left[\frac{\left({\sum }_{i=1}^{n} {g}_{i}\right)-1}{{\sum }_{i=1}^{n} {g}_{i}{\left({H}_{i}-{H}_{\text{mix}\text{ }}\right)}^{2}}\right]}^{1/2}$ Entropy-driven formation of stable single-phase solid solutions, where n is the total number of sampled geometrical configurations and gi are their degeneracies. Hi of the sampled configurations. [66]
LDI Lattice Distortion Index $LDI={\sum }_{i=1}^{n} \sqrt{{\left({x}_{i,a}-{x}_{i,0}\right)}^{2}+{\left({y}_{i,a}-{y}_{i,0}\right)}^{2}+{\left({z}_{i,a}-{z}_{i,0}\right)}^{2}}/n$ Parameters for the degree of lattice distortion in disordered systems, ( x,y,z ) is the atomic position. [77]
$\gamma $ The normalized geometric packing parameter for the metallic sublattice calculated $\gamma =\left\{1-{\left[1-\frac{{\left({r}_{\mathrm{S}}+\stackrel{‾}{r}\right)}^{2}-{\stackrel{‾}{r}}^{2}}{{\left({r}_{\mathrm{S}}+\stackrel{‾}{r}\right)}^{2}}\right]}^{1/2}\right\}/\left\{1-{\left[1-\frac{{\left({r}_{\mathrm{L}}+\stackrel{‾}{r}\right)}^{2}-{\stackrel{‾}{r}}^{2}}{{\left({r}_{\mathrm{L}}+\stackrel{‾}{r}\right)}^{2}}\right]}^{1/2}\right\}$ Evaluating how different metal atoms stack together in a crystal lattice, where rS and rL are the radii of the smallest and largest atoms. [78]
Table 1 Parameters and Descriptors Related to Theoretical Design.
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