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Page 10 of 17 Liu et al. J Mater Inf 2023;3:17 https://dx.doi.org/10.20517/jmi.2023.19

Figure 5. The temperature-dependent lattice thermal conductivity of (TaZrU)C and (YZrU)C.

Figure 6. The chemical bonding of investigated medium entropy carbides (MECs) characterized by the 3D and 2D views of bonding
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charge density isosurfaces (Δρ = 0.016 e Å ), (A) (TaZrU)C; (B) (YZrU)C. The green and the pink colors are utilized to highlight
those atoms presenting the negative and the positive charge, respectively.
contributions. In those investigated medium entropy ceramics, metal atoms exhibit different degrees of
electron gain and loss, with the order of the metal atoms receiving electrons being U > Y while the order of
metal atoms losing electrons being Ta > Zr. This observation suggests that metal atoms in MECs experience
varying degrees of electron gain and loss, which increase as their atomic size decreases. Since the higher Δρ
density corresponds to the stronger chemical bonds, it can be inferred that the hardness of (TaZrU)C is
larger than that of (YZrU)C, which is consistent with the analysis of the partial bulk modulus B in the
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previous section on thermodynamic properties.

In order to gain a deeper understanding of the bonding behavior of the two MECs, we conducted an
analysis of the charge density distribution on the (001) plane, and contour plots are shown in Figure 8. It