Multihyperuniformity in high-entropy MXenes

MXenes are a large family of two-dimensional transition metal carbides and nitrides that possess excellent electrical conductivity, high volumetric capacitance, great mechanical properties, and hydrophilicity. In this work, we generalize the concept of multihyperuniformity, an exotic state that can exist in a disordered multi-component system, to MXenes. Disordered hyperuniform systems possess an isotropic local structure that lacks traditional translational and orientational order, yet they completely suppress infinite-wavelength density fluctuations as in perfect crystals and, in this sense, possess a hidden long-range order. In particular, we evaluate the static structure factor of the individual components present in the high-entropy (HE) MXene experimental sample TiVCMoCr based on high-resolution scanning electron microscope imaging data, which suggests that this HE MXene system is at least effectively multihyperuniform (MH). We then devise a packing algorithm to generate MH models of HE MXene systems. The MH HE MXenes are predicted to be energetically more stable compared to the prevailing (quasi)random models of the HE MXenes due to the hidden long-range order. Moreover, the MH structure exhibits a distinctly smaller lattice distortion, which has a vital effect on the electronic properties of HE MXenes, such as the density of states and charge distribution. This systematic study of HE MXenes strengthens our fundamental understanding of these systems and suggests possible exotic physical properties, as endowed by the multihyperuniformity.