• bond theory;
  • boron;
  • ELF (Electron Localization Function);
  • elastic properties;
  • thermodynamics


Phase stability is important to the application of materials. By first-principles calculations, we establish the phase stability of chromium borides with various stoichiometries. Moreover, the phases of CrB3 and CrB4 have been predicted by using a newly developed particle swarm optimization (PSO) algorithm. Formation enthalpy–pressure diagrams reveal that the MoB-type structure is more energetically favorable than the TiI-type structure for CrB. For CrB2, the WB2-type structure is preferred at zero pressure. The predicted new phase of CrB3 belongs to the hexagonal P-6m2 space group and it transforms into an orthorhombic phase as the pressure exceeds 93 GPa. The predicted CrB4 (space group: Pnnm) phase is more energetically favorable than the previously proposed Immm structure. The mechanical and thermodynamic stabilities of predicted CrB3 and CrB4 are verified by the calculated elastic constants and formation enthalpies. The full phonon dispersion calculations confirm the dynamic stability of WB2-type CrB2 and predicted CrB3. The large shear moduli, large Young’s moduli, low Poisson ratios, and low bulk and shear modulus ratios of CrB4[BOND]PSC and CrB4[BOND]PSD indicate that they are potential hard materials. Analyses of Debye temperature, electronic localization function, and electronic structure provide further understanding of the chemical and physical properties of these borides.