By utilizing the first-principles method, the pressure-induced effects on phase transition, mechanical stability, and elastic properties of WS2/CrS2 are investigated in the pressure range from 0 to 80 GPa. Transitions from 2H(c) to 2H(a) for WS2 and CrS2 are found to occur at 17.5 and 25 GPa, respectively. It is found that both 2H(a) and 2H(c) phases of WS2 and CrS2 meet the mechanical stability criteria up to 80 GPa, suggesting that those structures are mechanically stable. The bulk and shear modulus anisotropy of the two phases of WS2 and CrS2 decrease rapidly under pressure and, finally, trend to isotropy. With increasing pressure, the elastic moduli (Y, B, and G), sound velocities (v(s), v(p), v(m)), and Debye temperatures (Theta) of 2H(a) and 2H(c) of WS2 and CrS2 increase monotonously. Moreover, the Debye temperature (Theta) of 2H(c) phase is higher than that of 2H(a) phase for both WS2 and CrS2. The bulk, shear, and Young's modulus, Poisson coefficient, and brittle/ductile behaviour are estimated. The percentages of anisotropy in compressibility and shear and the ratio of bulk to shear modulus (B/G) are also studied.

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