High-pressure single-crystal elasticity study of CO₂ across phase I-III transition

Sound velocities and elastic moduli of solid single-crystal CO₂ were measured at pressures up to 11.7(3) GPa by Brillouin spectroscopy. The aggregate adiabatic bulk modulus (K_S), shear modulus (G), and their pressure derivatives for CO₂ Phase I are K_S0 = 3.4(6) GPa, G₀ = 1.8(2) GPa, (dK_S/dP)₀ = 7.8(3), (dG/dP)₀ = 2.5(1), (d²K_S/dP²) ₀ = -0.23(3) GPa^-1, and (d²G/dP ²)₀ = -0.10(1) GPa^-1. A small increase of elastic properties was observed between 9.8(1) and 10.5(3) GPa, in agreement with the CO₂ I-III transition pressure determined from previous x-ray diffraction experiments. Above the transition pressure P_T, we observed a mixture dominated by CO₂-I, with minor CO₂-III. The CO₂-I + III mixture shows slightly increased sound velocities compared to pure CO₂-I. Elastic anisotropy calculated from the single-crystal elasticity tensor exhibits a decrease with pressure beginning at 7.9(1) GPa, which is lower than P_T. Our results coincide with recent X-ray Raman observations, suggesting that a pressure-induced electronic transition is related to local structural and optical changes.