We report the complete set of elastic constants and the bulk modulus for single-crystal $\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3$ (PMN) at room temperature obtained from Brillouin spectroscopy and molecular-dynamics (MD) simulations. The bulk modulus from Brillouin spectroscopy is found to be $103\mathrm{GPa}$, in good agreement with earlier x-ray studies. We also derived the refractive index along all principal axes and found PMN to be optically isotropic, with a refractive index value of $2.52\pm 0.02$. PMN shows elastic anisotropy with $A=1.7$. The MD simulations of PMN using the random site model overestimate the elastic constants by $20–50\mathrm{GPa}$ and the bulk modulus of $148\mathrm{GPa}$, but the elastic anisotropy matches the Brillouin results of $A=1.7$. We also determined the elastic constants for various models of PMN and we predict variation in the elastic constants based on chemical ordering.

• Received 28 December 2006

DOI:https://doi.org/10.1103/PhysRevB.75.144410