Influence of incommensurate structure on the elastic constants of crystalline Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ by Brillouin light scattering spectroscopy

Abstract

Brillouin light scattering spectroscopy was used to probe the room-temperature elasticity of crystalline high-$T_c$ superconductor Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$. A complete set of best-estimate elastic constants was obtained using established relationships between acoustic phonon velocities and elastic constants along with a simple expression relating crystal elastic constant $C_{22}$ to the corresponding constants of the constituent incommensurate sublattices. This latter relationship, which was derived and validated in the present work, has important implications for those studying incommensurate systems as it appears that it may be applied in its general form to any composite incommensurate crystal. The results obtained in this work are also consistent with sublattice assignments of Bi${}_2$Sr${}_2$O${}_4$ and CaCu${}_2$O${}_4$ reported in a previous Brillouin scattering study.

7 pages, 1 figure