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.

中文翻译：

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布里渊光散射光谱研究不通度结构对晶体Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$弹性常数的影响

布里渊光散射光谱用于探测结晶高$T_c$超导体Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$的室温弹性。使用声子速度和弹性常数之间建立的关系以及将晶体弹性常数 $C_{22}$ 与组成不相称的子晶格的相应常数相关的简单表达式，获得了一组完整的最佳估计弹性常数。后一种关系在本工作中得到并验证，对那些研究不相称系统的人具有重要意义，因为它似乎可以以其一般形式应用于任何复合不相称晶体。