The complete temperature-dependent elastic constants of superconducting crystals ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ (${\mathit{T}}_{\mathit{c}}$=84 K) are determined from sound-velocity data. The longitudinal modes ${\mathit{C}}_{11}$, ${\mathit{C}}_{22}$, and ${\mathit{C}}_{\mathit{L}}$ (propagating along the [110] direction) monotonically increase as temperature decreases from room temperature to ${\mathit{T}}_{\mathit{c}}$. The shear-mode elastic constants ${\mathit{C}}_{66}$ exhibit a weak variation (<1%) with temperature from 250 to 80 K except for three small softening minima around 240, 140, and 100 K. The in-plane shear mode C’(=[(${\mathit{C}}_{11}$+${\mathit{C}}_{22}$)/2-${\mathit{C}}_{12}$]/2) shows not only a relatively small absolute value, but also an overall trend of softening (11%) over a wide temperature range (200–100 K). The softening of the C’ mode is consistent with the local-atomic-displacements model proposed from pulsed-neutron-scattering results. A possible relation between the softening of elastic constants and superconductivity is discussed.

• Received 23 July 1992

DOI:https://doi.org/10.1103/PhysRevB.47.2806