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The dimerization of the Cu ions in the spin-Peierls state of ${\mathrm{CuGeO}}_{3}$ below 14 K has been determined by neutron-diffraction measurements. In addition to superlattice reflections with indices $\frac{h}{\frac{2kl}{2}}$ ($h$, $k$, $l$, all odd) recently observed in electron and x-ray diffraction studies, we also found peaks for which $k=5$ = even. Oxygen displacements in the $a\ensuremath{-}b$ plane of about 0.01 \AA{}, accompanied by comparable shifts of the Cu ions along the chain direction $c$, can be related to the dimerized spin state in a natural fashion.

High-resolution ultrasonic measurements have been performed on single-crystalline ${\mathrm{La}}_{1.86}$${\mathrm{Sr}}_{0.14}$${\mathrm{CuO}}_{4}$ in magnetic fields H up to 14 T. We found that by reducing temperature the transverse elastic constant (${\mathit{C}}_{11}$-${\mathit{C}}_{12}$)/2 starts to soften from about 50 K and continues to soften down to ${\mathit{T}}_{\mathit{c}}$(H), even when ${\mathit{T}}_{\mathit{c}}$(H) is reduced to 14 K by magnetic field. The softening turns to rapid hardening by the emergence of superconductivity. This behavior of C${(}_{11}$-${\mathit{C}}_{12}$)/2 is a consequence of the structural instability of the orthorhombic phase and disappearance of the instability caused by emergence of the superconducting state.

A novel resonant ultrasound technique is used to measure all elastic constants and their temperature dependence in single-crystal La{sub 1.86}Sr{sub 0.14}CuO{sub 4}. The in-plane shear modulus {ital c}{sub 66} drops by nearly half upon cooling to 227 K, an effect attributed to order-parameter fluctuations (of 2D Gaussian character) near the tetragonal-orthorhombic phase boundary. Implications for current models of the structural phase transition are discussed, as well as the effect of domains in the low-temperature orthorhombic state.

Using neutron-scattering techniques, we have studied the temperature dependence of the magnetic excitations at varied energies in a high-quality single crystal of ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$${\mathrm{CuO}}_{4}$. This crystal exhibits a sharp superconducting transition at 33 K with nearly 100% flux exclusion. For magnetic excitation energies of 9 meV and lower, the intensity drops dramatically with decreasing temperature for temperatures below \ensuremath{\sim}150 K. However, at 12 MeV the intensity is independent of temperature between 300 and 5 K.