  To leading order in displacement size, the scattering of electrons in a Cu-O
plane from O displacements perpendicular to that plane is due to spin-orbit
coupling. This scattering is investigated with the following results: (1) As a
consequence of time-reversal symmetry, spin fluctuations, which can strongly
enhance scattering from a spin impurity, do not enhance spin-orbit scattering;
and (2) for a superconductor with a $d_{x^2-y^2}$ gap function, pair-breaking
from spin-orbit scattering can be strong, particularly in a structurally
disordered phase in which locally CuO$_6$ octahedra tilt as in the orthorhombic
phase of La$_2$CuO$_4$, but globally the average structure is tetragonal. These
results are discussed in the context of the (La,Nd)-(Sr,Ba)-Cu-O system where
certain structural transitions are observed to suppress superconductivity.
