We investigate the coherent electron-positron pair creation by high-energy photons in a periodically deformed single crystal with a complex base. The formula for the corresponding differential cross-section is derived for an arbitrary deformation field. The conditions are specified under which the influence of the deformation is considerable. The case is considered in detail when the photon enters into the crystal at small angles with respect to a crystallographic axis. The results of the numerical calculations are presented for $mathrm{SiO}_{2}$ single crystal and Moliere parametrization of the screened atomic potentials in the case of the deformation field generated by the acoustic wave of $S$ type. In dependence of the parameters, the presence of deformation can either enhance or reduce the pair creation cross-section. This can be used to control the parameters of the positron sources for storage rings and colliders.
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