Model calculations of the static distribution of the electric-field-gradient tensor elements in substitutionally disordered ${\mathrm{Rb}}_{1\mathrm{-}\mathit{x}}$(${\mathrm{NH}}_4$${)}_{\mathit{X}}$${\mathrm{H}}_2$${\mathrm{PO}}_4$

The substitution of Rb by ${\mathrm{NH}}_4$ in ${\mathrm{RbH}}_2$ ${\mathrm{PO}}_4$ results in competing interactions of the ferroelectric-antiferroelectric type, which for a certain concentration range 0.22<×<0.78 inhibit the onset of long-range proton order. In this system the local random polarization of the protons p(x,t) couples linearly to the random-field variable h(x,t). There is, however, always a static temperature-independent component $h_0$(x) present which is due to the static random distribution of ${\mathrm{NH}}_4$ and Rb. Quadrupole-perturbed NMR is a very suitable tool to measure the random-field distribution since the random polarization is mapped into the NMR line shape. The temperature dependence of the line shape allows for a clear separation between the static and dynamic components. In order to elucidate the influence of the static random field on the line shape we have performed model calculations of the five irreducible electric-field-gradient tensor-element distributions as a function of concentration. We demonstrate that these distributions are uncorrelated Gaussian distributions.