Cubic-to-tetragonal phase transition in RbCaF_{3} investigated by diffraction experiments with neutrons, x rays, and γ rays from a Mössbauer source

The cubic-to-tetragonal phase transition of RbCa${\mathrm{F}}_3$ at $T_0=198\mathrm{}$ K has been studied on single crystals and powder samples utilizing diffraction techniques with various types of radiation. From our x-ray experiments we have determined the temperature dependence of the domain distribution. In particular an anisotropic distribution of domains was found close above $T_0$. The neutron-diffraction data obtained from powder samples were taken to extract the critical exponent $\beta$ free from the influence of domains. We find $\beta =0.25\mathrm{}\left(1\right)\mathrm{}$. We show that the bond lengths of the Ca-F bond exhibit a pronounced minimum at the transition. The fluctuations of the order parameter ${(〈{\varphi }^2〉-{〈\varphi 〉}^2)}^{0.5}$ are compared with $〈\varphi 〉$ to determine the critical region below $T_0$. A peak in $〈{\varphi }^2〉$ is found for the first time in the neutron experiments. The Mössbauer $\gamma$-ray-diffraction experiments were performed in order to separate elastic and inelastic scattering components from the central peak above $T_0$ and from the superlattice point ½${\mathrm{}\left(311\right)\mathrm{}}_{\mathrm{cubic}}$ below $T_0$ with an energy resolution of 60 neV.