The temperature dependence of the Debye–Waller factor near a phase transition: CsPbCl₃

By fitting effective one-particle potentials to Bragg neutron diffraction intensities measured by Sakata, Harada, Cooper & Rouse [Acta Cryst. (1980), A36, 7-15] for the cubic perovskite caesium lead chloride, CsPbCl₃, it has been established that, contrary to the results of Sakata et al., the effective one-particle potentials for the Cl ion are neither independent of temperature nor of a highly anharmonic form. To the resolution limit of the data, collected out to sin θ/λ = 0.58 Å^-1, the one-particle probability density function of the Cl ion is singly peaked. It is proposed that the strong temperature dependence of the effective one-particle potentials, and the accompanying anomalous temperature behaviour observed for the mean-square displacements of the Cl and Cs ions above the anti-ferrodistortive phase transition temperature, result from soft-mode vibrations. The temperature dependence of the mean-square displacement in the presence of soft modes is derived and it is shown for the first time that a significant temperature-invariant component will be the main additional effect at temperatures well above the critical temperature. The Cl and Cs ions in CsPbCl₃ obey this derived mean-square displacement relationship.