Paracrystalline lattice distortions and microdomains in manganese ferrites near the cubic-to-tetragonal transition

The line profiles of X-ray reflexions from different Mn_xFe_{3 − x}O₄ samples were investigated. Sample I (x = 1.66) is cubic with no anomalies; small paracrystalline distortions, g < 0.1%, cannot be excluded and are calculated to be of this magnitude from considerations of a simple volume effect of the larger Mn³⁺ ions. Samples II–IV (x = 1.88) show interesting effects which are closely connected with the development of the tetragonal structure, observed when x > 1.80. Sample II (quenched) shows paracrystalline distortions which can be quantitatively explained on the basis of the Jahn–Teller effect: the tragonally deformed single Mn³⁺O²⁻₆ octahedra are statistically oriented and statistically distributed over B sites and have a mean tetragonality = 0.014. In sample III (cooling rate 20°C.min⁻¹) about 26% of the volume consists of microdomains which result from a correlation between the orientations and positions of Jahn–Teller octahedra; quantitive agreement with the theory can be obtained by introducing a correlation factor γ = 2. In sample IV (cooling rate 7°C.min⁻¹) this correlation proceded in such a way that the crystal consisted of 74% tetragonal matrix which had already attained a value of c/a = 1.056, and about 22% of tetragonal microdomains oriented in two other directions with a value c/a < 1.056. In addition about 3 to 5% of a cubic phase is present. If the mean tetragonality of the microdomains is taken to be = 0.020 the experiments correspond quantitatively with the theory. The detailed study of sample III proves H_{¼ ¼ ¼} are the paracrystalline coordination statistics with a fluctuation α = 27 XU in the direction [111] and β = 38 XU perpendicular to it. This is explained by a model of the spinel structure having two kinds of blocks: a tetrahedral A-structure and Jahn–Teller affected octahedral subcubes at B sites; the separation distance is ¼ √3a = 3.7 Å.