Single crystal specimens of Fe 2.992 O 4 (magnetite), Fe 3– x – y Mn x □ y O 4 ( x ≤ 0.980) and Fe 3– x – y Ni x □ y O 4 ( x ≤ 0.513, □ denotes point defects) are prepared using a floating-zone technique, and changes in their structural parameter values with x are examined at room temperature. Preferences of Mn, Ni and point defects at A, B and B sites, respectively, are confirmed by single-crystal X-ray diffraction experiments, while preference of Mn at the A site is not perfectly accomplished in Fe 2.010 Mn 0.980 O 4 . Mean-square displacements of atoms along the 3 axis in 111 are peculiarly large at the B site in Fe 2.992 O 4 and the displacement decreased smoothly in both series, to nearly half in Fe 2.010 Mn 0.980 O 4 , with increasing amount of heteroatom. On the other hand, displacements normal to the direction show only slight convexity with x due to coexistence of the heteroatom. As a result anisotropy in displacements (dominant in 111 at x = 0) is inverted at x = 0.3 in FeMn series and would expectedly be inverted at x ≃ 0.55 in FeNi series. In spite of different locations of heteroatoms and slightly different inversion points on anisotropy, changes in mean-square displacements at the B site in 111 in these series are found on similar lines with changing amounts of heteroatom. In other words, the amount of this displacement is a function of the amount of Fe 2+ , or remnant electron from the itinerant-electron point-of-view, on the B-site substructure in these compounds. This characteristic lattice mode on the B-site substructure could be interpreted as an average of local distortion of the substructure due to `trimeron' Senn et al. (2012). Nature , 481 , 173–176 and some other modes such as distortion in 〈001〉 Siratori & Kino (1980). J. Magn. Magn. Mat . 20 , 87–90, which moves in the high-temperature structure.
Kitamura et al. (Thu,) studied this question.