Benchmark Crystal Structure of Defect-Free Spinel ZnFe2O4

Accurate structural models are of paramount importance for elucidating structure-property relationships in functional materials. Spinels (AB2O4) form a highly important family of materials with complex crystal structures, and subtle structural details have a critical bearing on understanding their physical properties. In some spinels, the space group symmetry is debated, and in general, point defects such as cation inversion and interstitials add complexity. Most studies of spinels concern powder materials, and this challenges deep structural characterization. In fact, most published spinel structures have dubious atomic displacement parameters (ADPs), which is a typical sign of problematic structural description in the refinement of diffraction data. Here, we use various X-ray and neutron diffraction techniques to establish a benchmark crystal structure for the essentially defect-free spinel ferrite ZnFe2O4, which is a widely studied frustrated magnet. It is shown that the appearance of Fd3̅m forbidden reflections in the ZnFe2O4 single-crystal neutron diffraction data is an artifact of multiple scattering rather than the loss of inversion symmetry. We then provide benchmark ADPs and demonstrate how strongly these parameters affect the refined cation inversion. The ADPs reported here may be used as reference data to test the soundness of refined structural models, possibly to constrain those based on suboptimal data quality, and thereby provide a more accurate fundamental understanding of the structure-property relationship in spinel-type materials.

Formation of breathing pyrochlore lattices: structural, thermodynamic and crystal chemical aspects

The structural diversity of breathing pyrochlore lattices was investigated on the example of ordered pyrochlores in terms of group-theoretical analysis, Landau thermodynamics and crystal chemistry.

Atomic order, electronic structure and thermodynamic stability of nickel aluminate

The atomic order, electronic structure and thermodynamic stability of nickel aluminate, NiAl2O4, have been analyzed using periodic density functional theory and cluster expansion. NiAl2O4 forms a tetragonal structure with P4122 space group. At temperatures below 800 K, it is an inverse spinel, with Ni occupying the octahedral sites and Al occupying both the octahedral and the tetrahedral sites. Some Niocta + Altetra ⇌ Nitetra + Alocta exchange occurs above 800 K, but the structure remains largely inverse at high temperatures, with about 95% Niocta at 1500 K. Various functionals, with and without van der Waals corrections, were used to predict the experimental formation energy, lattice parameters and electronic structure. In all cases, the NiAl2O4 is found to be ferromagnetic and a semiconductor with an indirect band gap along the Γ → M symmetry points. NiAl2O4 is found to be thermodynamically stable at operating conditions of 900-1000 K and 1 atm relative to its competing oxide phases, NiO and Al2O3.

Kinetics and Thermodynamics of Mg-Al Disorder in MgAl2O4-Spinel: A Review

The MgAl₂O₄-spinel has wide applications in various industries and in geosciences. It shows a significant inter-site Mg-Al cation exchange (denoted by the inversion parameter x), which modifies structural features, such as the unit-cell parameters and the sizes of the component polyhedra, and influences the physical and chemical properties. Previous studies mainly focused on the kinetics and thermodynamics of the Mg-Al exchange reaction, with the aim to ascertain the correlation between the inversion parameter and temperature; these studies, however, reached conflicting results. Here, we first reviewed the kinetics studies on the Mg-Al cation exchange reaction, and then reviewed all thermodynamic experiments, with special attention paid to the Mg-Al cation exchange equilibrium and the quench process, which might have modified the cation distributions once attained at high temperatures. We also assessed the accuracies in the temperature measurements and in the quantifications of the x by different analytical methods. With some necessary temperature correction and data removal, we have landed with a generally reliable x-T dataset covering the T-x space of 873 < T < 1887 K and 0.18(1) < x < 0.357(60) (71 data pairs in total). Fitting these x-T data to three most commonly used thermodynamic models, we have obtained more accurate model parameters. Further, we also evaluated the constituent items of the Gibbs free energy for the Mg-Al cation exchange reaction with experimental results from different research fields and reached the conclusion that highly possibly the TΔSD should not be neglected. Based on this review, we suggest that: (1) Further kinetics study on the Mg-Al exchange reaction should be performed at both low T (<~973 K) and high T (>~1173 K); (2) further Mg-Al exchange equilibrium studies should be carried out at relatively low T and ambient P, as well as in vast ranges of simultaneous high P and high T; and (3) direct experimental measures about the entropies or the enthalpies of the MgAl₂O₄-spinels disordered to different extents should be conducted with full characterization of the starting materials and detailed description of the experimental procedures.

Abnormal elastic and vibrational behaviors of magnetite at high pressures

Magnetite exhibits unique electronic, magnetic, and structural properties in extreme conditions that are of great research interest. Previous studies have suggested a number of transitional models, although the nature of magnetite at high pressure remains elusive. We have studied a highly stoichiometric magnetite using inelastic X-ray scattering, X-ray diffraction and emission, and Raman spectroscopies in diamond anvil cells up to ~20 GPa, while complementary electrical conductivity measurements were conducted in a cubic anvil cell up to 8.5 GPa. We have observed an elastic softening in the diagonal elastic constants (C₁₁ and C₄₄) and a hardening in the off-diagonal constant (C₁₂) at ~8 GPa where significant elastic anisotropies in longitudinal and transverse acoustic waves occur, especially along the [110] direction. An additional vibrational Raman band between the A_1g and T_2g modes was also detected at the transition pressure. These abnormal elastic and vibrational behaviors of magnetite are attributed to the occurrence of the octahedrally-coordinated Fe²⁺-Fe³⁺-Fe²⁺ ions charge-ordering along the [110] direction in the inverse spinel structure. We propose a new phase diagram of magnetite in which the temperature for the metal-insulator and distorted structural transitions decreases with increasing pressure while the charge-ordering transition occurs at ~8 GPa and room temperature.