Theoretical explanation of the uniform compressibility behavior observed in oxide spinels

Abstract

Simple algebraic equations show that the bulk compressibility in spinel-type compounds can be expressed by means of cation oxide polyhedral compressibilities and a term that accounts for the pressure effect on the internal oxygen position in the unit cell. The equations explain ͑i͒ the difference of compressibilities at octahedral and tetrahedral sites, ͑ii͒ why the macroscopic bulk modulus can be estimated as the average of these polyhedral bulk moduli, and ͑iii͒ the uniform behavior found in oxide spinels under hydrostatic pressure. Quantum-mechanical ab initio perturbed ion results on MgAl 2 O 4 , ZnAl 2 O 4 , ZnGa 2 O 4 , and MgGa 2 O 4 direct spinels and on MgGa 2 O 4 inverse spinel are reported to illustrate the interpretative capabilities of the proposed equations.

Origin of the low compressibility in hard nitride spinels

“…All these results indicate that the behavior of the group-IV nitride spinels resembles that of normal oxide ordered spinels with tetrahedra ͑octahedra͒ compressing more ͑less͒ than the bulk. 18 This conduct is confirmed by the calculated atomic sizes of the group-IV element since the tetrahedral ͑octahedral͒ interstices are occupied by the biggest ͑smallest͒ A atom ͑see Table II͒. Let us go now to the more distinctive findings enclosed in the electron density. A common feature of these nitride spinels is the existence of highly directional bonds governing the molecular graph and conferring them great resistance to pressure load.…”

“…13 Moreover, they are in concordance with our previous analysis in several oxide spinels. 18 Thus, the unit cell reduction under pressure is mostly achieved through AN 4 deformations. A complete partition of the unit cell in terms of empty and occupied polyhedra reveals other two remarkable results: ͑i͒ the average of the tetrahedral and octahedral bulk moduli is found to be a good estimation of the macroscopic bulk modulus due to the low variation of u with pressure in the three crystals, and ͑ii͒ those polyhedra with larger ͑smaller͒ volumes than in the ideal uϭ0.25 lattice show compressibilities larger ͑smaller͒ than the bulk value.…”

“…17 This simple partition is also related here to the more usual decomposition in terms of the elementary AN 4 and AN 6 polyhedra of the cubic spinel structures. 18 As a result, the linking between compressibility and chemical bonding is clearly established, and factors determining the difficulty in the synthesis of ␥-A 3 N 4 polymorphs are also derived.…”

Post-spinel transformations and equation of state inZnGa2O4: Determination at high pressure byin situx-ray diffraction

“…It should be said here, that a partial inversion between Zn and Ga sites could cause a decrease of the compressibility of the ZnO 4 tetrahedra. A decrease of this compressibility would necessary lead to an enhancement of B 0 if we compare it with that of the normal spinel [19]. Evidence of such pressureinduced cation inversion has been found in other oxide spinels upon compression; e.g.…”

Structure and stability ofZrSiO4under hydrostatic pressure

“…͑3͒ show that ͑i͒ SiO 4 Ͻ Ͻ ZrO 8 for all pressures studied ͑up to 60 GPa͒, ͑ii͒ the compressibilities of the bulk and the dodecahedra are similar in both structures, in concordance with the findings of Errandonea et al 36 quoted above, and ͑iii͒ the average of the compressibilities of these two types of polyhedra is not a good estimation of the compressibility of ZrSiO 4 , contrarily to AB 2 O 4 spinels. 44 The AIM analysis of the electron density of zircon and reidite provides further insight into the compressibility of these systems. The relevant properties at zero pressure appear summarized in Table IV.…”