# Spinel Oxides

## Introduction

The spinel structure of general formula AB2O4 is complex enough to offer an extraordinary versatility. Remarkable magnetic, electrical and physical properties have been obtained depending on the nature of the different cations and their distribution among the two tetrahedral and octahedral sublattices. Spinel phase materials are involved in several technical areas such as magnetic recording, batteries, catalysis, biomedicine,…

## Crystal Structure

Cubic Structure

Spinel type compounds AB2O4 tend to crystallize in the cubic crystal system with the Fd$$\bar{3}$$m (#227) space group. The unit cell contains 8 formula units, where 8 tetrahedral and 16 octahedral sites can be occupied either by cation A or B. Crystallographic data are give below:

Atom Symmetry Wyckoff x y z
A Td 8a 1/8 1/8 1/8
B Oh 16d 1/2 1/2 1/2
O C3v 32e ~1/4 ~1/4 ~1/4

In the so called “normal spinel” structure (A)[B2]O4, the cation A occupies 1/8 of the tetrahedral sites, and the cation B one-half of the octahedral sites, whereas in an “inverse spinel” (B)[AB]O4, alternatively 1/8 of the tetrahedral sites are occupied by cation B whereas A and B occupy each 1/4 of the octahedral site. Cations A and B can rearrange – therefore, the normal and inverse spinel distributions represent extrema. The degree of inversion x characterizes the cation distribution in a more general formula (A1-xBx)[AxB2-x]O4.

tetragonal Structure

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