Introduction to Magnetite

Magnetite, Fe$_3$O$_4$ is a member of the Spinel family of minerals, all of whose crystal structures are similar. Crystallographically magnetite takes a cubic inverse spinel form[49]. The oxygen ions form a close-packed cubic lattice with the iron ions located at interstices between the oxygen ions. There are two different interstices that the metal ions can take, tetrahedral (A) sites and octohedral (B) sites.

Chemically magnetite/maghemite can be represented by the formula

$$\mathrm{Fe}^{3+}\left[ \mathrm{Fe}^{2+}_{1-y} \,\mathrm{Fe}^{3+}_{1-y} \,\mathrm{Fe}^{3+}_{1.67y} \,\square_{0.33y} \right] \mathrm{O}_{4}$$

where $y=0$ for pure magnetite and $y=1$ for pure maghemite, and vacancies are represented by $\square$.[50]

Magnetite exhibits a variety of characteristics, dependent on its temperature. There are three regions of temperature where magnetite behaves differently:

1. between $0\ensuremath{\unskip\,\mathrm{K}}$ and $119\ensuremath{\unskip\,\mathrm{K}}$ (the Verwey transition temperature, $T_{v}$),
2. between $120\ensuremath{\unskip\,\mathrm{K}}$ and $840\ensuremath{\unskip\,\mathrm{K}}$ (the Curie temperature, $T_{c}$),
3. above $840\ensuremath{\unskip\,\mathrm{K}}$.

In region 3 magnetite is paramagnetic with metallic-like conductivity. In region 2 the A sites are populated by Fe$^{3+}$ ions and the B sites by Fe$^{3+}$ and Fe$^{2+}$ ions, with twice as many B sites populated as A sites. At these temperatures electron-hopping occurs between the B sites. This electron hopping occurs over a timescale of approximately $10^{-9}\ensuremath{\unskip\,\mathrm{s}}$. As the timescale of the Mössbauer event is $10^{-7}\ensuremath{\unskip\,\mathrm{s}}$ the nuclei at each site display an average charge state of $2.5+$ during this time interval. Thus a Mössbauer spectrum displays two distinct components: one from the Fe$^{3+}$ ions on the A sites and one from the Fe$^{2.5+}$ average on the B sites.

Below $T_{v}$ the electron hopping process stops and the ions on the B sites have a fixed charge. A Mössbauer spectrum now has three components: one from Fe$^{3+}$ ions on the A sites, one from Fe$^{3+}$ ions on the B sites and one from the Fe$^{2+}$ ions on the B sites.