What allows magnesium to substitute freely for iron in olivine?

Olivine is a mineral with the general chemical formula of (Mg, Fe)₂SiO₄. It belongs to the family of silicate minerals and is an important constituent of Earth's mantle and a common mineral in basaltic and ultramafic rocks. In the olivine structure, magnesium and iron can substitute for each other freely because they possess similar characteristics, which we will explain in detail below.

Olivine has an orthorhombic crystal structure, with isolated silicate \( (SiO_4)^{4-} \) tetrahedra, where each silicon atom is surrounded by four oxygen atoms in a tetrahedral arrangement. The metal cations (magnesium and iron) are located in octahedral sites between the silicate tetrahedra. The possible octahedral sites for Mg and Fe can be denoted as \( M1 \) and \( M2 \) sites, which are slightly different in size but can still accommodate both Mg and Fe.

One of the major reasons why magnesium can substitute freely for iron in olivine lies in the similar ionic radii of magnesium and iron in the crystal. The ionic radius of Mg²⁺ is approximately 0.72 Å, while the ionic radius of Fe²⁺ is approximately 0.78 Å. Due to their similar sizes, both cations can fit comfortably within the octahedral sites in olivine's structure.

Magnesium and iron share chemical and electronic similarities as well; both elements are divalent cations (Mg²⁺ and Fe²⁺) and lose two electrons to form a stable chemical bond with oxygen in the silicate structure. Their similar charge allows them to form similar ionic bonds with the oxygen in the silicate tetrahedra, which helps maintain the stability of the olivine structure when Mg and Fe are substituted for each other.

Because of the above-discussed factors (similar ionic radius, electronic configuration, and bonding with oxygen), the Mg-Fe substitution in olivine is an example of a solid solution series. The crystal lattice can accommodate a range of Mg-Fe compositions without any significant change in the crystal structure. Hence, minerals like forsterite (Mg₂SiO₄) and fayalite (Fe₂SiO₄) can form a complete solid solution series (olivine series) as their compositions vary between the two end-members. In conclusion, the ability of magnesium to substitute freely for iron in olivine is due to the similar ionic radius, electronic configuration, and bonding with oxygen that both Mg²⁺ and Fe²⁺ possess. As a result, the crystal structure of olivine can accommodate their substitution without any significant distortions or changes, allowing the formation of a complete solid solution series.