Question

Dalton’s “Law” doesn’t hold for a large class of chemicals. One example is the mineral olivine, for instance, has the formula (Mg_xFe_2–x)SiO₄, in which x can vary from 0 to 2 from one sample of the mineral to another. It is a single material, not a mixture. Olivine can be described as an ionic solid, with silicate (SiO₄^4–) anions, Mg²⁺ cations, and iron cations Fe²⁺. Thinking of Mg²⁺ and Fe²⁺ as simply spheres with 2+ charges, one can estimate an ionic radius. Use the “high-spin” Fe radius. Are the radii of these two cations similar (within 10%)? If so, can you rationalize why the strange looking formula (Mg_xFe_2–x)SiO₄is possible?

Answer 1

Every ionic solid has its own crystal structure. Every crystal lattice comprises of voids and lattice point (where you can put atoms). Atomic structure of olivine is built with the hexagonal close-packed array of oxygen atom. Hexagonal close-packed array produced 2 octahedral holes and 8 tetrahedral holes. Among them, half of the tetrahedral sites occupied with Magnesium (Mg)or Iron(Fe) atom which has similar radii and one-eighth of tetrahedral holes occupied with silicon atoms(Si). As a crystal is always a charge neutral species thus the interchanging of divalent Mg or Fe won't create a problem. Thus MgxFe2–x)SiO4 is justified.