1. the size (i.e., radii) of the ions
   • free substitution can occur if size difference is less than ~15%
   • limited substitution can occur if size difference is 15 - 30%
   • little to no substitution can occur if size difference is greater than 30%
2. the charge of the ions --> cannot differ by more than 1

Isomorphs: minerals with different chemical compositions; same crystal structure (belong to same crystal class)

Polymorphs: minerals with same chemical composition; different crystal structures

Solid Solution is defined as "a mineral structure in which specific atomic site(s) are occupied in variable proportions by two or more different elements." (Klein & Hurlbut, p.233)

Examples:

The Olivine group represents a complete solid solution series

Compositions range from a 100% Mg-rich "end member" (forsterite) to a 100% Fe-rich "end member" (fayalite), with all mixtures of these two elements possible (e.g., 90% Mg and 10% Fe)

• complete solid solution series because Fe and Mg have same charge and similar ionic radius

Plagioclase Feldspars also display a complete solid solution series ranging from a 100% Na-rich end member (albite) to a 100% Ca-rich end member (anorthite), with all intermediate compositions possible.

• Because Na has a charge of +1 and Ca has a charge of +2, a double substitution must occur to maintain the charge balance. The other cations in the feldspar composition are Al (charge = +3) and Si (charge = +4). (Al and Si are close enough in size for substitution to occur)For each substitution of Ca (+2) for Na (+1), an equal amount of Al (+3) is substituted for Si (+4)
  e.g., a 50/50 mixture would have the composition:
  Ca_0.5Na _0.5Al _1.5Si _2.5 O ₈

  charge balance: (+2 x 0.5) + (+1 x 0.5) + (+3 x 1.5) + (+4 x 2.5) = +16

  which is balanced by -16 from oxygen

In contrast Alkali Feldspars display only a limited solid solution series because the radius of K (1.33 Å) is significantly larger than that of Na (0.97 Å)

Some carbonates show a limited solid solution series (e.g., calcite & magnesite)

• to maintain the calcite-type structure, large cations (e.g., Ca radius = 1.08 Å) cannot be freely replaced by small ones (e.g., Mg radius = 0.66 Å); if too much Mg is substituted, the structure destabilizes and collapses
• dolomite: 50/50 mix of Ca and Mg
  *structurally completely different from calcite - has alternating Ca-rich and Mg-rich layers