In What Makes a Mineral you learned that a mineral is a natural solid with a definite chemistry and an orderly inner structure. In Ions you met atoms that have gained or lost electrons. Put the two together and you have the inside of most minerals: positive and negative ions stacked in a pattern that repeats in every direction.
Why it works
Opposite charges attract. In halite (rock salt), each $\text{Na}^{+}$ is surrounded by six $\text{Cl}^{-}$ and each $\text{Cl}^{-}$ by six $\text{Na}^{+}$, a pattern that repeats trillions of times. Two rules shape every mineral. First, the crystal as a whole must be electrically neutral: positive charges cancel negative ones. Second, ions must fit the spaces in the pattern, which depends on their size. So any ion with the same charge and nearly the same size can take another's place without breaking either rule.
- $\text{Mg}^{2+}$ (radius about 72 pm) and $\text{Fe}^{2+}$ (about 78 pm) trade places freely. That is why olivine ranges from $\text{Mg}_2\text{SiO}_4$ (forsterite) to $\text{Fe}_2\text{SiO}_4$ (fayalite), written $(\text{Mg},\text{Fe})_2\text{SiO}_4$.
- $\text{Na}^{+}$ (102 pm) is the right size to replace $\text{Ca}^{2+}$ (100 pm) but carries the wrong charge. In plagioclase feldspar the swap still happens, paired with $\text{Al}^{3+}$ replacing $\text{Si}^{4+}$ to keep the balance: a coupled substitution.
Key idea
A mineral is ions stacked in a repeating, electrically neutral pattern. Ions of similar size and the same charge can substitute for one another, so many minerals have a formula that varies within set limits.
Worked examples
Worked example: Balance a formula
Garnet (pyrope) has 3 $\text{Mg}^{2+}$, 3 $\text{Si}^{4+}$ and 12 $\text{O}^{2-}$ per formula unit, plus some $\text{Al}^{3+}$. How many aluminum ions?
- Known charges: $3(+2) + 3(+4) + 12(-2) = 6 + 12 - 24 = -6$.
- Aluminum must bring $+6$: $6 \div 3 = 2$ ions.
- The formula is $\text{Mg}_3\text{Al}_2\text{Si}_3\text{O}_{12}$.
Answer: 2 aluminum ions.
Worked example: A forsterite number
An olivine has 1.8 $\text{Mg}^{2+}$ and 0.2 $\text{Fe}^{2+}$ per formula unit. What fraction of its metal sites hold magnesium?
- There are always 2 sites: $1.8 + 0.2 = 2$.
- Magnesium fills $1.8 \div 2 = 0.90$ of them: geologists write Fo90.
- Olivine near Fo90 is typical of Earth's upper mantle.
Answer: $90\%$ (Fo90).
Common mistake
It is easy to think a mineral's formula is always exact, the way water is always $\text{H}_2\text{O}$. Many minerals are solid solutions: olivine can be any mix from all magnesium to all iron, and it is still olivine because the structure is the same. Check a substitution by asking two questions: is the charge the same (or balanced by a second swap), and is the size within about 15%?