The silica tetrahedron can stand alone or share corners. How many corners each tetrahedron shares sorts nearly all the crust's minerals into five families, and that one structural fact explains their formulas, their shapes and the way they break.
| Family | Shared corners | O per Si | Examples and how they break |
|---|---|---|---|
| Isolated tetrahedra | 0 | 4 | olivine, garnet: no cleavage |
| Single chains | 2 | 3 | pyroxene: two cleavages near 90° |
| Double chains | 2 or 3 | 2.75 | amphibole: two cleavages at about 60° and 120° |
| Sheets | 3 | 2.5 | mica, clay: one perfect cleavage into sheets |
| 3-D frameworks | 4 | 2 | quartz: none; feldspar: two near 90° |
Why it works
Count oxygens per silicon: each unshared oxygen counts 1, each shared one counts $\tfrac12$. With $s$ shared corners, oxygens per silicon $= 4 - \tfrac{s}{2}$. Cleavage follows the weakest bonds. Inside a chain or sheet, Si–O bonds are strong; between chains or sheets, only weaker bonds through metal ions hold things together, so the crystal splits there. In quartz, every oxygen is shared in all three directions, leaving no weak plane at all, so it breaks along curved, shell-like surfaces.
Key idea
Tetrahedra link as isolated units, single chains, double chains, sheets or frameworks. Oxygens per silicon $= 4 - \tfrac{s}{2}$ for $s$ shared corners, and cleavage runs between the strongly bonded chains or sheets.
Worked examples
Worked example: From formula to family
Talc is $\text{Mg}_3\text{Si}_4\text{O}_{10}(\text{OH})_2$. Which family is it?
- Count the oxygens bonded to silicon (leave out the OH): $\text{Si}_4\text{O}_{10}$.
- Ratio: $10 \div 4 = 2.5$ oxygens per silicon.
- 2.5 is the sheet ratio. Talc is a sheet silicate, which is why it is soft and slippery: the sheets slide past one another.
Answer: A sheet silicate.
Worked example: Why double chains give 2.75
In a double chain, half the tetrahedra share 2 corners and half share 3. How many oxygens per silicon?
- Average shared corners: $\tfrac{2 + 3}{2} = 2.5$.
- Oxygens per silicon: $4 - \tfrac{2.5}{2} = 2.75$, so the repeat unit is $\text{Si}_4\text{O}_{11}$.
Answer: $2.75$.
Common mistake
It is tempting to memorize the five family names without their structures, and then it seems arbitrary that mica peels into sheets while quartz has no cleavage. Tie each property to the linking: sheets peel, chains split along their length at angles set by their width, and a framework has no weak direction. Check yourself with feldspar: also a framework, but its aluminum and the large ions between tetrahedra leave two planes of weaker bonds, so it does cleave.