3 Crystallography: crystal structure and crystal systems

Crystal structure

• The atoms of a mineral are arranged in an orderly way, giving the crystal form.
• A crystal is a solid geometric body with flat outer surfaces called crystal faces.
• Example: halite (rock salt, NaCl) forms when ${\text{<span class="eqx" dir="ltr" style="direction:ltr;unicode-bidi:isolate;display:inline-block">Na</span>}}^{+}$ and ${\text{<span class="eqx" dir="ltr" style="direction:ltr;unicode-bidi:isolate;display:inline-block">Cl</span>}}^{-}$ ions combine in a repeated pattern, giving a cubic crystal.
• The crystal system controls the shape of the mineral and its physical and chemical properties.

Elements used to study crystals

• Crystal axis: a line through the centre of the crystal; when the crystal rotates around it, faces, edges or angles repeat two or three times. Axes are written $\mathrm{<span\; class="eqx"\; dir="ltr"\; style="direction:ltr;unicode-bidi:isolate;display:inline-block">a</span>},\mathrm{<span\; class="eqx"\; dir="ltr"\; style="direction:ltr;unicode-bidi:isolate;display:inline-block">b</span>},\mathrm{<span\; class="eqx"\; dir="ltr"\; style="direction:ltr;unicode-bidi:isolate;display:inline-block">c</span>}$ when their lengths differ and ${\mathrm{<span\; class="eqx"\; dir="ltr"\; style="direction:ltr;unicode-bidi:isolate;display:inline-block">a</span>}}_{\mathrm{<span\; class="eqx"\; dir="ltr"\; style="direction:ltr;unicode-bidi:isolate;display:inline-block">1</span>}},{\mathrm{<span\; class="eqx"\; dir="ltr"\; style="direction:ltr;unicode-bidi:isolate;display:inline-block">a</span>}}_{\mathrm{<span\; class="eqx"\; dir="ltr"\; style="direction:ltr;unicode-bidi:isolate;display:inline-block">2</span>}},{\mathrm{<span\; class="eqx"\; dir="ltr"\; style="direction:ltr;unicode-bidi:isolate;display:inline-block">a</span>}}_{\mathrm{<span\; class="eqx"\; dir="ltr"\; style="direction:ltr;unicode-bidi:isolate;display:inline-block">3</span>}}$ when equal.
• Angles between the axes: written $\alpha ,\beta ,\gamma$.
• Plane of symmetry: a plane that divides the crystal into two identical halves.

Systems with three axes

Systems with four axes

• Hexagonal: three horizontal axes of equal length crossing at equal angles; they are perpendicular to a fourth axis of a different length. The fourth (vertical) axis has hexagonal symmetry. It has vertical and horizontal planes of symmetry.
• Trigonal: three equal horizontal axes crossing at equal angles; the fourth axis is perpendicular to their plane and has three-fold symmetry. It has no horizontal plane of symmetry.