Unit Cell: The smallest subset of the lattice that still retains all of the physical, chemical, and symmetry properites of the mineral.

Axial Ratios: Distances measured in Å along the edges (axes) of the unit cell and ratio’d to the length of the unit cell along the b axes. This gives the ratio of the distances along the crystallographic axes expressed by a/b:b/b:c/b. By definition the relative length along the b axis will always be one.

For example native sulfur which is orthorhombic and has a=10.47 Å, b= 12.87 Å, and c= 24.49 Å. The ratios are then a=10.47/12.87, b=12.87/12/.87, and c=24.49/12.87. Thus the relative lengths of the unequal a,b, and c axis in this orthorhombic mineral are .813 (a) :1 (b) ; 1.903 (c).

Structure of the Unit Cell: The multiplicity of a unit cell is simply how many of the lattice nodes are shared with other cells. Each corner is shared by 8 adjacent cells, so only 1/8 of a specific corner belongs to a specific cell. Since each 3-D cell has 8 corners, the multiplicity of a primitive cell is 8 x 1/8 = 1. Centered faces are shared by only 2 cells, so add 1 (2x1/2) for each pair of centered faces. Body centered nodes (in the interior) are unique to each cell, so add 1 to each cell.

This becomes important when we try to figure out how to assemble a mineral. You will be combining the information from the Bravais lattice structure with charge information to decipher the pattern of bonding in the mineral structure. You should be able to calculate shared lattice nodes on the different Bravais Lattice types.

The difference in unit cell structure in different axial directions (even in the isometric system) gives rise to many of the interesting mineral properties. Many of these properties are influenced by uneven axial spacing, but they are more influenced by density of the atomic structure found along the particular axial direction.  

Vectorial Properties: Properties that vary in magnitude with crystallographic direction due to the different atomic arrangements along different crystal planes.

Continuous Vectorial Properties: Properties that have a fixed value along a specific crystallographic direction and vary continuously between unequal crystallographic directions. Examples are hardness, speed of light, electrical and thermal conductivity, and thermal expansion.

Discontinuous Vectorial Properties: Properties that do not have fixed values along a specific crystallographic axis and are also different between unequal crystallographic directions. Examples are growth rate, solution rate (both of which can change with time during crystallization), and cleavage (planes of weakest bonding, which occur periodically along a specific direction).