Chapter 3

Coordination Number (CN)

The number of nearest neighbors for a particular atom or the number of atoms touching a particular atom.

Stable ionic structures

Ionic structures that maximize the number of nearest oppositely charged neighbors.

r/R ratio

The ratio used to determine the coordination number; it compares the radius of the cation to the radius of the anion.

Lattice

A collection of points arranged in a periodic fashion, each point having identical surroundings.

Basis (Motif)

A group of at least one atom associated with each lattice point.

Bravais lattices

14 distinct lattice types grouped into seven crystal systems.

Unit Cell

The smallest repeating unit of a crystal lattice that possesses all structural characteristics.

Atomic Packing Factor (APF)

A measure of how efficiently atoms fill space within a unit cell.

Density of materials

Calculated using the formula: density = mass / volume, adjusting for the number of atoms per unit cell.

Isotropic properties

Properties that are identical in all directions.

Anisotropic properties

Properties that depend on the crystallographic direction along which the property is measured.

Miller indices

A notation system in crystallography for planes and directions in crystal lattices.

Polymorphism/Allotropy

The existence of two or more distinct crystal structures for the same material.