Question

1. Explain the terms: lattice, basis, structure, unit cell, Miller indices ?

Answer 1

Lattice - a 3D collection of points that divide space into smaller equally sized units.

Basis - a group of atoms associated with a lattice point. This may be one single atom or a group of atoms.

Structure - In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. A crystal structure is composed of a unit cell, a set of atoms arranged in a particular way; which is periodically repeated in three dimensions on a lattice.

Unit cell - The unit cell is defined as the smallest repeating unit having the full symmetry of the crystal structure. The geometry of the unit cell is defined as a parallelepiped, providing six lattice parameters taken as the lengths of the cell edges (a, b, c) and the angles between them (?, ?, ?).

Miller-indices - A shorthand notation to describe certain crystallographic directions and planes in a material.  

Lattice directions are in direct space and are denoted by [ ] brackets. A negative number is represented by a bar over the number.