Question

what is defined on a discrete lattice often on a square of simple cubic lattice

Answer 1

Answer:

In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (1850),[1] is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by:

{\displaystyle \mathbf {R} =n_{1}\mathbf {a} _{1}+n_{2}\mathbf {a} _{2}+n_{3}\mathbf {a} _{3}}\mathbf{R} = n_{1}\mathbf{a}_{1} + n_{2}\mathbf{a}_{2} + n_{3}\mathbf{a}_{3}

Answer 2

Discrete lattice is defined on a square of simple cubic lattice as Bravais lattice.

Explanation:

• Bravais lattice is named after Auguste Bravais
• It is an infinite array of discrete points which is generated by a set of discrete transitions.
• it is defined in three-dimensional spaces by $\mathbf{R} = n_{1}\mathbf{a}_{1} + n_{2}\mathbf{a}_{2} + n_{3}\mathbf{a}_{3}$ where
• $n_{i}$ are any integers and $a_{i}$ are primitive translation vectors or primitive vectors which lie in different directions (not necessarily mutually perpendicular) and span the lattice.
• The symmetrically aligned atoms which is the smallest group that can be repeated in an array in order to make up the entire crystal is called unit cell.