# Building up a body centered cubic lattice

  200 lightgrey Body_centered_cubic_lattice.xyz  A body centered cubic lattice
• Consider:
1. a cubic simulation box whose sides are of length $\left. L \right.$
2. a number of lattice positions, $\left. M \right.$ given by $\left. M = 2 m^3 \right.$, with $m$ being a positive integer
• The $\left. M \right.$ positions are those given by:
$\left\{ \begin{array}{l} x_a = i_a \times (\delta l) \\ y_a = j_a \times (\delta l) \\ z_a = k_a \times (\delta l) \end{array} \right\}$

where the indices of a given valid site $(i_a,j_a,k_a)$ must fulfill:

• $i_a, j_a, k_a$ must be either all odd or all even.
• $0 \le i_a \le 2 m$
• $0 \le j_a \le 2 m$
• $0 \le k_a \le 2 m$

and $\left.\delta l = L/(2m) \right.$

## Atomic position(s) on a cubic cell

• Number of atoms per cell: 2
• Coordinates:

Atom 1: $\left( x_1, y_1, z_1 \right) = \left( 0, 0, 0 \right)$

Atom 2: $\left( x_2, y_2, z_2 \right) = \left( l/2, l/2, l/2 \right)$

Cell dimensions:

• $a=b=c = l$
• $\alpha = \beta = \gamma = 90^0$