Building up a diamond lattice

[EN CONSTRUCCION]

• Consider:

1. a cubic simulation box whose sides are of length $L$
2. a number of lattice positions, $M$ given by $M=8m^3$,

with $m$ being a positive integer

• The $M$ positions are those given by:

$\{\begin{array}{c}{x}_a=i_a\times (\delta l)\\ y_a=j_a\times (\delta l)\\ z_a=k_a\times (\delta l)\end{array}\}$

where the indices of a given valid site are integer numbers that must fulfill the following criteria

• $0\le i_a<4m$
• $0\le j_a<4m$
• $0\le k_a<4m$,
• the sum of $i_a+j_a+k_a$ can have only the values: 0, 3, 4, 7, 8, 10, ...

i.e, $i_a+j_a+k_a=4n$; OR; $i_a+j_a+k_a=4n+3$, with $n$ is any integer number

• the indices $\{i_a,j_a,k_a\}$must be either all even or all odd.

with $\delta l=L/(4m)$