Building up a simple cubic lattice

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A simple 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 $\left.M=m^{3}\right.$ ; with $m$ being a positive integer

• The $\left.M\right.$ positions are those given by:

$\left\{{\begin{array}{ll}x=i\times (\delta l)&;i=0,1,\cdots ,m-1\\y=j\times (\delta l)&;j=0,1,\cdots ,m-1\\z=k\times (\delta l)&;k=0,1,\cdots ,m-1\end{array}}\right.$

where $\left.\delta l=L/m\right.$

Atomic position(s) on a cubic cell

• Number of atoms per cell: 1
• Coordinates:

Atom 1: $\left(x_{1},y_{1},z_{1}\right)=\left(0,0,0\right)$

Cell dimensions:

• $a=b=c$

• $\alpha =\beta =\gamma =90^{0}$