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 $L$
2. a number of lattice positions, $M$ given by $M=m^3$ ; with $m$ being a positive integer

• The $M$ positions are those given by:

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

where $\delta l=L/m$

Atomic position(s) on a cubic cell

• Number of atoms per cell: 1
• Coordinates:

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

Cell dimensions:

• $a=b=c$

• $\alpha =\beta =\gamma =90^0$