Building up a simple cubic lattice

• Consider:

1. a cubic simulation box whose sides are of length Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. L \right. }
2. a number of lattice positions, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. M \right. } given by Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. M = m^3 \right. } with Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m } being a positive integer

• The Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \delta l = L/m \right. }

Atomic position(s) on a cubic cell

• Number of atoms per cell: 1
• Coordinates:

Atom 1: X=0, Y=0, Z=0.

Cell dimensions:

• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a=b=c }

• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha = \beta = \gamma = 90^0 }