Building up a square lattice

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  • Consider:
  1. a square simulation box whose sides are of length \left. L  \right.
  2. a number of lattice positions,  \left. M \right. given by  \left. M = m^{2}    \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 \\
\end{array}

\right.

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

Atomic position(s) on a square cell[edit]

  • Number of atoms per cell: 1
  • Coordinates:

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