Building up a body centered cubic lattice: Difference between revisions
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\right\} | \right\} | ||
</math> | </math> | ||
where the indices of a given valid site <math>(i_a,j_a,k_a)</math> must be either all odd or all even. | where the indices of a given valid site <math>(i_a,j_a,k_a)</math> must fulfill: | ||
* <math> i_a, j_a, k_a </math> must be either all odd or all even. | |||
* <math> 0 \le i_a \le 2 m </math> | |||
* <math> 0 \le j_a \le 2 m </math> | |||
* <math> 0 \le k_a \le 2 m </math> | |||
and | |||
<math> | <math> | ||
\left. | \left.\delta l = L/(2m) | ||
\delta l = L/(2m) | |||
\right. | \right. | ||
</math> | </math> | ||
Revision as of 11:51, 20 March 2007
- Consider:
- 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. }
- 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 = 2 m^3 \right. } , with 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:
- 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\{ \begin{array}{l} x_a = i_a \times (\delta l) \\ y_a = j_a \times (\delta l) \\ z_a = k_a \times (\delta l) \end{array} \right\} }
where the indices of a given valid site 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 (i_a,j_a,k_a)} must fulfill:
- 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 i_a, j_a, k_a } must be either all odd or all even.
- 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 0 \le i_a \le 2 m }
- 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 0 \le j_a \le 2 m }
- 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 0 \le k_a \le 2 m }
and 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/(2m) \right. }