Building up a simple cubic lattice: Difference between revisions
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* Consider: | * Consider: | ||
# a cubic simulation box whose sides are of length <math>\left. L \right. </math> | # a cubic simulation box whose sides are of length <math>\left. L \right. </math> | ||
# a number of lattice positions, <math> \left. M \right. </math> given by <math> \left. M = m^3 \right. </math> with <math> m </math> being a positive integer | # a number of lattice positions, <math> \left. M \right. </math> given by <math> \left. M = m^{3} \right. </math> ; with <math> m </math> being a positive integer | ||
* The <math> \left. M \right. </math> positions are those given by: | * The <math> \left. M \right. </math> positions are those given by: | ||
Revision as of 12:19, 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 = 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:
- 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}{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: 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( x_1, y_1, z_1 \right) = \left( 0, 0, 0 \right) }
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 }