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:
  1. a cubic simulation box whose sides are of length
  2. a number of lattice positions, 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:


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 }
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