Building up a face centered cubic lattice: Difference between revisions

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* <math> 0 \le j_a < m </math>  
* <math> 0 \le j_a < m </math>  
* <math> 0 \le k_a < m </math>,
* <math> 0 \le k_a < m </math>,
 
*and the sum: <math> \left. i_a + j_a + k_a \right. </math> must be, for instance, an even number.  
and its sum: <math> i_a + j_a + k_a </math> must be an, for instance, even number.  


with
with

Revision as of 18:31, 19 March 2007

  • Consider:
  1. a Cubic Simulation box 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 = 4 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 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 are integer number that 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 0 \le i_a < 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 < 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 < m } ,
  • and the sum: 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. i_a + j_a + k_a \right. } must be, for instance, an even number.

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 \left. \delta l = L/(2m) \right. }

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