Building up a body centered cubic lattice: Difference between revisions

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m (New page: * Consider: # a Cubic Simulation box of length <math>\left. L \right. </math> # a number of lattice positions, <math> \left. M \right. </math> given by: : <math> \left. M = 2 m^3 \ri...)
 
mNo edit summary
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* Consider:
* Consider:
# a Cubic Simulation box 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:
# a number of lattice positions, <math> \left. M \right. </math> given by <math> \left. M = 2 m^3    \right. </math>, with <math> m </math> being a positive integer
 
: <math> \left. M = 2 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:
 
:<math>
<math>
\left\{ \begin{array}{l}
\left\{ \begin{array}{l}
x_a = i_a \times (\delta l)  \\
x_a = i_a \times (\delta l)  \\
Line 17: Line 12:
\right\}
\right\}
</math>
</math>
where the indices of a given valid site <math>(i_a,j_a,k_a)</math> must be all of them either odd or even.
where the indices of a given valid site <math>(i_a,j_a,k_a)</math> must be either all odd or all even.
 
with
<math>
<math>
\left.
\left.

Revision as of 18:36, 19 March 2007

  • Consider:
  1. a cubic simulation box whose sides are of length
  2. a number of lattice positions, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.M\right.} given by , 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}{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 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 \left. \delta l = L/(2m) \right. }

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