Building up a face centered cubic lattice: Difference between revisions

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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 = 4 m^3    \right. </math>,
 
with <math> m </math> being a positive integer
: <math> \left. M = 4 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)  \\
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</math>
</math>


where the indices of a given valid site are integer number that must fulfill:
where the indices of a given valid site are an integer number that must fulfill the following criteria


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


with
with

Revision as of 18:39, 19 March 2007

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

with being a positive integer

  • The positions are those given by:

where the indices of a given valid site are an integer number that must fulfill the following criteria

  • ,
  • the sum of must be, for instance, an even number.

with