Building up a face centered cubic lattice: Difference between revisions
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* Consider: | * Consider: | ||
# a | # 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 | |||
* 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 18: | Line 15: | ||
</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>, | ||
* | * 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:
- a cubic simulation box whose sides are of length
- 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