Building up a face centered cubic lattice: Difference between revisions

Revision as of 18:39, 19 March 2007

a cubic simulation box whose sides are of length $\left.L\right.$
a number of lattice positions, $\left.M\right.$ given by $\left.M=4m^{3}\right.$ ,

with $m$ being a positive integer

\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 an integer number that must fulfill the following criteria

$0\leq i_{a}<m$
$0\leq j_{a}<m$
$0\leq k_{a}<m$ ,
the sum of $\left.i_{a}+j_{a}+k_{a}\right.$ must be, for instance, an even number.

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

@@ Line 1: / Line 1: @@
 * 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:
-<math>
+:<math>
 \left\{ \begin{array}{l}
 x_a = i_a \times (\delta l)  \\
@@ Line 18: / Line 15: @@
 </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 j_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