Building up a diamond lattice: Difference between revisions

Revision as of 13:29, 20 March 2007

[EN CONSTRUCCION]

a cubic simulation box whose sides are of length $\left.L\right.$
a number of lattice positions, $\left.M\right.$ given by $\left.M=8m^{3}\right.$ ,

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 integer numbers that must fulfill the following criteria

$0\leq i_{a}<4m$
$0\leq j_{a}<4m$
$0\leq k_{a}<4m$ ,
the sum of $\left.i_{a}+j_{a}+k_{a}\right.$ can have only the values: 0, 3, 4, 7, 8, 10, ...

i.e, $\left.i_{a}+j_{a}+k_{a}=4n\right.$ ; OR; $\left.i_{a}+j_{a}+z_{a}=4n+3\right.$ , with $n$ is any integer number

with $\left.\delta l=L/(4m)\right.$

@@ Line 3: / Line 3: @@
 * Consider:
 # 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 <math> \left. M = 4 m^3    \right. </math>,
+# a number of lattice positions, <math> \left. M \right. </math> given by <math> \left. M = 8 m^3    \right. </math>,
 with <math> m </math> being a positive integer
@@ Line 19: / Line 19: @@
 where the indices of a given valid site are  integer numbers that must fulfill the following criteria
-* <math> 0 \le i_a < 2m </math>
+* <math> 0 \le i_a < 4m </math>
-* <math> 0 \le j_a < 2m </math>
+* <math> 0 \le j_a < 4m </math>
-* <math> 0 \le k_a < 2m </math>,
+* <math> 0 \le k_a < 4m </math>,
-* the sum of <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> can have only the values: 0, 3, 4, 7,  8, 10, ...
+i.e, <math> \left. i_a + j_a + k_a =  4 n \right. </math>; OR; <math> \left. i_a + j_a + z_a = 4 n + 3 \right. </math>, with <math> n </math> is
+any integer number
 with
 <math>
 \left.
-\delta l = L/(2m)
+\delta l = L/(4m)
 \right.
 </math>