Building up a face centered cubic lattice: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
mNo edit summary |
||
| Line 1: | Line 1: | ||
* 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 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. L \right. }
- a number of lattice positions, 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. } 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. M = 4 m^3 \right. } ,
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 are an integer number that must fulfill the following criteria
- 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 0 \le i_a < m }
- 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 0 \le j_a < m }
- 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 0 \le k_a < m } ,
- the sum of 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. i_a + j_a + k_a \right. } must be, for instance, an even number.
with
