Building up a body centered cubic lattice: Difference between revisions

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m (New page: * Consider: # a Cubic Simulation box of length <math>\left. L \right. </math> # a number of lattice positions, <math> \left. M \right. </math> given by: : <math> \left. M = 2 m^3 \ri...)
 
(Added a Jmol applet + category.)
 
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{{Jmol_general|Body_centered_cubic_lattice.xyz|A body centered cubic lattice}}
* 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 = 2 m^3    \right. </math>, with <math> m </math> being a positive integer
 
: <math> \left. M = 2 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 17: Line 13:
\right\}
\right\}
</math>
</math>
where the indices of a given valid site <math>(i_a,j_a,k_a)</math> must be all of them either odd or even.
where the indices of a given valid site <math>(i_a,j_a,k_a)</math> must fulfill:
* <math> i_a, j_a, k_a </math> must be either all odd or all even.
* <math> 0 \le i_a \le 2 m </math>
* <math> 0 \le j_a \le 2 m </math>
* <math> 0 \le k_a \le 2 m </math>


with
and
<math>
<math>
\left.
\left.\delta l = L/(2m)
\delta l = L/(2m)
\right.
\right.
</math>
</math>
== Atomic position(s) on a cubic cell ==
* Number of atoms per cell: 2
* Coordinates:
Atom 1: <math> \left( x_1, y_1, z_1 \right) = \left( 0, 0, 0 \right) </math>
Atom 2: <math> \left( x_2, y_2, z_2 \right) = \left( l/2, l/2, l/2 \right) </math>
Cell dimensions:
*<math> a=b=c = l </math>
*<math> \alpha = \beta = \gamma = 90^0 </math>
[[category: computer simulation techniques]]
[[category: Contains Jmol]]

Latest revision as of 13:28, 22 July 2009


<jmol> 

 <jmolApplet>
 <script>set spin X 10; spin on</script>
 <size>200</size>
 <color>lightgrey</color>
   <wikiPageContents>Body_centered_cubic_lattice.xyz</wikiPageContents>
</jmolApplet>
</jmol>
A body centered cubic lattice
  • 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 must fulfill:

  • must be either all odd or all even.

and

Atomic position(s) on a cubic cell[edit]

  • Number of atoms per cell: 2
  • Coordinates:

Atom 1:

Atom 2:


Cell dimensions:

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