Building up a simple cubic lattice: Difference between revisions

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{{Jmol_general|Simple_cubic_lattice.xyz|A simple 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 numer 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 = m^{3}    \right. </math> ; with <math> m </math> being a positive integer


: <math> \left. M = m^3    \right. </math>
* The <math> \left. M \right. </math> positions are those given by:  
 
:<math>
: with <math> m </math> being a positive integer
 
* The <math> \left. M \right. </math> positions are those given by:
 
<math>
\left\{ \begin{array}{ll}
\left\{ \begin{array}{ll}
x = i \times (\delta l) &; i=0,1,\cdots, m-1 \\
x = i \times (\delta l) &; i=0,1,\cdots, m-1 \\
Line 15: Line 11:
z = k \times (\delta l) &; k=0,1,\cdots, m-1  
z = k \times (\delta l) &; k=0,1,\cdots, m-1  
\end{array}
\end{array}
\right.
\right.
</math>
</math>


with:
where
<math>
<math>
\left.
\left.
Line 24: Line 21:
\right.
\right.
</math>
</math>
== Atomic position(s) on a cubic cell ==
* Number of atoms per cell: 1
* Coordinates:
Atom 1: <math> \left( x_1, y_1, z_1 \right) = \left( 0, 0, 0 \right) </math>
Cell dimensions:
*<math> a=b=c </math>
*<math> \alpha = \beta = \gamma = 90^0 </math>
[[category: computer simulation techniques]]
[[category: Contains Jmol]]

Latest revision as of 13:01, 22 July 2009


<jmol> 

 <jmolApplet>
 <script>set spin X 10; spin on</script>
 <size>200</size>
 <color>lightgrey</color>
   <wikiPageContents>Simple_cubic_lattice.xyz</wikiPageContents>
</jmolApplet>
</jmol>
A simple 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

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

  • Number of atoms per cell: 1
  • Coordinates:

Atom 1:


Cell dimensions:

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