Building up a face centered cubic lattice: Difference between revisions

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{{Jmol_general|Face_centered_cubic_lattice.xyz|A face 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 = 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:
* 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)  \\
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</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 integer numbers that must fulfill the following criteria


* <math> 0 \le i_a < m </math>
* <math> 0 \le i_a < 2m </math>
* <math> 0 \le j_a < m </math>  
* <math> 0 \le j_a < 2m </math>  
* <math> 0 \le k_a < m </math>,
* <math> 0 \le k_a < 2m </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
with
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\right.
\right.
</math>
</math>
== Atomic position(s) on a cubic cell ==
* Number of atoms per cell: 4
* 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( 0 , \frac{l}{2}, \frac{l}{2}\right) </math>
Atom 3: <math> \left( x_3, y_3, z_2 \right) = \left( \frac{l}{2}, 0, \frac{l}{2} \right) </math>
Atom 4: <math> \left( x_4, y_4, z_2 \right) = \left( \frac{l}{2}, \frac{l}{2}, 0  \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 09:58, 25 June 2012


<jmol> 

 <jmolApplet>
 <script>set spin X 10; spin on</script>
 <size>200</size>
 <color>lightgrey</color>
   <wikiPageContents>Face_centered_cubic_lattice.xyz</wikiPageContents>
</jmolApplet>
</jmol>
A face 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 are integer numbers that must fulfill the following criteria

  • ,
  • the sum of must be, for instance, an even number.

with

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

  • Number of atoms per cell: 4
  • Coordinates:

Atom 1:

Atom 2:

Atom 3:

Atom 4:

Cell dimensions:

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