Building up a diamond lattice - Revision history

Nice and Tidy at 10:00, 13 February 2008

2008-02-13T10:00:38Z

← Older revision		Revision as of 12:00, 13 February 2008
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	*<math> \alpha = \beta = \gamma = 90^0 </math>		*<math> \alpha = \beta = \gamma = 90^0 </math>
			[[category: computer simulation techniques]]

Carl McBride at 17:14, 4 June 2007

2007-06-04T17:14:03Z

← Older revision		Revision as of 19:14, 4 June 2007
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	~~[EN CONSTRUCCION]~~

	* Consider:		* Consider:
	# a cubic simulation box whose sides are of length <math>\left. L \right. </math>		# a cubic simulation box whose sides are of length <math>\left. L \right. </math>

Noe: /* Atomic position(s) on a cubic cell */

2007-03-20T16:42:21Z

Atomic position(s) on a cubic cell

← Older revision		Revision as of 18:42, 20 March 2007
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	== Atomic position(s) on a cubic cell ==		== Atomic position(s) on a cubic cell ==

	* Number of atoms per cell: 4		* Number of atoms per cell: 8
	* Coordinates:		* Coordinates:
	Atom 1: <math> \left( x_1, y_1, z_1 \right) = \left( 0, 0, 0 \right) </math>		Atom 1: <math> \left( x_1, y_1, z_1 \right) = \left( 0, 0, 0 \right) </math>
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	Atom 2: <math> \left( x_2, y_2, z_2 \right) = \left( 0 , \frac{l}{2}, \frac{l}{2}\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 3: <math> \left( x_3, y_3, z_3 \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>		Atom 4: <math> \left( x_4, y_4, z_4 \right) = \left( \frac{l}{2}, \frac{l}{2}, 0 \right) </math>

			Atom 5: <math> \left( x_5, y_5, z_5 \right) = \left( \frac{l}{4}, \frac{l}{4}, \frac{l}{4} \right) </math>

			Atom 6: <math> \left( x_6, y_6, z_6 \right) = \left( \frac{l}{4}, \frac{3l}{4}, \frac{3l}{4} \right) </math>

			Atom 7: <math> \left( x_7, y_7, z_7 \right) = \left( \frac{3l}{4}, \frac{l}{4}, \frac{3l}{4} \right) </math>

			Atom 8: <math> \left( x_8, y_8, z_8 \right) = \left( \frac{3l}{4}, \frac{3l}{4}, \frac{l}{4} \right) </math>

	Cell dimensions:		Cell dimensions:

Noe at 16:37, 20 March 2007

2007-03-20T16:37:58Z

← Older revision		Revision as of 18:37, 20 March 2007
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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>

Noe at 13:10, 20 March 2007

2007-03-20T13:10:44Z

← Older revision		Revision as of 15:10, 20 March 2007
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	* <math> 0 \le k_a < 4m </math>,		* <math> 0 \le k_a < 4m </math>,
	* the sum of <math> \left. i_a + j_a + k_a \right. </math> can have only the values: 0, 3, 4, 7, 8, 10, ...		* 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 + k_a = 4 n + 3 \right. </math>, with <math> n </math> is		i.e, <math> \left. i_a + j_a + k_a = 4 n \right. </math>; OR; <math> \left. i_a + j_a + k_a = 4 n + 3 \right. </math>, with <math> n </math> being
	any integer number		any integer number
	* the indices <math> \left\{ i_a, j_a, k_a \right\} </math>must be either all even or all odd.		* the indices <math> \left\{ i_a, j_a, k_a \right\} </math>must be either all even or all odd.

Noe at 12:25, 20 March 2007

2007-03-20T12:25:48Z

← Older revision		Revision as of 14:25, 20 March 2007
Line 23:		Line 23:
	* <math> 0 \le k_a < 4m </math>,		* <math> 0 \le k_a < 4m </math>,
	* the sum of <math> \left. i_a + j_a + k_a \right. </math> can have only the values: 0, 3, 4, 7, 8, 10, ...		* 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		i.e, <math> \left. i_a + j_a + k_a = 4 n \right. </math>; OR; <math> \left. i_a + j_a + k_a = 4 n + 3 \right. </math>, with <math> n </math> is
	any integer number		any integer number
	* the indices <math> \left\{ i_a, j_a, k_a \right\} </math>must be either all even or all odd.		* the indices <math> \left\{ i_a, j_a, k_a \right\} </math>must be either all even or all odd.

Noe at 11:32, 20 March 2007

2007-03-20T11:32:56Z

← Older revision		Revision as of 13:32, 20 March 2007
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	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		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		any integer number
			* the indices <math> \left\{ i_a, j_a, k_a \right\} </math>must be either all even or all odd.
	with		with
	<math>		<math>

Noe at 11:29, 20 March 2007

2007-03-20T11:29:35Z

← Older revision		Revision as of 13:29, 20 March 2007
Line 3:		Line 3:
	* Consider:		* Consider:
	# a cubic simulation box whose sides are 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 <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		with <math> m </math> being a positive integer

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	where the indices of a given valid site are integer numbers that must fulfill the following criteria		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		with
	<math>		<math>
	\left.		\left.
	\delta l = L/(2m)		\delta l = L/(4m)
	\right.		\right.
	</math>		</math>

Noe: New page: [EN CONSTRUCCION] * Consider: # a cubic simulation box whose sides are of length $\left. L \right.$ # a number of lattice positions, $\left. M \right.$ given by ...

2007-03-20T11:22:27Z

New page: [EN CONSTRUCCION] * 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 ...

New page

[EN CONSTRUCCION]

* 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>,
with <math> m </math> being a positive integer

* The <math> \left. M \right. </math> positions are those given by:

:<math>
\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\}
</math>

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 j_a < 2m </math>
* <math> 0 \le k_a < 2m </math>,
* the sum of <math> \left. i_a + j_a + k_a \right. </math> must be, for instance, an even number.

with
<math>
\left.
\delta l = L/(2m)
\right.
</math>