KevinYager at 22:48, 13 November 2016

2016-11-13T22:48:13Z

KevinYager: Created page with "'''SC''' or '''simple cubic''' is the simples and most generic cubic lattice. ==Canonical SC== ===Symmetry=== * Crystal Family: Cubic * [http://en.wikipedia..."

2016-11-13T22:47:11Z

Created page with "'''SC''' or '''simple cubic''' is the simples and most generic cubic lattice. ==Canonical SC== ===Symmetry=== * Crystal Family: Cubic * [http://en.wikipedia..."

New page

'''SC''' or '''simple cubic''' is the simples and most generic [[Lattice:Cubic|cubic]] lattice.

==Canonical SC==
===Symmetry===
* Crystal Family: Cubic
* [http://en.wikipedia.org/wiki/Lattice_system Crystal System]: [[Lattice:Cubic|Cubic]]
* [http://en.wikipedia.org/wiki/Bravais_lattice#Bravais_lattices_in_3_dimensions Bravais Lattice]: P (pcc)
* Crystal class: Hexoctahedral
* [http://en.wikipedia.org/wiki/Crystallographic_point_group Point Group]: m3m
* Space Group: Pm3m
* Particles per unit cell: <math>n=1</math>
* Volume of unit cell: <math>V_d=a^3</math>
* Dimensionality: <math>d=3</math>
* Projected ''d''-dimensional volume: <math>v_d=a^3</math>
* Solid angle: <math>\Omega_d=4\pi</math>
* Nearest-neighbor distance: <math>d_{nn}=a</math>
* Assuming spherical particles of radius ''R'':
** Particle volume fraction: <math>\phi=4 \pi R^3/\left(3a^3\right)</math>
** Maximum volume fraction: <math>\phi_{max}=\pi/6\approx0.524</math> when <math>R=a/2</math>
===Reciprocal-Space Peaks===
<pre>
peak q value h,k,l m f intensity
1: 6.283185307180 1,0,0 6 1 6
2: 8.885765876317 1,1,0 12 1 12
3: 10.882796185405 1,1,1 8 1 8
4: 12.566370614359 2,0,0 6 1 6
5: 14.049629462081 2,1,0 24 1 24
6: 15.390597961942 2,1,1 24 1 24
7: 17.771531752633 2,2,0 12 1 12
8: 18.849555921539 3,0,0 30 1 30
9: 19.869176531592 3,1,0 24 1 24
10: 20.838968152189 3,1,1 24 1 24
</pre>
[[Image:LatticePeaks-SC.png|450px]]

==Alternating Simple Cubic==
A simple cubic lattice where the particle identity (in every direction) alternates between two possibilities. Thus this lattice has 2 distinct particles, in a 1:1 ratio. The unit cell may be thought of as having 8 particles (4 of each type).

[[Image:Sc alternating.png|300px]]

===Examples===
====Atomics====
* [http://en.wikipedia.org/wiki/Sodium_chloride Sodium chloride (NaCl)] (''a'' = 5.6402 Å)

@@ Line 1: / Line 1: @@
-'''SC''' or '''simple cubic''' is the simples and most generic [[Lattice:Cubic|cubic]] lattice.
+'''SC''' or '''simple cubic''' is the simplest and most generic [[Lattice:Cubic|cubic]] [[lattice]].
 ==Canonical SC==
-===Symmetry===
+===[[Symmetry]]===
 * Crystal Family: Cubic
 * [http://en.wikipedia.org/wiki/Lattice_system Crystal System]: [[Lattice:Cubic|Cubic]]

Lattice:Simple cubic - Revision history

KevinYager at 22:48, 13 November 2016

KevinYager: Created page with "'''SC''' or '''simple cubic''' is the simples and most generic cubic lattice. ==Canonical SC== ===Symmetry=== * Crystal Family: Cubic * [http://en.wikipedia..."