CHEM 360 Handouts

 

 

Geometrical characteristics of the seven crystal systems.

 

  

System

Axial lengths and angles
Unit cell geometry

cubic

a = b = c, a = b = g = 90°

tetragonal

a = b c, a = b = g = 90°

orthorhombic

a b c, a = b = g = 90°

rhombohedral

a = b = c, a = b = g ≠ 90°

hexagonal

a = b c, a = b = 90°, g = 120°

monoclinic

a b c, a = g = 90°, b ≠ 90°

triclinic

a ≠ b ≠ c, a ≠ b ≠ g

 


Bravais Lattices

 

simple cubic

body-centered
cubic

face-centered
cubic

simple tetragonal

body-centered
tetragonal

simple
orthorhombic

body-centered
orthorhombic

base-centered
orthorhombic

face-centered
orthorhombic

rhombohedral

hexagonal

 

simple monoclinic

base-centered
monoclinic

triclinic

 


Some common directions in a cubic unit cell. The dot indicates the point where the vector exits the unit cell

 

 

 

 

Schematic representation of a close packed layer of equal sized spheres. The close packed rows (directions) are shown by the dashed lines.

 

 

Schematic represenation of two close packed layers arranged in A (dark grey) and B (light grey) positions. The alternative stacking of the B layer is shown in (a) and (b)

 

(a)

(b)

 

 

A schematic projection of the basal plane of the hcp unit cell on the close packed layers

 

 

 

Schematic represenation of the three close packed layers in a cubic close packed arrangement: A (dark grey), B (medium grey), and C (light grey).

 

 

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