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Geometry of packing in planar patterns.
Oblique, square, hexagonal
Four rotational symmetry elements
Mirror plane (reflection), fold axes (rotation), center of symmetry (i), rotoinversion (rotation + inversion)
Writing H-M symbols
Determine overall symmetry content of the crystal
list each symmetry element present
determine total of each element present
determine different # of kinds present ** most important
H-M rotation axes
Write in descending order using numbers only. Such as 4 2. list for how many times there are types. if there are 3 types of 2 fold axes 2 must be written 3 times (2 2 2)
H-M mirror planes
If a mirror plane is perpendicular to a fold axis, the m is placed under the rotation axis, as in a fraction. m is listed as many times as there are types. 4/m 2/m 2/m .
If mirror planes are not perpendicular to rotation axes, add the m to the end of the symbol such as 4m.
H-M center of symmetry
An overbar is added to the odd-fold axes to represent presence of center of symmetry. All even fold axes have perpendicular mirror planes so it is unnecessary to state i.
if there is no center of symmetry then its H-M symbol is 1.
Miller indicies
isometric form - textrahexahedron - 24
Wavelength and color on a graph
The lowest point is the color that is being transmitted and the highest point is peak absorption
Isometric crystal system
a1,a2,a3 - perpendicular mirror plane 2 kinds (9 total 2 kinds)
4/m 3 bar, 2/m
Tetragonal Crystal system
A4= C A2= A1, A2
3 types of mirror planes all perpendicular to fold axes.
4/m 2/m 2/m
Orthorhombic
a,b,c all perpendicular to 3 types of mirror planes. A2= a,b,c
2/m 2/m 2/m
Hexagonal crystal system
C, a1, a2, a3. 3 types of mirror planes all perpendicular to axes. A6(orA3)=C
A2= 2 axes
6/m, 2/m, 2/m
Other type- hexagonal rhombohedral - the 3 fold
Monoclinic crystal system
a not equal b not equal c
𝛼=Ɣ=90 β ≄ 90
A2=b
2/m
Triclinic
a,b,c all not equal no angles equal. only center of symmetry.
Bar 1
the geologist can find amazing ores quickly through correct data
Mohs Hardness scale
Hardness of a glass plate
H= 5.5