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Crystallography Flashcards

1
Q

What is symmetry?

A

The order of arrangement and orientation of atoms in minerals, and the order in the consequent distribution of mineral properties.

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2
Q

What are the 4 basic types of symmetry operations?

A

Reflection, Rotation, Inversion, Translation

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3
Q

What are the basic Point Symmetry Operations?

A

Reflection, Rotation, Inversion

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4
Q

What is Reflection?

A

Reflection refers to symmetry distributed across a plane

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5
Q

What is Rotation?

A

Rotation refers to symmetry distributed about an axis

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6
Q

What is Inversion?

A

Inversion refers to symmetry related through a central point

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7
Q

What is Handedness?

A

The nature of a second motif that is generated after a given symmetry operation

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8
Q

What are the symmetry operator, the symbol, and the handedness for Inversion?

A

inversion center/point
i
opposite

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9
Q

What are the symmetry operator, the symbol, and the handedness for Rotation?

A

Rotation axis
n
same

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10
Q

What are the symmetry operator, the symbol, and the handedness for Reflection?

A

Mirror plane
m
opposite

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11
Q

What is a motif?

A

Set of atoms arranged in a particular way/geometrical pattern (in respect to 2-D lattice)

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12
Q

What are the options of Rotational Symmetry?

A

n = 2, 3, 4 or 6
2 motifs about a 2-fold axis, 180° apart
3 motifs about a 3-fold axis, 120° apart
4 motifs about a 4 fold axis, 90° apart
6 motifs about a 6-fold axis, 60° apart

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13
Q

What is Translational Symmetry?

A

Space symmetry
symbol: t
Handedness: same
ALL minerals process translation!

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14
Q

What is the difference between point symmetry and space symmetry?

A

Point symmetry: collection of atoms around a central point (reflection,rotation,inversion)
Space symmetry: motifs are generated across large distances (translation)

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15
Q

What is Roto-Inversion Symmetry?

A

Combination of Rotation+Inversion that produces a unique symmetry element.
2-step process done in sequence
Symbol: bar n
Options: n= bar 2,bar 3,bar 4 (unique), bar 6

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16
Q

How many symmetry combinations are possible? What is the list called?

A

32 point groups/ crystal classes
(w/o translation)
Hermann-Mauguin Symbols

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17
Q

How many crystal systems are there?
What are their names?

A

7 crystal systems
Triclinic, Monoclinic, Orthorhombic, Tetragonal, Rhombohedral, Hexagonal, Isometric

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18
Q

Geometry of crystallographic axes

A

a - horizontal, + facing you
b - horizontal to the side, + to the right
c - vertical, + towards top
alpha: angle between b and c axes
beta: angle between a and c axes
gamma: angle between a and b axes

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19
Q

Triclinic

A

Least amount of symmetry
a ≠ b ≠ c all angles ≠ 90

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20
Q

Monoclinic

A

mono = one, clinic = inclined. a ≠ b ≠ c, alpha + gamma = 90, beta > 90

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21
Q

Orthorhombic

A

a ≠ b ≠ c all angles = 90

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22
Q

Tetragonal

A

a1 = a2 ≠ c all angles = 90

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23
Q

Hexagonal-Rhombohedral

A

a1 = a2 = a3, all angles equal but ≠ 90

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24
Q

Hexagonal-Hexagonal

A

a1 = a2 = a3 ≠ c a angles = 120 to each other, a and c axes are 90

25
Isometric
Also called cubic. Highest symmetry. a1 = a2 = a3 all angles = 90
26
What are Miller Indices?
Indicates the orientation of a particular crystal face in space. General symbol is (hkl). Each letter stands for an integer (whole number)
27
What is a form? What is a habit?
Form: set of faces related by symmetry element Habit: describes external shape of a crystal (fibrous,tabular,needle-like,equant,bladed...)
28
General forms to know
pinacoid (set of 2 parallel faces) Prism (set of faces parallel to 1 axis): rhombic, tetragonal, hexagonal Dipyramid: rhombic, tetragonal, hexagonal, scalenohedran (triangular faces)
29
Forms to know that are specific to a particular crystal system
Hexagonal-Rhombohedral system: rhombohedron Isometric System: cube, octahedron, dodecahedron, tetrahedron, pyrithohedron
30
What is a Holohedral?
Highest symmetry for each group/ all faces required by complete symmetry ("last one in each group")
31
What is a Lattice? What is a 2-D Lattice called? What is a 3-D Lattice called?
Imaginary points that form a repeating pattern. Nets Bravais Lattices
32
What are the 5 unique lattices in 2-D?
Square Net: a1 = a2 at 90, 4-fold Hexa Net: a1 = a2 at 60 (or 120), 6-fold or (3-fold) Ortho Net: a ≠ b at 90, 2-fold Centered Ortho Net: a ≠ b at 90 (w/center point) Clino Net: a ≠ b, no special angle, 1 or 2-fold
33
How many Bravais Lattices exist?
14 3-D Bravais Lattices derived from the 2-D nets.
34
What are the 14 Bravais lattices?
Triclinic P Monoclinic P C Orthorhombic P I C F Tetragonal P I Hex-Hexagonal P Hex-Rhombohedral R Isometric P I F
35
What is a primitive lattice?
Primitive lattices only have lattice points are the corners of the cell. Each corner contributes 1/8 of it's volume to the cell.
36
What lattices are Holohedral?
All lattices are holohedral, meaning they have the highest symmetry possible for that crystal system.
36
What are the general types of Bravais Lattices
P: Primitive. 1 lattice points per cell. 1/8 x 8 corners I: Body-Centered. 2 per cell. 1/8 x 8 plus 1 in center F: Face-Centered. 4 per cell. 1/8 x 8 plus 1/2 x 6 A, B or C End Centered. 2 per cell. 1/8x8 plus 1/2 x 2 R: Rhombohedral. 1 per cell. special type. 1/8 x 8
37
Tetragonal Primitive Lattice
3-D lattice that is consistent with a single 4-fold of rotation(c-axis). a1 = a2 ≠ c, angles all 90. Has 1 lattice points per cell (1/8 x 8 = 1). 4/m 2/m 2/m
38
Isometric Primitive Lattice
a1 = a2 = a3, all angles at 90. Has 1 lattice point per cell (1/8 x 8). 4/m bar 3, 2/m. "cubic"
39
Tetragonal Body-Centered Lattice
a1 = a2 ≠ c, all angles at 90. Has 2 lattice points per cell. (1/8 x 8=1 and 1 in the middle). 4/m 2/m 2/m
40
Isometric Body-Centered Lattice
a1 = a2 = a3, all angles at 90. 4/m 2/m 2/m. Has 2 lattice points per cell (1/8 x 1 and 1 in the middle)
41
Symbol for Body-Centered Symbol for Face-Centered
I = Innenzentriert (body centered) F = Flächenzentriert (face centered)
42
What are Glide Planes?
Combination of reflection (m) + translation in a 2 step process. Reflection flips the image, then translation moves the image. Opposite handed. Example: footsteps
43
What are Screw Axes?
Combination of rotation (n) + translation in a 2 step process. Rotation does NOT flip the image then translation moves the image. Same handed motif. Ex: tightening a screw, spiral staircase appearance
44
How to reduce space group to equivalent point group?
1. Drop letter that indicates lattice type (P I F, A-B-C, or R) 2. Convert any glide planes (a, b, c, n, d) to regular mirror plane (m) 3. Convert any screw axes to regular rotation axes (drop the subscripts) Example. Iba2 = mm2 (orthorhombic)
45
What are the building blocks in silicate minerals?
The fundamental building block in silicate minerals is an (SiO4)4- tetrahedron with oxygen at the corners and silicon in the center
46
Nesosilicates
Isolated tetrahedron Ratio 1:4 Example: Olivine, Garnet
47
Sorosilicates
Double tetrahedron Ratio: 1:3.5 Example: Tanzanite gem
48
Cyclosilicates
Tetrahedral ring/Ring silicates Ratio: 1:3 Example: Beryl
49
Inosilicates - single
Infinite chain of tetrahedra Ratio: 1:3 Example: Pyroxine
50
Inosilicates - double
Infinite double chain of tetrahedra Ratio: 1:2.75 Example: Amphiboles
51
Phyllosilicates
Infinite sheet/Sheet silicates Ratio: 1:2.5 Example: Micas, Clay
52
Tectosilicates
Infinite 3-D/Framework silicates (most polymerized) Ratio: 1:2 Example: Quartz, Feldspars
53
What are the Miller Indices for a cube
(100) (T00) (010) (0T0) (001) (00T)
54
What are the Miller Indices for a hexagonal prism with a pinacoid
(10T0) (T010) (01T0) (0T10) (T100) (1T00) (0001) (000T)
55
What are the Miller Indices for an octahedron
(111) (TTT) (T11) (1TT) (T1T) (1T1) (11T) (TT1)
56
What are the Miller Indices for a tetragonal prism with a pinacoid
(100) (T00) (010) (0T0) (001) (00T)
57
What is a unit cell?
All crystals are made of basic building blocks called Unit Cells (w/respect to 3-D lattice) -have any of the 7 (6) shapes (crystal systems!) - fit together in one of the 14 ways to make crystals - is defined by lattice points (who are substituted to represent a real motif)

EESC (4 decks)

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