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eesc > Crystallography > Flashcards

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
Q

Isometric

A

Also called cubic. Highest symmetry.
a1 = a2 = a3 all angles = 90

26
Q

What are Miller Indices?

A

Indicates the orientation of a particular crystal face in space. General symbol is (hkl). Each letter stands for an integer (whole number)

27
Q

What is a form? What is a habit?

A

Form:
set of faces related by symmetry element
Habit: describes external shape of a crystal (fibrous,tabular,needle-like,equant,bladed…)

28
Q

General forms to know

A

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
Q

Forms to know that are specific to a particular crystal system

A

Hexagonal-Rhombohedral system: rhombohedron
Isometric System: cube, octahedron, dodecahedron, tetrahedron, pyrithohedron

30
Q

What is a Holohedral?

A

Highest symmetry for each group/ all faces required by complete symmetry (“last one in each group”)

31
Q

What is a Lattice?
What is a 2-D Lattice called?
What is a 3-D Lattice called?

A

Imaginary points that form a repeating pattern.
Nets
Bravais Lattices

32
Q

What are the 5 unique lattices in 2-D?

A

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
Q

How many Bravais Lattices exist?

A

14 3-D Bravais Lattices derived from the 2-D nets.

34
Q

What are the 14 Bravais lattices?

A

Triclinic P
Monoclinic P C
Orthorhombic P I C F
Tetragonal P I
Hex-Hexagonal P
Hex-Rhombohedral R
Isometric P I F

35
Q

What is a primitive lattice?

A

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
Q

What lattices are Holohedral?

A

All lattices are holohedral, meaning they have the highest symmetry possible for that crystal system.

36
Q

What are the general types of Bravais Lattices

A

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
Q

Tetragonal Primitive Lattice

A

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
Q

Isometric Primitive Lattice

A

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
Q

Tetragonal Body-Centered Lattice

A

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
Q

Isometric Body-Centered Lattice

A

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
Q

Symbol for Body-Centered
Symbol for Face-Centered

A

I = Innenzentriert (body centered)
F = Flächenzentriert (face centered)

42
Q

What are Glide Planes?

A

Combination of reflection (m) + translation in a 2 step process. Reflection flips the image, then translation moves the image. Opposite handed.
Example: footsteps

43
Q

What are Screw Axes?

A

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
Q

How to reduce space group to equivalent point group?

A
  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
Q

What are the building blocks in silicate minerals?

A

The fundamental building block in silicate minerals is an (SiO4)4- tetrahedron with oxygen at the corners and silicon in the center

46
Q

Nesosilicates

A

Isolated tetrahedron
Ratio 1:4
Example: Olivine, Garnet

47
Q

Sorosilicates

A

Double tetrahedron
Ratio: 1:3.5
Example: Tanzanite gem

48
Q

Cyclosilicates

A

Tetrahedral ring/Ring silicates
Ratio: 1:3
Example: Beryl

49
Q

Inosilicates - single

A

Infinite chain of tetrahedra
Ratio: 1:3
Example: Pyroxine

50
Q

Inosilicates - double

A

Infinite double chain of tetrahedra
Ratio: 1:2.75
Example: Amphiboles

51
Q

Phyllosilicates

A

Infinite sheet/Sheet silicates
Ratio: 1:2.5
Example: Micas, Clay

52
Q

Tectosilicates

A

Infinite 3-D/Framework silicates (most polymerized)
Ratio: 1:2
Example: Quartz, Feldspars

53
Q

What are the Miller Indices for a cube

A

(100) (T00) (010) (0T0) (001) (00T)

54
Q

What are the Miller Indices for a hexagonal prism with a pinacoid

A

(10T0) (T010) (01T0) (0T10) (T100) (1T00)
(0001) (000T)

55
Q

What are the Miller Indices for an octahedron

A

(111) (TTT) (T11) (1TT) (T1T) (1T1) (11T) (TT1)

56
Q

What are the Miller Indices for a tetragonal prism with a pinacoid

A

(100) (T00) (010) (0T0) (001) (00T)

57
Q

What is a unit cell?

A

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)

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