CRYSTALLOGRAPHY Flashcards
What is Crystallography
branch of mineralogy that studies the long-range order or crystal structure of crystalline substances.
What is Crystal faces
Flat surfaces enclosing a crystal that are formed when enclosed minerals stop growing.
WHAT IS MOTIF
Smallest unit of pattern, that when repeated by a set of symmetry operations, will generate the long-range pattern characteristic of the crystal; Set of atoms arranged in a specific way.
MOTIF IS REPRESENTED BY _____
NODE
A SYMMETRY OPERATION IS
The repetition of these
fundamental units of pattern with long-range order.
TYPES OF SYMMETRY OPERATIONS
- Simple Symmetry Operations
- Compound Symmetry Operations
DEFINE TRANSLATION
A periodic repetition of nodes
in a systematic, linear displacement.
Unit Translation Vector
(t) – A specific length
and direction of systematic displacement by which the pattern repeats.
TYPES OF TRANSLATION
Two-Dimension 2D
Three Dimension 3D
Two-dimension 2D
A form of translation
defined by two-unit translation vectors: ta and tb, or t1 and t2.
Plane Lattice or?
Plane Mesh
Plane Lattice
is a two-dimensional array of pattern of nodes generated by the two-dimensional translation.
Three-dimension Translation
A form of translation defined by two-unit translation vectors: ta , tb and t1 , t2 and t3.
SPACE LATTICE
A three- dimensional array of pattern of nodes generated by the two- dimensional translation.
Rotation
(n) – A perfectly repetition of patterns in a complete 360°rotation around an axis of rotation.
Axis of Rotation
An imaginary line or axis where a pattern of nodes rotate around.
TYPES OF ROTATION
One Fold
Two Fold
Three Fold
Four Fold
Six fold
ONE FOLD AXIS ROTATION SYMBOLIC ROTATION AND DESCRIPTION
1 or A1
Description
Motif is Repeated only once during 360 rotation
TWO FOLD AXIS SYMBOLIC ROTATION AND DESCRIPTION
2 or A2
Repeated every 180 or Twice During a 360 rotation
THREE FOLD AXIS SYMBOLIC ROTATION AND DESCRIPTION
3 or A3
Motifs repeated every120 & three times during complete rotation
FOUR FOLD ACIS OF ROTATION
4 or A4
Motifs repeated every 90 & Four times during complete rotation
Six fold axis of rotation Symbolic notation and description
6 or A6
Motifs repeated every 60 & 6 times during complete rotation
REFLECTION
A form of symmetry operation in which every component of a pattern is repeated by reflection through a mirror plane.
Mirror plane
An imaginary line or axis where a pattern of nodes Reflects around.
INVERSION
(i)
The repetition of motifs by inverting them through a center called center of inversion.
Center of inversion
A point where the
“image” of the motif is inverted through.
TYPES OF SIMPLE SYMMETRY OPERATIONS
Translation
1. 2D
2. 3D
Inversion
GLIDE REFLECTION
The combination of translation with reflection across a mirror plane, producing a glide plane.
GLIDE PLANE
An imaginary plane where
nodes “glide” unto.
ROTOINVERSION
The combination of translation with reflection across a mirror plane, producing a glide plane.
SCREW ROTATION
The combination of translation parallel to an axis with rotation about the axis.
Types if compounds symmetry operations
GLIDE
ROTOINVERSION
SCREW ROTATION
PLANE POINT GROUP
Two-dimensional motifs that are consistent with the generation of long-range, two- dimensional arrays.
UNIT MESH
The smallest units of plane lattice which contain at least one node and the unit translation vectors. It contains all the information necessary to produce the only larger two-dimensional pattern
17 Place Lattice Groups
P1
P2
Pm
Pg
Cm
P2mm
P2mg
P2gg
C2mm
P4
P4mm
P4gm
P3
P3m1
P3lm
P6
P6mm
10 plane point group
1
2
M
2mm
4
4mm
3
3m
6
6mm
5 unit meshes
Oblique ( p)
Rectangle ( p & c )
Square ( p)
Hexagonal ( P) (rhombohedral)
Hexagonal ( p) (hexagonal)
Plane Lattice Groups
A set of 17 plane lattice groups formed through the combination of the 10 plane point groups and 5 unit meshes.
Space point group
Three-dimensional equivalents of two-dimensional equivalents plane point groups.
Space lattices
Three-dimensional patterns of nodes.
Crystal Classes
– The 32 three-dimensional motif symmetries defined by the arrangement of the space point groups.
Crystallographic Axes
A set of imaginary orientations used to describe the direction of a crystal’s propagation.
Crystal Systems
A classification of minerals based on the relative measurement of their unit edges (a, b, and c), and the angles between them (α, β, and γ).
ISOMETRIC LATTICE PARAMETER AND ANGLE
a = b = c
ã = b = y = 90%
TETRAGONAL LATTICE PARAMETER AND ANGLES
a = b ≠ c
a = b = y = 90
ORTHORHOMBIC LATTICE PARAMETER AND ANGLES
a ≠ b ≠ c
a = b = y = 90%
MONOCLINIC LATTICE PARAMETER AND ANGLES
a ≠ b ≠ c
a = y = 90 b = >120
TRICLINIC LATTICE PARAMETER AND ANGLES
a ≠ b ≠ c
a ≠ b ≠ y ≠ 90%
HEXAGONAL LATTICE PARAMETER AND ANGLES
a= b = c ≠ d
a = 120; B= y = 90
RHOMBOHEDRAL / TRIGONAL LATTICE PARAMETER AND ANGLES
a = b = c ≠ d
a = 120; B = y = 90%
