Crystallography Flashcards
What is symmetry?
The order of arrangement and orientation of atoms in minerals, and the order in the consequent distribution of mineral properties.
What are the 4 basic types of symmetry operations?
Reflection, Rotation, Inversion, Translation
What are the basic Point Symmetry Operations?
Reflection, Rotation, Inversion
What is Reflection?
Reflection refers to symmetry distributed across a plane
What is Rotation?
Rotation refers to symmetry distributed about an axis
What is Inversion?
Inversion refers to symmetry related through a central point
What is Handedness?
The nature of a second motif that is generated after a given symmetry operation
What are the symmetry operator, the symbol, and the handedness for Inversion?
inversion center/point
i
opposite
What are the symmetry operator, the symbol, and the handedness for Rotation?
Rotation axis
n
same
What are the symmetry operator, the symbol, and the handedness for Reflection?
Mirror plane
m
opposite
What is a motif?
Set of atoms arranged in a particular way/geometrical pattern (in respect to 2-D lattice)
What are the options of Rotational Symmetry?
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
What is Translational Symmetry?
Space symmetry
symbol: t
Handedness: same
ALL minerals process translation!
What is the difference between point symmetry and space symmetry?
Point symmetry: collection of atoms around a central point (reflection,rotation,inversion)
Space symmetry: motifs are generated across large distances (translation)
What is Roto-Inversion Symmetry?
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
How many symmetry combinations are possible? What is the list called?
32 point groups/ crystal classes
(w/o translation)
Hermann-Mauguin Symbols
How many crystal systems are there?
What are their names?
7 crystal systems
Triclinic, Monoclinic, Orthorhombic, Tetragonal, Rhombohedral, Hexagonal, Isometric
Geometry of crystallographic axes
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
Triclinic
Least amount of symmetry
a ≠ b ≠ c all angles ≠ 90
Monoclinic
mono = one, clinic = inclined. a ≠ b ≠ c, alpha + gamma = 90, beta > 90
Orthorhombic
a ≠ b ≠ c all angles = 90
Tetragonal
a1 = a2 ≠ c all angles = 90
Hexagonal-Rhombohedral
a1 = a2 = a3, all angles equal but ≠ 90