Lecture 11 Flashcards
What are the three different types of symmetry elements in 3D?
point: centers of symmetry, mirror planes, and inversion axes
translational: glide planes and screw axes
How many different space groups are there for 3d?
230
How are bravais lattices grouped?
through their point group symmetries into seven crystal systems
Do P F I cubic lattices have the same point group symmetry?
yes
What is a crystal habit?
external shape
What are the centrosymmetric groups?
What does centrosymmetric mean?
the crystal posses an inversion center
What two shapes have the same point group symmetry? How is that determined?
cube and octahedron
you go through all the options (ex 4-fold 3-fold 2-fold) if they have the same # of each they’re the same
Does a tetrahedron have more or less symmetry than a cube? octahedron?
less, both are more
What is the characteristic of the cubic crystal? What are three crystal shapes in this category?
four triads
cube, octahedral, tetrad
What does it mean when two crystals belong to the same crystal class?
they have the same point group symmetry (ex cube and octahedron)– not necessarily the same shape
In 3D, what is a point group called?
a crystal class
How many different 3D crystal classes are there? 2d point groups?
3D- 32
2D- 10
What is the notation for an identity? inversion center? mirror plane? rotation axis n-fold? rotoinversion?
what does an 1 hat inversion look like? what is it also called?
inversion center
What does a 2 hat (m) look like? Also called?
2-fold rotoinversion
inversion diad
What does a 4 hat look like? also called?
4-fold rotoinversion
inversion tetrad
what does a 3 hat look like? also called?
3 fold rotoinversion
inversion triad
What does it for crystals to be in the same class?
their outer shapes have the same point group symmetries
What does point group symbol notation indicate?
the main symmetry elements present (not all, but most important)
what is the minimum symmetry for the cubic system? how do you identify with the symmetry notation?
4 triads
3 bar is the second number written or 3 for non-centro
what is the minimum symmetry for the tetragonal system? which ones can it be? how do you identify?
1 inversion tetrad
Primitive, bcc (I)
4 is the first one listed in the notation
what is the minimum for orthorhombic? what is the centro symmetric notation? non?
3 diads
PICF
centro; mmm
non centro: 222, mm2^P
what is the minimum symmetry for trigonal?
1 rotation triad
trigonal=rhombohedral
R
what is the minimum symmetry for hexagonal?
1 rotation hexad (6 in the phrase)
By looking at the point symmetry notation, how do you kow if it’s centrosymmetric?
if it’s only one number and m’s
what is the minimum qualification for monoclinic? triclinic?
1 inversion diad
none
What does the order that the symmetry elements appear in the point group symbol depend on?
the crystal system
what does /m mean? mm?
the mirror plane is perpendicular to the rotation axis
mm: mirror planes parallel to rotation axis
what is the most common crystal class?
60% correspond to 2/m and m
what is the most symmetric class?
m3m- cubic
what does the addition of glide planes and screw axes make it called?
space groups
How many Bravais lattices are there in 3D space
14
What is body-centered in bravais notation
I
what is face-center in bravais notation
F
what is base-center in bravais notation
C
What are the 14 bravais lattices for 3D space?
the 14 lattices are in 7 crystal systems
What are the 7 crystal systems for the 14 bravais lattices?
- Cubic (3): simple cubic, BCC, FCC
- Orthorhombic (4): simple ortho, body-centered ortho, base-centered ortho, face-centered ortho
- tetragonal (2): simple tetrag, body-centered tetrag
- trigonal (1): rhombohedral
- hexagonal (1): hexagonal
- monoclinic (2): simple mono, base-centered mono
- triclinic (1): triclinic
How are bravais lattices grouped?
by their point group symmetries into the seven crystal systems
What are the different centrosymmetric crystal groups?
What is the qualification to belong in the cubic crystal sysem?
four 3-fold axes
What 3 3D shapes belong in the cubic system?
What is the difference between crystal system and crystal class?
system– same qualifier
class- all the same point group symmetry
In 2D, how many different crystallographic point groups are there? How many 3D point groups are there?
10- point groups
32- crystal classes
What does inversion look like?
What does inversion diad look like?
What does inversion tetrad look like
inversion triad
what is the minimum symmetry for cubic, tetragonal, orthorhombic, trigonal, hexagonal, monoclinic and triclinic?
How do you know the nomanclature order for different crystal classes?
the viewing directions listed on the chart
what is the least common crystal class?
m3m
