Lecture 9 Flashcards
another word to geometrical characteristics
symmetry elements
What is a crystal?
a solid composed of atoms that are arranged in a periodic pattern
What kind of symmetry do crystalline solids?
translational symmetry (composed of regular array of atoms)
Do amorphous solids have symmetry?
no, we consider them frozen liquids
What are the two components of crystal structure?
lattice + basis
What is a lattice?
an infinite and regular array of points in which the environment of each point is identical to the environment of
What kind of symmetry do lattice points have? what does this mean?
translational symmetry, so every point in the lattice can be generated by the addition of two lattice vectors, a and b
What is a unit cell?
the smallest repeating unit having the full symmetry of the crystal structure
What can the structure of a crystal be described in terms of?
a lattice; an atom (or group of atoms) – called the “basis” is “attached” to a single lattice point
When what is repeated in space does it form the crystal structure?
basis
What do lattice + basis look like when there’s a motif versus not?
What’s the best way to figure out if it’s a lattice or not?
see if you can draw the same vector to get from every point to it’s relative other one.
What is the difference between oblique and rectangular lattices?
different symmetry elements
How many lattices are there with different symmetries in 2D? Which ones?
6
triangle, square, rectangle, parallelogram, hexagon, rhombus
**triangle isn’t included in the 5 plane lattices
What are three shapes that don’t fill 2D space?
pentagon, decagon, octagon
What do you use to describe rotational symmetry in crystals?
n-fold = 360/n
ex: 1-fold = 360/1 = 260
What is a mirror line?
What is a 180 rotation, or 2-fold?
diad
What is 120 rotation, or 3-fold?
triad
What is 90 rotation, or 4-fold?
tetrad
What is 60 rotation, or 6-fold?
hexad
What do 2 mirror lines + diad look like?
What does mirror lines + triad look like?
What does a tetrad + 4 mirror lines look like?
What does a hexad + 6 mirror lines look like?
When identifying point groups, how do you denote a mirror, a rotation, or both?
any rotation- use the fold number (ex: 3) for a 3-fold triad
**put the number and then mm if it’s a mirror (unless triad then just one m)
(m) : mirror
mm - double mirror
mm or 2mm - diad or double mirror
4mm- tetrad + mirror
6mm - hexad + mirror
What are the 2D crystallographic point groups?
(all the ones we learned basically)
1, m, 2, 2mm, 3, 3m, 4, 4mm, 6, 6mm
What are the 5 plane lattices?
(all primitive)
1. oblique lattice
2. square lattice
3. rectangular lattice
4. hexagonal lattice
5. rhombus (centered rectangular lattice)
What is another “name” for a rhombus lattice
centered rectangular lattice
what does the oblique lattice look like?
the slanted horizontal one (parallelogram)
What would a primitive oblique lattice with 2-fold rotation look like?
p2
What to remember when trying to draw lattices with rotation?
the R’s are attached to the points
Is translation symmetry good for 4-fold in an oblique?
Is all rotation symmetry consistent with all the lattices?
no, sometime they don’t work
What kinds of rotation can an oblique crystal system allow?
1-fold and 2-fold
(can’t do 4 fold bc if you rotate the unit cell just 90 degrees the lines do not match up)
Do square lattices allow for 4-fold rotational symmetry?
yes
What is a glide?
reflection + translation (1/2 of lattice spacing)
how many total plane groups are there?
17
What are the 17 plane groups?
- 2 oblique
- 7 rectangle
- 5 rhombohedral
- 3 squares
What is the difference between oblique and hexagonal?
oblique sides aren’t even
When are glide lines created?
from the combo of point group symmetry with a lattice
What are the two different types of oblique?
p1 and p2
What are the 5 different options for rectangular plane groups?
pm
pg
cm
p2mm
p2mg
p2gg
c2mm
