Lecture 9 Flashcards

1
Q

another word to geometrical characteristics

A

symmetry elements

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2
Q

What is a crystal?

A

a solid composed of atoms that are arranged in a periodic pattern

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3
Q

What kind of symmetry do crystalline solids?

A

translational symmetry (composed of regular array of atoms)

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4
Q

Do amorphous solids have symmetry?

A

no, we consider them frozen liquids

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5
Q

What are the two components of crystal structure?

A

lattice + basis

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6
Q

What is a lattice?

A

an infinite and regular array of points in which the environment of each point is identical to the environment of

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7
Q

What kind of symmetry do lattice points have? what does this mean?

A

translational symmetry, so every point in the lattice can be generated by the addition of two lattice vectors, a and b

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8
Q

What is a unit cell?

A

the smallest repeating unit having the full symmetry of the crystal structure

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9
Q

What can the structure of a crystal be described in terms of?

A

a lattice; an atom (or group of atoms) – called the “basis” is “attached” to a single lattice point

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10
Q

When what is repeated in space does it form the crystal structure?

A

basis

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11
Q

What do lattice + basis look like when there’s a motif versus not?

A
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12
Q

What’s the best way to figure out if it’s a lattice or not?

A

see if you can draw the same vector to get from every point to it’s relative other one.

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13
Q

What is the difference between oblique and rectangular lattices?

A

different symmetry elements

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14
Q

How many lattices are there with different symmetries in 2D? Which ones?

A

6

triangle, square, rectangle, parallelogram, hexagon, rhombus

**triangle isn’t included in the 5 plane lattices

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15
Q

What are three shapes that don’t fill 2D space?

A

pentagon, decagon, octagon

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16
Q

What do you use to describe rotational symmetry in crystals?

A

n-fold = 360/n

ex: 1-fold = 360/1 = 260

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17
Q

What is a mirror line?

A
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18
Q

What is a 180 rotation, or 2-fold?

A

diad

19
Q

What is 120 rotation, or 3-fold?

A

triad

20
Q

What is 90 rotation, or 4-fold?

A

tetrad

21
Q

What is 60 rotation, or 6-fold?

A

hexad

22
Q

What do 2 mirror lines + diad look like?

A
23
Q

What does mirror lines + triad look like?

A
24
Q

What does a tetrad + 4 mirror lines look like?

A
25
Q

What does a hexad + 6 mirror lines look like?

A
26
Q

When identifying point groups, how do you denote a mirror, a rotation, or both?

A

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

27
Q

What are the 2D crystallographic point groups?

A

(all the ones we learned basically)

1, m, 2, 2mm, 3, 3m, 4, 4mm, 6, 6mm

28
Q

What are the 5 plane lattices?

A

(all primitive)
1. oblique lattice
2. square lattice
3. rectangular lattice
4. hexagonal lattice
5. rhombus (centered rectangular lattice)

29
Q

What is another “name” for a rhombus lattice

A

centered rectangular lattice

30
Q

what does the oblique lattice look like?

A

the slanted horizontal one (parallelogram)

31
Q

What would a primitive oblique lattice with 2-fold rotation look like?

A

p2

32
Q

What to remember when trying to draw lattices with rotation?

A

the R’s are attached to the points

33
Q

Is translation symmetry good for 4-fold in an oblique?

A
34
Q

Is all rotation symmetry consistent with all the lattices?

A

no, sometime they don’t work

35
Q

What kinds of rotation can an oblique crystal system allow?

A

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)

36
Q

Do square lattices allow for 4-fold rotational symmetry?

A

yes

37
Q

What is a glide?

A

reflection + translation (1/2 of lattice spacing)

38
Q

how many total plane groups are there?

A

17

39
Q

What are the 17 plane groups?

A
  • 2 oblique
  • 7 rectangle
  • 5 rhombohedral
  • 3 squares
40
Q

What is the difference between oblique and hexagonal?

A

oblique sides aren’t even

41
Q

When are glide lines created?

A

from the combo of point group symmetry with a lattice

42
Q

What are the two different types of oblique?

A

p1 and p2

43
Q

What are the 5 different options for rectangular plane groups?

A

pm

pg

cm

p2mm

p2mg

p2gg

c2mm