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Crystals > Lecture 8 > Flashcards

Lecture 8 Flashcards

1
Q

What is a crystal?

A

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

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2
Q

What kind of symmetry do crystalline solids have?

A

translational symmetry (are composed of a regular array of atoms)

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3
Q

Do amorphous solids have symmetry? What do we consider them?

A

they don’t. we consider them frozen liquids.

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4
Q

What is the crystal structure formed from?

A

crystal structure = lattice + basis

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5
Q

What is a lattice?

A

a lattice is an infinite and regular array of points (atoms) in which the environment of each point is identical

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6
Q

What kind of symmetry do lattice points have?

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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7
Q

What is a unit cell?

A

The minimum repeating unit that can fill all the space

The smallest repetitive volume which can be translated in three dimensions
- parallelepiped
- six parameters needed to describe the unit cell dimensions and angles

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8
Q

What are the six lattice constants or lattice parameters?

A

Length: |a|, |b|, |c|
* Angles between axes: alpha beta gamma

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9
Q

What are the lattice constants for cubic?

A
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9
Q

What are the lattice constants for tetragonal?

A
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10
Q

What are the seven crystal systems?

A
  1. cubic
  2. tetragonal
  3. orthorhombic
  4. rhombohedral
  5. hexagonal
  6. monoclinic
  7. triclinic
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11
Q

What are the lattice constants for orthorhombic?

A
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12
Q

What are the lattice constants for rhombohedral (trigonal)?

A

all sides the same and all angles the same but not 90

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13
Q

What are the lattice constants for hexagonal?

A

two sides the same, two angles are 90
one angle is 120

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14
Q

What are the lattice constants for monoclinic?

A

no sides are the same ,

two angles are 90

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15
Q

What are the lattice constants for triclinic?

A

no sides the same
no angles are 90

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16
Q

What are orthogonal systems? What are the three different types?

A

systems where alpha = beta = gamma = 90

*so all edges are perpendicular

simple cubic, simple tetragonal, simple orthorhombic (all same l, 2 same l, 3 dif)

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17
Q

What are the lattice vectors to describe the unit cell dimensions for orthogonal systems?

A

SC - all the same
S tetragonal - one dif.
S orthorhombic - all dif.

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18
Q

How do you calculate a crystallographic direction vector?

A
  1. subtract head - tail coordinates
  2. normalize
  3. reduce to the smallest integer value
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19
Q

How do you denote a family of directions?

A

< >

20
Q

what is a family of directions?

A

the distance between atoms along the directions are the same

ex: [100],[010],[001],[-100],[0-10],[00-1]
in the <100> family

21
Q

How is a crystallographic plane represented?

A

{ }

22
Q

How do you denote a family of lattice planes?

A

( )

23
Q

How do you calculate miller indicies?

A
  1. find the intersects with the xyz system
  2. calculate the reciprocals
  3. common factor
  4. enclose in ( )
24
Q

What are the common miller indicies for crystallographic planes?

A
25
Q

What would be the plane of this?

A
26
Q

if you can’t seem to figure out how to do miller indices, think about what?

A

remember it’s a family

translate it to the right or left one then identify it in the “family” – it’s still the miller indicie

27
Q

How do you draw a plane given the indicies?

A

take inverse of indicies

find intercepts

28
Q

What do the planes of the {100} family look like?

A
29
Q

What does the interplanar spacing look like with orthorhombic crystals (ones w all dif side lengths)?

A
30
Q

What are the different formulas for the interplanar spacing in orthorhombic, tetragonal, and cubic?

A

it’s always h2 k2 l2

correlate to dif side lengths– ortho (all dif), (tetragaonal a=b, so no b and group), cubic all same

31
Q

What formulas do you use to calculate interplanar distance?

A

interplanar spacing formulas– “d” spacing

32
Q

What do low hkl indicies mean?

A

larger d-spacing

33
Q

What is the pm to A conversion

A

100 pm = 1A

34
Q

in what system is [hlk] perpendicular to (hlk)

A

a cubic system

35
Q

What are the 3 bravis lattices in cubic systems?

A

simple cubc
BCC
FCC

36
Q

what are the 2 bravis lattices in tetragonal systems?

A

simple tetragonal

body-centered tetragonal

37
Q

what are the 4 bravis lattices in the orthorhombic system?

A

simple orthorhombic

body-centered orthorhombic

bass-centered orthorhombic

face-centered orthorhombic

38
Q

what bravis lattice is the trigonal system? what’s something to remember?

A

it can have either hexagonal or rhombohedral lattice

39
Q

what bravis lattice is in the hexagonal system?

A
40
Q

what two bravis lattices are in the monoclinic system?

A

simple monoclinic

bass-centered monoclinic

41
Q

is [hlk] generally perpendicular to (hlk)?

A

no, unless for cubic systems

42
Q

What are the two choices of hexagonal unit cells?

A
  1. primitive hexagonal unit cell ex: (110), (100), (010)
  2. hexagonal (four index) ex: (1100) (1010) (0110)
43
Q

What are Weber symbols/zone axis symbols?

A

<UVTW>

4 base vectors in 3D space
</UVTW>

44
Q

what are the formulas to remember for Weber symbols?

A
  • go through the patterns in your mind
45
Q

What are the end points of a hexagonal crystal lattice?

A
  • think about the patterns
  • top right start with neg
  • right diag starts with 2, middle has middle 2, left has end 2
  • they’re all the opposite signs of the other side
46
Q

How do you identify a crystallographic plane in a hexagonal crystal?

A

using miller-bravais indicies: h k i l

i = -(h+k)
**others are the same that you would think

47
Q

What’s another way to write miller-bravais indicie (always about planes) h k i l

A

h k . l

48
Q

How do you go about finding the miller-bravais indicies for a hexagonal crystal?

A
  • find where it intersects with a/x b/y/ and z
  • put that into () remember the negs
  • change to hkil by i = -(h+k)

Crystals (11 decks)

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