Lecture 8

Question 1

What is a crystal?

Answer 1

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

Question 2

What kind of symmetry do crystalline solids have?

Answer 2

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

Question 3

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

Answer 3

they don’t. we consider them frozen liquids.

Question 4

What is the crystal structure formed from?

Answer 4

crystal structure = lattice + basis

Question 5

What is a lattice?

Answer 5

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

Question 6

What kind of symmetry do lattice points have?

Answer 6

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

Question 7

What is a unit cell?

Answer 7

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

Question 8

What are the six lattice constants or lattice parameters?

Answer 8

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

Question 9

What are the lattice constants for cubic?

Answer 9

Question 9

What are the lattice constants for tetragonal?

Answer 9

Question 10

What are the seven crystal systems?

Answer 10

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

Question 11

What are the lattice constants for orthorhombic?

Answer 11

Question 12

What are the lattice constants for rhombohedral (trigonal)?

Answer 12

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

Question 13

What are the lattice constants for hexagonal?

Answer 13

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

Question 14

What are the lattice constants for monoclinic?

Answer 14

no sides are the same ,

two angles are 90

Question 15

What are the lattice constants for triclinic?

Answer 15

no sides the same
no angles are 90

Question 16

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

Answer 16

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)

Question 17

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

Answer 17

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

Question 18

How do you calculate a crystallographic direction vector?

Answer 18

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

Question 19

How do you denote a family of directions?

Answer 19

< >

Question 20

what is a family of directions?

Answer 20

the distance between atoms along the directions are the same

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

Question 21

How is a crystallographic plane represented?

Answer 21

{ }

Question 22

How do you denote a family of lattice planes?

Answer 22

( )

Question 23

How do you calculate miller indicies?

Answer 23

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

Question 24

What are the common miller indicies for crystallographic planes?

Answer 24

Question 25

What would be the plane of this?

Answer 25

Question 26

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

Answer 26

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

Question 27

How do you draw a plane given the indicies?

Answer 27

take inverse of indicies find intercepts

Question 28

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

Answer 28

Question 29

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

Answer 29

Question 30

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

Answer 30

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

Question 31

What formulas do you use to calculate interplanar distance?

Answer 31

interplanar spacing formulas-- "d" spacing

Question 32

What do low hkl indicies mean?

Answer 32

larger d-spacing

Question 33

What is the pm to A conversion

Answer 33

100 pm = 1A

Question 34

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

Answer 34

a cubic system

Question 35

What are the 3 bravis lattices in cubic systems?

Answer 35

simple cubc BCC FCC

Question 36

what are the 2 bravis lattices in tetragonal systems?

Answer 36

simple tetragonal body-centered tetragonal

Question 37

what are the 4 bravis lattices in the orthorhombic system?

Answer 37

simple orthorhombic body-centered orthorhombic bass-centered orthorhombic face-centered orthorhombic

Question 38

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

Answer 38

it can have either hexagonal or rhombohedral lattice

Question 39

what bravis lattice is in the hexagonal system?

Answer 39

Question 40

what two bravis lattices are in the monoclinic system?

Answer 40

simple monoclinic bass-centered monoclinic

Question 41

is [hlk] generally perpendicular to (hlk)?

Answer 41

no, unless for cubic systems

Question 42

What are the two choices of hexagonal unit cells?

Answer 42

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

Question 43

What are Weber symbols/zone axis symbols?

Answer 43

4 base vectors in 3D space

Question 44

what are the formulas to remember for Weber symbols?

Answer 44

- go through the patterns in your mind

Question 45

What are the end points of a hexagonal crystal lattice?

Answer 45

- 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

Question 46

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

Answer 46

using miller-bravais indicies: h k i l i = -(h+k) **others are the same that you would think

Question 47

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

Answer 47

h k . l

Question 48

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

Answer 48

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