Definitions

Question 1

symmetry

Answer 1

If an object has regular arrangement or pattern.

Question 2

name the different symmetry operations

Answer 2

Identity, inversion, rotation, rotoinvresion , mirror

Question 3

inversion

Answer 3

taking points (x,y,z) and turning into –> (-x, -y,-z)

Question 4

rotoinversion

Answer 4

combination of rotation and inversion

Question 5

property of a symmetry

Answer 5

all symmetries have the property that if you apply them enough times you get back to where you started

Question 6

The lattice

Answer 6

A lattice is an array of regularly spaced points which represent the translational symmetries of a system. They are defined in terms of basis vectors, for any n-dimensional system we require n non co-planar basis vectors.

Question 7

unit cell

Answer 7

the unit cell is any region of space which tessellates (fits together) when translated by a lattice vector

Question 8

primitive cell

Answer 8

primitive unit cell is a cell which contains only 1 lattice point

Question 9

name a primitive cell

Answer 9

wigner-seitz

Question 10

how many types of bravais lattice are there

Answer 10

14

Question 11

packing fractions

Answer 11

calculate the volume fraction of space filled assuming each lattice point is home to a sphere

Question 12

assumption when calculating packing fraction

Answer 12

• crystal is made up of ideal hard spheres sitting on the lattice points
• each sphere, just touches its neighbour, implying that the radius of the sphere is just half the distance between neightbouring lattice points

Question 13

vacancy

Answer 13

Vacancy are missing atoms in otherwise perfect structure

Question 14

substitution

Answer 14

Substitution is when an atom in a otherwise perfect structure is replaced with a different atom.

Question 15

interstitial

Answer 15

interstitial are atoms which sit between sites in normally unoccupied locations

Question 16

name different point defects

Answer 16

vacancy, substitution, interstitial

Question 17

Line defect

Answer 17

linear disruption in the ordering of a material

Question 18

examples of line defects

Answer 18

edge, screw

Question 19

why are line defects important

Answer 19

critical to defromation of material. As a material is compressed these defects are able to move.

Question 20

planar defect

Answer 20

interference between two regions of mismatched perfect crystal

Question 21

example of planar defect

Answer 21

grain boundary and twin boundary

Question 22

unit cell of the reciprocal lattice is called

Answer 22

the Brillouin zone

Question 23

property of Brillouin zones

Answer 23

They all have the same area

Question 24

reciprocal lattice have vectors…

Answer 24

have vector dimensions of inverse length so can be thought of as a wave vector

Question 25

each reciprocal lattice vector corresponds …

Answer 25

to a plane in the direct lattice

Question 26

official definition of X-ray

Answer 26

X-rays are photons which are generated by inner shell transitions within atoms

Question 27

new definition of x_rays

Answer 27

x-rays can be defined by specifying a wavelength range, typically 10pm -10nm corresponding to photon energies of around 0.1-100Kev

Question 28

what does the range of photons from x-ray definition do

Answer 28

makes them ideal for scattering from crystals

Question 29

when an x-ray interacts with an atom, one of two process may occur, what is the one covered in atomic course

Answer 29

The x-ray may be absorbed by the atom, prompting an inner shell electron to the continuum or an unoccupied energy level

Question 30

when an x-ray interacts with an atom, one of two process may occur, what is the NEW ONE

Answer 30

The photons may scatter from the electrons in the atom, changing its direction, but not in the classical limit, its energy.

Question 31

diffraction theory

Answer 31

Radiation with wavelength of order the lattice spacing will diffract from a periodic array of scattering

Question 32

what type of reaction is scattering, give example

Answer 32

elastic

i.e. the radiation wavenumber, K remains unchaged during scatterin

Question 33

The wigner-seitz cell

Answer 33

is the smallest volue enclosed by the perpendicular bisector of the central point to neighbouring cells

Question 34

strength of photon scattering

Answer 34

weak, but the atomic density of solids is high enough for results to be appreciable

Question 35

The Ewald sphere

Answer 35

A sphere intercepting points that fufil the Lave condition

Question 36

phonos

Answer 36

Phonos are quantised lattice vibrations that have energy and momentum

Question 37

Neutrons used in elastic scattering for what

Answer 37

to determine points on dispersion curve

Question 38

Dulong-Petit fails where

Answer 38

For Diamond and Beryllium and all materials at low temperatures

Question 39

Einsteins model does what

Answer 39

treats each atom as an independent quantum SHO

Question 40

Debye Model assumption

Answer 40

assumes equally spaced isotropic modes (in reciprocal space) and a linear dispersion

Question 41

Debye answers what question

Answer 41

The debye temperature is an answer to the question “how quantum is you’r system” and large values correspond to tight bindings

Question 42

Harmonic potential approximation

Answer 42

• higher temperatures have anharmonic regions

- odd terms in the Taylor expansion are asymmetric

Question 43

Free electron theory assumption

Answer 43

• Each electron follows a classical trajectory in a uniform potential, set up by ions and other electrinos
• Electrons do not scatter off each other only ions

Question 44

Scattering FET

Answer 44

Electrons are accelerated by f(t) until they collide and scatter

Question 45

Collide and scatter (FET)

Answer 45

• time between events is 1/tau

- the proprtion of electrons that scatter is dt/tau so (1-dt/tau) dont scatter

Question 46

Mathiessen’s rule

Answer 46

phonons and impurities cause electrons to scatter. phono is dependent on temperature

Question 47

Boin von Karmon boundary condition

Answer 47

The crystal is modelled as a ring so to avoid a difference of pi in phase

Question 48

pauli exlusion principle

Answer 48

No two fermions can occupy the same quantum state (including spin)

Question 49

edge defect

Answer 49

and edge dislocation is a line defect formed at the edge of missing or additional half plane of atoms in a structure

Question 50

A stacking fault

Answer 50

A stacking fault is a disruption to the normally regular arrangement of planes within a material.

Question 51

Two different types of stacking faults which is which?

Answer 51

intrinsic, missing. Extrinsic additional