Structures Of Crystalline Solids

Question 1

Name the 5 2D crystal lattice

Answer 1

square primitive, oblique primitive, rectangular primitive, rectangular centred, hexagonal primitive

Question 2

Conditions of unit cells

crystal unit cells

Answer 2

must be infinitely repeatable via translation.

Question 3

Difference between primitive and centred

Answer 3

Primitive does not have any lattice points inside the unit cell
Centred has a single lattice point in the cell and it is symmetrically equivalent to all corner lattice points

Question 4

Why not choose a primitive cell for a rectangular centred lattice

Answer 4

in a bravais lattice the rectangular centred unit cell reflects the maximum symmetry of the lattice and the primitive does not

Question 5

What is a Bravais lattice

Answer 5

A bravais lattice is a mathematical description of a crystal structure and reflects the macimum symmetry of a crystal lattice.
The unit cell must preserve as much symmetry as possible

Question 6

Square primitive lattice constants and their values

Answer 6

a=b, gamma=90 degrees

Question 7

Rectangular primitive and Rectangular centred lattice parameters

Answer 7

a≠b and gama=90

Question 8

Hexagonal primitive lattice parameter values

Answer 8

a=b and gamma=120

Question 9

Oblique primitive lattice parameter values

Answer 9

a≠b and gamma≠60,90,120

Question 10

What is a zone axis

Answer 10

its the common direction shared by the intersection of 2 or more crystal planes (A and B).
A x B = zone axis

Question 11

Weiss Zone Law

Answer 11

the plane (hkl) ∈ the zone axis [uvw], given that hu+kv+lw=0

Question 12

What are the bracket symbols for miller indices for directions and planes and their families

Answer 12

direction [hkl] - miller bravais [uvtw]
family of directions - <hkl> miller bravais [uvtw]
plane (hkl) - miller bravais (uvtw)
family of planes {hkl} - miller bravais {uvtw}</hkl>

Question 13

What are Miller Bravais Indices

Answer 13

used for hexagonal and rhombohedral/trigonal symmetry due to their 3 and 6 fold rotational azes

Question 14

How to transform miller bravais to miller indices

Answer 14

• mb 4 - m 3 index transformation:
• U = u-t, V=v-t, W = w
• m 3 - mb 4 index transformation:
• u = 1/3 (2U-V), v = 1/3 (2V-U), t= -(u+v), w=W

Question 15

What is rotational symmetry

Answer 15

An operation that on turning the crystal structure a certain number of degrees results in no change in position (given as n-fold symmetry)

Question 16

reflection symmetry - what is a reflection and what is a mirror plane’s role

Answer 16

reflection -> symmetry operation
mirror plane -> symmetry operator

Question 17

what is a glide plane

Answer 17

a combination of translations parallel to a plane. which may also be reflected across the plane.

Question 18

What is inversion symmetry

Answer 18

• operation with respect to a point known as the inversion centre
• the inversion centre is located in the middle of crystal
• results in similar crystal faces and atomic arrangements

Question 19

What are point groups and their notation

to do with symmetry of lattices and unit cells

Answer 19

• Collection of symmetry elements of an isolated shape/motif
• have the same origin/centre of mass point
• written by “nm” for non orthoganol mirror planes and “nmm” for orthogonal mirror planes
• 2mm, 4mm and 6mm
• m, 3m

Question 20

How to name 2D plane groups

pcmg

Answer 20

• 2D bravais lattice + 2D point group = 17 2D plane groups
• pcmg (primitive, centered no. of max rotational symmetry, mirror planes, glide planes)
• c is a number for the rotational symmetry
• everything is measured from the point centre
• gg and mm are orthogonal planes

Question 21

What are harmonic waves and what form does the equation take?

Answer 21

• Harmonic waves are simple waves propagating as a sine or cosine function.
• wave with amplitude “A” travelling at velocity “v”
• ψ(x,t) = A sin((2pi/λ)(x-vt))

Question 22

Interference of Waves (principle of superposition)

Answer 22

• when two waves interfere at a certain point, the displacement at that point is equal to the sum of the displacement of the individual waves

Question 23

what is the law of reflection

Answer 23

• for a monochromatic plane wave arriving at a surface, the reflected ray lies in the plane of incidence and the angle of incidence = angle of reflection

Question 24

what is the refractive index (n) equation

Answer 24

n = speed in vacuum / speed in medium

Question 25

What is Snell's law equation

Answer 25

n<1>sin theta<1> = n<2> sin theta <2>

Question 26

Neutron Diffraction | What is it, why is it more useful, what can it do

Answer 26

* beam of neutrons can be used to produce a diffraction pattern from a sample * neutrons are scattered by the nuclei of atoms (diffraction intensity is different for each element as it is dependent on atomic mass) * it is easier to distinguish different elements from neutron diffraction * useful for detecting magnetic fields due to spin of neutron which interacts with magnetic moments within the atom * can therefore reveal microscopic magnetic structure of material.

Question 27

What are the common applications of neutron diffraction

Answer 27

- locating light atoms in the presence of heavy atoms - differentiating neighbouring atoms in the periodic table that have similar no. of electrons and therefore x-ray scattering factor but distinct neutron scattering factor due to atomic mass differences.

Question 28

Advantages of Neutron Diffraction

Answer 28

- distinguishes between adjacent elements - scattering depends on isotope and does not produce a smooth curve with Z - sensitive to magnetic fields

Question 29

Disadvantages of Neutron Diffraction

Answer 29

- expensive - produced by a nuclear reactor - weak flux hence requires larger samples

Question 30

Simple Cubic allowed hkl reflections formula

Answer 30

All are allowed

Question 31

Body centred cubic allowed reflections formula

Answer 31

h^2+k^2+l^2= even number

Question 32

Face Centred Cubic allowed hkl reflections formula

Answer 32

h, k, l are all even or all odd

Question 33

Steps to determining the crystal structure from its diffraction pattern and angles

Answer 33

* use 2 theta to find sin^2(theta) * normalise all the values by dividing by the smallest value of sin^2(theta) * clear all the values to find the sum of h+k+l * determine the hkl values * determine the lattice type

Question 34

what is the relationship between a hkl plane's diffraction angle and the sum of the squared hkl values? | theta and (h^2+k^2+l^2)

Answer 34

the hkl plane with the smallest diffraction angle will have a smaller h^2+k^2+l^2 value.

Question 35

What is the lattice parameter "a" and what is its equation?

Answer 35

- lattice parameter describes the geometric properties of a crystal structure represented by symbol (a) - a = d x sqrt(h^2+k^2+l^2)

Question 36

What is the equation for the number of vacancies in a crystal structure

Answer 36

N_v = N_o x e^(-Q/(kT))

Question 37

What causes total internal reflection?

Answer 37

- When the angle of incidence is larger than the critical angle, the incident ray will be reflected back into the denser medium. - 2nd medium must have greater density than 1st medium

Question 38

Plane waves

Answer 38

- has the same value irrespective of y and z but whose value changes as a function of x