Structure Of Solids

Question 1

What is a bravais lattice?

Answer 1

It is an infinite arrangement of points with identical surroundings/environment (not necessarily isotropic). Each point has the same number of neighbours found at the same distance and distance and in the same direction (so not all lattices are bravais lattices e.g. The hexagonal lattice if you consider all points).

Question 2

How many ways are there of forming bravais lattices in 2D and 3D?

Answer 2

There are 5 ways to make a 2D bravais lattice and there are 14 ways to make one in 3D

Question 3

Name the 5 2D bravais lattices and their associated angles and lengths

Answer 3

Square P (a=b o=90)
Rectangular P (a |=| b o=90)
Rectangular C (a |=| b o=90) Cheg
Hexagonal (a=b o=120)
Oblique (a |=| b o=any)

There are only 4 unit cells since rectangular is used twice.

Question 4

PIFC?

C has two related arrangements A and B

Answer 4

Primitive
I = Body centered
Face centered 
C is base (ab face) centered (includes roof and base)
A is on the bc face (left and right) 
B is on the ac face (front and back)

Question 5

What are the 7 3D unit cells?

Answer 5

A is alpha B is beta C is gamma

Cubic a=b=c A=B=C=90
Tetragonal a=b;c A=B=C=90
Orthorhombic a;b;c A=B=C=90

Rhombohedral a=b=c A=B=C;90
Monoclinic a;b;c A=C=90 ;B
Triclinic a;b;c A;B;C

Hexagonal a=b;c C=120 A=B=90

Question 6

What are the 14 3D bravais lattices?

Answer 6

Cubic: simple(P), I, F, C
Tetragonal: simple(P) I
Orthorhombic: simple(P) I, F, C

Rhombohedral: simple(P)
Monoclinic: simple(P), C
Triclinic: simple(P)

Hexagonal: simple(P)

Rhombohedral is also called trigonal

Question 7

Name some FCC and BCC materials

Answer 7

FCC

Aluminium nickel copper platinum gold lead silver silicon germanium diamond gallium arsenide indium phosphide

BCC

Lithium sodium potassium chromium iron molybdenum tungsten manganese

Question 8

What’s the difference between great and small circles?

Answer 8

Great circles have the same circumference as the sphere they are on (lines of longitude) whereas small circles don’t (lines of latitude represent the angular distance from the North or South Pole

Question 9

Axes, planes, and centres of symmetry

Answer 9

An axis of symmetry is a line through a 3D solid around which the solid can be rotated to produce an identical image at least once. Every shape has an identity axis, then there are diads, triads, tetrads, and hexads. (The number of times the object is repeated = 1,2,3,4, and 6)

Planes are for mirroring

Center of symmetry is for inversion

Question 10

How many axes, planes, and centres of symmetry can a shape have?

Answer 10

Many axes and planes but only one center of symmetry/inversion