1.2 Crystals I

Question 1

Define a Crystal

Answer 1

A solid whose atoms are arranged in a regular repeating pattern that extends over a large distance

Question 2

Define a crystal lattice

Answer 2

An infinite set of points defined by integer sums of a set of linearly independent primitive lattice vectors (PLVs)

Question 3

What are the two 2D lattice types?

Answer 3

Square and Triangular (hexagonal)

Question 4

What is meant by the choice of PLVs not being unique?

Answer 4

They can be anything as long as you can reach every point with them

Question 5

Give an alternative definition for a crystal lattice which includes the environment

Answer 5

A lattice is a set of points where the environment of any given point is the same as that for any other point

Question 6

How can we describe a crystal structure using a basis?

Answer 6

Represent the periodic structure as a lattice of repeating patterns. Basis = repeated object
lattice + basis = crystal structure

Question 7

Define the unit cell

Answer 7

A region of space such that when identical units are stacked, it completely fills space
OR a PLV contains exactly 1 lattice point

Question 8

State the three types of cubic lattices

Answer 8

Simple cubic, FCC, BCC

Question 9

Describe the properties of a cubic lattice

Answer 9

All sides are equal, all angles are equal (90 deg)

Question 10

How many types of 3D lattices are there that satisfy all symmetry operations and periodic conditions, and what are they called?

Answer 10

Bravais lattices - 14

Question 11

Describe some symmetry operations

Answer 11

Translation, rotation, reflection

Question 12

Describe the atomic packing factor

Answer 12

• Place an atom on each lattice point
• Assume sphericicity, radius R
• Calculate the percentage of space filled

Question 13

What is the only element that has a simple cubic structure?

Answer 13

Po

Question 14

Describe the structure of a of a BCC

Answer 14

A simple cubic with an extra lattice point in the centre a/2

Question 15

Describe the structure of a of a FCC

Answer 15

Simple cubic with an extra lattice point at the centre of each face

Question 16

State how many lattice points are contained in a simple cubic, BCC, FCC

Answer 16

Simple cubic = 1
BCC = 2
FCC = 4

Question 17

What cubic structure are most elements found in and why?

Answer 17

FCC - densest possible packing method

Question 18

How do we describe directions when navigating a cubic and define a negative?

Answer 18

uvw. Use a bar for negative numbers (like a vector)

Question 19

Describe the movement for <100>

Answer 19

Along a unit cell axis

Question 20

Describe the movement for <110>

Answer 20

Along a face diagonal

Question 21

Describe how to treat <2 4bar 6>

Answer 21

Reduce to simplest form:

<1 2bar 3>

Question 22

Define a plane

Answer 22

A plane intercepts the axis at u’ w’ v’ or a/h b/k c/l for side lengths abc

Question 23

What is the traditional notation used in relation to planes and what must we note when writing them down?

Answer 23

The Miller indices hkl. They must all be integers

Question 24

State the 4 point defects which can arise during the formation of a crystal

Answer 24

Schottky defect, colour centre, frenkel defect, impurities

Question 25

Describe the Schottky defect

Answer 25

There is a vacancy - one atom is missing in the lattice which distorts it. no expected for N atoms at an energy Ev to remove a lattice:
n = N * exp(-Ev / kt) vacancies

Question 26

Describe the colour centre defect

Answer 26

The colour changing of a crystal due to lattice damage

- caused when crystal is irradiated by x-rays, gamma rays, electrons etc

Question 27

Describe the frenkel defect

Answer 27

When there is a vacancy and interstitial atom

• distorts atom
• needs 5-10x more energy than a normal vacancy

Question 28

Describe the impurity defect

Answer 28

When there is a different material on a lattice point

Question 29

State the two dislocations

Answer 29

Stacking faults/edge dislocations

Screw dislocations

Question 30

Define grain boundaries

Answer 30

Most materials are not single crystals, but many small crystallites orientated wrt to each other