1.2 Crystals I Flashcards

1
Q

Define a Crystal

A

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

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2
Q

Define a crystal lattice

A

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

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3
Q

What are the two 2D lattice types?

A

Square and Triangular (hexagonal)

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4
Q

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

A

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

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5
Q

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

A

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

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6
Q

How can we describe a crystal structure using a basis?

A

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

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7
Q

Define the unit cell

A

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

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8
Q

State the three types of cubic lattices

A

Simple cubic, FCC, BCC

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9
Q

Describe the properties of a cubic lattice

A

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

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10
Q

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

A

Bravais lattices - 14

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11
Q

Describe some symmetry operations

A

Translation, rotation, reflection

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12
Q

Describe the atomic packing factor

A
  • Place an atom on each lattice point
  • Assume sphericicity, radius R
  • Calculate the percentage of space filled
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13
Q

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

A

Po

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14
Q

Describe the structure of a of a BCC

A

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

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15
Q

Describe the structure of a of a FCC

A

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

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16
Q

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

A

Simple cubic = 1
BCC = 2
FCC = 4

17
Q

What cubic structure are most elements found in and why?

A

FCC - densest possible packing method

18
Q

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

A

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

19
Q

Describe the movement for <100>

A

Along a unit cell axis

20
Q

Describe the movement for <110>

A

Along a face diagonal

21
Q

Describe how to treat <2 4bar 6>

A

Reduce to simplest form:

<1 2bar 3>

22
Q

Define a plane

A

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

23
Q

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

A

The Miller indices hkl. They must all be integers

24
Q

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

A

Schottky defect, colour centre, frenkel defect, impurities

25
Describe the Schottky defect
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
26
Describe the colour centre defect
The colour changing of a crystal due to lattice damage | - caused when crystal is irradiated by x-rays, gamma rays, electrons etc
27
Describe the frenkel defect
When there is a vacancy and interstitial atom - distorts atom - needs 5-10x more energy than a normal vacancy
28
Describe the impurity defect
When there is a different material on a lattice point
29
State the two dislocations
Stacking faults/edge dislocations | Screw dislocations
30
Define grain boundaries
Most materials are not single crystals, but many small crystallites orientated wrt to each other