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MS2 > Crystal Defects > Flashcards

Crystal Defects Flashcards

1
Q

What is a vacancy (Schottky defect)?

A

An atom is removed from the crystal structure and notionally relocates to the surface (equally a vacancy migrates in from the surface).

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2
Q

What is an interstitial defect?

A

An atom is squeezed into a space in the crystal structure between the atoms on their lattice sites.

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3
Q

What is a Frenkel defect?

A

A combination of a self interstitial and a vacancy formed by an atom leaving a lattice site but remaining in a nearby interstice.

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4
Q

What is a substitutional defect?

A

A native atom is replaced by a foreign one.

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5
Q

What is a colour centre?

A

An anion vacancy where an electron takes the place of the vacant anion. It can give rise to the emission of characteristic wavelengths of lights.

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6
Q

List all types of point defects.

A 
Vacancy (Schottky pair)
Substitutional
Interstitial
Frenkel
Colour centre
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7
Q

Derive Fick’s first law.

A

Check derivation.

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8
Q

In Fick’s first law, what is D equivalent to?

A

1/(6τ) d^2

Where
τ is the jump frequency
d is the distance between planes.

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9
Q

Derivation of τ.

A

Check derivation.

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10
Q

Fick’s second law of diffuion is dependent on what?

A

Time.

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11
Q

Useful equation for Fick’s second law

A

x=sqrt(Dt)

where D is diffusion coefficient.

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12
Q

What is a stacking fault?

A

A region within a crystal where the regular stacking sequence is interupted for one or two layers.

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13
Q

What is an intrinsic stacking fault?

A

The removal of a layer.

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14
Q

What is an extrinsic stacking fault?

A

The insertion of a layer.

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15
Q

What is twinning?

A

A fault where two grains where all atoms either side of the grain are in ideal positions with respect to the lattice of both halves of the twinned crystal.

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16
Q

Mechanisms of twinning

A 
Mechanical shear process.
Annealing twins (growth accident).
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17
Q

What is a grain boundary?

A

Excess energy present in the material as a result of disturbance of a perfect lattice by misorientation between crystals.

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18
Q

What is the equilibrium condition of a triple junction?

A

stress1/sin(theta1)=stress2/sin(theta2)=stress3/sin(theta3)

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19
Q

What does the energy in an interphase boundary depend on?

A

The degree of lattice mismatch between the two phases.

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20
Q

What is an interphase boundary?

A

A boundary between two different phases of material.

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21
Q

What is an antiphase boundary?

A

In crystals of more than one atom type, where two domains of the same ordered phase are arranged such that atoms are next to their non-preferential nearest neighbours on the boundary.

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22
Q

What is a dislocation?

A

A line in a crystal structure where bonding (local atomic coordination) is incorrect.

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23
Q

How does bonding and coordination change due to a dislocation?

A

With the exception of the core itself, the bonding (coordination) is normal (though it may be distorted).

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24
Q

Derive an expression for theoretical shear modulus of a material by block shear.

A

Check derivation.

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25
Q

What happens when a dislocation moves?

A

The position of the extra half plane moves by one atomic spacing.
Atoms at core only move a short distance.
Energy fluctuations with position are small.

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26
Q

Describe an edge dislocation

A

Slip vector 90º to dislocation line. Slip vector and dislocation line define a unique slip plane.

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27
Q

Describe a screw dislocation

A

Slip vector and dislocation line are parallel. No unique slip plane can be define.

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28
Q

Similarities between edge and screw dislocations.

A

Dislocation divides slipped from unslipped material.
An applied stress causes dislocations to make more material slip.
Dislocations can only move normal to its line direction (otherwise “movement” is meaningless)

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29
Q

Whcih dislocations are glide dislocations?

A

Screw and edge.

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30
Q

What is climb of a dislocation?

A

If a vacancy diffuses to every bottom atom of the extra half plane on an edge dislocation, the dislocation has moved up by one atomic step.

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31
Q

Limiting condition that makes climb of dislocations slow?

A

A vacancy must diffuse to every atomic position along the whole line of the dislocation.

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32
Q

What convention is used for finding Burgers vector?

A

Dislocation into page with FS/RH convention.

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33
Q

Dislocations cannot be immutably labelled edge or screw so what are they?

A

Most dislocations are mixed with an angle between b and l between 0º and 90º

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34
Q

What is the line between slipped and unslipped material called?

A

The line vector of the dislocation.

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35
Q

For a mixed dislocation what can the line vector be broken up into?

A

Components of edge and screw.

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36
Q

Along the line vector what happens to the Burgers vector?

A

It remains the same.

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37
Q

At a dislocation node, what can be said about the sum of the Burgers vectors?

A

Equal to 0 due to conservation of the Burgers vector.

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38
Q

Where is the only place at which dislocations can end?

A

At crystal boundaries (surface or grain boundary).

39
Q

In TEM, where does the electron diffraction pattern form?

A

On the back focal plane

40
Q

What is the difference between bright field (BF) images and dark field (DF) images?

A

BF are formed using only the transmitted beam whereas DF are formed by using only one of the diffracted beams.

41
Q

How does a dislocation show on TEM?

A

Local variations in crystal structure such as strain fields result in changes to the intensity of the diffracted beams.

42
Q

Why do dislocations show on TEM?

A

Crystal planes close to the dislocation are bent and if the bulk of the material is set to a Bragg condition, the planes near the dislocation will not be well oriented so will appear dark.

43
Q

What is the invisibility criterion for a dislocation?

A

g.b=0

where
b is Burgers vector
g is reflection orientation

44
Q

Why does etching reveal dislocations?

A

The rate of removal of material at a dislocation is higher due to strained bonds near the core of the dislocation, resulting in an etch pit.

45
Q

What does a edge etch look like?

A

A conical pit due to symmetrical strain fields.

46
Q

What does a screw etch look like?

A

A spiral pit.

47
Q

What does a grain boundary etch look like?

A

A series of pits.

48
Q

How can a low tilt boundary be formed?

A

With a series of regularly spaced edge dislocations.

49
Q

How does spacing of edge dislocations along a grain boundary vary with θ?

A

Spacing is inversely proportional to misorientation angle θ.

tanθ≈θ=b/D

where
b is the smallest lattice spacing
D is the spacing between dislocations.

50
Q

Why does energy of grain boundary vary approximately linearly with angle in low angle grain boundaries?

A

Dislocations have a energy per unit length

since
dislocation energy α 1/D α θ.

51
Q

What happens when etching to reveal dislocation motion?

A

The repeating etching of an etch makes pit wider not deeper as dislocation is no longer in that position. Series of pits decreasing in width forms, decreasing in direction of dislocation motion.

52
Q

What’s the difference between sessile and glissile dislocations when repeatedly etched?

A

Sessile dislocations do not move so etch pit gets deeper and wider.
Glissile dislocation moves so when etched leaves a trace with older pits getting wider not deeper.

53
Q

What are causes of sessile dislocations?

A

Jogs, tangles from work hardening.

54
Q

How can dislocations in silicon be revealed using copper?

A

Thet can be decorated as copper diffuses very fast in silicon and the lattice is expanded at the dislocation core giving lower energy sites for copper. Silicon is transparent in IR but copper is not so appears under IR.

55
Q

Derive the shear strain of a screw dislocation.

A

Check deriavtion.

56
Q

Derive the line energy of a screw dislocation.

A

Check derivation

57
Q

What assumption is made about core energy when deriving line energy of a screw dislocation to the first approximation?

A

Due to it being highly strained but of small volume it us negligible.

58
Q

Result for self energy of an edge dislocation

A

E=(Gb^2)/(4π(1-ν)) ln(R/r0)

ν is Poisson’s ratio

59
Q

What is line tension of a dislocation?

A

Energy per unit length = force, so line energy is equivalent to line tension.

60
Q

Why is the Burgers vector most likely to be the shortest lattice vector?

A

Slip must move an atom to an equivalent position in the lattice.
Dislocation energy per unit length is proportional to b^2

61
Q

Why is the slip plane most likely to be the closest packed plane?

A

The planes are furthest apart so can slide over each other more easily.
The interatomic distances in close packed planes are smallest so the Burgers vector will be as small as possible.

62
Q

In more complex structures, what should dislocations not do?

A

The paths atoms follow as shear happens should not create transient situations with high energy. Should avoid situations in ionic materials where ions of the same charge move near to one another.

63
Q

In fcc materials, what is the slip planes and what are the slip directions?

A

{111}
and
<110>

64
Q

What is the length of the Burgers vectors in fcc?

A

a/sqrt(2)

65
Q

How many independent slip systems are there in fcc?

A

4 slip planes
3 slip directions in each
3x4=12 independent slip systems.

66
Q

Equation for Schmid’s Law

A

τ = F/A cosφcosλ = σcosφcosλ

φ is angle between stress direction and normal of slip plane
λ is angle between slip direction and stress direction

67
Q

What is the Schmid factor?

A

cosφcosλ

φ is angle between stress direction and normal of slip plane
λ is angle between slip direction and stress direction

68
Q

What does Schmid’s Law state?

A

Yeild will occur when the resolved shear stress on a slip system reaches a critical value.

69
Q

What is the condition for Schmid factor in order to find critical external stress?

A

cosφcosλ must be maximum.

70
Q

The OILS rule for fcc.

A

State tensile axis in form [UVW].
Of these indices identify highest H, intermediate I, and lowest L, ignoring signs.
Slip direction of <110> type in fcc where 0 is in the position of the intermediate index and the signs of the others are retained.
Slip plane {111} type in fcc where intermediate and highest signs are preserved but the lowest is reversed.

71
Q

The OILS rule for bcc.

A

State tensile axis in form [UVW].
Of these indices identify highest H, intermediate I, and lowest L, ignoring signs.
Slip plane of {110} type in bcc where 0 is in the position of the intermediate index and the signs of the others are retained.
Slip direction <111> type in bcc where intermediate and highest signs are preserved but the lowest is reversed.

72
Q

What does the OILS stand for?

A

zerO
Intermediate
Lowest
Sign

73
Q

What systems does the OILS rule apply to?

A

Cubic only

74
Q

How are diamond structures similar to fcc in terms of dislocations?

A

Slip planes are {111} and slip directions are <110>, but shortest vector is 1/4 <111> but it doesn’t lie in a close packed plane.

75
Q

How are diamond structures different to fcc metals in terms of dislocations?

A

Bonds must be broken and reformed for a disloocation to be moved and the bonds in a diamond structure are covalent. This makes it very difficult for a dislocation to move.

76
Q

What is a dissociated dislocation?

A

Where a perfect dislocation splits into two (Shockley) partial dislocations.

77
Q

What type of Burgers vectors do partial dislocations have in fcc?

A

a/6<112>

78
Q

What is formed between partial dislocations?

A

A stacking fault

79
Q

Compare energetics of a perfect and two partial dislocations.

A

Check comparison

Two partials should have lower energy making more favourable.

80
Q

Why are stacking faults extra energy?

A

A plane of atoms is in a non prefered stacking sequence.

81
Q

Will there always be a stacking fault with partial dislocations?

A

Yes as partial dislocations repel one another and seperate to an equilibrium distance to where lowering the energy of seperation is balanced by the increase in energy of widening the stacking fault.

82
Q

What is a Lomer-Cottrell Lock?

A

When two partial dislocations on different planes that intersect interact and lower their energy by forming a dsilocation of a strange Burgers vector. Since the Burgers vector is on neither slip plane the dislocation becomes sessile.

83
Q

What direction does a force act on a dislocation?

A

Perpendicular to the dislocation line.

84
Q

Derive the force per unit length acting on a dislocation.

A

Check derivation

85
Q

How does a shear stress act on a dislocation loop?

A

Since the whole loop has the same Burgers vector, the magnitude of the force on must be the same everywhere on the loop. The line vector is constantly changing but the force on the dislocation must always be normal to the line vector.

86
Q

Under what conditions will a dislocation loop expand or contract?

A

Expand-if stress favours the shear produced by the dislocation
Contract-if stress opposes the shear produced by the dislocation

87
Q

What happens to dislocations in annealing?

A

At high temperatures glide occurs more easily and dislocations of opposite signs will annihilate each other lowering dislocation density.

88
Q

What happens to dislocation density in deforming?

A

Increases

89
Q

What happens to dislocations in work hardening?

A

They obstruct each other’s movement making the metal harder to deform.

90
Q

Describe the Frank-Read mechanism.

A

A dislocation is anchored at both ends in the slip plane.
It responds to the force applied by blowing out.
Two dislocation line vectors of opposite sign touch and annihilate.
An outer dislocation loop is formed and will expand while the inner segment can expand causing a further loop.

91
Q

Derive the critical condition for a Frank-Read source.

A

Check derivation.

92
Q

Why is the critical condition for a Frank-Read source when the dislocation is a semicircle?

A

The curvature is greatest and shear stress is at it’s maximum.

93
Q

Derive an expression for vacancy concentration.

A

Check derivation

94
Q

How can vacancy concentrations be measured?

A

Electrical resitivity

Thermal expansion

MS2 (6 decks)

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