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GP2 > Electrical and Optical Properties of Materials > Flashcards

Electrical and Optical Properties of Materials Flashcards

1
Q

State Coulomb’s Law

A

Check L1 S4

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2
Q

State Coulomb’s law for multiple charged particles.

A

Check L1 S4

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3
Q

State what is meant by electric field.

A

The electric field at a point in space is defined as the force per unit positive test charge at that point

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4
Q

State an equation for electric field strength in terms of force and charge.

A

Check L1 S5

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5
Q

In what direction do lines of force go when showing a field.

A

They show the direction of the force acting upon a positive test charge.

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6
Q

State Gauss’s law

A

The electric flux out of a closed surface us equal to the charge enclosed within it divided by ε(0).

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7
Q

State expressions for field around a point charge, a charged wine and a plane by using Gauss’s law.

A

Check L1 S6

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8
Q

State an expression for electrical potential from electric field.

A

Check L1 S7

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9
Q

Relate electric field to electronic potential.

A

Check L1 S7

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10
Q

State an expression for electric dipole moment

A

Check L1 S8

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11
Q

What direction is a dipole arrow draw?

A
  • to +
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12
Q

Derive an expression for the Torque on a dipole in an electric field

A

Check L1 S8

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13
Q

State an expression for capacitance using charge and voltage.

A

Check L1 S9

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14
Q

Derive an expression for capacitance of a parallel plate capacitor in terms of area and distance.

A

Check L1 S9

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15
Q

State a set of expressions for the energy stored in a capacitor.

A

Check L1 S9

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16
Q

State an expression for the relative premittivity of a material.

A

Check L1 S10

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17
Q

What is polarisation P?

A

The dipole moment per unit volume.

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18
Q

Show the charge separations in a parallel plate capacitor with a dielectric.

A

Check L1 S10

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19
Q

State an expression for the total field in a dielectric in a capacitor.

A

Check L1 S10

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20
Q

Relate polarisation and electric field using electric susceptibility.

A

Check L1 S11

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21
Q

RElate relative permitivity and susceptibility of a dielectric.

A

Check L1 S10

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22
Q

What is the electric displacement?

A

A measure of the field due to the conduction charges only

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23
Q

Relate D, E and P

A

Check L1 S10

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24
Q

What is a piezoelectric material?

A

A material that exhibits electrical polarisation when a mechanical stress is applied.

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25
Q

What is a pyroelectric material?

A

A material where electrical polarisation can be modified by changing the temperature.

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26
Q

What is a ferroelectric material?

A

A non-linear material in which polarisation can be controlled with electric field.

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27
Q

What is the crystallographic condition that all piezo- pyro- and ferroelectric materials exhibit.

A

No centre of symmetry in there structure.

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28
Q

What must pyro- and ferroelectric materials contain in order to exhibit the effects.

A

Must contain permanent electrical dipoles which limits the crystal symmetries to this that are polar.

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29
Q

How do ferroelectric materials relate to pyroelectric materials?

A

Ferroelectrics are a sub-group of pyroelectrics in which the direction of spontaneous polarisation can be reverse with an electric field.

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30
Q

State the two expressions for polarisation and strain for piezoelectric materials.

A

Check L1 S14

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31
Q

State the expression for pyroelectric crystals.

A

Check L1 S15

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32
Q

How is wurtzite a pyroelectric crystal?

A

The Zn2+ ions are below the S2- ions leading to spontaneous polarisation along the c-axis.

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33
Q

Sketch an energy against Ti4+ position graph showing how BaTiO3 (perovskite) is a ferroelectric material.

A

Check L1 S16

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34
Q

What is a ferroelectric domain?

A

A region with the same polarisation.

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35
Q

A hysteresis loop can explore what in ferroelectric materials?

A

The relationship between growth of domains and the strength of the field applied.

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36
Q

State all of Maxwell’s equations in integral and differential form.

A

Check L1 S17

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37
Q

Derive the speed of light in a vacuum from the general wave equation and the electromagnetic wave equation.

A

Check L1 S18 and 1st year notes

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38
Q

Sketch how conductivity varies with temperature for metals, semiconductors and insulators.

A

Check L2 S20

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39
Q

State the temperature dependence of conductivity for metals, semiconductors and insulators.

A

Metals: σ α T^-1
Semiconductors: σ α exp(-E/kT). (E is Band gap)
Insulators: σ α exp(-E/kT) (E is the diffusion and vacancy formation energy).

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40
Q

State an expression fro the Drude model.

A

Check L2 S21

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41
Q

Where is the temperature dependence in the Drude model?

A

1/τ = 1/τ(impurity) + 1/τ(phonon) + 1/τ(grain boundary) + … (this is Matthiesen’s rule)

Since 1/τ depends on 1/τ(phonon) and τ(phonon) is proportional to T^5 for low T and proportional to T for the rest it means that there is a linear dependence between resistivity and temperature near RT.

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42
Q

State the conductivity equation for a semiconductor and which terms have T dependence.

A

Check L2 S24

n and τ have T dependence as n varies with T in a semiconductor.

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43
Q

Sketch a plot of logσ against 1/T for a semiconductor including different doping levels and label the dominant type of scattering etc.

A

Check L2 S24

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44
Q

If the band gap of a material exceeds what value, it becomes an insulator.

A

4 eV

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45
Q

By what mechanism can insulators conduct?

A

Ionic conductivity in the solid state.

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46
Q

Derive an expression for the concentration of vacancies in an ionic crystal.

A

Check L2 S26-28

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47
Q

Using Einstein model of a solid as an ensemble of independent quantum harmonic oscillators vibrating at the same frequency ν, drive the vibrational entropy associated with each vacancy in an ionic crystal.

A

Check L2 S29

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48
Q

What are the two main defect types in ionic crystals.

A

Schottky defects and Frenkel defects.

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49
Q

What is a Schottky defect?

A

Where there is an equal number of missing positive and negative charges in the lattice.

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50
Q

What is a Frenkel defect?

A

Where a positive or negative charge is missing in the lattice, but there is an equal of that charge in an interstitial site at some point in the lattice.

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51
Q

What materials are a good example of electrical conductivity in insulators (by ionic conductivity)?

A

Alkali halides (eg NaCl)

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52
Q

In an alkali halide, will there be an intrinsic vacancy density?

A

Yes and it is dependent on T. Vacancies can form by an ion migrating to the surface but charge neutrality is maintained otherwise there would be a large electrostatic energy formed.

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53
Q

How can vacancies form independent of T in alkali halides?

A

If a small amount of another compound was dissolved in the alkali halide (eg CaCl2 in NaCl) then a small number of Na+ sublattice points would be occupied by Ca2+ ions with an equal number of vacancies being created to maintain charge neutrality. (Much like doping in a semiconductor).

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54
Q

Use Fick 1 to show how diffusivity in a lattice can vary at high and low T.

A

Check L2 S34-36

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55
Q

Adapt Fick 1 to allow the formation of current density and electrical conductivity equations in a material that ionically conducts (eg NaCl).

A

Chekc L2 S37-38

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56
Q

Derive the Einstein relation for diffusivity.

A

Check L2 S39

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57
Q

How can we determine which ion vacancy is responsible for conductivity in an ionic solid.

A

Use slabs of M and M+X- and measure the mass before and after a potential is applied. The change in masses will indicate which ion vacancies are responsible for conduction.

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58
Q

Give an example of a superionic conductor

A

AgI

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59
Q

What phase change allows AgI to be a superionic conductor?

A

Below 420K it has a wurtzite structure, but above 420K it has an α-AgI structure with excess sites for Ag+ ions (interstitial) that allows the ions to move rapidly through the material.

60
Q

Describe the electron hopping (polaron) conduction mechanism.

A

Present in certain impure ionic solids.
For transition metals that can change ionised state.
Addition of another metallic ion (eg Li+) allows electrons to hop from one transition ion to another.
Check L3 S48

61
Q

Discuss the difference in temperature and activation energy between electron transfer through a semiconductor and a polaron.

A

Both have a logarithmic dependence of conductivity on 1/T and have an activation energy.

In semiconductors the exponential behaviour is due to the increase in carriers whereas in polaron conductors it is due to an increase in mobility.

The activation energy associated with motion of electrons in a polaron conductor is due to the lattice distortion that is caused around sites as they are polarised (diagram L3 S49)

62
Q

Can polymers show electrical conductivity?

A

Sometimes along certain directions.

63
Q

By what mechanism does polyacerylene conduct electricity?

A

Alternating double and single bonds in the chain. Their overlapping p-orbitals create a cyst em of delocalised π-electrons which results in conductivity.

64
Q

Do polymers emit light?

A

Those with a suitable band gap can emit light and be used in OLEDs.

65
Q

Why is there a critical point (percolation threshold) in composites when it comes to conducting electricity?

A

Below a certain weight percent there is no continuous pathway through the material to conduct electricity whereas above a continuous pathway can be formed. This is the percolation threshold.

66
Q

State the formula for capacitance of a parallel plate capacitor with no dielectric in terms of distance between plates and area.

A

Check L4 S2

67
Q

State the formula for capacitance of a parallel plate capacitor with dielectric in terms of distance between plates and area.

A

Check L4 S3

68
Q

What two advantages are there of placing a dielectric in a parallel plate capacitor?

A

The field within the dielectric is lower than the applied field this the plates can be moved closer together as the risk of breakdown is reduced (increases the capacitance).

The polarisation charge σ’ attracts more charge onto that plates (increases capacitance).

69
Q

Give an expression relating the polarisation and the local field in a material that has an applied electric field.

A

Check L4 S5

70
Q

Give an expression rating the local field, Lorentz field and the applied field in a material that has had an electric field applied.

A

Check L3 S5

71
Q

How do we combine the effect of polarisation mechanisms on a material?

A

We consider those that are acting and sum the α values of each.

72
Q

List the mechanisms that a material can become polarised by.

A 
Electronic 
Ionic
Orientation (fluids)
Orientation (ion jump)
Space charge
73
Q

Discuss the mechanism for electronic polarisation within a material that us under an applied field.

A

The atom of the applied field displaces the electron orbit slightly resulting in a dipole forming as the centre of the electron orbit no longer falls on top of the positive nucleus.

The time to switch polarisation is of the order of the reciprocal of the frequency of x-ray or optical emission from excited electrons on those orbits. We do not expect any loss during switching except at frequencies near those same frequencies.

74
Q

Discuss the mechanism of ionic polarisation of solids under an applied electric field.

A

The ions of an ionic solid maybe thought of as charged particles of various masses connected to their nearest neighbours by springs of various strengths.

Applied electric field displaces the ions to polarise the solid. Here we expect profound frequency dependence according to those charges, masses and spring constants in the ionic arrangements.

Sketch on L4 S7

75
Q

Discuss the orientation polarisation mechanism (fluids) in a material with under an applied electric field.

A

If molecules of the fluid have permanent electric dipoles they align with the applied field. It is analogous to the classical theory of paramagentism so through Langevin theory -α α 1/T

Frequency dependence is expected to follow the Debye equations.

At low frequencies molecules have time to respond so polarisation can be quite large. At high frequencies the molecules cannot respond quickly enough by virtue of their inertia and collisions they suffer so polarisation will be lower.

Diagram L4 S8

76
Q

Discuss orientation polarisation (ion jump) in solids under an applied electric field.

A

Possible in A+B- charged systems with C++B2- impurity in solution which leaves A+ vacancies present that can associate with C++ impurities to look like a dipole. Reorientation of this dipole in the field by the vacancy moving from site to site changes the state of polarisation.

On application of E the orientation becomes energetically favourable so polarisation occurs.

T dependence (from Langevin theory) and frequency dependence are expected.
The contribution will be small for frequencies greater than the frequency with which the ion jump takes place.

Diagram L4 S9

77
Q

Discuss the mechanism of space charge polarisation in a solid under an applied electric field.

A

In a multiphase solid where one phase has a very much larger electrical; resistance than the other, charges can accumulate at the interface (ie the material behaves like an assembly of interconnected resistors and capacitors) - the overall effect being the solid is polarised.

There is complicated frequency dependence in according to the range of capacitors and resistors involved (ie grain sizes and resistivities (highly sensitive to temperature)).

Certain ferrites and semiconductors exhibit this property,.

Diagram L4 S10

78
Q

Derive the Clausius-Mossotti relation.,

A

Check L4 S11

79
Q

Derive the orientation polarisation of polar fluids using the Langevin derivation.

A

Check L4 S12-13

80
Q

Show the frequency dependence of polarisation with a restoring force (electronic and ionic polarisation) by using the Clausius-Mossotti relation.

A

Check L5 S17-18

81
Q

Show that for electronic and ionic polarisation when frequencies are much greater than the resonant frequency, the polarisation mechanism is not activated and contributes nothing to the overall polarisability of the material.

A

Check L5 S19

82
Q

What materials does the resonance model work well for and not so well for?

A

Well for ionic solids but less certainty to molecular rotation bands and to the obviously quantum mechanics=cal situation of optical/x-ray transitions of individual atoms at very high frequency.

83
Q

State how orientation polarised materials relax with an expression.

A

Check L5 S20

84
Q

Derive the Debye equations for how a material responds to an oscillating applied electric field.

A

Check L5 S21-22

85
Q

Sketch a table of effect of temperature and effect of frequency on each type of polarisation in a material.

A

Check L5 S25

86
Q

What methods of loss are there in dielectric materials?

A

DC leakage.

AC loss.

87
Q

Describe DC leakage in a dielectric material.

A

Polar organic molecules are very low loss, while ionic solids have temperature dependent losses that may be considerable.

88
Q

Describe AC loss in a dielectric material.

A

Must choose dielectric in accordance to frequency range of interest.

For example, oils are used in transformers to prevent breakdown at very low frequencies.

At medium to high frequencies, ionic solids must be used because in the medium frequency range the oils may have Debye type losses and high frequencies are thus effectively infinite.

Both dielectric constant (ε’) and loss (ε’’) must be taken account and some compromise found for a particular frequency range.

89
Q

What is dielectric strength?

A

The ability of a dielectric to resist the conduction of electricity above a certain field strength.

90
Q

Describe Zener breakdoiwn.

A

If an electron A were able to change its position to B it would be in the conduction band (leaving a hole in the valance band) and it would have achieved this without an increase in its kinetic energy (potential energy used in this creation process). Now in large fields the distance Δx is decreased and electrons near the top of the valance band can tunnel through to the conduction band, producing the envisaged hole at A and the conduction electron at B.

91
Q

Describe the process of avalanche breakdown.

A

For larger fields (larger gap materials) it many be possible for an electron once in the conduction band to acquire such a large amount of energy that between its inevitable collisions sufficient energy can be given to a valance band electron to ionise it into the conduction band. The original electron loses that amount of kinetic energy but stays in the conduction band. The two electrons now generate more and so on producing an avalanche.

92
Q

What four types of breakdown are there for good insulators?

A

Collision breakdown
Thermal breakdown
Local discharge breakdown
Electrolytic breakdown

93
Q

Describe collision breakdown in a good insulator.

A

Same mechanism as avalanche breakdown in semiconductors as the unlikely event of an electron in the conduction band is bound to sufficiently multiply in large fields. (Zener breakdown is much less likely due to tunnelling lengths).

94
Q

Describe how thermal breakdown occurs in good insulators under DC conditions.

A

Once any conduction takes place, ohmic heating results because conductivity is so low high temperatures are attained locally. Higher T means more electrons are excited to the conduction band and more local heating as breakdown occurs.

95
Q

Describe the process of thermal breakdown of a good insulator under Ac conditions.

A

Any loss/lag mechanism dissipates energy and hence heats the material with the same result as the DC case where more electrons are excited to the conduction band which in turn heats the materials further as more energy dissipated eventually leading to breakdown.

96
Q

Describe the process of local discharge breakdown in a good insulator.

A

For solids with gas bubbles/porous, the field experienced in the gas is higher than that in the solid because of the continuity condition on electric displacement D.
The result is a microscopic arc discharge being initiated. Electrons and ions from the discharge bombard the inner surface and erode it allowing there cavity to grow which in turn increases the current in the arc, increasing the temperature and eventually causing breakdown.

97
Q

Describe the process of electrolytic breakdown in good insulators.

A

Local electrolytic (ie moving ions) current paths transport some conducting materials from the electronics to the interior of the dielectric. This process is frequently aided by humidity. Over time a very fine conducting path reaches the interiors reducing the local thickness of the dielectric material and thus increasing the field strength. An increased field strength then allows one of the other failure mechanisms to take over.

98
Q

State the equations that describe the properties of piezoelectric materials

A

Check L6 S37

99
Q

Describe how a strain on a piezoelectric material results in polarisation.

A

When a crystal is strained, any ionic charges within it are displaced from their equilibrium positions. In piezoelectric materials the displaced charges form electric dipoles resulting in a change of polarisation. In quartz the unstrained material has no permanent dipole, but strain displaces the ions such that a dipole is formed.

100
Q

Describe how a pyroelectric material works.

A

The crystals contain permanent dipoles. The magnitude of polarisation depends on positions of the ions in the unit cell. When the temperature is changed, the positions of the ions changes anisotropically and this alters the overall polarisation of the crystal.

101
Q

How can pyroelectric materials in theory be used for thermometry?

A

A polarisation only develops when the temperature is changed is accounted that although the crystals are always spontaneously polarised internally the resulting surface charges are cancelled out bu charges absorbed from the surroundings.

On heating or cooling the internal anisotropy changes causing internal polarisation to change in ways which lead to external compensating charges do not keep pace.

This is unreliable however in air.

102
Q

Is there a ferroelectric curie temperature?

A

Yes, above which a ferroelectric material is just a paraelectric.

103
Q

What is the ferroelectric catastrophe?

A

If the dipole is greater than the dipole which is producing it then the system will escalate to infinite polarisation.

104
Q

Derive the ferroelectric catastrophe.

A

Check L L6 S43

105
Q

What are the differences in hysteresis for the ferroelectric case compared to the ferromagnetic case?

A

1) Polarisation rotation cannot occur as the direction of the polarisation is fixed by the structure (ie there are a fixed number of crystallographic directions that polarisation can occur along).
2) In general, domain growth is favoured in the “forward” direction, ie long domains tend to grow even longer. This indicates that unlike the ferromagnetic case the “head-to-tail” coupling is stronger than sideways interactions. This means domains can be very narrow and has important implications for computer memories.

106
Q

Uses of piezoelectric materials?

A

Transducers
Oscillators
Mechanical actuators

107
Q

Uses of pyroelectric materials

A

Infrared sensors for detecting small changes in T.

108
Q

Applications of ferroelectric materials?

A

FRAM.

109
Q

Sketch the orientation of domains in a ferroelectric material before and after poling.

A

Check L6 S51

110
Q

How can we achieve high relative premittivioty materuals?

A

When a ferroelectric is close to its curie T, the displacement of an ion (eg Ti4+ in BaTiO4) is rather easy. Thus the application of electric fields leads to a large polarisation and the material has a large dielectric constant.

Modification of the composition of the material allows the Curie T to be around RT making them useful.

111
Q

Derive the differential form of the wave equation.

A

Check L7 S4

112
Q

Draw a table of Maxwell’s equations for a vacuum stating where they come from, both the integral and differential form and the meaning behind each.

A

Check L7 S5

113
Q

Derive the relation between the electric and magnetic parts of an EM wave from Maxwell’s equations with both time and position dependence then use the differential form of the wave equation to derive the speed of an EM wave in a vacuum.

A

Check L7 S6-9

114
Q

How is the plane of polarisation defined?

A

Using the electric field vector and the direction of motion.

115
Q

State an expression for the speed of light through a transparent insulating medium?

A

Check L7 S14

116
Q

When a EM wave enters a medium what properties change and don’t change?

A

Change: Speed and wavelength

Don’t change: Frequency.

117
Q

Derive an expression for an EM wave travelling through a conducting medium?

A

Check L7 S15

118
Q

DErive an expression for skin depth of a conducting material.

A

Check L7 S16

119
Q

What does skin depth describe?

A

The tendency of an alternating current flowing in a conductor to be restricted to the surface regions of the conductor.

120
Q

Show that in a conductor, the magnetic field is zero in the middle of the mateiral when an EM wave is incident.

A

For more than a few δ, the amplitude of the magnetic field becomes nearly zero. From Ampere’s law this implies that the current flowing in these regions is also nearly zero, hence current flow is restricted to the surface regions.

121
Q

Explain why AC current is limited to the surface of a conducting material?

A

The AC current generates a changing magnetic field that penetrates the conductor and acts in such a way as to prevent the current changing (Lenz’s law). This effect us greatest towards the Cente of the conductor and most strongly hinders current flow there. This drives the current to the surfaces of the conductor.

122
Q

How is skin depth exploited in power cables?

A

Want to minimise skin depth effects by using multiple separated components for each cable rather than a single wire.
Manufacture each part from a steel core for strength and use aluminium cladding for electrical current carrying capacity.

The poor electrical properties of steel core are largely irrelevant as little current flows there.

123
Q

How does skin depth affect submarine communications?

A

Salt water is a conductor so radio frequencies must be used to penetrate that deep.
Use extremely low frequencies (76Hz for US military).
Data transition rate is slow and ariels need to be long.
For thus reason submarines only receive and do not transmit data.

124
Q

Derive Snell’s law from conservation of transverse momentum.

A

Check L8 S21

125
Q

State the condition of Snell’s law for total internal reflection.

A

Check L8 S21

126
Q

What are the conditions for best transmission of a light down an optical fibre.

A

Must have smooth surfaces to avoid attenuation.
Must have a low dispersion
Use of grading of refractive index to ensure the pulses remain in phase.

127
Q

List the basic requirements for an optical fibre.

A 
High core refractive index
Low core dispersion
Low cladding refractive index
Smooth interface between core and cladding
Sufficient cladding thickness
Good flexibility
Good transmission efficiency
128
Q

Use a handwavey method to derive the reflection and transmission coefficients for the s-polarisation.

A

Check L8 S25

129
Q

Use a handwavey method to derive the reflection and transmission coefficients for the p-polarisation.

A

Check L8 S26

130
Q

State the Brewster condition.

A

Check L8 S26

131
Q

What is the Brewster angle?

A

At a certain angle, no p-polarised radiation is reflected, so all reflected radiation is s-polarised.

132
Q

State the solutions for s and p polarised transition and reflection under the condition of normal incidence.

A

Check L8 S27

133
Q

State expressions for the reflected and transmitted power of EM radiation when incident on an interface.

A

Check L8 S27

134
Q

List the methods for producing plane polarised light?

A

Selective reflection of plane polarised light

Birefringence

135
Q

Describe how selective reflection can produce plane polarised light.

A

Using Brewster’s angle, light incident at Brewster’s angle is plane polarised in reflection.
The amplitude of the plane polarised reflected light can be increased by using multiple layers of material to reflect more light.

136
Q

Describe how birefringence can produce plane polarised light.

A

Birefringence is where different polarisations have different refractive indexes and the material has a lower symmetry than cubic.
When unpolarised light enters the crystal it splits into two plane polarised portions that propagate according to two different refractive indices.

137
Q

How can selective absorption of different polarisations of light be used

A

Dichroism (differential absorption of different polarisations) was used in Polaroid who developed a system of dichroic crystals in a plastic sheet that were aligned in production.

138
Q

State the expressions of Malus’ Law for transmission through a polariser and analyser.

A

Check L8 S35

139
Q

Show that the greater the number of analysers in series to achieve rotation of a polarised wave, the greater transmission is.

A

Check L8 S36

140
Q

What is a liquid crystal?

A

A group of materials which display a “double” melting point. At the melting point the solid “melts” but in at least one dimension is maintained until the higher melting point is achieved at which point the material becomes truly liquid.

141
Q

What type of liquid crystals are used in electronics and describe them.

A

Nematic crystals are used.
The have rod shaped molecules that tend to line up parallel to each other locally (enhanced by electric fields polarising them). They also align with respect to a true solid surface with which they are in contact with.

142
Q

Describe how an LCD cell can allow light to be transmitted.

A

A cell with nematic crystal material inside aligned with surfaces.
E field is applied between two plates on outside that twists the crystals reducing the amount of polarised light to be transmitted.

143
Q

Describe how a twisted nematic display works.

A

Orientation of crystals on each side of LCD cell at 90° and gradually twist between each side.
The plane of polarisation of the light is able to be rotated.
under no field the light is rotated and passes through.
Under field the gentle rotation of crystals is disrupted and no polarised light is rotated.

144
Q

Sketch the setup of a reflected nematic display

A

Check L8 S40

145
Q

How can a dielectric mirror be made?

A

By making use of constructive or destructive interference, multiple layers of dielectrics can be stacked to either enhance transmission of a particular wavelength (eg for lenses) or to reflect a particular wavelength. These work over a narrow range of wavelengths.

146
Q

State the reflection of a dielectric mirror under normal incidence.

A

Check L8 S41

GP2 (4 decks)

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