Materials for Devices Flashcards
Angle between C-C bonds
109.5 degrees
Polymers
Built up of repeating units (monomers)
Chem drawing for polymers (with (un)shaded triangles)
Shaded triangle = bond comes out of the page
Lined triangle = bond retreating into the page
Ends of carbon chains
The last carbon at the end of a carbon chain isn’t bonded to 2 carbons, only 1. So, you have to bond it with 2 extra bonds e.g. 2 extra hydrogens to maintain 4 bonds each
Random walk
Used to model the actual length of a polymer since they gets tangled up and don’t lie perfectly straight.
Proof on BH6
Kuhn length
Polymer chains are stiffer than they shown by the random-walk model. Bonds aren’t free to move in all directions.
The kuhn length is the length for which polymer chains are effectively straight and rigid.
Kuhn length in the random walk model
Length squared = (n/k)(l*k)^2
where n is the number of bonds, k is the kuhn length and l is the length of 1 of the bonds
So the rms length = n^(1/2) * k^(1/2) * l
How side-groups affect the stiffness of polymers
Increase the stiffness because they limit foldability
Crystalline materials
Have long range order i.e. are anisotropic
Anisotropic
Properties may differ depending on the direction of measurement
Liquids
No long range order i.e. are isotropic
Isotropic
Properties are invariant depending on direction
Liquid crystals
Anisotropic liquids
Molecules are free to move relative to each other i.e. no long range positional order
Molecules tend to line up i.e. there is orientational order
Orientational order in a LC
Defined by a vector called a director
Degree of orientational order depends on the temperature of the LC:
At low temperatures, the LC may crystallise and have long range positional order
At high temperatures, the thermal agitation overcomes the alignment interaction
Order parameter (Q)
Used to describe the degree of orientational order
x = mean of (cosy)^2
where y is the angle between a molecule and the director
Q = (3x - 1)/2
With all molecules aligned, Q = 1 since x = 1
With molecules randomly orientated, x = 1/3 so Q = 0
How light interacts with a polymer as it passes through it and how this is affect by long range order or lack of it
EM waves travelling through a sample interact with the electron clouds around a polymer.
Along the long axis of the polymer, there’s a lot of interaction; perpendicular to this axis, there’s a lot less interaction.
This has no effect if the molecules are randomly orientated.
There is a net effect if the molecules are aligned preferentially. The axis along which there’s more interaction is the slow axis. The axis with little interaction is the fast axis. Refractive index is different for the different axes.
PVDs
Permitted vibration directions
The axes along which light can travel along a molecules
Birefringence
The difference between the refractive indices of PVDs
How polarising filters work
Aligned polymers with large birefringence. The light along the slow PVD is absorbed
Optical path difference
How far behind the slow beam is when the fast beam reaches the end of a birefringent block.
(birefringence)*(thickness)
When light through a birefringent material will pass through crossed polars
The optical path difference is (n + 1/2) wavelengths i.e. the phase difference is pi
Plane of polarisation is perpendicular to before
When light through a birefringent material will not pass through crossed polars
The optical path difference is n wavelengths i.e. the phase difference is 0
Plane of polarisation is parallel to before
Complementary colour
When white light passes through a birefringent material, 1 or more wavelengths of light will be absorbed by the analyzer and the optical path difference is an integer number of wavelengths.
Light observed is the full optical spectrum minus these wavelengths
Why Michel-Levy chart becomes less vivid in higher order
More and more wavelengths begin to be absorbed by the analyzer as there are more combinations of integer values of wavelengths that are possible
Extinction positions
Occur when the incident plane polarised light oscillated entirely along 1 PVD. There is no phase change and so the analyser absorbs all the light
Determination of which PVD is fast and which is slow
Align sample and compensator so both PVDS are 45 degrees to the polarizer/analizer.
Fast aligns with fast or slow aligns with slow:
Optical path difference increases and observed colour moves up Michel-Lecy chart
Fast aligns with slow:
Optical path difference decreases and observed colour moves down Michel-Levy chart
Compensator
An anisotropic crystal with a known birefringence e.g. quartz
What happens if light is polarised along the director in a LC
The section is isotropic
PVDs in an LC
PVDs are perpendicular and parallel to the director
Domains in LCs
LCs don’t have single, uniform directors. They are broken into smaller, differently orientated regions
Disclinatior
When domains meet in an LC
Schlieren texture
Observed when an LC is under crossed polars
Dark regions are in extinction since the director is parallel to the plane of polarisation of the light
Light regions have a uniform director that isn’t parallel to the light’s plane of polarisation
Maltese crosses occur when all point towards a single centre: the centre of the cross
Smectic LCs
Molecules organise themselves into layers –> organisational order with some positional order
Chiral nematic aka cholesteric
Molecules align themselves into a helical twist
Director rotates in a plane. Therefore, the plane of polarisation of light rotates too
Pitch
The distance along the axis of a chiral nematic LC for a complete 360 degree rotation of the director
Depends on how close the stiff part of the molecules is to the chiral centre. The further it is away, the steepness decreases and the pitch increases.
Chiral molecules
Lack inversion symmetry
Chiral nematic LCs under crossed polars
Light polarised perpendicularly to the axis of the helix produces a stripy pattern like a finger print
When director is in the plane of polarisation, there’s extinction.
When the director is perpendicular to the plane of polarisation, there’s a bight spot.
The pitch is the distance between 3 subsequent dark spots
How to encourage the director of an LC to be in a certain direction
Create grooves on the surface the LC is in contact with
An LC sandwiched between 2 surfaces with grooves perpendicular to each other will twist.
Chiral nematic dopant
Helps to encourage the director of an LC to twist
LC cells
Analyzer and polarizer are parallel to the grooves on the 2 surfaces that the chiral nematic LC is sandwiched between.
Normally, all the PPL is transmitted through the analyzer as the plane of polarisation twists 90 degrees.
If an electric field is applied across the LC cell, there’s an induced dipole moment and the molecules align with the field. Molecules near the grooves maintain with orientation. Twisting of the plane of polarisation is disrupted and the analyzer doesn’t transmit light.
Freedericksz Transition
If an electric field is applied across the LC cell, there’s an induced dipole moment and the molecules align with the field.
Dielectric material
Electrical insulator for that it can support electrostatic charge
Polarisation
Dipole moment per unit volume
Mechanisms of polarisation
Distortion of the electric cloud about a nucleus
Change the relative position of positive and negative ions
Rotate pre-existing permanent dipole moments
Dipole moment
A vector
individual charge * displacement between then
Charge density of a material aka displacement field
Sum of the polarisation of a material and the free space component.
= permitivity of free space * electric field + polarisation
= Electric field * permitivity of the material
Dielectric constant of a material
permitivity of a material / permitivity of free space
Capacitance
The units of charge a material can store per unit of potential difference across it
Unique direction
A lattice vector which isn’t repeated anywhere else by the symmetry present
Centrosymmetric
Every component is reflected through the centre of symmetry
Polar material
demonstrates dielectric polarisation
must contain a unique direction
Piezoelectricity
e.g. quartz
A stress applied to the material induces a shape change which moves the centres of positive and negative charge relative to each other and creates a dipole moment. Overall, there is a net change in polarisation.
e.g. igniters or flashing lights in trainers
OR
An electric field is applied to the material moves the ions which changes the shape of the material
e.g. displacement transducers
Pyroelectricity
As the temperature of the material changes, the relative positions of positive and negative charges changes. There is polarisation
e. g. thermal imaging cameras or burglar alarms
e. g. ZnS
Ferroelectrics
Application of an electric field can leave the crystal permanently polarised and this can only be reversed by applying an electric field in the opposite direction.
Ions in a crystal sit in double well potentials. An electric field pushes the ions to specific energy wells. When it’s removed, the ions remain in an energy well, so they don’t move and the material remains polarised.
e.g. BaTiO[3]
Why there’s no polarisation of free space across a piezoelectric
There’s no external voltage since the voltage developes within the sample due to an applied stress. So, there’s no polarisation of free space as there’s no voltage across free space
Curie Temperature (ferroelectrics)
Temperature at which the unit cell in a ferroelectic material spontaneously acquires a dipole moment due to a change from high to low crystallographic symmetry
What effects the dielectric constant of ferroelectric materials
- Dopants or impurities
- Temperature:
Approaching the Curie temperature as the sample cools, the dielectric constant increases rapidly. The small ions in interstitial sites vibrate less as they cool and there’s more space left to displace them and create a dipole.
After passing the Curie temperature as the sample cools, the crystal system gets a greater packing efficiency at expense of symmetry. So, the interstitial sites are smaller. There’s less space to displace the ion into, so the crystal is harder to polarise. Dielectric constant falls rapidly.
The dielectric constant increases again after more cooling.
Energy balance of domains
Stray field energy is balances by domain wall energy.
The smallest total energy is optimal
Poled ferroelectrics
Dipoles are preferentially aligned along the crystallographic direction that’s most close to parallel to the field.
Hysteresis for ferroelectrics
- No E-Field, no polarisation = randomly orientated domains
E-Field increases:
- Reversible domain wall motion
- Favourably orientated domain grow and non-favourably orientated domain diminish
- Saturation polarisation: 1 single domain lined up along the crystallographic direction that most closely aligns with the field
E-Field decreases:
Polsarisation remains principally aligned.
With no E-Field, there’s the remanent polarisation
Reverse Field increases:
- Oppositely orientated domain grow.
- Coercive field is the strength of the E-Field required to reach 0 polarisation again
- Domains aligned with the reverse field continue to grow.
- Saturation polarisation in reverse direction
Saturation polarisation
One single aligned domain in the ferroelectric
What affects the size of the hysteresis loop
Domain walls can be pinned by crystal defects.
Area of the loop is proportional to the energy required to switch polarisation
How reverse domains nucleate and grow
- Reverse field is applied
- oppositely polarised domains grow at the edges of existing domains
- Reverse domains grow along the direction of the field
- Reverse domains grow laterally aka perpendicularly to the field
- Polarisation is reversed when all domains form 1 domain
Why ferroelectric is good
- Low voltage
- Non-volatile
- Radiation hard
- Small size and cost
Why it’s good to keep a ferroelectric at a phase boundary
Can deform along more crystallographic directions and better align with an applied field as it can deform in both lattices
Magnetic dipole
Produced by spinning electrons about a nucleus.
Depends on electrons in incomplete shells as these don’t all have partners with opposite spin.
Magnetisation
Magnetic moment per unit volume (Am^2 / m^3)
Magnetic field
Applied across a sample
Magnetic moment
Current * Area
Diamagnetism
No unpaired electrons
With no external field, no net magnetic moment
In an applied magnetic field, electron orbits react to oppose the field
Susceptibility is negative
e.g. graphite
Paramagnetism
Some unpaired electrons –> dipoles exist, but they align randomly
With no external field, the overall moment is 0
With an external field, there is partial alignment and moments in the direction of the field
Susceptibility is small but positive
e.g. Na
Ferromagnetism
Many unpaired electrons
Strong interaction between moments
Moments tend to align as parallel moments have the lowest energy.
Moments align with an applied field and orientation becomes permanent
Susceptibility is high and positive
e.g. Fe
Antiferromagnetism
Many unpaired electrons
Strong interaction between moments
Moments tend to align BUT antiparallel moments have the lowest energy.
Net magnetic moment = 0
e.g. Cr
Ferrimagnetism
Many unpaired electrons
Strong interaction between moments
Moments tend to align BUT antiparallel moments have the lowest energy.
Moments in opposite directions are NOT equal magnetudes
Net magnetism
e.g. magnetite
Curie Temperature (ferromagnets)
Susceptibility becomes very high around the Curie temperature
As temperature increases, vibration of ions increases and coordination of electron spin states decays. Ferromagnetic materials becomes paramagnetic at the Curie temperature
Magnetocrystalline anisotropy
Preferred direction of the magnetic moment depends on the crystalline direction.
Energy is lowest when the magnetisation points along a specific crystallographic direction.
There are easy and hard directions along which to magnetise a material
Shape anisotropy
Easier for magnetisation direction to be along a long, thin sample than perpendicular to the long side of the same sample
Magnetostriction coefficient
fractional change in length on changing magnetisation from 0 to saturation
Magnetostriction
A magnetised crystal will deform
An applied stress to a crystal can lead to magnetisation
Domain walls in magnetised materials
Can either transition between anti-parallel domains abruptly or through gradual twisting.
- Exchange interaction energy: Misaligned domains have high energy
- Magnetocrystalline/anisotropy energy: Moments misaligned with the easy axis have high energy.
Depending on the material, the optimal scenario is found from 1 and 2
Ferromagnetic hysteresis
Increasing applied field:
- Reversible domain wall motion (domain walls don’t reach crystal defects)
- irreversible wall motion as favourably orientated domain grow along the easy access that fit best to the field’s direction
- Moment rotates from the easy axis to the direction of the field. Saturation magnetisation is reached
Removing the field:
Spontaneous magnetisation is achieved. Magnetic dipole rotates back to the easy axis. Still 1 single domain
When there’s 0 field, there’s the remanent magnetisation. Small oppositely orientated domains nucleate to reduce the large stray field energy.
Increasing reverse field:
- Reverse domains grow
- Coercive field is required to reach 0 magnetisation again
- 1 single dipole along easy axis
- domain rotates to the direction of the field
Area of the magnetic hysteresis loop
proportional to energy required for 1 cycle i.e. double the energy needed to switch magnetisation
How imperfections in ferromagnetic materials affect the coercive field
Pin domain walls and increase the coercive field
Shapes of magnetic hysteresis loops that fit different needs
Large area: permanent magnets that don’t demagnetise easily
Square loop: well defined switches for memory devices
Tall and thin: High saturation magnetisation and low coercive field for transformer cores
Making magnetically soft materials
Small hysteresis loop area
Get rid of imperfections
Use long heat treatments to grow perfect crystals or use homogeneous materials with no crystalline structure as these can’t have imperfections
Making magnetically hard materials
Want to incorporate infections to pin domain walls
Either quench the material (rapid cooling) or compress fine powders as these are independent particles
Shottky defect
Equal number of anion and cation vacancies. Overall neutrality
Frenkel defect
Ion moved from where it should be to an interstitial site leaving behind a vacancy
Why ion conduction is affected by temperature
Ions vibrate more at higher temperatures.
Have more energy and can migrate through a lattice more easily.
What ion mobility depends on
Number of interstitial sites
Energy barrier between adjacent sites
Factors that create an ionic current flow
- concentration gradient (of ions or vacancies) gives rise to a diffusion current
- An external electric field gives rise to a drift current
Diffusion current density
Charge of individual ion * diffusivity * concentration gradient
ONLY applies to solid-state diffusion in a uniform concentration gradient
Ions move down the concentration gradient (oppositely charged vacancies move in the opposite direction) by random diffusion
Activation energy
Energy barrier between lattice points (i.e. from an energy well to the maximum energy between it and the subsequent energy well)
EITHER in Joules per mole
OR in eV per atom
Drift current
Addition of an electric field reduces the activation energy in 1 direction (by rotating the energy profile)
When to use the Nernst-Einstein equation
When diffusion current density is equal to drift current density.
Yttrium Stabilized Zirconia
Doping zirconia (ZrO[2]) with yttrium to create oxygen vacancies
Zirconia has cations in an FCC lattice with anions filling all the tetrahedral interstices
Y^(3+) ions replace Zr^(4+) ions
2 replacements creates 1 oxygen vacancy
Undoped zirconia is monoclinic at room temperature
Doping with Y[2]O[3] allows the cubic form to be stabilised over a wider range of temperatures including room temperature
delta - Bi[2]O[3]
FCC lattice with on average 6 tetrahedral sites filled with oxide ions. i.e. on average there are 2 oxygen vacancies per unit cell
Oxygen Concentration cell
Porous platinum electrodes to catalyse reactions and conduct electrons
If there are different concentrations of oxygen at each electrode, oxygen is transported from high to low concentration.
On the side with a greater oxygen concentration, oxygen is reduced and forms oxide ions.(cathode) These ions are transported across a solid electrolyte e.g. YSZ. At the other side (anode), oxide ions gain electrons.
In databook, oxygen ions flow from pO[2] to pO[1]. Of flow is in the opposite direction, E will be negative
Lamdba sensors
Measure oxygen levels in vehicle exhausts to make fuel combustion as efficient as possible
Self-generated voltage shows the difference in oxygen concentration between the exhaust and the atmopshere
Small e.m.f = lean burn, fuel should be added
Large e.m.f. = fuel rich, add oxygen
Air-to-fuel ratio by weight is 14.6 Aiming for (measured ratio)/14.6 = 1
Oxygen pump
Oxide ions driven across a membrane using an applied potential
Used for removing oxygen from molten metals
Fuel cell
Produces electricity from direct oxidation of fuel. Doesn’t have as many stages for electricity generation and so can be more efficient.
Cathode:
Oxygen is reduced to form oxide ions
Oxide ions travel across solid electrolyte
Oxide ions oxidise fuel (Hydrogen to water or methane to carbon dioxide and water)
Pros:
If hydrogen is used, there’s no polluting emissions
No noise
High efficiency
Requirements:
For effective conduction, electrolyte must be kept at high temperatures to maintain high ion conductivity and low electron conductivity.
Anode must be porous and electrically conducting –> conducting ceramic (cer-met)
Cathode must be permeable to oxygen, not oxidise at high temperatures and electrically conducting –> doped porous manganite
Cons:
High operating temperatures: need stability, no inter-reaction or inter-diffusion and matched thermal coefficients of expansion of all components
Polymer electrolyte membrane fuel cells
Conduct protons and operate at lower temperatures
e.g. sulphonated fluoropolymer membrane
Has a hydrophilic end that form clusters where water collects.
Proton on hydrated end moves between molecules
How to produce hydrogen
electrolyse water: requires energy input
pass fossil fuels and water over a heated catalyst: separates in carbon dioxide and hydrogen
Easy –> hard crystallographic axes for common ferromagnetic materials
Fe (BCC):
Easy <100> –> <110> –> <111> Hard
Ni (FCC):
Easy: <111> –> <110> –> <100> Hard
Co (hex):
Easy: <001> –> <100> Hard
Magnetite - reverse spinel
Ferrimagnetic
Fe(3+) ions have magnetic moments that all cancel
Fe(2+) ions have magnetic moments that remain
Arrhenius equation
Diffusivity = D
D = D[0] * exp(Q/RT) if Q in J/mol
D = D[0] * exp(Q/kT) if Q in J/atom
