Mark Senn 1-6

For the sake of general knowledge, can you explain how each of the points work, or what is used.

microphone:

Touch screen:

non volatile storage

GPS aerial

microphone: piezoelectrics

Touch screen: capacitors, moisture from finger

non volatile storage:NAND flash memory

GPS aerial: high specification ceramic dielectrics

OLED and LC displays are usually for what (bg) and what material is used for screen usually

OLED: each pixel emit its own light

LCD: uses backlight behind liquid crystals

Tin oxide lets screen detect ur fingers while letting light go pass thru

What part of phone is responsible for memory

RAM for temporary storage

NAND for long term storage

and doped semi conductors

Some rocksalt revision, These are important because of most functional material are crystals

Rocksalt

Rutile

Corrundum

Perovskite

Spinel

rocksalt: AO

rutile AO2

corrundum: A2O3

Perovskite: ABO3

Spinel: AB2O4

identify what each are below
NiO

Mn₃O₄

Cr₂O₃

CrO₂

AlFe₂2O₄

NiO :rock salt

Mn₃O₄ is Spinel

Cr₂O₃ is corrundum

CrO₂ is rutile

AlFe₂O_{4 is spinel}

difference between metal, insulator and semiconductor in terms of fermi level

Metal fermi level is close

insulator, large gap

semi conductor a little gap

why is this metal N a conductor (recap)

The N has a configuration of 1s_²2s²2p⁶3s_¹ The one on 3s, shows its a partially filled, so electrons can move easily under electric field, hence making it conductive. Because conduction happens at 3s, it does not need to jump to 3p to have conduction

what is a factor that can affect semiconductors distribution of atomic orbitals

Temperature

difference between an insulator and semiconductor

Both have a zero density of state at fermi level, but semi has smaller band gap

What are the three classes that make bad dieelectric material

Conductors (metals)

narrow band gap semi conductors (doped Si)

transition metal that have part filled d orbitals that contribute to the valence band, as they likely to be metallic or narrow band gap

How does this show if V3+ is a good dielectric or not

So, V3+ is 4s²3d³ making V3+ makes it 3d² now looking at diagram, the gap between 3d and O₂ is large. Large band gap means can be dielectric

Explain if TiO₂ is a good dielectric

Ti charge here is +4. That makes the configuration 4s²3d^2. Making it 3d0 after. So nothing filled means no electron, hence large BAND gap, so its dielectric. Dielectric are basically insulators, where their band gap is bigger than semiconductor (narrow). Dieelectric also require polarisation to work not electrons. hence why 3d0 works. The Ti shifts one way and O2 shifts another. Bc Ti-O bonds are highly polarizable

What makes something polarisable

1)Large soft electron clouds I- is more polarisable than F- bc outershell is farther away

2)Highly charged ions can distort neighbors, In Ti4+, has high charge and small in size, so interacts with oxygen electron clouds, creating polarizable bonds

3) empty d orbitals, empty low energy orbital exists

Predict the following dielectrics

Cr2O3 → 3d3

ZnO→3d10

Ga2O3→3d10

Cr→ dielectric, the repulsion makes it big. cuz each filled in t2g first one way up

ZnO→ filled, no repulsion, so no bc, band gap is around 3.3 v, so narrow and

Ga→ 3d10, so no but electrons move so becomes metal conductor cuz of 4p1

Between TiO2 and LaCoO₃ which would make a poorer dielectric and why?

Ti has 4+ and the p orbital spins are all filled.

LaCoO₃ has 3d6, and thats 6/10 filled, making it a narrow band gap between the band. hence it will be a weaker dielectric

What is ε_r

Measure of how good the material is at screening + and - from each other. Also described as capacitance

What is capacitance C1 and C0

C0 is reference and C1 is relative to reference

How can you measure C which in turn measures Epsilon

C=Q/V. so you run charge through built up per unit voltage.

Er= C1/C0

What increases capacitance when it comes to parallel plates

When a material is put inbetween because it develops dipoles that screen the applied field

Air has Er of 1.006

teflon is 2

TiO2 is 94, with these values what can you interpret

Most insulating Er values are <30. bigger than 30 can be functional dielectrics in electronic devices

What is the bulk polarisation(P)

• A material contains positive and negative charges.

• When an electric field is applied, those charges shift slightly.

• This creates tiny dipoles inside the material.

• The combined effect of all those dipoles across the whole material = bulk polarization.

What is P equation

P=ξ0 × Xe ×E

So now we have a big P and a little p. what is the difference

little p is polarisation of an atom, dipole etc. the equation is p=αxE(local) and big P is polarisation of many

what are the three polarisability and its terms

Ae, is usually general for excite electron clouds of substituet atoms (e for evertyhing)

Ai, usually high for materials with ions of large charge that can easily vibrate with large amplitudes (ions and ionic)

Ad, is high for materials with large permanent dipoles, that can easily orinetate/ rotate in applied field (dipoles)

Diamon ξr= 6

CaF2 ξr=7

H2O ξr=80

what are the dominant mechanisms contributing

Diamond= usually covalent and mainly carbon, so mostly Ae

CaF2 is usually ionic so mostly Ai and Ae

and H2O is dipoles so Ad

whats typically the magnitude of order of the capacitance contribution

Ae<ei<ed but below 300mhz, all mechanism contribute

what is εopt

in short its how to measure ae, estimated from optical limit from refractive index.

εopt =n²

n=refractive index

What is the difference between εstat and εopt

Estat is the sum of all E acting on it. so electronicc+ ionic+dipolar +space charge.

E opt is the dielectric constant measured withing the optical light phase (10^14-10^15 Hz). can be known as E electronic too.

Answer, why is Estat and e opt similar for diamond.

what does the large difference between E stat and opt tell you

why is this difference larger in LiCl

1) the only contribution is Ae. electronic. because diamond has no ionic.

2)has ions in NaCl so the vibration contribution is large.

3)LiCl has higher cloud density, so higher vibration. Higher cloud means (+1 charge packed into a small volume, think of shells)

what is this equation specifically used for

• εr​ = relative permittivity (dielectric constant)

• α = polarizability of the ion/atom

• Va​ = volume per atom (or molecular volume)

• What it essentially shows is links microscopic atomic/ions interaction have on the effect of the whoole entire material. so an atom to a crystal.

what determines high dielectric constant

large polarisability of ionic

small atomic or unit cell volume

therefore large a/V ratio produce high Er

If ZrO2 was 33.7 as Va. what is the Er. The electroneg of O is 2.01and Zr is 3.25

In alternate electric filled, what happens to the capacitors and then the polarisation

during alternating, the capacitor plates alternate from pos and neg, the polarisation of the materials in between try to keep up with the change by driving relevant ionic vibrations (and dipole rotation). this causes energy loss thru heat giving ride to dielectric loss.

Whats a dielectric resonator

its like a ceramic tuning fork for electromagnetic waves. It can be used to filter phones by vibrating strongly at one microwave frequency filtering others out. So wifi 2.4hz can be tuned to just respond to 2.4hz. Low Er is large ceramic puck. and so on. a ceramic puck is like a cavity.

However, Q, quality factor,measures how good the resonator is. small loss→ large Q. but its temerpature dependant sometimes.

So phone heat up, dimension changes, u dont want 2.4→2.3 everytime warm so Tf, should be small

Tf=| (∆V-/V0)/ ∆T | <3×10⁻⁶

For a resonator to be detected at 5G, so V0=1 Ghz, what is the maximum Δv0 that can be tolerated per 1 kelvin

Ba₃MgTa₂O₉ is the most suitable dielectric resonator material because it has a moderate-high dielectric constant, allowing miniaturisation, while also having the highest Qν0Q\nu_0Qν0​, meaning low dielectric loss and high frequency selectivity. MgO has lower losses but too low a dielectric constant, while SrTiO₃ has a very high dielectric constant but poor Qν0Q\nu_0Qν0​, making it too lossy.

So what are ferrorelectrics and why are they of interest

ferrorelectirc have giant εr. which in theory can make 6G. but it also has high dielectric loss and lack temerpature stability. however they have relevant properties to low frequency AC and DC electric fields

BaTiO3 has anamolousy high εr. using its structure perovskite, can you explain why?

As we heat up the crystal, and cool it, distortion occurs on the edge and soon BaTi is making and breaking the distortion which results in a diff Er. Apply an electric field, Ti, the centre can move even further. between 300-400k tetragonal shape is where most BaTiO3 is used.

what exactly is this showing

Ti⁴⁺ is d⁰, so its empty t₂g orbitals can mix with filled O²⁻ 2p SALCs. Moving Ti off-centre increases this mixing, lowers the total energy, and therefore the crystal spontaneously distorts. This off-centre Ti displacement creates the large polarization responsible for the huge dielectric constant of BaTiO₃.

Can you simplify what this is saying

In centrosymmetric [TiO6]⁸⁻, the occupied O 2p SALCs (t1u,t2u and empty Ti t2g​ orbitals have opposite parity and cannot mix. Off-centre displacement of Ti removes inversion symmetry, allowing these orbitals to mix, lowering the energy of the occupied states and stabilizing the distorted structure. This is the second-order Jahn-Teller (pseudo-Jahn-Teller) effect responsible for ferroelectric distortion in BaTiO₃.

alright. KTaO3, will this have a Second Order Jahn teller effect

So Ta would become +5. Because its group 5, d=0.

look at the image. this basicaly means it will

SrMnO3

Mn is +4, Group 7, so d=3. There is a cancel on bonds so less susceptible to occur. look at image why

NaNbO3

Nb is group 5, has +5, so D=0. so no change per say

YTiO3

Ti is 3+, but in group 4. so 1+. has d=1. so some distortion not favourable as it starts filling t2g

WO₃

W is +6. its in group 6. so d=0. but theres a bit of distortion cuz its not perovskite.

why might not all the materials you predict to have SOJT effect end up having an associated polar structural distortion

Firstly, symettry, if the t2g is filled then it can’t occur. not rly expected to know

at high temps, originally BaTiO3 adopts an octahedral/cubic structure, but at room temperature, Ti shifts as shown in the picture. It has a C4v symettry. this also means that inversion is not allowed. because of this t2g and u can mix. The O 2p SALCS are allowed to mix with empty Ti d orbitals which lower the energy. the mixing allows energy lowering and makes distorted structure more stable and then a dipole moment gets created , spontaneous polarisation and this makes something ferooelectric.

its basically asking "Why can't normal (1st order) Jahn-Teller distortion explain ferroelectricity like BaTiO₃ does

First-order Jahn-Teller distortions remove electronic degeneracy by elongating or compressing bonds but typically retain inversion symmetry (e.g. Oh→D4). Because inversion symmetry remains, no permanent dipole moment is generated and the distortion is non-polar. Therefore first-order Jahn-Teller effects do not usually produce the large spontaneous polarization or anomalously high dielectric constants associated with ferroelectric materials such as BaTiO₃, where a second-order Jahn-Teller distortion removes inversion symmetry and creates a polar structure.

Exam shortcut for identifying sojt or fojt

d⁹ → FOJT
d⁰ /d 10→ SOJT

FOJT → bond length changes
SOJT → metal moves off-centre

FOJT → usually non-polar
SOJT → can be ferroelectric (inversion symettry is usually gone)

non centrosymettric materials, give me an insight of what they are

we have met already ferroelectric.

other technology is piezoelectricity and circular dichroism

In this lecture, there are 3 things or numericals to describe crystals what do they entail

lattice parameters, one of the 7 crystals, one of the 32 crystallographic point symmetries

what is the use of the table here.

So if someone was to be like H-M was mmm, you see that that is D2h. then u ask does D2H have inversion symettry. yes it does. so NOT polar. so not ferroelectric. thats kind of the use of this

Main difference between centrosymmetry and non centrosymettric and piezoelectric

centro has inversion symettry. cannot be polar.

non centro doesnt have inversion, can be polar

piezo: apply pressure you get a voltage.

what is neumanns principle

The symmetry elements of a crystal must also be present in its physical properties.

Therefore crystal symmetry determines which properties (e.g. polarization, piezoelectricity, ferroelectricity) are allowed or forbidden.