Succeeding Polystyrene

Do we get marks for participating after the exam? :)

I read about this in the National Geographic magazine for June: a group in the USA created 'ultralight metallic microlattices. 'Ultralight' refers to < 10 mg per cubic centimetre. Of course, styrofoam already exists, but it isn't particularly strong because of the rather disordered structure of the ultralight-version of the material.

These microlattices apparently overcome this weakness because they can be created using much more regular internal structures. The way they did this: a self-propagating photopolymer was grown as a template, the template was coated with nickel via 'electroless' plating (not sure what this is yet...) and then etching away the template.

Ultralight materials are useful because of their thermal and kinetic insulating abilities, and now because they can be used as light structural supports.

Here is the doi and other stuff:
Science 18 November 2011: 
Vol. 334 no. 6058 pp. 962-965 
DOI: 10.1126/science.1211649


Josh Harbort

PS: Has anyone though that doi would be pronounced "DOO-ee"? :)

Today's exam (Monday 18th June)

This is just a reminder that the final exam will be in room 407 physics annex (conference room) at 2:30 pm today.

Please note that you are allowed a formula sheet that must be no longer than two sides of a single A4 sheet of paper and contain no more than 40 equations.

Semiconductors and synthetic biology

 I know points have been added and everything, and not that I've been distracted or anything, but there is an interesting (news) article: Artificial cells evolve proteins to structure semiconductors(snazzy title!)
This is based on PNAS article pubished in April (there's a very exciting intro in this).
(The news article seems much more optimistic/daring than the article)

The claim is that they have biofabricated silicon dioxide and titanium doxide (which they point out is in solar cells!).

From what I understand, they're taking advantage of biomineralisation -> sort of like skeleton of sea sponge (and humans and bones).
They place a seed inside a cell (fungus). DNA will then wrapped around the bead, which grows the material (the function of this DNA string). The proteins from these genes have been produced.

I suppose it's not too far-fetched of an application, but now the genes that could involved with making SiO2 and TiO2, have been identified and proteins synthetised.
It's not a big step to suggest we could use these proteins on a small labscale - on a larger scale is a different question entirely. Perhaps with regards to manufacturing very small structures, biofabrication would be most useful.

I suppose one must also question the efficiency of engineering bacteria to make such materials compared to convential methods.


Sidenote: the comments with the news article are interesting, and quite entertaining.

Classical Hall Resistance

Hello everyone, I was working through the mid semester exam again, and in Question 3 (d) we are required to find the classical Hall resistance in 2D by analogy with the 3D case. I'm not sure which quantity this Hall resistance is exactly, though, because of the 'hints' given in the question. The question itself seems to suggest use of the Drude relation, is this right?

Good work too, everyone, on passing so far! :)

Formative assessment marks

Marks are out of 100.
First three numbers are the last 3 numbers of student number

712 - 63.5
653 - 62
375 - 90
235 - 91.5
762 - 69.5
613 -59.5
398 - 70


Good news. Everyone scored more than 50 and so no one has an automatic fail.
Maxwell Smart says Extra good news for agents  no. 375 and 235. 
Because of they scored above 85 this enhanced the effect of their summative marks. e.g. they only need 45% to pass and 75% to get a 7. (see course profile for more details).
Consistent engagement pays off!

Marks for student presentations

These were well done.


Marks are out of 10.
First three numbers are the last 3 numbers of your student number

712 - 8.3
653 - 7.9
375 - 8.8
235 - 7.5
762 - 7.3
613 -7
398 - 7.8

Final exam location

It will be in room 407 physics annex [conference room]
at 2:30pm monday June 18

Josh's Slides from Talk, at last!

Hello everyone, sorry for not getting these up earlier! I had terrible troubles with Google Docs and infinite redirect loops, but I think that I've found a temporary solution... don't use Google Chrome for Google docs....

Here is the link to the document: https://docs.google.com/presentation/d/1Pr2rWBp_ujcko5YNP-wQKz-wRiZrbQGgx8KfUczHr_k/edit
Enjoy! :)

Three most important equations

Related to the essay, but I figured I'd go through what I considered to be the three most important equations of the course.  Reckon it would be interesting to see if they differ from others opinions.  I apologise for the notation in advance, it'll probably be set out how I would write it in matlab

Fermi wave vector: n = (kf^3)/(3*pi^2)

Might seem like a bit of an odd one, but the construction of the Fermi surface and the subsequent Fermi wave vector has so many implications in all of the solid state that we dealt with.  This definition first appeared in chapter 2 using the Sommerfield model, but was still used once the crystal lattice was introduced.

Bloch's Theorem:  psi_nk(r+N*a) = exp(i*N*k.*a)psi_nk(r)

Bloch rocks, need I say more?

Semiclassical equations of motion:  dr/dt = 1/hbar * de_n(k)/dk
                                                          hbar* dk/dt = -e(E + 1/c * dr/dt * B)

Grouped these two together, but with them we can determine the dynamics of electrons in magnetic and electric fields with certain energy levels defined by e_n(k).  Requires just a few assumptions about position and momentum.

Anyway they're my three equations, and with them i feel you can describe most of the dynamics of electrons and ions in a crystal lattice.  Any major disagreements with my choices?

Optional revision session

Thursday June 7
1-2pm
Interaction room.

n.b. I will be overseas from June 9 onwards.

Final exam date?

Please talk amongst yourselves and propose a possible date.

Dirac points

During my presentation, the Dirac point was mentioned.
This also popped up in Andy's paper.


From an article:  Pairs of bands are degenerate at a point of high symmetry of the Brillouin zone.
Electromagnetic one-way edge modes were first predicted in 2008, 2006, to occur in systems possessing Dirac points.
Here, they take a Dirac point to be points s.t. modes near each degeneracy point can be described by Dirac Hamiltonian. (We may recall Dirac Hamiltonian from Quantum, similar to Schrodinger, but with spin with

We may interpret the Dirac points to be points of high symmetry of the Brillouin zone, which is where electrons can be described by the Dirac equation. This is consistent with description given in another article of where two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions.
The points of high symmetry would be the centre and corners of the Brilouin zone (wikipedia), verified in graphene since this is where the kx and ky must be equal (in magnitude), with the periodic nature of Bloch model.


This was related to my presentation with the plot Dave pointed out on Page 9, this figure, with the band structure of of the Bi2Se3.

 

For Figure a, we see our Dirac point is at the centre of the Brillouin zone. We see our surface band meets our bulk band at the one point at the Dirac point, which is a condition for being a topological insulator.

We have the yellow for a high electron density of states. Then there is a higher density of states at the bulk band, which we can infer as most electrons are in the bulk state, i.e. insulating. Thus there are fewer states in the surface state, i.e. conducting

This the conduction is small compared to the insulation, as we would expect since conduction is only at the edges.

Sidenote: Figure b would be the dispersion relation for the material. Resembles the cone of graphene.

So our Fermi surface would be circles, of diameter proportional to the Fermi energy/wavenumber.

Fun reading!

Continuing on a series of interesting arxiv articles,
Clarification as to why alcoholic beverages have the ability to induce superconductivity in Fe_{1+d}Te_{1-x}S_x claims to have investigated the key components in alcoholic beverages and clarified the mechanism to induce superconductivity in Fe1+dTe1-xSx.

Actually reading this, I agree that they have investigated the key components in alcoholic beverages.
They have mentioned previous work with that material, specifically regarding the presence (necessitating absence) of iron in that material to achieve superconductivity.

Also, they have not experimentally induced superconductivity in that material.

Procedure:
They considered the concentrations of three acids: malic acid, citric acid and β-alanine and water (which are major components of their drinks).

Temperature susceptibility measured to 2K.
Shielding volumes were calculated for the drinks showing increase proportional to concentrations of of the three acids.
X-ray diffraction shows that the drink solutions does not decompose the crystal structure.

So reasonable question  (which they mention) would be how does/why would malic acid, citric acid and β-alanine make things superconduct?
They mention Fe content is interesting, bu these three acids don't contain Fe.

Their procedure raises a question which they have not addressed/supported: what's shielding volume and how is it relevant?
I suppose superconductivity involves conduction without loss, so there's some term that must shield a current from the outside?

Anyway, if alcoholic beverages had the ability to induce superconductivity, that'd be a pretty good party trick...


Sidenote: There are some great articles on arXiv...
"How many zombies do you know?" Using indirect survey methods to measure alien attacks and outbreaks of the undead
(footnotes...)

Further remarks on the thermoelectric paper

Here is my final blogpost for Condensed Matter (there might a few more after this).

In my talk, I mentioned that to have a good thermoelectric material, you need to have high electrical conductivity and low thermal conductivity. The simplest reason I could think of is that  we want to maintain the temperature difference so we do not want the temperature at both ends to equalize quickly-hence the need for low thermal conductivity.

While I was thinking about thermal conductivity, I was wondering how do they measure the thermal conductivity. It turns out that measuring thermal conductivity is not an easy as measuring electrical conductivity. Several methods are listed on wiki and one of the most widely used one was laser flash analysis whose basic working principle is basically heating up one side of the material and measure the temperature change at the other side.

This makes you think about the uncertainties of the measurements that they made of the thermoelectric efficiency which depends on how accurately you can measure electrical conductivity, thermal conductivity and thermopower (hopefully everyone memorized the formula). It was mentioned in the paper that uncertainty in each quantity may vary between 5% to 20% which means the uncertainty of  zT (the maximum efficiency) might  be as high as 50%! Hence, the guys measuring those stuff need to make careful with measurements so that results of high zT would be actually meaningful.

Andys Presentation

This is it:
Presintashon

Dave's Presentaion

Presentation!

Course summary

Write 10-15 pages summarising the main points learnt in the semester. Each point must contain one figure and one equation.

The summary must be emailed as a .pdf file to me. 
It may be run through Turnitin in order to test for plagiarism.


This assessment piece counts for 10% of the summative assessment.


This is officially due at 5pm this friday June 1.

I may not start marking until tuesday morning.

Birth of topological insulators!!

Slides for my presentation!

Here a link to my slides.

https://docs.google.com/presentation/d/1OcztPPBoxEhgPVTbcdryazAjZtcNiodDdbLW-Ka0k_4/edit
Inform me if it does not work. Cheers.

Talk Slides - Dale

Hi all, the slides to my talk can be found here

Umklapp scattering

So this wasn't really mentioned in the notes, but it popped up a few times in my paper, and is in chapter 25 'anharmonic effects in crystals' in the book.  It's a bit of a step back to Brillouin Zones and interactions, and whilst a simple concept it comes across as quite counter intuitive!

So say we have two phonons that lie within the first brillouin zone, and they scatter off each other to produce a third phonon with a different wavevector k3.  If this third wavevector lies within the first brillouin zone, then this is just a simple scattering situation.  Umklapp scattering occurs when the wavevector lies outside of this zone.  However, as any wavevector lying outside the FBZ can be equally well described by a wavevector lying inside of it, it is possible to have two phonons interact, and have a third phonon that appears almost reflected from the scattering.  This is a bit clearer with this diagram here

http://en.wikipedia.org/wiki/File:Phonon_nu_process.png

Obviously this has implications about the phonons momenta, although at first glance I can't find anything related to conservation of it.  Anyway, a little aside concerning phonons and scattering!

Energy bands and semiconductors

Just thinking about the band structures we learnt with the Bloch model.
Bands determine the state, so insulator, metal, semimetal, semiconductor by the filling (or not filling) of electrons or holes.

We saw the band structures again in Paul's last set of lectures on semiconductors.

We were introduced to the donor and acceptor bands, also the valance and conduction bands.

How are these bands related to the energy bands from the Bloch picture?
Are they the same thing?


Also, I still don't quite understand the distinction between the valance/conduction bands and the donor/acceptor bands?
 I take it that the donaor accept are within the conduction/valance pair, but why are there two pairs of them?


Final set of questions, when we consider these two sets of bands, their expressions (p592-3 A&M) no longer contain the Fermi energy. Are they related to the Fermi energy, else where has the Fermi gone?

Apologies for all the questions.
Thanks.

Conduction mechanisms

Differences in conduction mechanisms between different classes of materials can lead to some interesting differences. For instance, the conductivity of silicon decreases with temperature. This is because as you heat silicon, the crystalline of the structure is degraded. As we know, it is the crystalline structure that allows such a well defined band structure, leading to conduction electrons.

Conversely, organic semiconductors rely on a different type of conduction. Electrons are conducted via "hopping" between molecules. This can only happen when molecules are very close to each other. An increase in temperature increases the rate of these phononic interactions, thus increasing the conductivity.

I think that this is a good example of how a relatively simple experiment, like temperature dependence of conductivity, can lead to some insight into much more fundamental electronic processes. Can you guys think of some other examples? Or perhaps some other fundamental differences between seemingly similar materials?

Presentation logistics

Each presentation will be 15 minutes plus 5 minutes for questions.
Time limits will be rigidly enforced.


I expect you all to attend all the presentations.


I also expect you to fill out the feedback and assessment forms I will provide.
i.e. you will be grading each others presentations. Paul and I will take this into account when assigning your final mark.


It is your responsibility to bring a laptop and to check beforehand that you can get it to work with the data projector. 


On the same day as your talk please post on the blog your Powerpoint slides.


The material below is from John Wilkins one page guides and should be read and applied before giving your talk.

• Preparing a talk. [html ], [postscript ]
• Talk Grit [html], [postscript] (Jim Garland)
• How to give a Terrible Talk 
• Viewgraphs Preparation: NOT 

Schedule is 

Monday 11am   Kiran, Josh, Dale
Tuesday 11am   Andy, Joseph
Wednesday 11am  Ann, Dave      + course evaluation

Isotope effect

One of the key ideas that pointed out that phonons are the pairing mechanism for BCS superconductors is the isotope effect -why the critical temperature was lower for heavier metal isotopes (elements with the same number of protons but different number of neutrons).

I have read somewhere before a simple explanation on how BCS theory accounts for this. A simple mental picture of the BCS theory is as follows. When electron moves through the lattice made up of positively charge metal ions, it distorts the ion lattice, since it attracts the ions creating a relatively positive region. This region then attracts another electron with the opposite spin and both electrons form what is known as a Cooper pair! Since heavier ions are harder to move, they are less attracted by the electrons. This results smaller binding energy between the Cooper pairs which means lower critical temperature for heavier isotopes.

Overhauser and DNP

An interesting fact I just discovered whilst reading about dynamic nuclear polarisation on Wikipedia: apparently, when Albert Overhauser first described the process in his paper (which just talked about using DNP on copper centres in organo-metallic complexes, all the rage in the 50s and 60s), famous physicists like Norman Ramsey and Felix Bloch (and 'other renowned physicists of the time', Wikipedia) initially criticised Overhauser because they thought the process was 'thermodynamically improbable' (Wikipedia). Obviously their Force senses were clouded by the Dark Side since Overhauser essentially invented NMR and worked out its equations... :) and it works. Then when Carver and Slichter gave experimental confirmation, Overhauser apparently received an apology from Ramsey (via mail) in the same year! Fortunately, DNP most definitely does exist, I've witnessed it!

More facts: originally, the term 'dynamic' was used to represent the random and time-dependent nature of Overhauser cross-relaxation. It has been kept in the name so that we now have a cool acronym for my project! :)

What is this 'cross-relaxation' you may ask? (Ask, or else!) :).
Solution state DNP (i.e. liquid, so that molecules can move around a lot) works by coupling molecular motion to the relaxation energies of the electron spin. With a nucleus and an electron, your system has 4 levels, 2 corresponding to the nuclear spin transition and 2 corresponding to the electron spin transition. The nuclear spin transition is of much lower energy than the electron spin transition due to the smaller gyromagnetic ratio of nuclei compared with electrons. The process the works like this:
1. Nucleus and electron are in low energy state
2. Electron is excited via microwave radiation (the wavelength appropriate for the temperatures and fields of normal electron paramagnetic resonance).
3. Electron has two choices: it can decay back to its original state (with nuclear spin unchanged) or it can decay to a state where the nuclear spin changes from low to high energy ('cross-relaxation'); because the nuclear transition energy is smaller than the electron transition energy, these two choices are not much different in energy. This cross-relaxation can occur if the energy of the electron decay with the nuclear spin flip is equal to the energy of molecular motions (hence the need for solution state), and if the cross-relaxation process is faster than the other relaxation (no nuclear spin flip) the nuclei are polarised in the high-spin state.

Now you have 'hyperpolarised' nuclei! Hooray! After doing all of this work, we now have a greater nucleus spin population difference between low and high spin states, and so our NMR signal is enhanced (the Force is strong with this one). :)

Hey all,

Just a question in class today about how the interaction between electrons can be strong even though they are moving in opposite directions. Remember that in classical superconductors the electron-electron interaction is mediated by phonons. I.e. the actual paring interaction is electron-phonon interaction. An electron can interact with the phonon field at any point in space. This interaction can propagate in the phonon field until it reaches the other electron (i.e. the only electron with the exact opposite wave vector sign and spin) when it interacts with it. Giving an effective long distance paring between the two spatially separated electrons.

This is kinda similar to what we have been doing in quantum with the field interactions. I.e. we have an electron field interacting with a phonon field. Giving effective electron, electron interactions mediated by a virtual phonons.

Semiconductors lecture slides

You can download a copy of my lecture slides on semiconductors here. I recommend reading chapters 28 and 29 from A&M.

Why no Copper superconductors?

This intrigued me in the last (or second last?) lecture. The question is; why do Copper, Silver, and Gold, three very good conductors not superconduct?

Well, it seems that it is due to them not being able to form Cooper pairs, required by BCS theory. These elements all have a free conduction electron which they can easily use to conduct well. However, they all have a FCC lattice structure which prevents eletron-phonon coupling required to form a cooper pair.

For a basic overview, I thought this site was pretty cool: http://www.superconductors.org/
It's aimed at beginners, but is surprisingly concise, and has some nice, comprehensive tables of superconducting materials.

On another note, A&M says in one of the footnotes that amorphous Bismuth superconducts at higher temperatures than crystalline Bismuth. This is all kinds of crazy! I decided to have a quick look around, and I found a couple of papers:

http://prl.aps.org/pdf/PRL/v22/i11/p526_1
These guys talk about the phonon spectrum of Bismuth and Gallium. To be perfectly honest, I don't really understand what the phonon spectrum is (perhaps some series of resonances within the crystal?). If anyone can shed some light on this is would be great. Speaking of shedding light, this paper:

http://iopscience.iop.org/0305-4608/5/11/034/pdf/0305-4608_5_11_034.pdf

looks at the optical properties of both amorphous and crystalline Bismuth films. I haven't had time to properly read this one yet, but it seems pretty interesting. Also, I'm sure it'll have a reference to a paper talking about electronic properties of the two types as well. In saying that, this paper is not particularly thoroughly referenced, which is slightly irritating. These guys;

http://iopscience.iop.org/0305-4608/11/3/013/pdf/0305-4608_11_3_013.pdf

talk about Bismuth films, both amorphous and crystalline, which are pretty interesting. Also, this paper is from 1980, as opposed to 1968 and 1975 for the last two, so maybe they have a better idea about the theory. However,  the first ceramic superconductors weren't around until 1986, and the first with Tc>77K were discovered a year later. I guess what I'm trying to say is that these guys were in for a surprise...

Essay

I was just wondering if anyone knows the exact date that this is due?  It says in the course notes end of semester, but isn't any more specific than that.  Is that end of week 13, or swot-vac, or possibly up until our exam on the 18th?  I know I have been a bit bad and haven't been to a few lectures lately, was just wondering if it's come up in any of them.

Thanks!!!

Crystal Defects

Throughout this course we have come across a couple of examples where a metal possessing defects actually leads to some pretty interesting features, most notably the quantum Hall Effect.  Chapter 30 goes into a bit more detail about these, but as it's not required reading I shall summarise a few key points here.

Firstly, whilst any disruption from the perfect crystal state is a defect, only two are considered in this chapter.  They are:

1) Vacancies and Interstitials
2) Dislocations

The first are known as point defects, as the imperfection bounds this one point in three dimensions (as opposed to a line or surface).  Examples of these are the addition of removal of additional ions from the crystal structure, the former of these known as a Schottky Defect.  This particular defect can arise naturally without disrupting any thermodynamic laws as long as the number of vacancies n is given by

n = N*exp(-(E+Pv)/kT)

Here N is the total number of ions, E is the derivative of (U-TS) with respect to n, where U is the potential energy, T is Temperature and S Entropy, P is pressure, v velocity and k is the boltzmann constant!

Consequences of this type of defect include changes in the electrical conductivity and optical properties.  Similar consequences arise if an additional ion was at the lattice point, if particular ions were polarons or excitons (polarised or excited state ions).

Dislocations, on the other hand, refer to line defects, where the imperfection is bounded in two dimensions.  This defect is important as it helps explain why a much smaller force is necessary to deform a crystal than predicted by all the previous theories.  There are two kinds, screw and edge dislocations, and the diagram for these is on page 632.  The basic requirements for this type of dislocation are (from page 634)

1) Everywhere else in the crystal except at the point of dislocation the crystal can be described as perfect
2) In the region around the dislocation the atomic positions differ substantially to that predicted by a pure crystal
3) There exists a nonvanishing Burgess Vector, defined as a loop of vectors that when mapped out in the perfect lattice return one to their starting point, but when the same vectors are traversed in the dislocation region one ends up at a different lattice.

As well as describing the weakness of crystals, these dislocations also affect the rate at which a crystal can grow.

Magnetic photons

There is an interesting article about magnetic photons:

Homeopathic Potencies Identified By A New Magnetic Resonance Method: Homeopathy’”An Energetic Medicine

Their claim is that magnetic photons are responsible for the potency of homeopathic solutions.

From what we have learnt in our undergrad years, a photon is a packet of electromagnetic wave.
We understand electromagnetic waves to be self-sustaining disturbance in the electric and magnetic field.
Here's our magnetic field.

I'm finding it a bit difficult to read, but it is bizarre. From what I understand:

Premise: information is carried an oscillatory wave
Premise: Tesla coil produces longitudinal wave
Premise: solution in Tesla coil gives nonzero response
Conclusion: this response is the information
?


There is something relating the frequency spectrum (power spectral density?) to the homeopathic information.
The figures from 3 and onwards could be clearer. Anyone?


Relation back to our work on the magnetism:could what they're measuring be the diagmanetic response?
Homeopathic solutions contain water...and you can levitate a frog with diamagnetism...levitate the solution?




Big sidenote:

Sort by magic!!