Talk on mathematics and physics of virions

Tonight I will be giving my first seminar via zoom.
Here are the slides.

It is for the Pandemic Seminar of the UQ School of Mathematics and Physics. 

Here is the recording.

The central role of symmetry in condensed matter

I have now finished my first draft of chapter 3, of Condensed Matter Physics: A Very Short Introduction. 

I welcome comments and suggestions. However, bear in mind my target audience is not the typical reader of this blog, but rather your non-physicist friends and family. 

I think it still needs a lot of work. The goal is for it to be interesting, accessible, and bring out the excitement and importance of condensed matter physics.

This is quite hard work, particularly to try and explain things in an accessible manner.

I am also learning a lot.

I have a couple of basic questions.

How is the symmetry of the rectangular lattice and the centred lattice different?

When was the crystal structure of ice determined by X-ray diffraction?

[Pauling proposed the structure in 1935.]

Don't confuse necessary and sufficient conditions

In Carl Caves recent UQ Quantum Science Seminar "Quantum metrology meets Quantum Information Science" as an aside he also made an important side point.

People often erroneously assume that the converse of a statement is true (i.e.  A implies B means that B implies A). This came up because a few referees had said that some of the results he presented in the seminar were "obvious". Roughly speaking, this concerns the issue of trying to determine what input quantum state to an interferometer will produce a "physical" output state. He found that the input state had to be "physical" (by some well-defined technical criteria). Showing this is non-trivial. However, it is obvious a physical input state is sufficient to produce a physical output state. But, that does not mean it is necessary. Showing this turned out to be quite non-trivial.

I can immediately think of two other cases where scientists made similar errors of conflating necessary and sufficient conditions.

The first case is the existence of quasi-crystals. It was well known that a periodic array of atoms is sufficient to produce sharp diffraction peaks. However, many people erroneously assumed that this was also necessary. I emphasise this point when I teach undergraduates about quasi-crystals.

The second concerns Angle-dependent MagnetoResistance Oscillations in quasi-two-dimensional metals. Not long after their experimental discovery AMRO was explained in terms of a coherent interlayer transport and a three-dimensional Fermi surface. It was subsequently more or less assumed that observing AMRO was evidence for a three-dimensional Fermi surface.  However, in 1998, Perez Moses and I showed that a 3D Fermi surface was not necessary for the existence of AMRO.

Enhanced teaching of crystal structures

This past week I taught my condensed matter class about crystal structures and their determination by X-rays. This can be a little dry and old. Here, are few things I do to try and make things more interesting and relevant. I emphasise that many of these developments go beyond what was known or anticipated when Ashcroft and Mermin was written. Furthermore, significant challenges remain.

Discuss whether the first X-ray crystallography experiment the most important experiment in condensed matter, ever?

Take crystal structure "ball and stick" models to the lectures.

Give a whole lecture on quasi-crystals.

Use the bravais program in Solid State Simulations to illustrate basic ideas. For example, the equivalence of each reciprocal lattice vector to an X-ray diffraction peak, to a family of lattice planes in real space, and to a Miller indice.

Show a crystal structure for a high-Tc cuprate superconductor and an organic charge transfer salt. Emphasize the large number of atoms per unit cell and how small changes in distances can totally change the ground state (e.g. superconductor to Mott insulator). Furthermore, these small changes may be currently beyond experimental resolution. This is very relevant to my research and that of Ben Powell.

Very briefly mention the Protein Data Bank, and its exponential growth over the past few decades. It now contains more than 100,000 bio-molecular structures. Mention the key concept that Structure determines Property determines Function. Mention that although many structures resolve bond lengths to within 0.2-0.6 Angstroms, that this just isn't good enough to resolve some important questions about chemical mechanisms related to function. I am currently writing a paper on an alternative "ruler" using isotopic fractionation. 

Next year I may something about the importance of synchrotrons and neutron sources, and crystallographic databases such as the Cambridge Structural Database, which contains more than 700,000 structures for small organic molecules and organometallics.

Pauling's last blackboard

Today I visited the Linus Pauling Archives at Oregon State University.
[I was actually on vacation in Corvallis visiting my sister-in-law but I just had to take a visit].

They have assembled a lot of fascinating material online, which is worth perusing. For example, how a funding agency convinced him to start working on proteins, and the details of correspondence about his (erroneous) ideas about quasi-crystals.

But, in the actual library there is a small display featuring Pauling's last blackboard, his desk, some molecular models, some calculators, his two Nobel Prize medals, and his signature beret.

Pauling is definitely one of my scientific heroes. He made multiple landmark contributions. Most of us would be happy to do just one of the things he is known for. He was truly the master of multi-disciplinarity. He brought quantum physics to chemistry, structural chemistry to biology, and molecular biology to medicine. But he had "clay feet", failing to see problems with his ideas about the triple helix for DNA, vitamin C and quasi-crystals.

Curious fact: I was allowed to touch the Nobel Prize medals but my brother-in-law asked if I could have my picture taken with Pauling's signature beret. The librarian said no!

2011 Nobel Prize in Chemistry

I was pleased to see that the Chemistry prize was awarded to Dan Shechtman for the discovery of quasi-periodic materials that led to a new definition of crystal (quasi-crystals). Back in 2003 APS News published a nice discussion of the background to the paper which appeared in PRL in 1984 and is the 8th most cited PRL of all time.

An earlier post discusses why I teach undergraduates about quasi-crystals. It illustrates the fundamental logical principle that A implies B does not mean that B implies A. Specifically, just because a periodic arrangement of atoms is a sufficient condition for a discrete X-ray pattern does not mean that it is a necessary condition. It also shows students that what they read in textbooks may be wrong.

Shechtman is not the first condensed matter physicist to be awarded the Nobel Prize in chemistry. Other recent examples include Walter Kohn and Alan Heeger.

What is a crystal?

You would have thought such a basic question would have been settled a very long time ago. Solid state physics textbooks written before 1980 certainly give that impression. But no, as recently as 1991, the International Union of Crystallography revised its definition.

After undergraduates learn about crystal structures it is good to teach them about Quasi-crystals. Several good reasons are:

• they are beautiful and fun
• it is a story which should encourage students to question conventional wisdom and not just believe everything in the textbook or that their lecturers tell them
• it illustrates the simple (but sometimes overlooked) truth that just because property A implies property B the converse does not necessarily apply

Here are the slides for my lecture.

The most useful website I found was Introduction to Quasicrystals produced by Steffen Weber. It includes software for producing different tiling patterns and making fourier transforms.

An aside: there is also an interesting 2007 article in Science by Peter Lu and Paul Steinhardt, Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture. The article generated some "lively" correspondence which you can read online.

I welcome suggestions of other online resources.