Bad crystals can be bad in many ways


The standard way of studying the structures of crystals on atomic lengthscales, is X-ray diffraction. We fire X-rays at a sample and then detect the X-rays that bounce off the sample, as a function of the angle X-rays come out. This gives us what is called a structure factor, S(k), where k is called the wavector, which has dimensions of inverse length, i.e., m-1.

Above are calculations for a toy model (one-dimensional) crystal, with atoms spaced on a lattice with a spacing between one atom and the next of one unit (i.e., I am working in units of the lattice spacing, typically a few tenths of a nanometre, not metres, for simplicity). For an infinite perfect crystal, the Platonic ideal of a crystal, the structure factor is a series of spikes (called delta functions) at 2π (~6.3), 4π (12.6), 6π (18.9), etc.

Now, often, for example in some substances people want to make cheap solar panels out of, the crystals are not infinite but only perhaps tens of atoms across. Then the peaks are still quite sharp but are not simple spikes. The structure factor for a perfect crystal of 31 layers is shown by a cyan curve above. Note that each of the three peaks is the same height, and that the peaks are all the same width. The width is about 2π /31, i.e., inversely proportional to the size of the lattice.

Real crystals are not of course perfectly periodic. The atoms of each crystal will be moving around due to their thermal energy, they may also be defects. These defects can really affect the properties, e.g., in a solar panel, so people are really interested in them. Above, there is a red dashed curve, that shows what happens when the lattice still repeats perfectly across the 31 layers in the sense that there is no average drift away from the spacing of one unit, but where each atom is little off to the left or to the right.

The only difference between the cyan and red curves is that the red peaks are lower than the cyan peaks by an amount that becomes larger and larger as we go from the first to the second and then to third peak. This sort of noise, basically just flattens the peaks at large values of k.

But what if successive layers do tend to drift away from the period of the perfect crystal, this is a different sort of noise, and its consequence is shown in the green curve. Just as with the red curve, the peaks at high k are flattened. But there is also a new effect, the peaks also become broader and broader as increases.

Crucially, this broadening is different from the broadening due to the small size of the crystal. Broadening due to small crystal size affects all peaks equally, that due to noise in the positions of the atoms that breaks the periodicity, broadens the peaks at high much more.

In a toy model this is very clear and neat, size and noise in the atom positions have affects that are easily distinguished. Apart from being kind of interesting, a group in Stanford is pushing using this idea on real X-ray patterns, to infer not just how bad their crystals are but how they are bad: Are they really tiny, or a bit bigger but with a messed up lattice? Real crystals are a lot more complex than my toy model, so it is a bit hard to see how well it works, but it is a nice idea.

What effect do gravitational waves have on your body?

The biggest news in physics this year was the discovery of gravitational waves a couple months ago. Waves in time-and-space are cool, but they are very weak, the detectors measured a distortion in space of one part in 1021 (or 1 in 1,000,000,000,000,000,000,000). That’s a small effect. On the one hand this is bad, as it made them very very hard to detect; the scientists on the LIGO collaboration must be experimental science ninjas and it still took them decades.

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Taking the Doctor’s advice

coxtestUnderstanding how crystals start to form is tricky. We can’t see how it happens as crystals start off microscopic, it is very sensitive to pretty much every aspect of the experimental set up, and the standard theory (called classical nucleation theory) has basically zero ability to predict anything. So we are a bit stuck. But we don’t have the toughest job around, arguably the most complex, and hardest to understand, thing around is the human body, so perhaps the toughest job belongs to medics and biomedical scientists studying diseases.

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Chicken Little comes home to roost

Zoo chicken roostingTwo years ago I wrote a blog post expressing amusement at Altmetric’s top papers for 2013. Now that Altmetric is rating a paper of mine #5 of 13,240 outputs (from the journal publisher and as of time of writing), it is clearly time for me revisit my position on Altmetric. Surely, anything that ranks my collaborators and me that highly must be on to something? Altmetric is software that collects references in the news media, blogs and on twitter, to a research paper, and then both provides links to them, and ranks the paper.

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The right tool for the job

I almost titled this post Daily Mail celebrates work of immigrants shocker but as they have written a pretty accurate article on work I am part of, that would be a bit ungrateful. Yesterday a paper came out in Physical Review Letters that I am really rather proud of, although I made only a small contribution to it. Most of the credit should go to Andrea Fortini, who discovered the effect the paper describes, and to Nacho Martin-Fabiani and Joe Keddie who did the experiments to show that it works in the real world too. Andrea found the effect in computer simulations. We also had help from collaborators in Lyon who made the particles Nacho used.

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Reducing the risk of heart disease with the aid of Russian Roulette

It is almost always easier to borrow ideas and techniques from other fields than to reinvent them. A PhD student, another academic and I, are studying two competing processes. These are crystallisation into two different crystals, called alpha and gamma, of a small molecule called glycine. The formation of alpha and gamma appear to be mutually exclusive, one or the other forms, not both. Crystallisation is statistical, it is at least partly random, and they are irreversible, once a crystal forms it persists.

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One hundred and twenty five billion reasons to care about crystallisation

Atorvastatin-3D-ballsLipitor is a cholesterol-lowering drug sold by the pharma multinational Pfizer. People who want to lower their cholesterol take it every day for years or decades. High cholesterol is a common problem, bacon and cakes are just too tasty, and so the market for drugs like lipitor is absolutely enormous. It has been estimated that over fifteen years, Pfizer made $125 billion from lipitor. That’s a lot of money. I don’t have the figures but presumably a billion plus of that was in the UK (i.e., paid for by the NHS). So if you are a taxpayer even if you haven’t taken it, you’ve paid for it. So I’ve paid for it, but I am also interested in lipitor as I study crystallisation, and like most drugs lipitor tablets contain the drug in crystalline form.

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Iron & Steel

ttSteel is not pure iron, it contains a small fraction of carbon that transforms the soft pure iron into the much tougher steel. I guess I have known that for a long time. But I have not really thought about how the carbon is incorporated into the crystalline iron. Dissolving salt in liquid water is straightforward. The ions of sodium and chloride just diffuse around in the liquid surrounded by the diffusing molecules of water. This is a liquid solution, a solution of salt in liquid water. Steel is a solid solution, it is carbon dissolved in solid iron.

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