Computer Simulation of the Thermal Epitaxial Nucleation of Crystals

Lead Research Organisation: University of Surrey
Department Name: Physics


Crystallisation lies at the heart of a vast array of natural phenomena and technological processes, including scale-formation, the production of new drugs, and the formation of ice in the atmosphere. The earliest stage of the formation of a crystal is called nucleation. Nucleation can control crucial features of a crystal, such as its structure, its orientation, and its size. Despite this, our understanding of these crucial nucleation events is poor.

Crystals almost always nucleate on solid surfaces, usually the surfaces of the microscopic impurities that are always present - no real system is 100% free of all impurities. The process of nucleation on a surface is known as heterogeneous nucleation. Most solid impurity particles will be crystalline. Thus we have one crystalline substance with one crystal lattice nucleating on another with its own crystal lattice. If the two crystal lattices are sufficiently similar the two lattices can be in step with each other, this is called epitaxial nucleation. This is believed to be why silver iodide is so good at inducing at the crystallisation of water. However, epitaxial nucleation is not well understood. In experiment the nucleus is perhaps only a few billionths of a metre across and exists for a fraction of a second, and therefore has never been observed.

We will get round the problem of not being able to see the nucleus in an experiment by studying nucleation in a computer. A computer simulation of nucleation can observe the nucleus forming in molecular detail. The proposed research will try and answer basic but so-far unanswered questions about epitaxial nucleation, with the aim of understanding which crystal surfaces are good at inducing crystallisation, and which are bad, and why this is. The proposed research is to undertake the first quantitative computer simulation study of the nucleation rates and microscopic behaviour of the thermal nucleation of a crystal on a crystalline substrate.

We hope that by increasing our understanding of epitaxial nucleation, in the future we will be able to better control the nucleation of crystals. Crystallisation is important to us for many reasons. Through the formation of snow it affects our climate. Also, many of the materials we rely on are crystalline and crystallisation is at the hear of many industrial processes. Crystallisation control is important even in places where you might not expect it, for example in making both pharmaceuticals and chocolate.

Some of the questions we hope to answer are as follows. How does the speed of nucleation vary if we vary the difference between the crystal lattice of the surface and that of the nucleating crystal? It is known that if the two lattices are very similar then nucleation is fast. Also, crystal surfaces have steps and terraces. We want to know: Does a new crystal start on a flat part of the surface or at a step? Finally, all solids have defects in their crystalline lattices, places where the lattice is not perfect. We will see if nucleation is faster or slower at these defects.

Planned Impact

The immediate beneficiaries will be people working on understanding crystallisation in near-equilibrium systems where nucleation is a rare thermal fluctuation. These scientists are a mixture of academic scientists working on the fundamentals (the field of the PI) and more applied university scientists and industry-based scientists who need to understand crystallisation better in order to better control it. Many industries rely on the controlled crystallisation of molecules, ions, metals, etc. The pharmaceutical industry is the industry with the largest R&D presence in this area, but other examples range from bulk chemicals to the food industry. Also, crystallisation control is crucial in new areas such as molecular electronics.

At the moment, nucleation is understood by most scientists crystallising substances via the simple classical nucleation theory. Also, those scientists who specifically consider epitaxial nucleation typically evaluate a substrate's ability to induce nucleation by calculating the lattice mismatch between the substrate and nucleus crystal lattices. This does not appear to be working. Silver iodide has a very good epitaxial match with ice and induces ice nucleation at low supersaturations, but this is an isolated success. The strategy of picking a substrate with a good epitaxial match to induce crystallisation has not worked. This lack of control/understanding is a source of frustration in the crystallisation community.

It is possible that at least part of the problem is that epitaxial nucleation is occuring not on perfect planar parts of the substrate (which are what is currently used to estimate lattice mismatches) but near steps and/or defects. If the proposed research confirms this I hope to disseminate this finding (e.g., to the UK community at BACG meetings) so that the field can move on. Scientists in the field could then consider epitaxial nucleation on stepped/defected substrates and consider how such an imperfect substrate can be selected to optimise it to induce controlled crystallisation. Whatever the findings, I will be able to show the community what epitaxial nucleation looks like in molecular detail for the first time, and hence move the search for substances to induce thermal epitaxial nucleation onto a more informed and systematic footing.

Another route to impact of the research will be through the RA. At the end of the programme, the RA will have experience of leading-edge computational techniques, and an understanding of how to apply them to a problem of great industrial importance and academic interest. Industry requires skilled computational scientists to model their processes, and the RA at the end of the proposed research will have the perfect skill set.
Description Some results of the grant can be summarised in simple terms as follows: It may be harder to know when crystallisation has occurred than you, or I, would hope. A simple unarguable crystalline material is common salt. A salt crystal is trillions of atoms of sodium and chloride ions arranged in a beautifully symmetric repeating lattice. This is great. And about a hundred years ago scientists realised that as the spacing between the ions was about the size of the wavelength of X rays, we could use these X-rays to probe the structure of crystals, and of the liquids they grow from. The pattern obtained from X-rays going through the salt crystal above is very different from that either molten salt, or salt dissolved in water. So, here X-rays allow us to tell how crystallisation is getting on. Very useful.

In the systems studied for the grant, life is not so simple. In these systems, three different types of crystals can form (these are usually called polymorphs). In itself that would be fine, indeed, X-rays can easily distinguish between one crystal and another. However, our system doesn't pick one of the three crystals, and just form that one, instead it forms a mish-mash of all three. The three are so mixed that an atom in a piece of one crystal type is maybe only 3 or 4 atoms from a piece of the one of the other two types of crystal. This mess of crystals mixture looks to X-rays not like a crystal but like the liquid.

Now, we studied this via computer simulation, so we can see what it really looks like as we can track every atom. Experimentalists cannot do that - real atoms are very very small, which is why they often rely on X-rays. So for our system, an experimentalist relying on X-rays would see very little happening during crystallisation. The X-ray pattern would hardly change.

Indeed, in some sense it is questionable whether we are observing crystallisation at all. Can a state that has the X-ray pattern of a liquid actually be called a crystal? This kind of depends on what you mean a crystal. If by solid you mean a substance where the atoms or ions are fixed in a repeating lattice such they are regularly spaced over thousands or millions of atoms, then what we see is a not a crystal. But if by crystal you mean something where each atom is surrounded by a regular arrangement of, in our case eight or twelve, neighbours then we have a crystal.

This is not just an academic exercise, these weird states between conventional crystals and liquids are common. When iron rusts such states can form, and crystalline calcium carbonate (what the White Cliffs of Dover are made of) forms via what may be a similar state.
Exploitation Route To apply the findings to real materials, experimental work will be required. This is difficult as we don't have the techniques to probe structure on these lengthscales and in this detail, for molecular/ionic systems. However, model colloidal systems could be studied.
Sectors Environment,Pharmaceuticals and Medical Biotechnology