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1st Intensive School in Physical Crystallography: From Phonons to Phase Transitions

Mark S. Senn
[Meeting attendees]
The Physical Crystallography Group (PCG) of the British Crystallographic Association was pleased to be able to offer its first residential school in physical crystallography in Abingdon, Oxfordshire, UK, from 18 to 21 June 2018. Planning for the School started back in January 2017 when the organising committee consisting of myself, Mike Glazer, John Claridge and Nick Funnell undertook the initial task of shortlisting topics for the school. We quickly homed in on the key material that we felt would be most beneficial to the community, from which everything else followed naturally. We decided for the first run of the PCG School we would focus on phase transitions, since the study of this topic is what unites all physical crystallographers. We were keen to include topics such as phonons and Landau theory in this that are not so commonly taught as part of postgraduate courses. We were delighted that Martin Dove and Michael Carpenter were willing to take on these topics and keen to be involved in this new project. The course was structured to follow the path of a soft-mode phase transition, with the final line-up of Mike Glazer for a review of symmetry and reciprocal space, Martin Dove for phonons, myself for irreducible representation analysis, Michael Carpenter for Landau theory, and John Claridge for incommensurate phase transitions. Our ambitious plan was now to fit this program into a 3.5-day intensive residential school. We were very fortunate in receiving substantial sponsorship from the ISIS Neutron and Muon Source, as well as contributions from Diamond Light Source and the Institute of Physics. This meant that we could hold the event with a substantially reduced residential registration fee of £240, whilst still being able to make use of STFC's unique Cosener's House venue situated in the picturesque town of Abingdon on Thames. Special thanks go to Nick Funnell here, who took on the bulk of the local organising leading to a seamlessly run school.

On midday on 18 June 2018, after months of planning, we were finally ready to welcome the 40 school participants, many who had travelled from afar. Registration for the School had far exceeded our expectation, making it a tough process shortlisting the candidates for the school. The final list of course participants included PhDs, post docs and early career academics from the Netherlands (5), Germany (2), USA (1), South Korea (1), Australia (1), Spain (1), France (1) and Republic of Ireland (1), with the rest coming from all around the UK.

Mike Glazer opened the school with a review of point-group and space-group symmetry for his first lecture, before developing the idea of reciprocal space, the appreciation of which would be crucial for the students' understanding in the following lectures. After a coffee break during which the sunshine and beautiful surroundings of Cosener's House could be enjoyed, it was back to work. Mike had prepared a lovely practical exercise helping the students gain familiarity in identifying symmetry elements, and helping them appreciate how International Tables of Crystallography Volume A is constructed.

As we had promised the students, the school would be intensive, which meant that after a three-course meal served back in the main building of Cosener's House, we returned to work. This time it was a poster session giving students the chance to present their work to each other, and it was also a great chance for the lecturers to get an idea of the research areas that the students were working in. I particularly enjoyed this session and was impressed by both the breadth and diversity of research topics covered by the course participants, and by how many students stayed on well past the point at which the free drinks ran out!

On Tuesday morning, fuelled by a full English breakfast, Martin Dove took the reins. He started out with a nice historical introduction to the field of lattice dynamics, before diving into the detail behind phonons and normal modes. The link between the theory of soft-phonon-mode phase transitions and Landau was beautifully made, and Martin finished his lectures with some nice examples of the effect of rigid-unit-mode motion on phonon dispersion and diffuse scattering. This tour de force, followed by a practical session using GULP, took the students through from 9am to 5pm - interspersed with plenty of breaks of course!

I was up next. I was a little nervous, not least as I had scheduled my lectures for the shift before and after dinner in what I appreciate was already a very long day for the students. My goal was to describe the language through which symmetry-breaking events can be classified according to irreducible representations. I was keen for the students to grasp that this symmetry breaking could be instantaneous, such as the dynamic fluctuations induced by phonons, or that it could be related to the order parameters describing the long-range ordering occurring at phase transitions. My tutorial session, which saw the students return fresh-faced on the Wednesday morning, sought to reinforce these concepts through several exercises, using ISODISTORT to analyse phase transitions and degeneracy in phonon-dispersion curves.

It was then over to Michael Carpenter who gave a very nice illustration of how the coupling between primary order parameters and strain can be used to study the nature of phase transitions, within the framework of Landau theory. As well as providing practice at performing this kind of analysis, the tutorial sessions explored how, once the Landau potential has been constructed, a host of other thermodynamic quantities can be derived and interrogated. It was particularly impressive to see the enthusiasm and stamina of the students throughout these sessions, who, even come the evening, were still working hard at problems and asking questions.

We felt it was also important for the students to appreciate how experimental measurements probing lattice dynamics can be made and interpreted, and in this respect we were very lucky to have two guest speakers on Wednesday afternoon from the ISIS Neutron and Muon Source. David Voneshen and Matthias Gutmann talked about their research interests around inelastic neutron scattering and diffuse scattering, providing an extra dimension to the school's curriculum. Even after such an action-packed Wednesday, I was pleased to see that a substantial number of students found the energy to soak up the last rays of sunshine by the river Thames, over a drink or two at the Nags Head Pub.

On Thursday morning it was over to John Claridge who gave an introduction to the superspace formalism and incommensurate crystallography, before diving into many intriguing examples of incommensurate phase transitions in functional materials. These ranged from site-occupancy modulation in thermoelectrics, to lone-pair and incommensurate tilt ordering in ferroelectric materials. For the final tutorial session, the students were let loose on refining incommensurately modulated structures in the program Jana2006.

As lecturers, we were very impressed by the calibre of the students and their enthusiasm, which was sustained up until the final session. For me, this is what really made the school so special. We hope to return for the 2nd PCG School in Physical Crystallography in 2020, but in the meantime the lecture material is available here for all to enjoy.

 

27 July 2018

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