Martin Dove

The central idea of the RUM model is that any low-energy distortion of a network structure can be described as a normal mode in which the tetrahedra move without distortion. If we set up a model in which the only terms are those that describe the energy of the distortions of the tetrahedra, the RUMs will have exactly zero frequency. This model allowed us to set up a molecular lattice dynamics method for the determination of the complete set of RUMs of any structure for any wave vector [web]. The first success of this model was to be able to explain the origins of a phase transitions in a number of framework materials, such as quartz [1,2,3], cristobalite [1,2,3] and tridymite [1].

Subsequently we have used the RUM model to explore the structures of high-temperature disordered phases, dynamics of silicate glasses [1,2,3], deformations in zeolites [1,2], and negative thermal expansion [1,2,3,4].

The RUM model has been subject to a number of experimental tests. The first tests were to match the predictions of the RUM model against patters of diffuse scattering in transmission electron diffraction measuremens. Other experimental tests include total neutron scattering experiments analysed by the Reverse Monte Carlo method, and inelastic neutron scattering measurements.

There is one aspect of the RUM mdel we still do not understand. The distributions of RUMs across reciprocal space in many systems take on very unusual shapes, as can be seen in our gallery of RUM surfaces. This has been verified in TEM measurements.

I am pleased to acknowledge collaboration with Volker Heine, Andrew Giddy, Ian Swainson, Kenton Hammonds, Alix Pryde, Manoj Gambhir, Matt Tucker, Dave Keen, Kostya Trachenko and Stephen Wells. This research has been supported by the NERC and the EPSRC.

My inclination is towards the soft mode picture, but there are systems with clear evidence that this has to be too simple. One of my favourite systems is the cristobalite polymorph of silica (SiO₂). The high-temperature phase has a highly symmetric cubic structure that appears to have linear Si–O–Si linkages (which are not chemically reasonable, since in almost all structures and in quantum mechanical calculations the Si–O–Si bond angle would rather be neared 145°), and distances between nearest-neighbour Si and O atoms that are shorter than typical Si–O distances. These observations can be reconciled with a model in which the SIO₄ tetrahedra are actually significantly rotated from their apparent orientations in the average high-symmetry structure. The question is how this can be accomplished within the constraints of the average model.

In brief, we have proposed that the disordered structures of high-temperature phases can arise from the existence of Rigid Unit Modes (described left). In this model, the higher symmetry of the high-temperature phase allows more RUMs to be created, and their low energies mean that they have high amplitude. Detailed analysis of configurations generated by the Reverse Monte Carlo method shows that the RUMs can account for more than 90% of the structural disorder, and that the RUM contribution to the disorder declines on cooling through the phase transition [1,2]. This model is consistent with the results of inelastic neutron scattering measurements.

I am pleased to acknowledge collaboration with Volker Heine, Andrew Giddy, Kenton Hammonds, Alix Pryde, Manoj Gambhir, Matt Tucker, Dave Keen, Kostya Trachenko and Stephen Wells. This research has been supported by the NERC and the EPSRC.

Provided that the experiment can perform a complete integration over all energy (or time) scales, a measurement of the total scattering pattern (Bragg + diffuse scattering) can provide information about a structure over both short-range and long-range length scales. This, of course, is exactly the type of experiment carried out to investigate the structures of liquid and amorphous phases (although there is no equivalent of the long-range order capture in the Bragg scattering). The initial diffraction study of cristobalite led to the development of a major project to harness total scattering measurements for the study of disordered crystalline materials.

Our analysis of the total scattering data is focussed on the use of Reverse Monte Carlo methods, which we have adapted specifically for the study of crystalline materials using pulsed neutron sources such as ISIS [1,2].

Among the systems we have studied and written up are quartz [1,2], cristobalite [1] and tridymite [1]; other systems include SF₆, perovskites, carbonates and nitrates, zirconium tungstate and zirconium phosphate.

I am pleased to acknowledge collaboration with Matt Tucker and Dave Keen. This research is being supported by the EPSRC [proposal 1, report 1, proposal 2].

The Cambridge Mineral Sciences group has developed a major interest in understanding the nature of radiation damage in crystalline ceramics. The motivation is to develop the possibility of using ceramics for the long-term storage of high-level radioactive waste. The group has developed a broad experimental approach using X-ray diffraction, spectroscopy and NMR. We have developed a simulation programme of work in support of the experimental programme.

We use large scale molecular dynamics techniques (up to 300k atoms) to simulate the response due to a high-energy recoil of an atom following alpha decay. With some development of the approach we are able to simulate realistic recoil events. Our first work has been concerned with the mineral zircon, ZrSiO₄, which is a natural example of a material that has contained radioactive elements.

Some of the radioactive decay events we have simulated have been converted into animations, which are available for download [www]. These graphically illustrate the processes that occur in such events. In particular, we have observed that the local structure resulting from an event is a lower-density core region surrounded by a shell of polymerised SiO₄ tetrahedra. This shell may act as a barrier between the low-density region and the rest of the matix.

Based on our simulations, we have developed a model to explain the large volume swelling of zircon following damage from radioactive decay. This uses results from percolation theory. With only a single fitting parameter (namely the factional volume change at large dose, which in turn scales as a parameter with a value which we have shown to be consistent with local effects in the simulations) we have been able to completely describe the non-trivial dependence of volume change on radiation dose [1].

I am pleased to acknowledge collaboration with Kostya Trachenko. This research is being supported by the CMI [proposal] and BNFL.

We have performed a lot of work on crystalline silicates in the context of our Rigid Unit Mode model. We initially shied away from looking at silicate glasses because we suspected that they would not be interesting from the RUM perspective. However, inspired by a NATO workshop organised by Mike Thorpe, we decided to try looking at silica glass, and to our surprise we found that it has as many RUMs as many crystalline phases (but we still do not understand why!). We have built upon this initial work to use the RUM model to explore a number of features of silica and silicate glasses.

The first study was of tunneling states in silica glass, which are believed to give rise to anomalous thermal properties at low temperature. We observed significant local rearrangements of the glass structure in molecular dynamics simulations that could be described as large amplitude RUM motions, since these rearrangements did not require distortions of tetrahedra or breaking of bonds [1,2]. These rearrangements can be viewed as animations [www]. By using the simulation results to obtain values for certain critical parameters, we developed a model that could explain why the low-temperature heat capacity varies with temperature as T^1.3, in contrast to a linear dependence for simple two-level tunneling models, and in contrast to T³ for a normal Debye solid [1].

Experimental work using both total neutron scattering and inelastic neutron scattering has shown that both the structure and dynamics of silica glass are surprisingly close to disordered crystalline silica phases (such as b-cristobalite). We have proposed that this is related to the existence of RUMs in both the crystalline and amorphous phases. This work has led us to understand that the so-called "Boson peak" seen as a feature in spectroscopic measurements at around 5 meV (1 THz or 30 cm^–1) is not a special feature of the amorphous state.

We have extended our study of silica glass to high pressures. We have studied rebonding events to explain irreversibility. We believe that we have shown that there is not a phase transition at high pressure, contrary to earlier reports, but instead the effects attributed to the existence of a phase transition can be explained in terms of irreversibility effects. In order to properly quantify the behaviour of silica glass under pressure, we have noted the existence of three clear pressure regimes. For P < 3 GPa, there are not rebonding events and the structure supports a number of RUMs. Large amplitude RUM rearrangements can take place in different parts of the structure. We have managed to explain, and quantify, the origin of the surprising negative gradient of the bulk modulus in this model. For 3 < P < 5 GPa there are initial rebonding events, which lead to a gradual decrease in the number of RUMs. For P > 5 GPa, there are no RUMs because there are too many higher coordinated silicon atoms, with rigid links between some of the polyhedra. The lack of RUMs means that the structure has stiffened, and for P > 5 GPa the volume changes with pressure are smaller than for P < 5 GPa. In addition to these results, we also find that for 3 < P < 5 GPa there is an enhanced reversibily for changes in temperature.

I am pleased to acknowledge collaboration with Kostya Trachenko, Mark Harris and Erika Palin. This research has been supported by the EPSRC [proposal, report].

Our work in this area began when increases in computational power allowed us to perform large sets of calculations of the energies of configurations with different degrees of order. From these databases of energies we could determine the energies associated with exchanging cation positions, e.g. the energy associated with breaking two Si–O–Al linkages to form an Al–O–Al linkage plus an Si–O–Si linkage. These exchange energies allow us to construct a model Hamiltonian, which we can study using Monte Carlo techniques. We apply the method of thermodynamic integration to determine the temperature dependence of thermodynamic functions with changing degree of order.

The first systems we studied were for Al/Si ordering, with the objective of understanding why there is a large variation of transition temperatures for long-range order (in spite of the fact that Al and Si cations behave similarly in most aluminosilicates). We understood that in some cases the onset of order is not determined by nearest-neighbour exchange interactions, but by more distant exchange interactions, and that there are many ways in which particular structures can accommodate short-range order (often in a one-dimensional sense) without needing to generate long-range order.

We have also applied our methods to study more complex cation order problems, as in pyroxene solid solutions and, more recently, in layer silicates and amphiboles.

Much of our work is based on empirical models of interatomic potentials, but we know that there are situations when these are inappropriate. In such cases we use quantum mechanics methods. In our work on non-convergent Al/Mg ordering across the tetrahedral and octahedal sites in spinel, MgAl₂O₄, we used only quantum mechanics methods to determine exchange interactions and chemical potentials, and we were able to reproduce the experimental measurements of long-range order. For other cases, such as Mg/Al ordering in the amphibole glaucophane, we used a combination of quantum mechanics and empirical models, the former to determine the values of chemical potentials and the latter to determine the values of the exchange interactions.

I am pleased to acknowledge collaboration with Volker Heine, S Thayaparam, Eva Myers, Simon Redfern, Anne Bosenick, Michele Warren, Charles Geiger, Erika Palin and Ignacio Sainz-Diaz. This research has been supported by the NERC [report] and the Royal Society.

We were able to demonstrate the ability of the equipment to generate pressures up to 7 GPa and temperatures in excess of 1500 K. Our first test experiment was on deuterated brucite, and we have followed this up with experiments on calcite and spinel. Our objective now is to extend the maximum pressure to 12 GPa and the maximum temperature to 2000 K.

One of the novel developments in our work was to determine the sample temperature using neutron radiography. This involves measuring the resonance absorption of high-energy neutrons in a thin metal foil held in the centre of the sample. The square of the resonance line width increases with temperaure in a way that is relatively straightforward to calibrate. So far this gives a precision of ±20 K in the measurement of temperature.

I am pleased to acknowledge collaboration with Simon Redfern, Yann Le Godec, Bill Marshall, Mark Welch and Matt Tucker. This research has been supported by the NERC [proposal, report], and is being supported by the Royal Society [proposal] and the Leverhulme Trust [proposal].

The fact that many materials with negative thermal expansion can be described as frameworks of corner linked structural polyhedra (such as ZrO₆ octahedra and WO₄ tetrahedra in ZrW₂O₈) has led us to apply our Rigid Unit Mode model to this problem. It is easy to show that a RUM system that does not have significant structure relaxation on changing temperature, and in which the polyhedra do not expand on heating, will automatically shrink on heating due to increased amplitude of rotational motions of the polyhedra. The question is whether these constraints are sufficently relaxed in real systems to allow the structure to have a positive coefficient of thermal expansion instead.

Our first work in this area was a study of the negative thermal expansion in the ambient pressure and high pressure phases of ZrW₂O₈ [1,2]. This was followed by a more formal general study [1] and a study of negative thermal expansion in quartz [1]. We believe that these studies have confirmed our basic ideas based on the RUM model. More recently we have been looking at negative thermal expansion in some zeolites from the same perspective.

I am pleased to acknowledge collaboration with Volker Heine, Alix Pryde and Patrick Welche.

The orientational order/disorder in calcite and sodium nitrate are easily seen in animations we have produced from molecular dynamics simulations [www]. We have studied these phase transitions using inelastic neutron scattering. In calcite we discovered an unusual dynamic process which appears to represent a coupling between a phonon and a relaxation process [1,2,3,4].

The ferroelastic phase transition in sodium carbonate is a rare example of a second order transition with softening of the acoustic modes in a whole plane of reciprocal space. This is predicted to lead to a divergence of the mean-square displacements along the hexagonal [001] direction, and hence to the vanishing of all Bragg peaks with Miller index l &Mac173; 0. We observed this feature quite by accident as part of a more general study of sodium carbonate, and then went on to characterise the phase transition and show how the theoretical predictions matched our data [1,2,3].

I am pleased to acknowledge collaboration with Ian Swainson and Mark Harris, and was supported by the EPSRC.

The applications we are planning include developments of studies of radioactive waste encapsulation, absorption of pollutant cations and organic molecules on mineral surfaces, weathering of mineral surfaces, and scaling by precipitation of minerals.

I am pleased to acknowledge collaboration with colleagues in Cambridge, London, Bath and Reading. This work is being funded by the NERC [proposal].