Martin Dove has been a lecturer in Mineral Physics at the University of Cambridge for 10 years. His research interests have mostly been concerned with phase transitions in inorganic materials, which he has studied using computer simulations, neutron scattering, and from a theoretical perspective. Over the last few years he has worked with Prof Volker Heine on the theory of phase transitions in crystalline silicates. This work has led to the development of the "Rigid Unit Mode" model which is central to the present project. The Rigid Unit Mode project was supported by a grant from NERC, and the final report on that grant was rated
α
5. Martin Dove has been a regular user of ISIS, mixing both diffraction and inelastic scattering experiments. He is on the GEM Scientific
Advisory Committee.
Relevant example papers:
ÒLow-frequency floppy modes in
β
-cristobaliteÓ
I. P. Swainson and M. T. Dove, Phys. Rev. Lett.
71 , 193-196, (1993)
ÒObservation of lattice melting at the ferroelastic phase transition in Na
2
CO
3
Ó
M. J. Harris, R. A. Cowley, I. P. Swainson and M. T. Dove, Phys. Rev. Lett.
71 , 2939-2942, (1993)
ÒMolecular dynamics simulation of α - and β -cristobaliteÓ
I. P. Swainson and M. T. Dove, J. Phys.: Condensed Matter 7 , 1771-1788, (1995)
ÒRigid unit phonon modes and structural phase transitions in framework silicatesÓ
K. D. Hammonds, M. T. Dove, A. P. Giddy, V. Heine and B. Winkler, Am. Mineralogist 81 , 1057-1079, (1996)
ÒFloppy modes in crystalline and amorphous silicatesÓ
M. T. Dove, M. J. Harris, A. C. Hannon et al.
, Phys. Rev. Lett.
78 , 1070-1073, (1997)
ÒHow floppy modes give rise to adsorption sites in zeolitesÓ
K. D. Hammonds, H. Deng, V. Heine and M. T. Dove, Phys. Rev. Lett.
, 78 , 3701-3704, (1997)
ÒTheory of displacive phase transitions in mineralsÓ
M. T. Dove, American Mineralogist, 82 , 213Ð244, (1997)
Some recent invited talks:
ÒObservation of Floppy Modes in SilicatesÓ at ÒAmerican Physical Society Spring MeetingÓ, St Louis, USA, March 1996
ÒSoft Modes in SilicatesÓ, course of lectures given at the NATO Advanced Study Institute on ÒAmorphous insulators and
SemiconductorsÓ, Bulgaria, May-June 1996
ÒDynamic Disorder and Phase Transitions in Framework SilicatesÓ at ÒGordon Conference, Order/Disorder in SolidsÓ, USA,
July 1996
ÒShort-range disorder and long-range order: implications of the ÔRigid Unit ModeÕ modelÓ. At workshop ÒLocal structure from diffractionÓ Traverse City, Michigan 10-14th August 1997
David Keen is the instrument scientist for the SXD diffractometer at the ISIS Spallation Neutron Source and is responsible for the development of diffuse scattering studies on SXD. Prior to joining ISIS in 1989 he worked as a
DPhil student at the Clarendon Laboratory, Oxford investigating the short-range order associated with fast-ion behaviour. He has continued this work at ISIS looking at fast-ion materials at high temperatures and pressures
(with a SERC grant reference P:AK:113 C2). He has developed computer simulation techniques for determining structural disorder from powder diffraction patterns including the use of combined neutron and X-ray measurements. The main theme of his work is the determination of structural disorder in materials using neutron diffraction and computer modelling methods. A considerable part of this work has involved development of the
Reverse Monte Carlo method, particularly incorporating structural constraints. The aims of the proposed work are well aligned to his existing interests and he has considerable experience of methods which will be used and developed in this project.
Relevant example papers:
ÒStructural modelling of glasses using reverse Monte Carlo simulationÓ
D. A. Keen & R. L. McGreevy Nature 344 423Ð425 (1990)
ÒStructural disorder in AgBr: Reverse Monte Carlo analysis of powder neutron diffraction dataÓ
D. A. Keen, R. L. McGreevy, W. Hayes & K. N. Clausen Phil. Mag. Lett.
61 349Ð357 (1990)
ÒHigh pressure polymorphism of the copper(I) halides: a neutron diffraction study to ~10 GPaÓ
S. Hull & D. A. Keen Phys. Rev.
B 50 5868Ð5885 (1994)
ÒHigh pressure phase of copper(I) iodideÓ
M. Hofmann, S. Hull & D. A. Keen Phys. Rev.
B 51 12022Ð12025 (1995)
ÒStructural evidence for a fast-ion transition in the high-pressure rocksalt phase of silver iodideÓ
D. A. Keen, S. Hull, W. Hayes and N. J. G. Gardner Phys. Rev Lett.
77 4914Ð4917 (1996)
ÒRefining disordered structural models using reverse Monte Carlo methods: application to vitreous silicaÓ
D. A. Keen Phase Transitions 61 , 109Ð124 (1997)

Some recent invited talks:
ÒDiffuse scattering studies using neutron time-of-flight Laue diffractionÓ
D. A. Keen ACA annual meeting , Albuquerque, New Mexico USA, 23Ð28/5/93
ÒRMC modelling of disordered magnetic structuresÓ
D. A. Keen Workshop on RMC methods for structural modelling , NFL Studsvik, Sweden 14Ð15/6/94
ÒStructural disorder in fast-ion conducting materials at high temperature and pressureÓ
D. A. Keen Solid State Physics Seminar , Clarendon Laboratory, Oxford, 9/11/95
ÒRefining Structural Disorder using Reverse Monte Carlo ModellingÓ
Seventeenth European Crystallographic Meeting, Lisbon 24-28th August 1997
ÒRefining Structural Disorder using Reverse Monte Carlo ModellingÓ.
Workshop on ÒLocal structure from diffractionÓ Traverse City, Michigan 10-14th August 1997
Our collaboration brings together our mutual interests in phase transitions, disordered materials, silica, and diffraction, which are reinforced by our individual skills in modelling, neutron experiments, data analysis, amorphous systems, and theory of phase transitions in silicates. In our work to date, using total neutron scattering measurements performed at ISIS, we are nearing the completion of a major study of the different phases of silica.
Part of this work on the phase transition in cristobalite, which led to our first paper, is described in the main case.
We have also focused on relating local distorted atomic configurations in the different crystalline phases to the local structure of amorphous silica (i.e. over length range 0Ð10 •), and have shown that some the disordered phases of cristobalite and tridymite have structural elements that are more closely related to silica glass than the corresponding ordered phases or quartz. This result is significant since it quantifies the relationship between the glass and crystalline phases for the first time. A paper has been submitted to Nature. The work has also allowed us to analyse the relationships between the local structures of two phases related by a displacive phase transitions, and as a result we have shown that domain models of high-temperature phases are not appropriate. The experimental results on both the relationship of crystalline to amorphous silica and the displacive phase transitions were backed up by applications of our rigid unit mode model, which enabled our quantitative results to be properly understood.
Our work made considerable use of the Reverse Monte Carlo method. It was through this work that we developed certain significant modifications, such as the use of constraints derived from the data, and the comparison of calculated three-dimensional diffuse scattering with experimental measurements, which allowed us to adapt the method as a refinement method. However, as a result we have come to appreciate that there are a number of ways in which the method can be developed to give a significant improvement in the quality of the results. We have charted these improvements, and they form part of the core of this proposal.
We have also appreciated how powerful our approach is for the study of disordered crystals in a more general sense, and this has heightened the urgency to develop the methods further, since we believe that there are many potential beneficiaries. This sense of urgency also comes because of the new GEM diffractometer funded by
EPSRC which should come on line during the course of the proposed project. It should be noted that we are both members of the GEM CRG and are involved in different ways in the development of the GEM project.
As noted above, the success of our collaboration was recently recognised by the invitation to give back-to-back talks at a workshop on ÒLocal Structure from DiffractionÓ in the USA.
ÒDirect measurement of the Si-O bond length and orientational disorder in β -cristobaliteÓ
M. T. Dove, D. A. Keen, A. C. Hannon and I. P. Swainson, Phys. and Chem. of Minerals 24 , 311Ð317, (1997)
ÒComparing the local structures of amorphous and crystalline polymorphs of silicaÓ
D. A. Keen and M. T. Dove, submitted to Nature

In recent years, disorder in crystalline materials has received increased attention. This is, in part, because important physical properties of many new materials have been shown to be intimately related to the disorder in the crystal lattice: the giant magneto-resistive effect is linked to the formation of polaronic defects [1], high temperature superconductivity is critically dependent on oxygen disorder [2] and molecular rotations give rise to some of the interesting properties in carbon-60 [3]. Also, it is now possible to make very high quality diffraction measurements from which very subtle aspects of crystalline structure may be extracted. The purpose of this grant application is to develop emerging techniques for determining local structural disorder from powder neutron diffraction data.
We aim to obtain structural information in the short (0-10•) range, paying particular attention to distances above ~4• which are not accessible to EXAFS experiments and which are often the key distances for determining disorder in structures with strongly bound local environments that do not change significantly through disordering transitions.
Although these techniques will have significant benefit to a wide range of scientific areas (see below), we will establish them by concentrating on a small number of key experiments in areas where we have considerable expertise and interest. The techniques will also be important for the full exploitation of data from existing and next generation neutron time-of-flight powder diffractometers such as the funded (CRG Grant ref: GR/K58203) GEM diffractometer at ISIS which will become operational in 1999. We are both members of the GEM CRG.
The structural information which can be obtained from Rietveld refinement of diffraction patterns from powdered crystalline materials is well documented [4]. Time-averaged mean atom positions are obtained from the analysis of
F hkl
, the structure factors obtained from the Bragg intensities, together with the variance in the distribution function of instantaneous positions that reflects the thermal motion or the partial occupancy of a number of possible sites.
Similarly, the methodology of Fourier transforming the total scattering structure factor, F(Q) , of liquid or amorphous materials is well understood [5]. The Fourier transform of F(Q) , known as the total radial distribution function, G(r) , gives information about short-range atom-atom correlations such as characteristic distances and coordinations. Extracting details about longer-range (but still 4-10 •) correlations are difficult and usually involve computer modelling methods [6]. Crystalline materials also display diffuse scattering (see for example [7]) which may be dominant in cases of extreme disorder, and if this diffuse scattering is ignored, very misleading structures can result (see [8,9] and case study below). The average structure may be very different to the actual arrangements of atoms on a local scale and in particular, the average positions may suggest contact distances that are rather shorter than actually realised. It is therefore necessary to utilise the total scattering (Bragg plus diffuse) to reliably describe the structure of disordered crystalline materials, harnessing the interpretations based on Rietveld refinement and radial distribution functions. This grant proposal sets out to establish the latter and can be broadly subdivided into the areas of the next three sections.
The principle objective of this project is to use total scattering measurements to extract detailed structural information over the length scale 0-10 • in cases where we expect the local structure to be significantly different from the average structure deduced from Bragg peak interpretation. This work can be applied to a whole range of disordered crystalline materials, many of which are important technological ceramics, and each is in an area of research where the UK has an established record of international excellence:
¥ Relaxor ferroelectrics, where local ordering of cations leads to local strain fields. These are phases of perovskite with significant levels of cation doping, which broadens the Bragg peaks and smears out the ferroelectric phase transition over a wide range of temperatures. It is believed that there is a mesoscopic inhomogeneity of the crystal structure, with small islands of different chemical composition.
¥ Rotational disordered molecular crystals, such as methane, CBr
4
, SF
6
and nitrogen. In these materials it is known that the orientations of neighbouring molecules are coupled, and there is a coupling between orientations and local strains, yet these couplings cannot be determined by Bragg diffraction. There is frequently considerable diffuse scattering in these materials that has been shown must be due to correlated motions, and only total scattering measurements will be able to determine these correlations.
¥ Crystals which have been damaged by nuclear radiation giving rise to a reduction in Bragg intensity and increase of diffuse scattering from the local strains around radiation-induced defect sites. Zircon is one such material which is important to the nuclear industry as a ceramic used in the containment of radioactive materials. It is known that radiation damage destroys the long-range crystallinity, producing an amorphous phase. It is probable that the local atomic arrangement in the amorphous structure resembles the actual crystalline structure, and that there are coexisting islands of the amorphous and crystalline phases.
¥ Crystals which transform via solid-state amorphisation. The most familiar examples are the pressure-induced amorphous phases, and it seems as if perhaps most crystalline silicates can be transformed to quenchable amorphous phases at high pressure (e.g. the silica phases quartz and cristobalite, leucite KAlSi
2 with compositions between NaAlSi
3
O
8
and CaAl
2
Si
2
O
8
O
6
, and feldspars
), but there are also examples of silicates that transform between different crystalline phases via an amorphous phase at high temperature. Amongst the latter are

dehydrated analcime, NaAlSi
2
O
8
, on which we have already performed a pilot study using LAD to determine F(Q) and hence G(r) , and the stishovite phase of silica.
¥ Silicate crystals with large unit cells, including zeolites where we know from our rigid unit mode analysis that there must be considerable structural flexibility. Here it is quite likely that the structure over a short-range length scale will be rather different from the average structure determined from diffraction. This is exactly as we have observed with cristobalite (see case study below).
¥ Materials with displacive phase transitions, such as perovskite, to see whether the local order in the hightemperature phase resembles the structure of the low-temperature phase and to determine the length scales of local order. We have already begun a programme of work using total scattering measurements on the disordered hightemperature polymorphs of silica ( β -cristobalite, the hexagonal phase of tridymite and β -quartz) which have already produced interesting new results (see case study below).
¥ Fast-ion conductors, to investigate the distortions in the structure around the defect conducting ion.
β
2
Like all the low pressure phases of SiO linked SiO
4
2
, cristobalite is composed of corner-
tetrahedra. However, in β -cristobalite these SiO
4
appear orientationally disordered in spite of the constraints of the linkages to neighbouring tetrahedra. Standard crystallographic analysis of the Bragg intensities yields an average structure with a linear Si-O-Si inter-tetrahedral bond and a Si-O bond length which is smaller than other silicate materials under comparable conditions. Both theory and experiment show this to be a highly unfavourable configuration. The orientational disorder is indicated by larger than expected oxygen temperature factors [8]. We have made an initial analysis [9] of the local structure of cristobalite using total neutron scattering measurements from the LAD diffractometer at ISIS. The positions of the three peaks in G(r) (the
Fourier transform of the total scattering structure factor F(Q) ) at shortest distances immediately show that the SiO
4
tetrahedra in β -cristobalite are not significantly distorted and instead are rotated from their average orientations by
~17¼ with a more favourable Si-O-Si bond angle of ~146¼ (see figure on right).
0
2
4
6
0 2 4 6 h 00
8
20
15
10
5
0 r
Si–O r
O–O r
Si–O r
O–O r
Si–Si r
Si–Si
T = 475 K,
α
-phase
T = 575 K,
β
-phase
15
The data show unambiguously that the medium-range order of the ordered lowtemperature α -phase of cristobalite is significantly different from the β -phase
10
5 which precludes the popular model for the high-temperature disorder based on averaged ordered domains. Indeed in many respects the medium-range order is more akin to that
0
0 2 4 r (•)
6 8 10 of glassy silica. Preliminary computer models using reverse Monte Carlo refinement [10,11] of the three-dimensional local structure of β -cristobalite
0 k 0
β
-cristobalite
T = 575 K based on these data yield strong diffuse scattering in [110] and [100] directions
(see Figure on left) consistent with the diffuse scattering calculated from low-
8 energy rigid unit modes and seen in electron diffraction [11,12]. Further RMC modelling of cristobalite and other silica phases has given the orientational distribution and correlation functions, and has shown the relationships between the local structures in each phase with that in amorphous silica [13].
The physical measurement and data correction are identical to the methods routinely used for measurement of total scattering from liquids and amorphous materials [14]. However we emphasise four aspects which are crucial to the successful completion of this project.
¥ First , we will work with powdered samples because large single crystal samples are often either not available
(e.g. cristobalite does not form large single crystals) or do not survive the disordering transitions.
¥ Secondly , we require a good real-space resolution. This is governed by the range of momentum transfer,
Q=4 π sin θ
/
λ ( θ is half the scattering angle and λ is the neutron wavelength), accessible by the instrument. For this reason we will use time-of-flight neutron diffraction where the lack of form-factor fall off (compared with X-ray scattering) and availability of short wavelength neutrons (compared with reactor-based neutron instruments) means that Q ≤ 50•
-1
(with corresponding real space resolution of ~ 0.13•) is routinely possible. Time-of-flight neutron diffraction will also simultaneously give good reciprocal space resolution for Rietveld structure refinement.
¥ Thirdly , we must develop new methods for obtaining G(r) . In order to avoid serious truncation ripples in G(r)
(which are seen most clearly at small r , as in the case study Ð it should be noted that with proper control of other sources of noise this is the most serious cause of noise on the computed G(r) ), the forward transformation
F(Q) → G(r) either relies on F(Q) becoming constant at the maximum measured Q or requires some form of

modification function which reduces the real-space resolution. A recent alternative approach which has been successful is to use the inverse transformation where G(r) calc.
is iteratively changed until its transform F(Q) calc.
is in good agreement with F(Q) expt.
[15]. We propose to develop this inverse method further to account for the instrumental resolution broadened Bragg peaks in our F(Q) . This broadening has the effect of suppressing the oscillations in G(r) at long distances and convoluting G(r) calc.
with the resolution functions prior to transformation to F(Q) calc.
will produce better data in the important ~4-10 • range. We also need to develop the method to use data from different banks of detectors (in effect, multiple sets of data with different ranges of Q with different resolution functions) simultaneously.
¥ Fourthly , the ultimate challenge is to develop structure models of the disordered crystals from G(r) . The problem is that G(r) contains information only about pair correlations, and three-dimensional structures are defined by the higher-order correlations that are not included in G(r) . Our approach will be to use computer modelling based on both the Bragg and diffuse scattering, as we now describe.
There have been attempts to use the total scattering structure factor F(Q) or its Fourier transform G(r) for structural interpretation of disordered crystalline powders and we intend to build on the recently established method of reverse Monte Carlo (RMC) modelling [10,11,16]. This method reconstructs a three-dimensional model of the local structure which is then used to investigate three-body correlations, such as bond-angle distributions, which cannot be obtained directly from the diffraction data alone. We have used RMC modelling methods to investigate the defects associated with high ionic conduction in, amongst others, AgBr [17], and to model the orientational disorder of SiO
4
tetrahedra in different crystalline and amorphous phases of silica. Also the Ôpair distribution functionÕ approach has been applied to a number of materials [18]. For the systems which we propose to study (see
Section 2.1)) we prefer the RMC method, since it allows for the greatest flexibility in the resultant structural model.
This strength is also one of its greatest drawbacks when applied to crystalline systems since chemical reasonableness and the known average structure have to be explicitly built into the model. It is this area which we will develop (see ¤2.3), extending our initial work [10,11,13] by developing new RMC-based programs to determine local disorder constrained by the average structure given by the intensities of the Bragg peaks.
Our present use of RMC has evolved from the original objectives. For modelling disordered crystals we view the
RMC method as a refinement method. We now routinely use constraints on short-range interatomic coordinations from the G(r) (e.g. for silicates we use the SiÐO bond lengths from G(r) ), and in the RMC procedure we progressively change the balance of weighting between the constraints and the fitting to F(Q) , and we do not allow the structure topology to change significantly.
This project requires three main resources. First , beamtime on a time-of-flight neutron diffractometer. The best instrument for these total scattering measurements will be the forthcoming GEM diffractometer at ISIS and until
GEM is operational the LAD instrument at ISIS is most appropriate. Secondly , we require a workstation to provide sufficient computing resources for developing and running new computer codes and thirdly we require an experienced PDRA capable of carrying out the diverse tasks in this project (exploitation of new instrumentation, novel experiments, new analytical methods and computer modelling).
The main focus of the project is to develop methods to extract structural information about disordered crystals from neutron diffraction data, and there are two main components of this. The first component is the set of experiments to be performed at ISIS (¤2.2), which will augment the sets of data we have already obtained on the crystalline phases of silica. The second component is to develop the analysis methods (¤2.3). This latter aspect is closely linked to the development of the GEM instrument as a replacement to LAD at ISIS, and we will place some weight on the service component of the work in order to develop a Ôuser-friendlyÕ method.
The proposed experiments cover a range of some of our own interests, and are also selected to cover a range of interests in the UK and international science work. Furthermore, we have selected examples which will stretch the analysis in different ways. When taken as a suite of examples together with our recent datasets on the crystalline phases of silica (e.g. quartz), we have examples ranging from a high degree of crystalline order and one end, to examples with rotational disorder, partial amorphisation, disorder from chemical substitutions, and large scale thermal disorder. Some examples lead to strain fields (e.g. perovskites), and other examples have orientation correlations. For the modelling work where we plan to take full account of the Bragg peaks, the more ordered systems will be extremely useful.
¥ Crystalline silicates that transform from one phase to another via an intermediate amorphous phase. Total scattering measurements will be able to probe the changes in the local order that accompany the loss of long-range order. These transitions are sufficiently slow that we envisage being able to provide the link between microscopic structure and kinetics. We propose to perform detailed measurements of the temperature-induced amorphisation of stishovite (7 days) which transforms at around 600 ¡C to an amorphous phase with a higher density than melt-

quenched glass [19], and a suite of measurements on recovered high-pressure amorphous phases of cristobalite (4 days) which are believed to have six O-atoms coordinated to Si [20]. Since it will only be possible to produce small quantities of sample at high pressure, we propose to carry out these measurements on the GEM instrument.
¥ Rotationally disordered crystalline phases of molecular crystals. We are planning to perform measurements of the disordered phase SF
6
, for which powder diffraction experiments have shown strong diffuse scattering with marked Q -dependence (2 days). Simulation work [21] has proposed correlations between the orientations of neighbouring molecules which are inconsistent with the average structure. In SF
6
the average atom positions would have neighbouring S-F bonds lying along a common vector leading to too short F...F contacts. It is likely that the molecules will have to rotate in order to avoid close contacts and models suggest that neighbouring bonds precess about each other. Total scattering experiments will pin down these correlations accurately.
¥ Silicate crystals with large unit cells, including zeolites, which show considerable structural flexibility. Our
RUM calculations on Zeolite A and ZSM-5 [22] have shown that these systems have a large number of low energy vibrations giving rise to large-amplitude atomic motions. In some cases this results in a negative thermal expansion
[23]. We are proposing to perform measurements on a number of carefully calcined zeolite samples (6 days).
¥ Radiation-damaged zircon, ZrSiO
4
and titanite, CaTiSiO
5
. We plan to perform total scattering measurements on a suite of samples with different degrees of amorphisation following different exposure to nuclear radiation (3 days) and to anneal the most disordered samples at modest temperature to follow the recrystallisation process (3 days). We will use naturally produced amorphous (metamict) samples, which form during long exposure to low doses and do not pose a serious radiological hazard.
¥ Relaxor ferroelectrics, where local ordering of cations leads to local strain fields and a mesoscopic inhomogeneity of the crystal structure, with small islands of different chemical composition. Total scattering experiments will be able to isolate these regions. We will perform total scattering measurements on a suite of samples with different chemical composition in the family of Pb(Zr,Ti)O
3
, with small amounts of doping with La
2
(PZT/PLZT) , which has the perovskite structure with doping on the octahedral site (4 days).
¥ The first stage will be to develop methods to obtain G(r) from the neutron data. The approach will be based on
Alan SoperÕs inverse transformation method [15] (¤1.3). The extension to include separate datasets from different detectors is relatively straightforward. To account for resolution, including the line broadening due to particle size
(and other factors associated with high-resolution diffraction), will require determination of the lineshape of the
Bragg peaks using standard methods (e.g. pattern fitting using the Pawley method [24]). Some work will be required to determine the best strategy, and to automate this process within the data reduction stage. Methods to obtain G(r) do not usually take account of the presence of Bragg peaks. In the transformation to G(r) from digitised
F(Q) data the Bragg peaks do not present any difficulties, but in the reverse transformation from G(r) the function needs to be sufficiently extensive in r in order to recover the sharp Bragg peaks in F(Q) . Some work will be required in order to find the optimum approach (taking account of computer time and memory).
¥ The second stage is to develop the RMC method to include the information contained in the Bragg peaks. At the present time the Bragg peaks are folded into the total scattering and the particular information they contain is not used explicitly. The Bragg peaks give information about the ÔaverageÕ structure (i.e. averaged over all unit cells), and the probability distribution functions of atomic positions. Our proposed approach is to extract the intensity of the Bragg peaks from the diffraction data directly, using the Pawley method from conventional powder diffraction
[24], and building into the RMC method the requirement that the calculated structure factors of the Bragg peaks should match the measured structure factors. In principle this approach seems straightforward, but some effort will be required to reduce ambiguities in the extracted Bragg intensities in the presence of a strong oscillatory background of diffuse scattering. From the modelling perspective, there will be fluctuations in the calculated Bragg peaks that will scale with the sample size, and the RMC method needs to take account of these. Therefore some work will be required to obtain the best strategy, and to tune the balance between the relative weighting put on the total scattering, the constraints from the Bragg structure factors, and the constraints on local bond lengths and angles. We want to change the approach to incorporate fitting against both G(r) , obtained using the new method outlined above, and multiple datasets for F(Q) taking resolution into account. Although the data are from an equivalent source, by balancing the fitting in both r and Q we effectively weight different parts of the data separately. This will need optimisation. We also want to be able to take proper account of experimental errors.
¥ It is inevitable that the analysis will also require some work on the data reduction from GEM, in order to get the data into a usable form in a routine manner. The analysis will therefore interface closely against the raw data coming from GEM.
¥ The end result should be a suite of programs that will be Ôuser-friendlyÕ for general use with data from GEM, thereby considerable extending the scope of ÔroutineÕ analysis of data from this instrument. This task is essential
2 service-oriented and will require some effort to ensure a satisfactory end result.
A summary of the proposed timetable is described in the table accompanying this proposal. In addition MTD and the PDRA will hold regular weekly meetings, with everyone meeting formally every 4 months at either ISIS or
Cambridge.

1. The PDRA and DAK, with assistance from Alex Hannon and Paulo Radaelli (ISIS), will be responsible for running the LAD and GEM experiments and developing data reduction software.
2. The PDRA, DAK and MTD will be responsible for developing methods to maximise the information that will be extracted from these experiments. They will consult regularly with R. L. McGreevy (Studsvik, Sweden) and A. K.
Soper (ISIS) during the development of inverse methods for transforming F(Q) to G(r) .
3. The PDRA, MTD and DAK will be responsible for the structural interpretations.
4. The PDRA and MTD will be responsible for sample preparation, in collaboration with A. Pawley, (Manchester
University) for preparation of samples at high pressures.
5. MTD and DAK will support the project with Molecular Dynamics simulations where appropriate.
¥ All the science issues we are proposing to address are of direct importance to a large number of different scientific communities. We will be obtaining information that will be of considerable importance but cannot be obtained by other methods. Our preliminary work on cristobalite [8,9,11Ð13] illustrates this.
¥ The results from this project will highlight the importance of structural disorder in the physical properties of materials and provide methods for characterising the disorder which will be of considerable benefit to a number of industries concerned with the properties of ceramics, including ferroelectric ceramics, glass and silicate ceramics.
The work on radiation damaged materials will also be important for the nuclear industries.
¥ The methods we will develop will be of considerable benefit to the neutron scattering community. We are proposing to deliver to the wider scientific community a new method for routine analysis of disordered crystalline materials. So that the community is able to use the method, we will ensure that all components are Ôuser-friendlyÕ and automated as appropriate, and will ensure that they are properly documented in manuals and on the WWW.
¥ A large part of our work will be of considerable benefit to the science programme on the GEM diffractometer at
ISIS which has been largely funded by EPSRC. Our work will extend the versatility of the scientific work possible on GEM for materials research.
First , the potential of the method to extract information about local order in disordered crystals has been clearly demonstrated in our pioneering work on cristobalite and other silica phases [9,11Ð13]. The information cut clearly to the heart of some of the important issues concerned with the nature of the high-temperature β -phase. Given this demonstration result, there is now a whole field of work in which to develop and exploit the methods, as illustrated by the broad range of examples given in Section 1.2. Secondly , the GEM diffractometer will open up many new possibilities, with a greatly increased data collection rate. It is essential to pioneer the methods outlined in this proposal before the GEM diffractometer is completed so that we will be able to begin this new line of science from the moment GEM becomes operational in September 1999 and so that we can influence the commissioning of the instrument. In order to obtain data before LAD is decommissioned, and to prepare the methods before GEM comes on-line, it is essential that the project is supported with a minimum of time delay .
2
¥ We will publish our results in the top scientific journals, in line with our present practice. We specifically target our publications at the intended audiences in a strategic manner.
¥ Similarly we have an extremely good record of invitations to speak at conferences and summer schools, an extremely valuable mechanism for stimulating applications of our ideas by other workers.
¥ Both Cambridge and ISIS have close contacts with likely industrial beneficiaries. Indeed our Department at
Cambridge offer regular seminars for industrial partners.
¥ We routinely place our programmes and main results on the world-wide web for people to use freely , and we will continue to follow this practice.
1. PDRA . The PDRA will be involved in all aspects of this work over the whole three-year period. This project is very demanding because it encompasses both science and method development and because of the timeliness there will be considerable urgency to make progress to tie in with the LAD/GEM changes. Accordingly it is essential that the manpower for this project be supported at a senior PDRA level which will also give us the necessary flexibility to appoint the best available applicant.
2. ISIS Neutron beamtime . This project relies entirely on results from total scattering measurements. For reasons described above (Section 1.3), time-of-flight neutron powder diffraction is the ideal method for obtaining total scattering structure factors, giving the best possible data for subsequent analysis. The number of days beamtime required for each of the experiments outlined in Section 2.2 has been determined in consultation with the appropriate ISIS instrument scientists and takes account of the reduced detector complement on GEM in the first year of operation (Total 29 days).

3. Computer . The data reduction procedures which we propose will need considerable computer resources. The inverse Fourier transform methods for obtaining G(r) involve Monte Carlo techniques with large data arrays for efficient computation. Convoluting G(r) with the instrumental resolution before transforming G(r) → F(Q) will result in an even larger computational overhead. The reverse Monte Carlo modelling methods are also computer intensive. Calculations based on our experience suggest that we will require a fast workstation with at least 128
MBytes of memory to carry out the necessary calculations in a reasonable timescale. We also require a
DECCampus licence for software and compilers. Our department requires that the funding of a computer officer in support of research be covered by research grants: we are requesting one monthÕs computer officer support.
4. Travel and Consumables . We will need travel funds for regular liaison between Cambridge and ISIS and for attendance at conferences and workshops in line with effective communication of our results to the wider scientific community. In addition to the visits to ISIS during scheduled experiments, and in particular in the period between operation of LAD and GEM, the PDRA will need longer stays at ISIS, averaging to about two weeks per year. It is also important to have sufficient funds to purchase the necessary materials for sample preparation without which we cannot carry out the neutron experiments.
[1] S.Billinge et al ., ÔDirect observation of lattice polaron formation in the local structure of La
1-x
Ca x
MnO
3
Õ, Phys.Rev.Lett.
, 77
715-718 (1996)
[2] H.F.Poulsen et al ., ÔRelation between superconducting transition T and oxygen ordering in YBa
2
Cu
3
O
6+x
Õ, Nature , 349 594-
596 (1991)
[3] W.I.F.David et al ., ÔCrystal structure and bonding of ordered C
60
Õ, Nature , 353 147-149 (1991); R.Glas et al.
,
ÔExperimental observation of static disorder in C
60
by diffuse neutron scatteringÕ, Phys. Rev.
B, 50 692-697 (1994)
[4] J.I.Langford & D.Lou‘r, ÔPowder diffractionÕ, Rep. Prog. in Phys.
, 59 131-234 (1996)
[5] A.C.Wright, ÔNeutron scattering from vitreous silica.V.Õ, J.Non-Cryst.Sol.
, 179 84-115 (1994)
[6] D.A.Keen & R.L.McGreevy, ÔStructural modelling of glasses using reverse Monte Carlo simulationÕ, Nature , 344 423-425
(1990); L.F.Gladden, ÔMedium-range order in v -SiO
2
Õ, J.Non-Cryst.Sol.
, 119 318-330 (1990)
[7] R.Fayos et al.
, ÔDirect experimental evidence of the relationship between intermediate-range order in topologically disordered matter and discernible features in the static structure factorÕ, Phys. Rev. Lett.
, 77 3823-3826 (1996)
[8] W.W.Schmahl, I.P.Swainson, M.T.Dove & A.Graeme-Barber, ÔLandau free energy and order parameter behaviour of the
α / β phase transition in cristobaliteÕ, Zeit.Krist.
, 201 125 (1993); I.P.Swainson & M.T.Dove, ÔLow-frequency floppy modes in
β -cristobaliteÕ, Phys.Rev.Lett.
, 71 193 (1993);Ð, ÔMolecular dynamics simulation of α - and β -cristobaliteÕ, J.Phys.:CM , 7 1771
(1995)
[9] M.T.Dove, D.A.Keen, A.C.Hannon & I.P.Swainson, ÔDirect measurement of the SiÐO bond length and orientational disorder in β -cristobaliteÕ, Phys. Chem. Min.
, 24 , 311Ð317 (1997)
[10] D.A.Keen, ÔRefining disordered structural models using reverse Monte Carlo methods: application to v -SiO
2
Õ, Phase
Trans . 61 , 109Ð124 (1997)
[11] D. A. Keen, ÔRefining Structural Disorder using Reverse Monte Carlo ModellingÕ, to appear in ÒLocal structure from diffractionÓ, ed M. F. Thorpe and S. J. L. Billinge (Plenum, 1998)
[12] M. T. Dove et al., ÔShort-range disorder and long-range order: implications of the Rigid Unit Mode modelÕ, to appear in
ÒLocal structure from diffractionÓ, ed M. F. Thorpe and S. J. L. Billinge (Plenum, 1998)
[13] D. A. Keen and M. T. Dove, ÔComparing the local structures of amorphous and crystalline polymorphs of silicaÕ submitted to Nature
[14] M.A.Howe et al.
, ÔThe analysis of liquid structure from time-of-flight neutron diffractometryÕ, J.Phys.: CM , 1 3433-3451
(1989)
[15] A.K.Soper et al.
, ÔReconstruction of orientational pair-correlation function from neutron diffraction data: the case of liquid hydrogen iodideÕ, Phys. Rev.
E, 47 2598-2605 (1993)
[16] R.L.McGreevy & L.Pusztai, ÔReverse Monte Carlo simulation: a new technique for the determination of disordered structuresÕ, Mol. Simul.
, 1 359-367 (1988); R.L.McGreevy, ÔRMC: progress, problems and prospectsÕ, Nucl. Instr. and Meth.
A, 354 1-16 (1995)
[17] D.A.Keen, W.Hayes & R.L.McGreevy, ÔStructural disorder in AgBr on the approach to meltingÕ, J.Phys.:CM , 2 , 2773-
2786 (1990); V.M.Nield, D.A.Keen, W.Hayes & R.L.McGreevy, ÔStructure and fast-ion conduction in α -AgIÕ, Solid State
Ionics , 66 247-258 (1993)
[18] S.J.L.Billinge et al.
, ÔDeviations from planarity of copper-oxygen sheets in Ca
0.85
Sr
0.15
CuO
2
Õ, Phys.Rev.
B, 43 10340-
10352 (1991)
[19] M.Grimsditch et al , ÔTemperature-induced amorphization of SiO
2
stishoviteÕ, Phys.Rev.
B, 50 , 12984-12986 (1994)
[20] X.Zhang & C.K.Ong, ÔPressure-induced amorphisation of β -cristobaliteÕ, Phys.Rev.
B, 48 , 6865-6870 (1993)
[21] M.T.Dove & G.S.Pawley, ÔA molecular dynamics simulation study of the orientationally disordered phase of sulphur hexafluorideÕ, J. Phys.
C, 17 , 6581-6599 (1984)
[22] K.D.Hammonds, M.T.Dove et al.
, ÔHow floppy modes give rise to adsorption sites in zeolitesÕ, Phys.Rev.Lett.
, 78 , 3701-
3704 (1997)
[23] J.W.Couves et al , ÔVerification of a predicted negative thermal expansivity of crystalline zeolitesÕ, J.Phys.:CM , 5 , l329-
1332, (1993)
[24] G. S. Pawley, ÔUnit-cell refinement from powder diffraction scansÕ J. Appl. Cryst . 14 , 357-361 (1981)