Cristobalite, cubic-SiO2

Silica, SiO2, is one of the most common materials on the Earth's crust. The most common form is quartz, which is the material that keeps the time in everyone's watch and clock. At high temperature quartz transforms to the phase known as cristobalite. In its crystal structure the silicon atoms occupy  the same places in the diamond structure (like crystalline silicon), with the oxygen atoms half-way  between neighbouring silicon atoms. As a result, each silicon atom is surrounded by four oxygen atoms to make SiO4 tetrahedra, and all tetrahedra are connected together in one near-infinite network sharing corners.

The figures above show the arrangement of atoms (left; blue are silicon and red are oxygen) and SiO4 tetrahedra (right).

It can be seen from the picture that the bonds between oxygen atoms and two neighbouring silicon atoms line in straight lines. This arrangement is not common in similar silicate materials, and calculations show that it is energetically unfavourable. These materials prefer a bond angle of around 145° rather than 180°. To achieve this the oxygen atoms must be displaced in there perpendicular direction, giving rise to disorder in the crystal structure. At low temperature the cubic structure transforms into a lower-symmetry tetragonal structure which has the normal Si–O–Si bond angles. But at high temperature, the disorder is dynamic.

We have looked at the phase transition in cristobalite and the structure of its high-temperature phase using a variety of methods. Using molecular dynamics simulations and neutron total scattering methods coupled with the Reverse Monte Carlo method we have 

Methods

Crystal structures were analysed by neutron powder diffraction. Cristobalite was the first material I studied using the neutron total scattering method and to which we applied the Reverse Monte Carlo method. 

Collaborators

My first collaborator in the study of cristobalite was Ian Swainson, one of my first PhD students in Cambridge. Neutron total scattering and RMC work was carried out in collaboration with Matt Tucker (now Oak Ridge National Laboratory, USA) and David Keen (ISIS neutron tactility, UK).

References

Landau free energy and order parameter behaviour of the α/β phase transition in cristobalite. WW Schmahl, IP Swainson, MT Dove and A Graeme-Barber. Zeitschrift für Kristallographie 201, 125–145, 1992 (https://doi.org/10.1524/zkri.1992.201.1-2.125)

Low-frequency floppy modes in β-cristobalite. IP Swainson and MT Dove. Physical Review Letters 71, 193–196, 1993 (https://doi.org/10.1103/PhysRevLett.71.193)

Direct measurement of the Si–O bond length and orientational disorder in β cristobalite. MT Dove, DA Keen, AC Hannon and IP Swainson. Physics and Chemistry of Minerals 24, 311–317, 1997 (https://doi.org/10.1007/s002690050043)

Rigid Unit Modes and dynamic disorder: SiO2 cristobalite and quartz. M Gambhir, MT Dove and V Heine. Physics and Chemistry of Minerals 26, 484–495, 1999 (https://doi.org/10.1007/s002690050211)

Crystal structure of the high-pressure monoclinic phase-II of cristobalite, SiO2. MT Dove, MS Craig, DA Keen, WG Marshall, SAT Redfern, KO Trachenko, MG Tucker. Mineralogical Magazine 64, 569–576, 2000 (https://doi.org/10.1180/002646100549436)

Dynamic structural disorder in cristobalite: Neutron total scattering measurement and Reverse Monte Carlo modelling. MG Tucker, MD Squires, MT Dove and DA Keen. Journal of Physics: Condensed Matter 13, 403–423, 2001 (https://doi.org/10.1088/0953-8984/13/3/304)

Infrared and Raman spectroscopy studies of the α–β phase transition in cristobalite. IP Swainson, MT Dove, and DC Palmer. Physics and Chemistry of Minerals, 30, 353–365, 2003 (https://doi.org/10.1007/s00269-003-0320-8)

Malononitrile, CH2(CN)2

Malononitrile has a special place in my heard because it was the material I studied, in its crystal form, for my PhD.

It's crystal structure as you find it "out of the bottle" has quite low symmetry, with the structure shown below (black is carbon, blue is oxygen, pink is hydrogen).

The crystal structure as drawn has monoclinic symmetry. There are two phase transitions to a triclinic phase – at 141 and 295 K – which are rather interesting because the symmetries of the high and low temperature phases are identical. Such a sequence of phase transitions is called re-entrant, and there are not many examples.

There is a fourth phase and we recently deduced its crystal structure, shown below using the same colour scheme.

This has tetragonal symmetry and is quite unlike the monoclinic phase.

Methods

We used the techniques of x-ray and neutron powder diffraction with the Rietveld method to refine the crystal structure, and simulations using density functional theory to calculate the crystal structures and the lattice dynamics of the monoclinic and tetragonal structures.

Collaborators

My PhD supervisor Alistair Rae (University of Birmingham), then later Keith Refson (Royal Holloway University of London) who developed the DFT phonon software, and my PhD student Lei Tan (Queen Mary University of London).

References

Structural phase transitions in malononitrile. MT Dove and AIM Rae. Faraday Discussions 69, 98–106, 1980 (http://doi.org/10.1039/DC9806900098)

The re-entrant phase transitions in malononitrile: specific heat capacity. MT Dove, G Farally, AIM Rae and L Wright. Journal of Physics C: Solid State Physics 16, L195–L198, 1983 (https://doi.org/10.1088/0022-3719/16/6/005)

A new theoretical model for the re-entrant phase transitions in malononitrile. AIM Rae and MT Dove. Journal of Physics C: Solid State Physics 16, 3233–3244, 1983 (https://doi.org/10.1088/0022-3719/16/17/010)

The re-entrant phase transitions in crystalline malononitrile, CH2(CN)2: a neutron powder diffraction study. MT Dove. Journal of Physics: Condensed Matter 23, 225402, 2011 (https://doi.org/10.1088/0953-8984/23/22/225402)

Structural phase transitions in malononitrile, CH2(CN)2: crystal structure of the δ phase by neutron powder diffraction, and ab initio calculations of the structures and phonons of the α and δ phases. L Tan, K Refson and MT Dove. Journal of Physics: Condensed Matter 31, 255401, 2019 (https://doi.org/10.1088/1361-648X/ab11a1)