This work developed from an accidental discovery, and turned out to be rather novel. Na2CO3 has a second-order ferroelastic phase transition at 760 K, involving a symmetry change from hexagonal to monoclinic. This symmetry change is very important, since it can be driven by softening of the C44 elastic constant of the hexagonal phase. This in turn is associated with the softening of the transverse acoustic modes with wave vectors in the a*-b* plane, and polarisation along [001]. There has been a theory around for a little while that predicts that an acoustic mode softening over a plane of wave vectors will produce a divergence of the Debye-Waller factors. In effect, for a second-order phase transition, the Debye-Waller factors will shoot up to infinity, causing the Bragg peaks to vanish. The Bragg peaks will then be replaced by broad peaks of diffuse scattering. Until our work there were no examples of this in practice, mostly because most candidate phase transitions are first-order, so the divergence of the Debye-Waller factors is never realised.
In a simple neutron powder diffraction experiment performed at ISIS we observed this behaviour at the ferroelastic phase transition in Na2CO3. I will confess that this was simply good luck, for until this point we had not made the connection between the theory and Na2CO3. However, the effect is really striking, and at the transition temperature the Bragg peaks disappear completely (there are some expected exceptions that are discussed in the papers). We then obtained more detailed neutron powder diffraction measurements at Chalk River, which were used to quantify the effect in general terms.
Following our first experiments, we have performed neutron diffraction and inelastic neutron scattering experiments using single crystals of Na2CO3. The results have been analysed in terms of the theory developed by Mayer and Cowley. Actually the theory ties the data together quite nicely, and a consistent picture has emerged.
Full credit goes to Mark Harris, who really ran the PRISMA experiments, and Ian Swainson who helped with the first powder diffraction study at Chalk River. Kevin Godfrey grew the single crystals.
Our papers on this subject include (in reverse chronological order):
M J Harris, M T Dove and K W Godfrey, "A single crystal neutron scattering study of lattice melting in Na2CO3". Journal of Physics: Condensed Matter 8, 7073-7084, 1996.
This paper presents details of our single crystal neutron diffraction measurements and our inelastic neutron scattering measurements.
M J Harris, M T Dove and K W Godfrey, "Observation of lattice melting in a single crystal: The ferroelastic phase transition in Na2CO3". Physical Review B51, 6758-6760, 1995.
This is our first report of our single-crystal neutron diffraction measurements.
I P Swainson, M T Dove and M J Harris "Neutron powder diffraction study of the ferroelastic phase transition in sodium carbonate". Journal of Physics: Condensed Matter 7, 4395-4417, 1995.
This gives the full details of our powder diffraction measurements.
M J Harris and M T Dove, "Lattice Melting at Structural Phase Transitions". Modern Physics Letters B9, 67-85, 1995.
For some reason we were asked to write a review paper following our first paper!
M J Harris, R A Cowley, I P Swainson and M T Dove, "Observation of lattice melting at the ferroelastic phase transition in Na2CO3". Physical Review Letters 71, 2939-2942, 1993.
This gives our first neutron powder diffraction measurements.
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