Shedding light on phase transitions hidden in higher dimensions

Garry McIntyre (ANSTO), Marie-Hélène Lemée-Cailleau (Institut Laue-Langevin) and Bertand Toudic (Rennes)
Recent visitors to ANSTO would have noticed the series of banners around the roundabout that depict various neutron-scattering patterns to celebrate the United Nations International Year of Light.  Two of these banners display spectacular starbursts so typical of neutron Laue patterns.
The Laue patterns come from a recent experiment [1] on KOALA on n-nonadecane-urea one of a family of aperiodic misfit composite crystals. Aperiodic crystals have been very much in the limelight following the award of the Nobel Prize in Chemistry to Dan Schechtman in 2011 for his discovery of quasicrystals in the early 1980s.  


Higher dimension figure 1
Figure 1. Schematic of a self-assembled aperiodic alkane-urea composite. The projection in the ab plane, normal to the channels in the urea host, is commensurate. Along the channels the irrational ratio chost/cguest = α leads to aperiodicity manifested by additional Bragg reflections at multiple values of α in the c* direction.
The family of n-alkane-urea inclusion compounds consists of guest alkane molecules of various lengths confined in the honeycomb-like network of channels formed by the host urea molecules (Figure 1). Because the ratios of repeat lengths along the channel axis (the c axis) and the alkane guests are usually irrational, these crystal structures are mostly incommensurate along the c axis, i.e. aperiodic.  This is not just a mathematical crystallographic curiosity, but also of physical interest since the incommensurability gives rise to such unusual phenomena as free or ser-frictional sliding of the alkane molecules along the channels.
Some of the present investigators previously observed for the first time in n-nonadecane-urea that there exist phase transitions where the structural changes correspond just to degrees of freedom hidden in the internal (super)space of such an aperiodic material [2]. A key factor in the discovery of this type of the transition [3] was the examination of the diffraction pattern in 3D, only possible at the time on a four-circle triple-axis neutron spectrometer, with the analyzer set at zero energy transfer to reduce the background and improve resolution. Despite the greater accessibility in reciprocal space, the weak intensity of the superlattice reflections limited the volume of reciprocal space that could be explored. 
Modern neutron Laue diffractometers with large image-plate detectors, like VIVALDI at the Institut Laue-Langevin and KOALA on the OPAL reactor at ANSTO, permit rapid and extensive exploration of reciprocal space with high resolution in the two-dimensional projection and a wide dynamic range with negligible bleeding of intense diffraction spots [3]. A preliminary experiment on VIVALDI showed that the weak superlattice reflections of n-nonadecane-urea could indeed be observed by the neutron Laue technique which led to a full experiment on KOALA.
Higher dimension figure 2
Figure 2. Typical neutron Laue patterns from KOALA for n-alkane-urea at 170 K, 140 K, and 4 K. The red circle surrounds the most prominent Laue spots that signal the appearance of Phase V below 80 K.
Surveying n-nonadecane-urea with neutron Laue diffraction on KOALA from 300K to 4K revealed further detail of the superspace-driven phase, notably a significant increase in misorientation in the plane perpendicular to the composite misfit axis, as well as a first-order transition to a new phase at lower temperature (Figure 2). Complementary monochromatic X-ray examination, again using a high-resolution image-plate detector, reveals that this new phase corresponds to additional ordering of the guest alkane subsystem [1]. Unfortunately, there are only a few unique new reflections observed by neutrons or X-rays, and the data, even if combined, are presently insufficient to allow refinement of the structure in Phase V. In fact, because of twinning and guest-molecule disorder determination of the structure of n-nonadecane–urea remains a very difficult task in all phases.
Higher dimension figure 3
Figure 3. Pressure- temperature phase diagram of n-alkane-urea. The new phase detected in this work is Phase V which shows the hysteresis depicted in the inset. The data points are the integrated intensities of one of the new reflections that appear in Phase V (in red: cooling; in blue: heating).
The link to the International Year of Light is not just via a tenuous use of false colour to display these patterns. The raw data may be recorded as two-dimensional distributions of intensity, i.e. on a grey scale, on neutron-sensitive image plates, but there is spectral information there if we could just access it. In the Laue diffraction experiment, the single crystal is irradiated by a beam of neutrons with wavelengths from (in this case) 0.74 Ä to 5 Ä, and each reflection selects the wavelength that satisfies the Bragg diffraction condition. If we had a wavelength-sensitive area detector we would see the pattern as a kaleidoscope of spots which would not just be pleasing to the eye but would also remove the main uncertainty in Laue experiments, determination of the absolute atomic unit-cell volume (Figure 4). 
Higher dimension figure 4
Figure 4. The simulated 170K Laue pattern of Figure 2 with colour coding according to the neutron wavelength that excites of the lowest harmonic Bragg reflection contributing to each spot. 82% of the spots correspond to just one Bragg reflection and thence just one wavelength.
As a final aside, we often see the colour in the Laue experiment in everyday life in a quite unexpected way.  Who is not fascinated by the play of colour in opals, the namesake of our modern nuclear reactor at Lucas Heights?
It turns out that the change of colours that you see as you turn an opal is no less than the Laue diffraction of light from the voids in the small lattices of amorphous nanoscale SiO2 spheres that make up an opal. This was demonstrated by renowned CSIRO scientist, John Sanders, in 1968 in a simple yet landmark experiment [4] using a thin beam of white light and a glass sphere as detector that is so reminiscent of the first X-ray Laue experiment of 1912. A historic example that ties together the International Years of Crystallography and Light
  1. Neutron Laue and X-ray diffraction study of a new crystallographic superspace phase in n-nonadecane/urea, S. Zerdane, C. Mariette, G.J. McIntyre, M.-H. Lemée-Cailleau, P. Rabiller, L. Guérin, J.C. Ameline, and B. Toudic, Acta Cryst. B 71 (2015) 293-299
  2. Hidden degrees of freedom in aperiodic materials. B. Toudic, P. Garcia, C. Odin, P. Rabiller, C. Ecolivet, E. Collet, P. Bourges, G.J. McIntyre, M.D. Hollingsworth, T. Breczewski (2008). Science 319, 69-71.
  3. High-speed neutron Laue diffraction comes of age, G.J.  McIntyre, M.-H. Lemée-Cailleau, C. Wilkinson (2006). Physica B 385-386, 1055-1058. 
  4. Diffraction of light by opals, J.V. Sanders, Acta Cryst. A 24 (1968) 427-434