I was particularly fortunate in that my research career developed entirely in terms of my private interests. I was able to chose my own M.Sc and Ph.D. topics of research, which were unsupervised. This meant that I was free to explore many interesting topics. This system led me to develop an interest in Mineral Physics and subsequently a serious interest in the theory of order-disorder phase transformations and related incommensurate behaviour. These topics are particularly well developed and studied in minerals of the feldspar group. Research on incommensurate phases has now taken me into group theoretical aspects of quantum theory. This important aspect of my career will be dealt with under the heading of recent research.
My research for M.Sc. and Ph.D. dealt with the intense thermal metamorphism of sedimentary rocks that were associated with a group of three basalt feeder pipes at Ballycraigy, north of Larne in Co. Antrim. I studied the contact with chalk and, having found an unexposed contact, I took a large number of specimens from a shallow trench approximately six feet long. My specimens contained a large number of extremely rare minerals including the cement phases larnite and bredigite and the complete assemblage formed the basis of my Ph.D. studies in Cambridge.
I was very fortunate In studying in the Mineralogy Department since it had excellent facilities for X-ray diffraction, and extremely competent workshop facilities. I taught myself crystallography and was able to establish the chemical composition, space group and cell dimensions of the very rare mineral scawtite from Ballycraigy. An important aspect of my studies was an investigation of the nature of the natural hydration products of the cement minerals larnite and bredigite in relation to the bonding medium in set cement. The crystal structure of the related mineral tobermorite was determined with funds from the Cement and Concrete Research Association which was extremely interested in my research.
My initial interest in incommensurate behaviour originally related to the fact that Dr’s Peter Gay and Mike Bown, both lecturers in Crystallography in the Mineralogy Department, were investigating incommensurate diffraction in the plagioclase feldspars and published their results in 1958. The phenomena were originally observed in routine structural studies on feldspars in the Cavendish.
This incommensurate behaviour occurred in the middle of the continuous triclinic solid solution series between the plagioclase minerals albite, NaAlSi3O8, and anorthite CaAl2Si2O8 that differ in their Al/S ratio. The additional diffracted k waves comprised pairs of satellite reflections convoluted with absent superlattice reflections, relating to ordering in the end member anorthite, and described as the e reflections. A second set of paired satellite k waves were convoluted with the normal diffraction maxima, and described as the f reflections. Ordering in this binary system involved the relocation of Al atoms in a common, three dimensional, (Al,Si)O4 tetrahedral framework structure.
At this point we may define an important condition. Each dynamic k vector necessarily relates to two functions which may be expressed as cosine and sine terms. Since these functions are linear in x it is possible to define a gradient invariant determinant as a symmetry operation. This is only possible where the relevant functions are linear. Further, this symmetry condition must necessarily apply to the entire set of k vectors in the corresponding symmetry group that describes the order-disorder transition. This condition provides a basis for a quantum model for the order-disorder transition.
Here there should be a link to electron optical photographs of both the incommensurate e and f modulations and captions.
The suites of additional e and f reflections combine to define a periodic structure with a wavelength of the order of 5nm which changes continuously with composition and hence is necessarily incommensurate with the basic reciprocal lattice repeats. At this stage I taught myself to use the electron microscope and, in a Nature Letter, in 1963 119 , 586, using electron optics, I resolved the incommensurate structure in a plagioclase feldspar for the first time. I identified it as an ordered anti-phase domain system related to the ordering in the anorthite end member, in analogy with similar behaviour, observed by Glossop and Pashley in metal alloys.
The general study of transformations in minerals also involved my building a hydrothermal laboratory in which mineral processes could be studied in the temperature range up to 1000o C and pressures, in the presence of water vapour, of several kilobars. Thus it was possible to combine hydrothermal experiments with both X-ray diffraction and electron optics to provide a time-temperature-transformation analysis of mineral transformations.
In the early 1970s many scientists were interested in applying these techniques to solving problems in the extremely important plagioclase feldspar group. In a NATO feldspar conference in 1971 I provided a time-temperature-transformation account of the incommensurate and the related transformation behaviour throughout the plagioclase series of minerals This material was published in the NATO Conference proceedings in 1974. These proceedings may not readily be available, but my data were cited in detail in a major publication by J.V. Smith, The Feldspar Minerals, Volume 1 Springer-Verlag, Berlin Heidelberg New York 1974, on all aspects of the complete feldspar group of minerals.
In the early 1970’s it was evident that a proper theory of the origin of incommensurate structures did not exist in the field of condensed matter or elsewhere. In response to this situation I began to think about a possible theoretical approach to the problem and decided to invest time in studying group theory as applied to condensed matter problems. First and foremost I studied Landau’s approach to second order transitions in terms of the existence of special points at the origin, or on the surface of the Brillouin zone. I was also aware of Lifshitz’s description, in Soviet J. Phys. 6, 61-73 251-263, of an order-disorder gradient invariant associated with Landau’s second order theory, which implied that a second order transition might not necessarily exist. This gradient invariant, α dβ/dx-βdα/dx, where α and β were order parameters for two different ordering modes, provided me with a model for incommensurate behaviour in which I proposed that the component interacting modes could be described in terms of cosine and sine functions. The important concept of gradient invariants was later discussed at length in a paper on incommensurate structures which was published in Phil. Trans. R . Lond. A (1991) 114, 425- 437.
Using group theory, I found it possible to establish practical solutions to the structure of many incommensurate structures. An excellent example of the use of space group theory to establish component phases is provided by my study, published in Z. Kristallogr. 214 (1999) 457-464, of the incommensurate structure of äkermanite, a mineral in the melilite group. This phase with formula Ca2MgSi2O7 , and space group P͞͞͞ ͞421m, had a small amount of Fe2+ replacing Mg in the single tetrahedral site for Mg. The incommensurate structure was characterized by the presence of an associated double Mossbauer signal and the presence of k vectors in positions ±0.29(a*-b*) and ±0.29(a*+b*) in reciprocal space. A group theoretical analysis established that the component structures responsible for the Mossbauer signal had space groups P ͞4 and P21212, associated with rotation, and diode distortion of the Mg tetrahedron. It is relevant to note, for future reference, that these two product space groups are related as gradients.