Date Published: March 01, 2019
Publisher: International Union of Crystallography
Author(s): Marc de Boissieu.
Ted Janssen’s contributions to the field of aperiodic crystals are reviewed.
Ted Janssen, 81 years old, passed away on 29 September 2017 of a rapid leukaemia (Souvignier, 2018 ▸). With him, crystallography lost the last of the founding fathers of n-dimensional crystallography (or superspace crystallography) after Pim de Wolff (Janssen & Tuinstra, 1998 ▸) and, most recently, Aloysio Janner (Janssen, 2016 ▸). This article reviews some of the major contributions Ted Janssen made to the field his scientific life was fully dedicated to: aperiodic crystals.
Soon after the discovery of X-ray diffraction by von Laue and its use for structure determination by the Braggs (son and father), detailed investigations of the observed diffraction photographs pointed to broad and diffuse spots or streaks, first observed by Friedrich et al. (1913 ▸), which could not be interpreted as regular Bragg peaks. Following an interpretation proposed by Faxen in 1923 ▸, these streaks and diffuse spots were shown to be the result of thermal vibrations and phonons by two independent studies (Laval, 1939 ▸; Preston, 1939 ▸); this is the well known thermal diffuse scattering. A detailed historical description of this discovery can be found in the article by Lonsdale (1942 ▸).
A very good account of the history and birth of superspace crystallography can be found in the review article by Janssen & Janner (2014 ▸). In the late 1960s and early 1970s, A. Janner and T. Janssen worked theoretically, in Nijmegen, on the problem of crystallographic groups in space and time and thus in 4D. At the same time, P. M. de Wolff, in Delft, studying the incommensurate phase Na2CO3, came to the idea of describing this phase in a 4D space. At the IUCr Congress held in 1972 in Kyoto they both presented their results and realized they were talking about the same theory. The superspace theory of aperiodic crystals was born with its two essential ‘ingredients’: (i) a description in a space with dimension larger than three, named superspace, where the structure is described as a decorated periodic structure; and (ii) the derivation of the symmetry of the aperiodic phase in the superspace and its superspace group leading to specific constraints for the modulation polarization, for instance, and to possible extinctions in the diffraction pattern (de Wolff, 1977 ▸; Janner & Janssen, 1977 ▸, 1980a ▸,b ▸; de Wolff et al., 1981 ▸). An illustration of the procedure and concept, with a simple example of the 1D displacive modulated chain and its representation in a 2D periodic space, is given in Fig. 3 ▸.
What is the influence of the long-range aperiodic order on physical properties? Are there new and characteristic signatures of the long-range aperiodic order on physical properties? In particular, what are the excitation spectrum and the dynamics of an aperiodic crystal? What are the driving forces stabilizing the aperiodic long-range order? Can aperiodic long-range order propagate with only finite-range forces?
The study of aperiodic crystals is expanding in many directions. Aperiodic crystals are found everywhere in almost all systems, and the superspace crystallography approach is the way to understand their atomic structure and their crystal chemistry. The boundaries sometimes made between the different classes of aperiodic crystals, namely incommensurately modulated structures, incommensurate composite crystals and quasicrystals, are rather artificial and the entire field should really be considered as a unique one, as was constantly promoted by Ted Janssen. Indeed, large-amplitude incommensurate modulations, multiple q modulations, anharmonic ones, incommensurate composites with large intermodulations and quasicrystals certainly share similar structure and raise similar questions and problems.