T. Janssen

Soft modes and phonon interactions in studied by means of neutron scattering

This paper presents an inelastic neutron scattering study of the proper ferroelectric and elastic neutron scattering results on the satellite diffraction pattern which characterizes the modulated phase. The temperature dependences of the satellite intensities and modulation wavevector are in fair agreement with results from previous x-ray experiments. Close to the incommensurate-to-ferroelectric transition temperature , an unexpected intensity overshoot is observed, similar to that seen in birefringence and dilatation experiments. The relationship between the lattice dynamics and the observed phase transition sequence is examined. The dispersion of the ferroelectric soft optic phonon (-polarization) and of the acoustic phonons is followed along the and -directions. In the ferroelectric phase, the TO mode shows a considerable softening as the incommensurate phase is approached from below. In the paraelectric and incommensurate phases, the response from the TO (-polarization) and TA ( strain) branches has been investigated via a series of constant-q scans in the -direction (approximately the modulation wavevector direction). The combined inelastic line-shapes, as observed in a number of non-equivalent Brillouin zones, could all be analysed in terms of a coupled-mode damped harmonic oscillator model. In addition, a diverging, resolution-limited, central peak is observed close to . It is suggested that the TO-TA coupling lies at the origin of the incommensurate instability. A phenomenological free energy is developed, in the continuum approximation, in which the TO-TA interaction is included via a pseudo-Lifshitz term of the type .

Report of a Subcommittee on the Nomenclature of n-Dimensional Crystallography. I. Symbols for point-group transformations, families, systems and geometric crystal classes

The notation of crystallography in arbitrary dimensions is considered. Recommended symbols for point-group transformations, geometric crystal classes, families and systems are presented.

Report of a Subcommittee on the Nomenclature of n-Dimensional Crystallography. II. Symbols for arithmetic crystal classes, Bravais classes and space groups

The Second Report of the Subcommittee on the Nomenclature of n-Dimensional Crystallography recommends specific symbols for R-irreducible groups in 4 and higher dimensions (nD), for centrings, for Bravais classes, for arithmetic crystal classes and for space groups (space-group types). The relation with higher-dimensional crystallographic groups used for the description of aperiodic crystals is briefly discussed. The Introduction discusses the general definitions used in the Report.

Phonons and internal friction in incommensurate composites

The non-linear dynamics involved in sliding modes in an incommensurate composite is studied in the double chain model. The coupling between the chains leads to phonons in which the two chains participate in various ways. For displacements beyond the harmonic approximation it is shown that, for a coupling small enough to leave the modulation functions continuous, there is a dynamic transition from a practically frictionless regime to a regime with strong dissipation. In the cross-over region resonances lead to an oscillatory motion of the subsystems with respect to each other. In the regime of discontinuous modulation functions there is strong dissipation and a transition from a pinned to an unpinned state. The unpinned motion is a non-linear wave in superspace.

Nonlinear dynamics of dimers on periodic substrates

Abstract:We study the dynamics of a dimer moving on a periodic one-dimensional substrate as a function of the initial kinetic energy at zero temperature. The aim is to describe, in a simplified picture, the microscopic dynamics of diatomic molecules on periodic surfaces, which is of importance for thin film formation and crystal growth. We find a complex behaviour, characterized by a variety of dynamical regimes, namely oscillatory, “quasi-diffusive” (chaotic) and drift motion. Parametrically resonant excitations of internal vibrations can be induced both by oscillatory and drift motion of the centre of mass. For weakly bound dimers a chaotic regime is found for a whole range of velocities between two non-chaotic phases at low and high kinetic energy. The chaotic features have been monitored by studying the Lyapunov exponents and the power spectra. Moreover, for a short-range interaction, the dimer can dissociate due to the parametric excitation of the internal motion.

Fifty years of aperiodic crystals

Historians often have debates about the beginning and end of a certain era. The same discussion can be had about the history of aperiodic crystals. There are reasons to claim that in 2012 one may celebrate the 50th anniversary of this field. A short description is given of the development of this branch of crystallography. It is argued that the most important point in its history is the discovery of quasicrystals, which has been recognized by awarding the Nobel Prize in Chemistry 2011 to Dan Shechtman.

Order-disorder versus soft mode behaviour of the ferroelectric phase transition in

This paper explains the coexistence of the displacive and the order-disorder features of the ferroelectric phase transition in crystals. Both have been observed in experiments. The height of the potential barrier hindering the order parameter fluctuations, estimated from experimental data, shows that the phase transition in is actually very close to the theoretical case of the order-disorder versus displacive crossover. Moreover, previously performed model calculations can be used for the analysis of the temperature dependence of dielectric susceptibility and other physical properties which do not obey the predictions of standard Landau theory.

Models for incommensurate phases in crystals withPcmn symmetry

A discussion is given of the relation between different models for systems with incommensurate phases. Moreover, a generalisation of such models is introduced, which shows an alternative explanation for similar phase diagrams. To get this one may vary the range of the interactions and the numbers of degrees of freedom per site.Another generalization involves coupling to elastic degrees of freedom. Such a coupling may change the type of the incommensurate phase transition.

Theory of Phasons in Aperiodic Crystals

The possibility of embedding a quasi-periodic structure into a higher-dimensional superspace gives rise to an interpretation of certain dynamical excitations as motions in the additional space. These excitations then are called phason excitations. There is always infinite degeneracy of the ground state of an aperiodic quasi-periodic system, but this degeneracy leads only to zero frequency modes if the atomic surfaces are smooth. If this is not the case, there is a phason gap. When the atomic surfaces are continuous, the linear phason excitations with low frequency may get an arbitrary amplitude. The excitations are almost frictionless when the velocity is below a threshold value. Above that value there is dissipation (i.e. energy transfer to phonons) even for smooth atomic surfaces.

Dynamics of modulated and composite aperiodic crystals: the signature of the inner polarization in the neutron coherent inelastic scattering

Abstract:We compare within an unifying formalism the dynamical properties of modulated and composite aperiodic (incommensurate) crystals. We discuss the concept of inner polarization and we define an inner polarization parameter β that distinguishes between different acoustic modes of aperiodic crystals. Although this concept has its limitations, we show that it can be used to extract valuable information from neutron coherent inelastic scattering experiments. Within certain conditions, the ratio between the dynamic and the static structure factors at various Bragg peaks depends only on β. We show how the knowledge of β for modes of an unknown structure can be used to decide whether the structure is composite or modulated. The same information can be used to predict scattered intensity within unexplored regions of the reciprocal space, being thus a guide for experiments.