Désordre linéaire dans les cristaux (cas du silicium, du quartz, et des pérovskites ferroélectriques)

Abstract

Many crystals produce a diffuse scattering of X-rays which is localized in a series of relplanes. It is shown that the corresponding linear disorder in the crystal may have various origins. In silicon, the scattering is due to thermal vibrations and is well explained by the elastic properties of the crystal. In neutron irradiated quartz the radiation damage is responsible for the major part of the scattering. The case of BaTiO3 and KNbO3 is discussed in detail. A linear disorder is proposed which accounts better for the different distributions of the scattering in the 4 allotropic phases than the alternative explanation of the soft mode. In spite of some neutron inelastic scattering results it is not yet possible to distinguish between static and dynamic disorder.

Macroscopic response and directional disorder dynamics in chemically substituted ferroelectrics

“…We focus on the correlation between the degrees of order (disorder) and four long-range symmetry phases in the temperature range 25-320 K. The anisotropic features are specifically investigated by considering the structural phases along the three main crystalline directions. Remarkably, the distribution of the macroscopic order/disorder state is found to be in agreement with the microscopic so-called eight-sites model developed by Comès et al [19,20]. This model was introduced to account for diffused photon scattering in xray studies of BaTiO 3 and KNbO 3 and implies that some perovskites never actually form high-temperature crystalline phases, have order/disorder transitions, and have a built-in capability of hosting disorder.…”

“…Local symmetries and order transitions of the crystal cell have been studied with x-ray diffuse scattering measurements on prototypical perovskite crystals BaTiO 3 and KNbO 3 by Comès et al [19,20]. These authors showed that in these compounds an intrinsic disorder is a consequence of the dynamic displacement of the B cation on eight energetically equivalent sites along the diagonals of the cubic cell, whose allowed directions of the displacements are dependent on the given crystalline phase (see the scheme in Fig.…”

“…Altogether these phenomena are able to cause a local symmetry breaking in what would be normally considered a high-symmetry paraelectric phase, a breaking that generates a wide landscape of PNR-driven properties whose nature and temperature dependence is still under study. The local ordering and crystalline symmetry of PNRs have been extensively investigated using various techniques, the principal being diffractometric [20,[27][28][29][30][31][32][33][34][35]. Results indicate that the behavior and response of PNR-hosting samples is strongly affected by disorder [5,13,21,36,37].…”

“…How exactly a crystal is able to host a dynamic population of dipoles is still an open question, and its understanding evidently lies at the heart of future applications [5,11,12]. In fact, it is well known that in a perovskite structure the ion disposition in the ABO 3 lattice may be distorted, causing local inherent or internal dipolar disorder [19,20]. When a substitutional disorder is simultaneously present, below the so-called Burns temperature T B , its combination with this internal disorder can give rise to lattice distortions, strains, and local electric fields [21], which then lead to PNRs [3,5,[22][23][24].…”

Doping and temperature-dependent optical properties of oxygen-reducedBaTiO3−δ

“…12 Another channel of electron scattering in BaTiO 3 that, until now, has been completely ignored is related to the positional disorder of Ti ions. Comes et al 13 proposed an order-disorder model of the phase transitions in BaTiO 3 based on the 8-fold off-center positional degeneracy of Ti ions (Figure 1 teristic Debye frequency of the central (relaxation) mode associated with the off-center Ti dynamics is of the order of 100 cm −1 which is comparable with the eigenfrequency of the low-energy (soft) phonons. 14 In view of extremely large amplitude of Ti off-center displacements (e.g., 0.19Å) one may expect strong dynamic perturbation of the conduction band width at the onset of the Ti disorder.…”