Volume 220, Issue 8 - Phase Transitions

The adsorption systems Pb/Ge(111) and Sn/Ge(111) exhibit temperature induced structural phase transitions. We report here a phenomenological analysis of these phase transitions starting from Landau theory. On the basis of symmetry arguments, we show that essential differences are expected theoretically for the critical behav ior of the two interfaces. The influence of hopping defects in these systems is treated using a Landau-like approach. This approach gives us a consistent and general manner to interpret the existing experimental data for these interfaces.

The basic concepts of the phenomenological approach to reconstructive transitions are illustrated by a working example, and their specific properties are outlined. A theoretical approach to morphotropic transformations, which are transitions between phases with different stoichiometries, is introduced through the description of the vanadium-oxide system.

A surface relaxation is a topology preserving distortion of a crystal surface. Investigations of simple models with harmonic interactions between planes of atoms, and simulations of the surface structure of crystals show that the distortion of the crystal structure at the surface is not restricted to the layers immediately adjacent to the surface, but instead the magnitude of the distortion decays exponentially with distance from the surface. Thus relaxations can mediate short range interactions between surfaces, destabilising symmetrical growth morphologies in favour of platelet morphologies. The relaxations that occur when a twin wall intersects a surface are also of interest since twin walls are sites of fast diffusion, high reactivity and novel properties. The surface structure of twin walls are affected by surface relaxations of the order parameter and by the coupling of secondary strains to the order parameter.

Structural pseudosymmetry is a fundamental property to be considered when trying to predict structural phase transitions at high temperatures. In the present work, two methods for detecting and characterizing pseudosymmetry, the here-called atomic displacements and electron density methods are briefly introduced, analyzed and compared. Conceptually both approaches are similar: the pseudosymmetry check is carried out with respect to a supergroup of the crystal space group. However, due to the different way of estimating the deviations between the initial and the possible high-symmetry structure, the two approaches study distinct and, to a certain extent, complementary aspects of the pseudosymmetry problem. This conclusion is also confirmed by the lack of functional relationship between the corresponding quantitative parameters used to estimate the structural pseudosymmetry. Several examples illustrate the main features of the two methods. The temperature dependences of the two parameters and their empirical relations with the transition temperature in ferroelectric transitions are discussed. Algorithmic procedures based on the two approaches have been implemented in two computer programs. They form part of the Bilbao Crystallographic Server as free web tools.

Quantum mechanical calculations based on density functional theory and a generalized gradient approx imation have been used to study the pressure-induced B1 to B2 structural phase transition in YbN, YbP and YbAs. The phase transitions are predicted to occur at 137 GPa in YbN, at 25 GPa in YbP, and at 20 GPa in YbAs. These values are significantly lower than those predicted by empirical poten tial model calculations. Bulk moduli are predicted to be 136, 70 and 63 GPa for YbN, YbP and YbAs, respectively.

Results of X-ray scattering intensities and peak profiles of lawsonite single crystals are presented in a wide temperature range including the antiferrodistortive phase transition Cmcm – ( T c ∼ 270 K) → Pmcn . In the integrated intensities of the superlattice reflections above T c pronounced pretransitional tails similar to those detected recently in birefringence [P. Sondergeld et al., Phys. Rev. B 62 , 6143 (2000)] and in excess entropy data [S. A. Hayward et al., Eur. J. Min. 14 , 1145 (2002)] are observed. These tails correspond to diffuse Lorentzian shaped scattering peaks. The temperature variation of the diffuse scattering intensity and profile can be well described within a Landau-Ginzburg model. In combination with entropy data we obtain a complete set of free energy parameters. Using these coefficients we are able to fit the spontaneous part and the precursor tails of the integrated intensities, the excess birefringence and entropy in a broad temperature range outside a temperature interval of about ±3 K around T c . In the vicinity of T c the experimental data are in excellent agreement with the predictions of a crossover model, the effective critical exponent α eff ( τ ) varying from the classical ( α eff = 0.5) to the 3d Ising limit ( α eff = 0.11). Lawsonite therefore represents an ideal system to study the crossover from classical to critical behavior.

CaZrOGeO 4 has been synthesized and its structure has been refined from X-ray powder diffraction data as triclinic, A 1̅ ( P 1̅). A displacive structural phase transition to a monoclinic structure of the titanite aristotype with space group symmetry A 2/ a ( C 2/ c ) is observed near 488 K. The non-symmetry breaking spontaneous strain below the phase transition corresponds to a contraction of the structure normal to the octahedral chain direction. The coordination of Ca changes from 7-fold in the high temperature phase to 8-fold in the triclinic low temperature phase. A limiting monoclinic-angle is postulated below which compounds of the titanite topology and general stoichiometry CaMOXO 4 distort to triclinic symmetry.

The crystal structure of sodium bismuth titanate, Na 0.5 Bi 0.5 TiO 3 , as a function of pressure is reported. From a combination of neutron powder diffraction experiments using the instrument POLARIS at the ISIS pulsed neutron facility and synchrotron X-ray powder diffraction experiments at ID30 at ESRF, it is found that the rhombohedral ambient pressure perovskite structure (space group R 3 c on average) transforms to a lower-symmetry structure which has a strong resemblance to the CaTiO 3 structure and is described by space group Pnma , at 40 kbar and above. A new refinement of earlier angle-dispersive neutron data collected at ambient pressure and temperature at D2B of the ILL, which gives Bi—O bond-lengths closer to the values suggested by subsequent EXAFS experiments, is also reported. This yields a model for disorder on the bismuth site within the ambient-pressure phase, average symmetry R 3 c , with locally triclinic displacements of the Bi atom off the (pseudocubic) [111] direction along the (pseudocubic) [10-1] direction.

Powder patterns of samples resulting from ferroelastic phase transitions generally show typical line profiles: asymmetry into the direction of the position of the corresponding hypothetical high symmetry reflection and strongly anisotropic line broadening. An approximate model is presented that describes the characteristic distribution of individual line widths based on the variation of lattice spacings within the domain walls. The variation with temperature is governed by the competition of decreasing spontaneous strain and increasing wall widths and/or wall densities. It is argued that conventional Rietveld refinements can easily lead to erroneous results and a simplified method is proposed to approximate the actual line profiles via the introduction of a second phase with anisotropic strain broadening to take into account the scattering fom the domain walls.

The sequence of ferroelectric phase transitions ( Pm 3̅ m — P 4 mm — Amm 2) in BaTiO 3 has been studied as a function of temperature (298 K–130 K) at a fixed pressure (3.2 GPa). The same sequence of transitions is observed as for ambient pressures, but the transition temperatures are reduced. The spontaneous strains of the non-cubic phases are determined. Whilst the structure of the tetragonal phase at high pressure is qualitatively similar to the ambient structure, both the spontaneous strain and the Ti displacement are smaller in the high pressure structure than the ambient structure.

Structural transformations that take place on cooling down in Pb-based relaxor ferroelectrics are investigated on the basis of polarized Raman spectroscopy and far infrared ellipsometry applied on single-crystal samples of PbSc 0.5 Ta 0.5 O 3 (PST) and PbSc 0.5 Nb 0.5 O 3 (PSN). The temperature evolution of phonon anomalies reveals different preferred ferroic species in PST and PSN. Near the dielectric constant maximum cooperative shifts of Pb atoms in respect to the oxygen sheets perpendicular to the cubic body diagonal occur in larger spatial regions for PST than for PSN. On cooling down this structural modification becomes preferential for PST, thus giving rise to highly anisotropic ferroelectric domains. In PSN the temperature decrease favours B -cation deviations from the B O 6 -octahedral centres, which leads to formation of small-sized polar clusters distributed in the isotropic matrix. Near 180 K PST undergoes an additional phase transition that involves reduction of the rotation symmetry. The nanoscale phase transformations in PST are affected by the presence of point defects rather than by the degree of long-range B -site ordering. The spectroscopic data give some evidence that in PSN additional multiplication of the unit cell takes place, besides the common perovskite-structure doubling Pm 3̅ m – Fm 3̅ m .

Nanoscale structural features of amorphous zircon and pyrochlore produced by self-irradiation induced amorphization have been characterized by small-angle X-ray scattering (SAXS). Electron density fluctuations were observed in the untreated samples and studied as a function of annealing temperature (up to 1300 °C). In untreated zircon, density fluctuations were found to have a characteristic length-scale of approximately 1 nanometer diameter. A clear scattering maximum develops at ∼3 nm –1 as a function of the degree of damage, but only for amorphous fractions higher than 70%. For the untreated pyrochlore sample such a strong signal was not observed in the scattering function. As annealing temperature increases, phase segregation is observed in zircon with a clear nucleation at 850 °C of zirconia grains. The SAXS contribution, however, points towards a lower nucleation temperature, ca. 700 °C. In the pyrochlore structure, at temperatures as low as 300 °C the appearance of a first crystalline phase, Ca 2 Nb 2 O 7 , is observed, with the subsequent crystallization of TiO 2 at 800 °C. Observed electron density variations are compared between the two structures and discussed in terms of nanoscale phase segregation phenomena.