B. Wruck

Order-parameter saturation and low-temperature extension of Landau theory

The temperature evolution of the structural order parameter in displacive phase transitions with high transition temperatures (e.g. quartz, As2O5, LaAlO3, CaCO3, NaNO3, Pb3(PO4)2 etc.) follows a Landau-type behaviour over large temperature intevals. Below a saturation temperatureTs, however, the order parameter tends to become temperature independent. A quantitative analysis shows the correlationkBTs=ħΩ/4, where Ω is the frequency of the relevant local excitation atTs. A general Landau-type expression for the Gibbs energy is given which includes the effects of order-parameter saturation.

Phonon spectra of alkali feldspars; phase transitions and solid solutions

Abstract The phonon spectra of IR-active vibrations in alkali feldspars have been systematically investigated in the spectral range 50-2000 cm-1 at temperatures between 20 and 900 K. Samples with high degrees of Al-Si Order display IR absorption line profiles with spectral line widths that are systematically smaller than those for samples with low degrees of Al-Si order. Phonon frequencies depend in a nonlinear manner on the Na-K content, indicating nonideal mixing properties. The mode Grüneisen parameters are largest for low-frequency lattice modes and Si-O stretching modes; some negative Grüneisen parameters were found at phonon energies below 430 cm-1. The temperature evolution of the phonon spectra shows clear indications of the C2/m-C1̅ transition in Al-Si disordered Na-rich samples. An anomaly for highly Al-Si ordered microcline at 270 K is confirmed.

Phase transition(s) in titanite CaTiSiO5: An infrared spectroscopic, dielectric response and heat capacity study

The structural phase transition in titanite near 500 K (averaged symmetries A2/a→P21/a) and a second anomaly around 900 K have been studied using infrared spectroscopy on single crystals aqnd powder samples, measurements of the dielectric properties and the specific heat. The same synthetic single crystal was used in all experiments.The phase transition near 500 K is associated with a break in the temperature evolution of phonon frequencies and absorption intensities. Some phonon signals decrease rapidly under further heating and their extrapolated intensities disappear at ca. 850 K. The most dominant temperature effect relates to Ti-O phonons with amplitudes along the crystallographic a axis. These phonons show large LO-To splitting and continue to soften under heating even at temperatures above the transitions point (ca. 500 K).The softening of these modes correlates directly with the increase of the real part of the dielectric constant with a well-pronounced anomaly at 500 K. The dielectric losses also increse with increasing temperature. Measurements under strong field do not show antiferroelectricity. The transition at 500 K generates a small but sharp λ-anomaly in the excess specific heat. A second, weaker anomaly was found near 850 K. The results are discussed in terms of thermodynamic models.

On the thickness of ferroelastic twin walls in lead phosphate Pb3(PO4)2 an X-ray diffraction study

Abstract The effective thickness of ferroelastic twin-walls (W-walls) in Pb3(PO4)2 at room temperature ( 0.7 T c ) was determined by X-ray diffraction. The diffraction profiles were analysed using a wall profile e=eotanh x/w where W is the effective wall thickness including the effects of wall bending and surface relaxations. The experimental value W is around 10 unit cells which is larger than expected from standard renormalization arguments. The limitations of such experimental studies are discussed.

In situ observation of the polytypic phase transition 2H-12R in PbI2: investigations of the thermodynamic structural and dielectric properties

A reversible phase transition between the two polytypic phases 2H and 12R was found in PbI2 near 367K which proves that these polytypes are thermodynamic equilibrium phases and not the result of growth processes. Disordered stackings were observed in samples which were annealed at temperatures above 420K. The phase transition is kinetically hindered with an activation energy of 3.8 eV. The character of the phase transition is first order with a latent heat of around 276 J mol-1. The absence of dielectric anomalies with electric fields along the hexagonal c axis indicates that dipole-dipole interactions are not involved in the transition mechanism. The nature of the inter-layer forces are exclusively based on short-range interactions leading to a description of the phase transition in terms of pseudo-spin models. The elastic energy released during the phase transition is 1.2 J mol-1 as determined from the observed jump of the c lattice parameter. A thermodynamic description of the phase transition leads to the conclusion that its driving forces are related to the gain of phonon energy and elastic energy during the transformation. The entropy gain is due to the differences of the phonon frequencies between the two phases. Higher polytypes, if thermodynamically stable phases, can be described as mixtures of structural elements of the basic polytypes with additional stabilisation energies. The temperature evolution of the free energies of the different phases is anticipated. The experimental results are expressed in terms of the Landau theory which shows that the phase transition 2H-12H must be first order as observed. The Landau theory also explains the disordered polytype as a common para-phase for all ordered polytypes. Further insight into the origin of polytypism can be derived from the current understanding of ANNNI models.

Influence of lattice imperfections on the transition temperatures of structural phase transitions: The plateau effect

Abstract The influence of defects on the apparent phase transition temperature has been studied over a large range of defect concentrations. An interval was found for low concentrations (around 1 mol%) in which the transition temperature depends only weakly on the number of defects and where defect tails occur. This interval is called the plateau. For higher defect concentrations we find that chemical mixing leads to strong variations of the transition temperature which are well described in the approximation of a homogeneous crystal.

On the displacive character of the phase transition in quartz : a hard-mode spectroscopy study

The temperature evolution of the frequencies and absorption cross section of the infrared-active phonons near 795 cm-1 and 695 cm-1 and the Raman-active mode near 355 cm-1 follow that of the symmetry-breaking order parameter of the alpha - beta phase transition in quartz. The IR signal at 695 cm-1 and the Raman signal at 355 cm-1 are symmetry forbidden in the beta phase. The experimental results show that these signals do, indeed, disappear at T>Tc+10 K. No signal related to microdomains of the alpha phase was found at these temperatures. Transition models based on the beta phase being a time-averaged structure with local alpha states and lifetimes of clusters being much longer than phonon times are incompatible with these observations. The experimental results affirm the displaciveness of the phase transition although the existence of small amounts of alpha or INC phase in matrix of beta structure cannot be ruled out.

Kinetic rate laws derived from order parameter theory IV: Kinetics of Al,Si disordering in Na-feldspars

AbstractThe kinetic rate laws of Al-Si disordering under dry conditions (T = 1353K, 1253 K, 1223 K, 1183 K) and in the presence of water (p = 1 kbar, T = 1023 K, 1073 K, 1103 K) were studied both experimentally and theoretically. A gradual change of the degree of order was found under dry conditions. For intermediate degrees of order broad distributions of the order parameter Qod occur. The variations of Qod are correlated with structural modulations as observed in the transmission electron microscope. The time evolution of the mean value of Qod can be well described by the rate law:

Ferroelastic phase transition and renormalization effect in diluted lead phosphate, (Pb1-xSrx)3 (PO4)2 and (Pb1-xBax)3 (PO4)2

\frac{{dQ_{od} }}{{dt}} = - \frac{\gamma }{{RT}}\exp \sum\limits_{i = 1}^n {X_i^2 } \left[ {\frac{{ - (G_a^0 + \varepsilon (\Delta Q_{od} )^2 )}}{{RT}}} \right]\frac{{dG}}{{dQ_{od} }}