Polarized Raman, IR and time-domain THz spectroscopy of orthorhombic lead zirconate single crystals yielded a comprehensive picture of temperature-dependent quasiharmonic frequencies of its low-frequency phonon modes. It is argued that these modes primarily involve vibration of Pb and/or oxygen octahedra librations and their relation to particular phonon modes of the parent cubic phase is proposed. Counts of the observed IR and Raman active modes belonging to distinct irreducible representations agree quite well with group-theory predictions. The most remarkable finding is the considerably enhanced frequency renormalization of the y-polarized polar modes, resulting in a pronounced low temperature dielectric anisotropy. Results are discussed in terms of contemporary phenomenological theory of antiferroelectricity.PACS numbers: 77.80.Bh, 77.84.Cg Although the ferroelectric and antiferroelectric materials have a lot in common, the latter have been much less investigated. An obvious reason is the absence of the direct linear coupling of the antiferroelectric (AF) order parameter to the macroscopic electric field.At the same time, a nonlinear coupling to the macroscopic electric field is still present. Therefore, AF materials actually do provide interesting functionalities, as well. In fact, the AF oxides are promising materials for high-energy storage capacitors, high-strain actuators and perhaps even for electrocaloric refrigerators [1][2][3]. The interest in the improvement of our understanding of AF oxides has been expressed recently [1,2,4,5].Lead zirconate, PbZrO 3 , is the best known example of an AF oxide -it is an end-member of technologically relevant solid solutions with PbTiO 3 (piezoelectric PZTs) [1,2,4,[6][7][8]. The parent paraelectric phase is a simple cubic perovskite with a 5-atom unit cell (P m3m, Z=1). Below the AF phase transition (T C ∼ 500 K), it goes over into an orthorhombic P bam (Z=8) structure [10,11]. The space-group symmetry change can be well understood[1] as a result of the condensation of two order parameters [1,4,9,12]. One of them is a polarization wave of a propagation vector Q Σ = (0.25, 0.25, 0) pc , the other order parameter is a Q R = (0.5, 0.5, 0.5) pc oxygen octahedra tilt mode (here pc stands for pseudocubic lattice, see Figs. 1-2).Superpositions of Q Σ , Q R include also Γ, X, M and Q S = (0.25, 0.25, 0.5) pc cubic-phase Brillouin zone points. All of these points become Brillouin zone centers in the P bam phase (see Fig. 2). Nevertheless, recent inelastic X-ray scattering experiments [4] have clearly demonstrated that the critical scattering occurs only in the vicinity of the Γ-point. Based on this experimental result, it was proposed that the AF phase transition is driven by a single mode, the Γ-point ferroelectric soft mode [4]. Within this model, the condensation of the Q Σ -point mode can be ascribed to the flexoelectric coupling with the ferroelectric mode, and the condensation of the Q R -point mode can be explained as due to a biquadratic coupling with the Q Σ m...

The Aurivillius compound Bi 4 Ti 3 O 12 exhibits a single phase transition from a tetragonal high-temperature phase to a ferroelectric state. By means of first-principles calculations guided by a complete symmetry analysis of the experimental distortion, we confirm B1a1 as the ͑monoclinic͒ symmetry of the room-temperature phase but show that the transition involves a complex interplay of six different normal modes belonging to four different irreducible representations. Three of them are necessary for the observed symmetry break. We do not find any feature in the energy landscape that would force the simultaneous condensation of these three order parameters and cause such an avalanche transition, so we suggest that further experimental work might be able to detect intermediate phases. On the other hand, the necessary condensation of pairs of normal modes of the same symmetry already puts Bi 4 Ti 3 O 12 outside the standard soft-mode paradigm and has important structural implications. In particular, the approximate rigidity of the BiO 6 octahedra is due to anharmonic couplings of these modes. In addition, a comparison of the energy calculations and the behavior of the bond-valence global instability index is presented.

The range of validity of Landau freeenergy potentials with the usual approximation of constam coefficients for terms higher than quadratic has recently been questioned (L Phys.: Condenr. Marter 1 (1989) 8327). The frequent observation in real systems, within large temperature intervals, clearly outside any possible critical region, of power laws of the type IC -TI" for the order parameter has also been pointed out as an indication that certain simple general features in phase transitions, not related at all ta critical phenomena, are beyond the usual approximations included in L Landau free-energy expansion. In particular, the value of the exponent h has been proposed to be related to the displacive and order-disorder degree of the system. In order to elucidate these questions, the temperature dependence of the Landau free energy corresponding to the three-dimensional O4 model has been investigated using a straightforward Monte Carlo method. Different model parameteis have been considered, ranging from typical displacive panmeters to those approaching a pure order-disorder system. Following its formal definition, the Landau free energy at each temperature has been directly derived from the order panmeter distribution in a Metropolis statistical sample. En ContriLCt with other numerical methods used in previous literature, no approximation is introduced in the calculation, except inherent to the numetical method employed. It is shown that the temperature dependence of the L m d u potential coefficients follows smooth simple laws that are outside the usual assumptions in Landau theory and can be related to the order-disorder degree of the system. The quadratic coefficient in the Landau potential exhibits a linea tempelatUE dependence in large temperature intervals but shows a marked change in slope about the transition temperature.The quatic coefficient is shown to depend on tempentlrre as strongly as the quadratic coefficient having a minimum around the transition point. The strong temperature dependence of this quartic coefficieht is responsible for the 'non-classical' behaviour of the order panmeter, which wn be described by a power law.

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AbslneL Inelastic neutron scattering experimenls in KzSeO,, CySeO, and KzCIQ are reported. ?be lowest CI-& phonon branches along the a*-axis in their plmm phase have teen characterized for the three mmpounds. lle mulls are mmpared with recent lattice dynamical simulations using rigid-ion models. Potassium chroma=, that simulations suggested to be incommensurate at low temperatures, evidences no s t ~~l ~r a l phase transition down to 12 K, but ik lowest Cz phonon branch exhibits a significative softening and decreases more than XI% as the temperature is lowered from MO K to 36 K . ? r e snflening mechanism m this "pound and in polassium selenate is related to an increase of the effective interaction between an amustic and an o p t i d branch.

New superspace models with different modulation amplitudes indicate that any degree of ordering, from disordered to ordered, can be observed in mullite.

Numerous materials with the general formula A2BX4, where A and B are cations and X is the anion, are isomorphous to Il-K2SO4 (space group Pnam) at high temperatures. A considerable number of them exhibit a structural instability leading to an incommensurately modulated phase with identical superspace symmetry. K&Se04 is the archetypical example. From the analysis of the incommensurate structures, the polarization vector of the unstable frozen mode can be determined, being similar in all investigated compounds. We report here a comparative energetic study and lattice-dynamics analysis of a set of compounds in this family. The set of materials K2SO4, R12Se04, Cs2Se04, Cs2ZnC14, Cs2ZnBr4, K2Cr04, K2Se04, K~ZnC14, Rb&ZnC14, and Rb~ZnBr4, includes compounds with and without an incommensurate phase. An empirical rigid-ion force model has been used with only three adjustable parameters, the tetrahedral BX4 groups being reduced to rigid bodies. The adjusted force model, optimized for each compound with use of only static structural data, is sufficient to explain the eventual presence of an incommensurate lattice instability at lower temperatures. The calculated phonon dispersion curves of those compounds with an incommensurate phase include an unstable X2 phonon branch with a minimum close to -, ' a*. In the simulations, the unstable or soft-mode branch is always an optical branch in the extended zone scheme or the consequence of an anticrossing of an optical branch with the X3 X2 acoustic branch; this result discredits any attempt to explain the soft-mode mechanism in terms of a one-dimensional model with an acoustic soft branch. The polarization vectors of the soft or unstable modes obtained in the simulations fairly agree with the experimental ones. They are rather insensitive to the details of the interactions, explaining their strong similarities. On the other hand, the form of the soft branch depends strongly on the material, and clearly distinguishes those materials having the BX4 groups disordered in the normal phase, from those having a soft-mode mechanism. The simulations indicate that the static and dynamic features of potassium chromate are similar to those of potassium selenate, raising the possibility that potassium chromate could exhibit a similar mode softening at low temperatures. The existence of an incommensurate lattice instability in these compounds depends basically on the effective volume of the A cations compared with the size of the BX4 tetrahedra. The charge distribution within the tetrahedral anion groups also plays a significant secondary role; smaller values of the charge of B tend to stabilize the Pnam structure. The static energy of some of the compounds has been investigated in a restricted configuration subspace, which includes the order-parameter distortion. The energy maps obtained show a clear "multiple-well" structure, that can be quantitatively related with the transition temperatures by means of a local-mode model.