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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