Antiferrodistortive Phase Transition Research Articles

Multicritical points in structural phase transitions

Abstract Recent theoretical (renormalization group) results on phase diagrams and multicritical points in systems undergoing structural phase transitions are reviewed. Particular attention is given to (a) the effects of anisotropic stress on cubic systems, e.g. perovskites undergoing antiferrodistortive phase transitions (bicritical, tricritical, Potts model, Lifshitz points, etc.), (b) phase diagrams of alloys, (c) the effects of electric fields on anisotropic antiferroelectrics.

Raman scattering investigation and symmetry analysis of ferroelectric/ferroelastic Sb5O7I polytype 2MA

The polytype 2MA (β-Sb5O7I) has the simplest acentric structure of the antimony oxideiodide family. It undergoes an antiferrodistortive phase transition at 438K and is both ferroelectric and ferroelastic below that temperature. The complete polarized Raman spectra in the ferroic phase have been measured and compared with those of the ferroelastic, centric polytype 2MC (α-Sb5O7I). Several lines could be attributed to Sb—0 and Sb—I vibrations. A factor group analysis has been performed and compatibility relations have been established connecting phonon species in the low and high temperature phase. As a function of temperature the spectra revealed a strongly temperature dependent central line and several phonon lines whose intensities vanish aboveT c . Using these phonon line intensities the temperature variation of the order parameter could be determined. The experimental results indicate that the phase transition is of first order.

Lifshitz-Point Critical and Tricritical Behavior in Anisotropically Stressed Perovskites

The antiferrodistortive phase transitions of some perovskite crystals, driven first order by strongly cubic order-parameter fluctuations, are shown to become continuous at finite anisotropic stresses favoring ordering of one order-parameter component. The associated critical and tricritical behavior will be that of one of a spectrum of uniaxial Lifshitz systems, its precise character reflecting the form of the anisotropy in the soft-mode dispersion. Our predictions are in substantial accord with recent experiments on RbCa${\mathrm{F}}_{3}$.

1H chemical shift tensor in squaric acid: C 4O 4H 2

The proton chemical shift tensor in squaric acid, which undergoes an antiferrodistortive phase transition at T c = 97°C, has been determined by means of a multiple-pulse NMR experiment. No change of the shift tensor is observed, when going through the phase transition, indicating a purely order—disorder type transition. The principal values of the shift tensor are: — 26.5, —20.2 and 1.0 ppm with respect ti TMS.

On the coupling between order parameter and temperature fluctuations in structural phase transitions

Starting from a model Hamiltonian for ferro- or antiferrodistortive structural phase transitions, a microscopic theory above Tc is derived for the retarded two point order parameter Green function occurring in the van Hove scattering function. Couplings between order parameter and temperature fluctuations are found and therefore a central mode near the Lambda -point of the Brillouin zone in addition to the soft optical mode doublet. The critical dynamic is discussed in the ferrodistortive case.

New excitations in systems undergoing displacive antiferrodistortive structural phase transitions?

A two-dimensional model system exhibiting antiferrodistortive structural phase transitions is considered. It covers the displacive and order-disorder regime. Using a molecular-dynamics technique, various spectral densities were calculated and new excitation branches were found close to the transition temperature and close to the displacive limit. These new branches appear in addition to the expected phonon resonances. One branch is traced back to the cluster dynamics and the other one to a two-phonon process. At the appropriate wavevectors they collapse into a central peak.

Model for tricritical points in distortive structural phase transitions

We show rigorously ($T=0$) that tricritical points in systems exhibiting ferro- or antiferrodistortive structural phase transitions are included in a two-dimensional model system covering the order-disorder and displacive regimes. For $Tg0$, our analysis is based on the mean-field approximation. Antiferroelectric systems turn out to be favorable candidates for investigation of the occurrence of tricritical points among real systems undergoing distortive structural phase transitions.

Properties of the one-particle-displacement probability distribution in systems undergoing antiferrodistortive structural phase transitions

Using the Hartree approximation, a high-temperature expansion, and the molecular-dynamics technique, we study some properties of the one-particle probability distribution ${F}_{1}({U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}})$ of the displacement ${U}_{x}$ of particle one in a model system. The system is two dimensional and subjected to constraints in such a way that it exhibits antiferrodistortive structural phase transitions. It covers the displacive and order-disorder regime, including the Ising and displacive limit. We present evidence that ${F}_{1}({U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}})$ or its symmetrized analog ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}_{1}({U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}})=\frac{1}{2}[{F}_{1}({U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}})+{F}_{1}(\ensuremath{-}{U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}})]$, being a very useful property to elucidate the regime to which a particular antiferrodistortive transition belongs. In the displacive regime, the ratio ${a}_{s}=\frac{{\left(\frac{d}{d{U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}}}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}_{1}({U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}})\right)}_{max}}{{\left(\frac{d}{d{U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}}}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}_{1}({U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}})\right)}_{min}},$ for ${U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}}$ either negative or positive, is shown to diverge at some temperature ${T}^{*}$, because ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}_{1}({U}_{x}^{\stackrel{\ensuremath{\rightarrow}}{1}})$ exhibits for $T<{T}^{*}$ a double-peak structure disappearing at $T={T}^{*}$. In the order-disorder regime, the ratio $\frac{{T}^{*}}{{T}_{c}}$ is infinite and decreases in the displacive regime by approaching the displacive limit to some value $\frac{{T}^{*}}{{T}_{c}}<1$. As M\"uller and Berlinger have shown, the key quantity ${a}_{s}$ can be measured, close to ${T}_{c}$ by means of the electron-paramagnetic-resonance technique.

Raman study of soft zone-boundary phonons and antiferrodistortive phase transition in BaMnF 4

We have discovered that the 255 K phase transition in BaMnF 4 involves a doubling of the primitive unit cell, that the phase transition is second-order (or very nearly so), and that it is characterized by a soft or unstable optical phonon at the Brillouin zone boundary of the orthorhombic C 12 2 V phase. The soft mode has a low-temperature energy of about 40 cm -1; it remains underdamped below 210 K, but is heavily overdamped near T c = 255 K. The doubling of the chemical unit cell below 255 K, previously unknown, permits the possibility (below T N = 26 K) of a linear magneto-electric effect in this class of materials, which has been the subject of some controversy.