Localized modes and central peak at displacive phase transitions

The influence of defects, which raise locally the transition temperature, on structural transitions is studied. At the local transition temperature $\text{T}{}^{\mathrm{<mtext>l</mtext>}}{}_{\mathrm{c}}$ a localized phonon condenses. The resulting cluster couples linearly to the band phonons and gives a central peak.     

The role of elastic strains at non-ferroelastic displacive phase transitions

The role of elastic strains at structural phase transitions is illustrated within the Landau theory and its first-order corrections due to critical fluctuations and defects are described. The Landau theory is sufficient to demonstrate the impossibility of bulk nucleation in a supercooled symmetrical phase and the absence of heterophase fluctuations in solids. The critical fluctuations are known to convert a second-order transition in an Ising-like system in a solid to a first-order one. Close to the mean-field tricritical point the effect can be described, for displacive systems, within a first-order perturbation theory and takes place for the Heisenberg systems as well. The influence of defects on these transitions is mediated essentially by the elastic strains. Defects smear the transition. For the “random local field” defects and an incommensurate (Heisenberg-like) transition this effect is so strong that first-order perturbation theory leads to a divergence.     

Critical behaviour at the displacive limit of structural phase transitions

For a special critical point at zero temperature,T _c =0, which is called the displacive limit of a classical or of a quantum-mechanical model showing displacive phase transitions, we derive a set of static critical exponents in the large-n limit. Due to zero-point motions and quantum fluctuations at low temperatures, the exponents of the quantum model are different from those of the classical model. Moreover, we report results on scaling functions, corrections to scaling, and logarithmic factors which appear ford=2 in the classical case and ford=3 in the quantum-mechanical case. Zero-point motions cause a decrease of the critical temperature of the quantum model with respect to the classicalT _c , which implies a difference between the classical and the quantum displacive limit. However, finite critical temperatures are found in both cases ford>2, while critical fluctuations still occur atT _c =0 for 0<d≦2 in the classical case and for 1 <d≦2 in the quantum model. Further we derive the slope of the critical curve at the classical displacive limit exactly. The absence of 1/n-corrections to the exponents of the classical model is also discussed.     

On the hydrodynamic theory of central peak in displacive structural phase transitions

A model involving nonlinear coupling between the overdamped phonon mode and temperature fluctuations is studied using the dynamic renormalization group method. It is shown that the behavior of the central peak in the dynamic form factor depends on the specific heat exponent α. For α < 0 and as T → T_c the central peak is found to merge with the over-damped phonon mode and the coupling goes to zero at T_c as (T ? T_c)^?α. An argument on the intensity of the central peak in the critical region in presented and it is concluded that the hydrodynamic coupling may not be the dominant mechanism of the central peak in SrTiO₃.     

General rule for displacive phase transitions in perovskite compounds revisited by first principles calculations

A recent high pressure experiment on LaAlO3 has revealed that the compound is an exception for the "general rule" of displacive phase transition associated with zone-boundary phonons. In the present study, the experimental result is successfully confirmed by first principles calculations. The pressure dependence of phonon frequencies as well as the phase transition pressure is quantitatively well reproduced. We found that the behavior is not peculiar to LaAlO3 but rather ubiquitous. RAlO3 (R = La, Nd, Sm, and Gd) and LaGaO3 can be classified in the same group.     

A characteristic critical quantity in nonequilibrium phase transitions

The bit-number variance, a generalization of specific heat, which was already introduced in earlier papers [7-10] is discussed, with respect to the critical behaviour in equilibrium-and nonequilibrium phase transitions. In the considered mean field examples it shows a uniform behaviour dependent on to which of two classes the system belongs. With it a new characteristic critical quantity is found appropriate for the comparison of different nonequilibrium phase transitions. New arguments are given with respect to the connection between critical correlations and the bit-number cumulants.     

A relation between critical exponents for the lambda phase transition in liquid helium

A relation between critical exponents is derived which permits the experimental determination of a so far unknown combination of critical exponents for theλ phase transition in liquid helium.     

Light scattering from moving cluster walls in a model of displacive phase transitions

We calculated the spectrum of light scattered from moving cluster walls which were recently found to be important excitations for strongly anharmonic one-dimensional models exhibiting displacive phase transitions at T_c = 0. It is found that the scattering spectrum consists of a Gaussian central peak.     

Pressure-induced crossover between diffusive and displacive mechanisms of phase transitions in single-crystalline alpha-GeO2

We present the first example of the phase transition occurring via the different kinetic mechanisms, displacive or diffusive, competing with each other in quartz-like alpha-GeO2 single crystals. Upon room-pressure heating, alpha-GeO2 transforms to the rutile-type phase (the alpha-->r transition) via the diffusive mechanism. With increase of the treatment pressure the diffusive mode of the temperature-induced alpha-->r transition is substituted at approximately 4 GPa by a displacive-like mode, and then at approximately 6 GPa the transition type changes from the alpha-->r sequence to a displacive martensitic-like transition to a distorted rutile-like phase (alpha-->r'. A crossover between diffusive and displacive transition modes suggests a new way to control the meso- and nanometer-scale morphology of high-pressure phases.     

A microscopic derivation of macroscopic sharp interface problems involving phase transitions

Macroscopic free boundary problems involving phase transitions (e.g., the classical Stefan problem or its modifications) are derived in a unified way from a Hamiltonian based on a general set of microscopic interactions. A Hamiltonian of the form + _x,x J(x–x)(x)(x) leads to differential equations as a result of Fourier transforms. Expanding the Fourier transform ofJ in powers ofq (the wave number), one can truncate the series at anarbitrary orderM, and thereby obtainMth-order differential equations. An asymptotic analysis of these equations in various scalings of the physical parameters then implies limits which are the standard macroscopic models for the dynamics of phase boundaries.     

Towards a microscopic theory of phase transitions: residual rays,correlation radii and critical indices

Bonds between atoms/molecules of condensed substances must be described within the framework of quantum electrodynamics (QED) as an exchange of virtual photons. Such representation is supported by the known conformity of latent heat with residual infrared (IR) rays and the possibility of latent heat removal by characteristic frequencies. These bonds are virtual if the duration of photons’ formation (their ‘dressing’) τ exceeds the duration of free path in substance ??=?1/σ _tot N, i.e. if τ?>??/c. It is assumed that reversing this inequality corresponds to bond breakage and phase transitions. With low σ _tot and τ frequencies, it leads to the universal radius of correlations, R _c?～?ω ^?ν, ν?=?2/3, and allows refinement of the Ginzburg–Landau model of phase transitions by expansion of thermodynamic potentials over R _c (instead of temperature distance), which results in the correct system of critical indices. Such a consideration offers an opportunity for the stimulation of definite phase transitions by resonant frequencies.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Constraints,phase transitions and critical indices

The notion of first order phase transitions is examined for systems under external constraints. It is emphasized that only discontinuities with respect to “natural” variables (additive extensive variables and their conjugate internal forces) should be regarded as first order transitions. The Baker-Essam model is accordingly reviewed, and it is shown that the transition is always of the second order. Fisher's conjecture about renormalization is shown to be correct also for this model.     

Manifestation of critical behavior at first-order phase transitions

We present in this Letter further results which are in good agreement with our earlier observations on the critical behavior at a strong first-order phase transition. More elaborate data analysis has been used here. A quantitative measure of the strength of the transition within the context of Landau theory is also given.     

Discontinuity of the dynamic critical exponents ofO(n)-symmetric systems

Then-component model of Sasvári, Schwabl, and Szépfalusy is analyzed by means of renormalized field theory to two-loop order. Singular two-loop contributions have a significant effect on the nature of the stability boundary of the dynamic scaling region in then—d plane. Along this boundary the dynamic critical exponents exhibit unexpected discontinuities.