Anharmonic phonons and central peaks at structural phase transitions

Recent light scattering studies of solids undergoing structural phase transitions clearly demonstrate that the “central peak” phenomenon is not one, but several processes (both static and dynamic) contributing in different degrees to the spectra observed for different types of transition. Our own work on Pb₅Ge₃O₁₁, SrTiO₃, K₂SeO₄ and BaMnF₄ is reviewed and the studies by other on KDP, KH₃(SeO₃)₂, KD₃(SeO₃)₂ are discussed briefly.     

Soft phonons and the central mode at structural phase transitions

Applying Landau's quasi-particle picture to an interacting phonon system it is shown that the softening of phonon modes is connected with an enhancement of the quasi-particle interaction. This in turn leads to a critical slowing-down of fluctuations around local equilibrium which may give rise to an additional central peak in the scattering function.     

Anharmonic relaxation of phonons

Using the Ziman scheme of considering a drifting Planck’s distribution, as the eigenvector of the linearized phonon collision operator, the anharmonic relaxation of phonons is discussed. The earlier arbitrariness in the phonon-phonon coupling parameters is removed by formulating explicit expressions for different allowed processes in terms of measurable quantities. Low and high temperature approximations of relaxation rates are also discussed: the results differ from earlier calculations. At low temperatures superthermal or high frequency phonons, which have temperature-independent and equal N- and U-relaxation rates, play important roles in thermal conduction in pure insulators. Presently working as University of Wales Fellow in the Applied Physics Department, UWIST Cathays Park, Cardiff CF1 3NU, U.K.     

Crystalline phase transitions and acoustic phonons behaviour of polymorphic ethanol

Ethanol shows a complex scenario of different crystalline phases in the temperature range between its glass transition at T_g = 97 K and its melting point at T_m = 159 K. Brillouin spectroscopy has revealed capable of observing and assessing acoustic phonon changes related to these phase transitions between different crystalline phases (either a plastic-crystal phase or different monoclinic phases). By combining this technique and calorimetric experimental data, we are able to corroborate the existence of at least two stable and two metastable (monoclinic) crystalline phases of pure ethanol.     

Anharmonic oscillator model for first order structural phase transition

Exact solutions for the motion of a classical anharmonic oscillator in the potentialV(φ)=Bφ ² ? |A|φ ⁴ +Cφ ⁶ are obtained in (1 + 1) dimensions. Instanton-like solutions in (imaginary time) which takes the particle from one maximum of the potential to the other are obtained in addition to the usual oscillatory solutions. The energy dependence of the frequencies of oscillation is discussed in detail. This can be used as a model for the first order structural phase transition in the mean field approximation. The high and low temperature behaviour of the static susceptibility is obtained. Finally, a qualitative explanation is offered for the observed central peak in ferroelectrics like SrTiO₂.     

Lattice dynamics and structural phase transitions

Results of lattice dynamics, or atomic motions in a solid, explain many of the thermodynamic properties of solids. Inelastic neutron scattering conveniently explores the atomic motions, quantized as phonons. Of particular interest are materials that undergo structural phase transitions. The soft mode theory has been successful in relating anomalous phonon behavior to structural changes in solids. One such example is the ferromagnetic shape memory alloy, Ni₂MnGa, which undergoes a sequence of phase transitions leading to a magnetic, incommensurate modulated, tetragonal phase as the ground state. The experiments, coupled with first principles calculations, provide evidence that strong electron–phonon coupling is the driving mechanism of the phase transformation.     

Anharmonic effects of phonons with Kohn anomalies

In a quasi-one-dimensional conductor, the phonons with anomaly at the Fermi diameter, 2k_F, cause the phonons at 4k_F to soften via the three-phonon coupling, mainly due to the phonon modulation of the Coulomb interaction between tight-binding electrons on different sites. The 2k_F phonons also cause strong second-order scatterings of X-rays or neutrons. These results may explain the recent observations of phonon anomalies at 4k_F in TTF-TCNQ.     

Interaction of optical phonons with magnons in orthorhombic crystals and the effect of magnetic field on structural phase transitions

The interaction of polar optical phonons with magnons in RMn₂O₅ manganates (R is a rare earth ion) has been studied in the approximation of collinear antiferromagnetic ordering of manganese sublattices. The effect of magnetic field on the structural phase transitions in these oxides has been analyzed.     

Spontaneous local distortions and structural phase transitions

Xray Absorption Fine Structure (XAFS) measurements of the local atomic structure of perovskite crystals undergoing various structural phase transitions are summarized and discussed. The results show that the local structure of crystals undergoing ferroelectric antiferroelectric and antiferrodistortive transitions is distorted in a disordered fashion far above the transition to the high symmetry phase. The size of the distortions is a large fraction of the distortion at temperatures far below T _c. Based on these results we propose a model of ferroelectricity which accounts quantitatively for the temperature dependence of the dielectric function the soft mode frequency, the imaginary part of the dielectric constant and the central peak in PbTiO₃ and KNbO₃.     

On structural phase transitions from a hypothetical phase

Examples known so far of structural phase transitions which can be treated as an instability of a hypothetical parent phase are enumerated. Physical requirements for being reasonable to consider such hypothetical phase are pointed out. The possibility of using this concept for explanation of successive structural phase transitions in Rochelle salt and langbeinites is discussed.The author thanks Dr. V.Janovec for many valuable remarks to this paper.     

Acoustic dispersion near structural phase transitions

We show on various examples, that elastic constant measurements provide a valuable tool for studying the dynamics of solids near phase transitions. Many experimental methods used in the investigation of phase transitions (NMR, neutron scattering, etc.) are able to give information on the dynamics, but in different regions of q- and ω-space, thereby probing different dynamical processes.

A comparison of the dynamics obtained from the elastic measurements with other techniques (NMR) demonstrates this very clearly for the cases of KSCN and C_60.     

Theory for photoinduced structural phase transitions

A general concept for photoinduced structural phase transitions is developed in terms of the hidden multistability of the ground state and the proliferations of optically excited states. Taking the ionic→neutral (I - N) phase transition in the organic charge transfer crystal, TTF—CA, as a typical example for this type of transition, we, at first, theoretically show an adiabatic path of this transition, which starts from a single charge transfer exciton in the ionic phase, but finally reaches a neutral domain with a macroscopic size. In connection with this I—N transition, the concept of the initial condition sensitivity is also developed so as to clarify experimentally observed nonlinear characteristics of this material. In the next, using a more simplified model for the many-exciton system, we theoretically study the early time quantum dynamics of the exciton proliferation, which finally results in the domain formation of a large number of ex-citons. For this purpose, we derive a stepwise iterative equation to describe the exciton proliferation, and clarify the origin of the initial condition sensitivity.     

Hierarchical microstructure in structural phase transitions

We consider a model in the context of martensitic materials in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential in local deviatoric (rectangular) strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symmetry allowed compositional fluctuation-induced strain gradient terms. The last term favors branching of domain walls which enables communication between macroscopic and microscopic regions essential for shape memory. Below the transition temperature (T₀) we obtain the conditions under which branching of twins is energetically favorable. Above T₀ a hierarchy of branched domain walls also stabilizes tweed formation (criss-cross patterns of twins). External stress or pressure modulates (“patterns”) the spacing of domain walls. Results based on 2D time-dependent Ginzburg-Landau simulations are shown for twins, tweed and hierarchy formation.     

NMR-NQR studies of structural phase transitions

Moving dislocations in II–VI semiconductors carry a large electric charge. This charge is not in thermal equilibrium, but is due to the sweeping up of electrons from point defects. Its movement produces a dislocation current during plastic deformation, and conversely, the application of an external field changes the flow stress. This paper reviews the structure and properties of these dislocations, the theory of their charge and the phenomena which are a consequence of the strong mutual interactions of the dislocation and electronic sub-systems in these crystals. The materials show a large photoplastic effect (a change in flow stress under illumination), and related effects due to the injection of electrons at an electrode. Deformation produces reversible changes in the conductivity, pulsed and continuous luminescence and the emission of electrons from the surface.     

Jahn-Teller solitons, structural phase transitions, and phase separation

It is demonstrated that under common conditions a molecular solid subject to Jahn-Teller interactions supports stable Q-ball-like nontopological solitons. Such solitons represent a localized lump of excess electric charge in periodic motion accompanied by a time-dependent shape distortion of a set of adjacent molecules. The motion of the distortion can correspond to a true rotation or to a pseudorotation about the symmetric shape configuration. These solitons are stable for Jahn-Teller coupling strengths below a critical value; however, as the Jahn-Teller coupling approaches this critical value, the size of the soliton diverges signaling an incipient structural phase transition. The soliton phase mimics features commonly attributed to phase separation in complex solids.     

Crystal imperfections and structural phase transitions in perovskites

High‐resolution X-ray scattering measurements of the antiferrodistortive phase transitions in the perovskites SrTiO₃, RbCaF₃ and KMnF₃ have recently revealed the existence of two length scales in the critical scattering above T_e . Here we review these observations and discuss how they might be related to the well known existence of two time scales (the "central peak" problem) in the critical dynamic response function above T_e . We reach the tentative conclusion that within a few degrees of T_e both the time and length scales of the fluctuations are strongly influenced by defects and that the intrinsic critical behaviour is swamped by these effects in most crystals.