On Landau theory and symmetric energy landscapes for phase transitions

The aim of this presentation is the development of a general approach for modelling the global complex energy landscapes of phase transitions. For the sake of clarity and brevity the exposition is restricted to martensitic phase transition (i.e., diffusionless phase transitions in crystalline solids). The methods, however, are more broadly applicable. Explicit energy functions are derived for the cubic-to-tetragonal phase transition, where data are fitted for InTl. Another example is given for the cubic-to-monoclinic transition in CuZnAl. The resulting energies are defined globally, in a piecewise manner. We use splines that are twice continuously differentiable to ensure sufficient smoothness. The modular (piecewise) technique advocated here allows for modelling elastic moduli, energy barriers and other characteristics independent of each other.     

Thermoelectric power and phase transition of polycrystalline As2Te3 under pressure

The pressure dependence of the thermoelectric power of monoclinic As₂Te₃ is measured up to 10 GPa using a Mao-Bell diamond anvil cell. The thermoelectric power never reaches an absolute value greater than the ambient pressure value of 242 μV/K. Evidence of a phase transition is present between 6 and 8 GPa where the thermoelectric power reaches an absolute value of 225 μV/K after passing through a minimum of S≈75 μV/K. X-ray diffraction experiments confirm that the resulting structure is β-As₂Te₃, which is isostructural with Bi₂Te₃ and Sb₂Te₃.     

High-pressure X-ray diffraction study of SrMoO4 and pressure-induced structural changes

SrMoO₄ was studied under compression up to 25 GPa by angle-dispersive X-ray diffraction. A phase transition was observed from the scheelite-structured ambient phase (space group I4₁/a) to a monoclinic fergusonite phase (space group I2/a) at 12.2(9) GPa. The unit-cell parameters of the high-pressure phase are a=5.265(9) Å, b=11.191(9) Å, c=5.195 (5) Å, and β=90.9(1)°, Z=4 at 13.1 GPa. There is no significant volume collapse at the phase transition. No additional phase transitions were observed and on release of pressure the initial phase is recovered, implying that the observed structural modifications are reversible. The reported transition appeared to be a ferroelastic second-order transformation producing a structure that is a monoclinic distortion of the low-pressure phase and was previously observed in compounds isostructural to SrMoO₄. A possible mechanism for the transition is proposed and its character is discussed in terms of the present data and the Landau theory. Finally, the room temperature equation of states is reported and the anisotropic compressibility of the studied crystal is discussed in terms of the compression of the Sr-O and Mo-O bonds.     

Crystallography of the tetragonal-to-monoclinic phase transformation in ceria-zirconia

A detailed understanding of the transformation toughening process in zirconia-containing ceramics requires the application of the crystallographic theory of martensitic transformation. Therefore, the crystallographic analysis of the tetragonal-to-monoclinic transformation in ceria-zirconia was performed by using both the infinitesimal deformation approach and Wechsler–Lieberman–Read phenomenological crystallographic theory. All crystallographic parameters such as the habit plane orientation, orientation relationship between the parent and product phases, the direction of the total shape deformation, the amount of the lattice invariant strain, etc. were calculated. The results obtained from the infinitesimal deformation approach were in agreement with those calculated from phenomenological crystallographic theory and also with experimental observations.     

An Infinitesimal Deformation Approach to the Crystallographic Theory of the Martensite Phase Transformation: Application to Au-Cd,Fe-Ni AND In-Tl Alloys

Using the infinitesimal deformation approach, a crystallographic analysis of the austenite-martensite transformation from the cubic to orthorhombic phase - which predicts crystallographic parameters such as habit plane, orientation relationship between austenite and martensite, rotation matrix and total shape deformation matrix - is derived from a knowledge of the crystal structures of the initial and final phase only. The numerical values coming from orientation relationships obtained for Au-47.5 Cd Fe-Ni and In--Tl alloys are compared with predictions of the phenomenological crystallographic theory, infinitesimal deformation approach and experimental data.     

Granular flows

We review both experimental and theoretical works concerning granular flows. We successively address the regime of slow deformations, which is mainly governed bystericinteractions and frictionforces, thenthe rapid flow regime, whichdeals with inelastic collisions, and lastly the regime of intermittent avalanches.     

Waves and patterns in ring lattices with delays

We investigate the existence and the stability of waves and phase locked states in rings of coupled oscillators with delayed interactions. Using center manifold reduction and the normal form method, we reduce the equation governing the dynamics of the whole network to an amplitude-phase model (i.e. a set of coupled ordinary differential equations describing the evolution of both the amplitudes and the phases of the oscillators). Then we prove the existence of traveling waves, in-phase and anti-phase locked oscillations, in both one-dimensional and two-dimensional lattices. The influence of the interaction strength and the number of oscillators is investigated, and the possible coexistence of waves and phase locked oscillations is shown.     

Global view on a nonlinear oscillator subject to time-delayed feedback control

We apply time-delayed feedback control to stabilise unstable periodic orbits of an amplitude-phase oscillator. The control acts on both, the amplitude and the frequency of the oscillator, and we show how the phase of the control signal influences the dynamics of the oscillator. A comprehensive bifurcation analysis in terms of the control phase and the control strength reveals large stability regions of the target periodic orbit, as well as an increasing number of unstable periodic orbits caused by the time delay of the feedback loop. Our results provide insight into the global features of time-delayed control schemes.     

Lowest order QED radiative corrections to five-fold differential cross section of hadron leptoproduction

The contribution of exclusive radiative tail to the cross section of semi-inclusive hadron leptoproduction has been calculated exactly for the first time. Although the experience of inclusive data analyses suggests us that the contribution of radiative tail from the elastic peak is of particular importance, similar effects in the semi-inclusive process were only recently estimated in the peaking approximation. The explicit expressions for the lepton part of the lowest order QED contribution of exclusive radiative tail to the five-fold differential cross section are obtained and discussed. Numerical estimates, provided within Jefferson Lab kinematic conditions, demonstrate rather large effects of the exclusive radiative tail in the region at semi-inclusive threshold and for high energy of detected hadron.     

Soft photon problem in leptonic B-decays

We point out at the peculiarity of B→μν_μ decay, namely the enhancement of the soft photon events which originate from the structure dependent part of the B→μν_μγ amplitude. This may be a dominant source of systematic uncertainty and compromise the projected experimental uncertainty on Γ(B→μν_μ). We show that the effect of these soft photons can be controlled if the experimental cut on identification of soft photons is lowered and especially if the better resolution in identifying the momentum of muon emerging from B→μν_μ is made. A lattice QCD computation of the relevant form factors would be highly helpful for a better numerical control over the structure dependent soft photon emission.