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Emmanuel Farhi

Habilitation a diriger des recherches (HDR) 2nd PhD thesis

Habilitation a Diriger des Recherches (HDR), long term PhD (pdf) Defence: Feb 10th 2014

"Virtual experiments as a data analysis tool for neutron scattering measurements"


This work demonstrates the use, and the limitations, of virtual experiments with applications to a liquid He4 ultra-cold neutron moderator study, a liquid Indium neutron inelastic experiment, and a neutron Rietveld refinement methodology. Extension to other topics are discussed.
The main tools used for this study are McStas <> and iFit <>.

Emmanuel Farhi: You can here get my thesis

date: Thu Jan 13, 1999


This is the Ultimate Version (in French).
Files are PDF. French document. 207 pages, 82 figures, 11 tables, 191 citations.

You may equally access the 'thèses-EN-ligne' server from the CNRS/SPM in section 'Thèses de physique statistique sur les transitions de phase'. Direct link is here (defense on the 14 Dec 1998).

If you appreciate this work, have any questions about it, want some details, etc.
just send me a kind e-mail to : farhi(at)

Quantum Paraelectric anomalies in KTaO_3 pure and Na-doped crystals

The full manuscript is available as a single PDF here (in French).

keywords : quantum paraelectrics, KTaO3, SrTiO3, Brillouin scattering, neutron scattering, second sound, multiphonon processes, phonon dampings, computer simulations.

Erratum : p 119 (Chapter 3) an error for indexes in Hanis matrix-Va block was corrected

Some associated publication preprints are available HERE.

French (short) Abstract

Le KTaO3 est un cristal dont la transition ferroelectrique est stoppee a basse temperature : le mode critique associe (TO) devient mou, mais ne se condense pas. Nous avons concentre cette etude sur les anomalies vibrationnelles observables a basse temperature (T < 100 K) par spectroscopie Brillouin dans le cristal pur et dope au sodium. Une parametrisation des nappes de phonons basse frequence a partir de mesures de diffusion inelastique de neutrons a permis dÕevaluer numeriquement la largeur des phonons, la vitesse du second son, dans la cas ou il serait visible, et le spectre de diffusion par difference de deux phonons dans le cristal pur, pour T < 100 K. Ce dernier processus semble pouvoir rendre compte de la forme singuliere des spectres Brillouin experimentaux. L'existence du second son dans KTaO3 est aussi possible.

English (long) Abstract

The object of the work was to study Quantum Paraelectric anomalies in KTaO_3 pure and Na-doped crystals, with E. Courtens and A.K. Tagantsev.

What are quantum paraelectrics (QPE, also called incipient ferroelectrics)? They are crystals (such as KTaO_3 and SrTiO_3) that should be ferroelectric under a certain Curie-Weiss temperature T_c, but they aren't ! At low temperature, the ferroelectric fluctuations are controlled by a zone-center transverse optic mode (TO) called ferroelectric mode which softens (tends to zero frequency) as the temperature decreases. This phonon is associated with the polarization fluctuations induced by the vibration of the cell-center ion (Ta or Ti) inside the octaedral oxygen cage. Around T_q (37 K for SrTiO3 and about 10 K for KTaO3), the related variation of the dielectric constant epsilon deviates from the normal Curie-Weiss divergence for ferroelectrics, and stabilizes at a large but finite value below T_q. Thus, ferroelectricity is not achieved. It is usually considered to be prevented by zero-point quantum fluctuations which are about the same amplitude as the would-be ferroelectric displacements. This corresponds to a quantum paraelectric state which remains stable down to the lowest temperatures. Moreover, the softening of the TO branch depresses the transverse acoustic phonon (TA), due to a strong TO-TA coupling. KTaO_3 was chosen for this study because it remains cubic down to the lowest temperature (and SrTiO_3 becomes tetragonal at about 105 K). It is then considered to be 'simpler' than other QPE's.

When decreasing temperature in KTaO_3 crystals, some unexpected features appear on Brillouin scattering spectra : (i) a broad quasi-elastic central peak, first reported by Lyons and Fleury (1976), which is usually interpreted as second order scattering, and (ii) a new doublet recently observed over the quasi-elastic central peak of QPE's, which was associated to second sound phenomena (propagation of heat) with acoustic phonons (Hehlen 1995).

I first measured precisely inelastic low energy phonons along high symetry axis (C_2, C_3 and C_4) in pure KTaO_3 (IN14, with B. Hehlen and R. Currat), in order to look for those up-mentionned anomalies near Brillouin zone center by neutron scattering experiments. But, except for the strong TA-TO coupling, no particular 'strange' behaviour showed up.

Then an extensive Brillouin characterisation of low frequency excitations (acoustic phonons, central peak, doublets) in the vicinity of Brillouin zone center was performed in pure and Na-doped KTaO_3 crystals. Many anomalous features were reported, and the effect of doping, eventually leading to ferroelectric transition, was also studied.

Using both neutron and Brillouin data, a phenomenological parametrisation of low frequency phonon sheets was successfully applied to the center part of Brillouin zone (|q| < 0.3 rlu). This emphasized the unusual anisotropy of phonons, specially for acoustic phonons along C_2 and C_4 axis (low energies and group velocities, some kind of 'valleys'), whereas C_3 axis are rather up-hill shaped (higher energies and group velocities).

This model was first used in order to compute a lower value of three phonon electrostrictive normal processes dampings for the five lower energy phonons over the center part of Brillouin zone. The phonon energy anisotropy is also visible in dampings. Comparison with experimental data shows reasonable agreement.

Then, the second sound hypothesis for the origin of doublet was tested. We here notice than second sound is the collective propagation mode of thermalised phonons : phonons whos normal dampings are greater than the secound sound frequency constitute thermal waves in which temperature is well defined and quasi-momentum is conserved (no resistive processes : defects, Umklapps, ...). Those waves can interact with light, and show up as doublets on Brillouin scattering spectra (Wehner and Klein, 1972). We computed second sound Brillouin zone center velocity with temperature, which is found to be in excellent agreement with experimental measurements of doublet frequency obtained through Brillouin spectroscopy. But secound sound intensity estimations could not fit with observations (either in value or in anisotropy).

Consecutively, we looked for an alternative interpretation of doublets in terms of phonon density fluctuations. When phonon dampings are smaller than the secound sound frequency, the collective mode cannot propagate. But light can still couple to over-damped second sound (usual central entropy fluctuation Rayleigh peak, diffusion of heat) and pairs of phonons (two-phonon difference scattering). The latter process was computed for low energy phonons, using energy parametrisation and damping evaluations. The resulting Brillouin spectra are in excellent agreement with measured ones, in all directions and for all temperatures below 100 K.

The doublet and the broad central peak can then be associated to two-phonon difference scattering processes from transverse acoustic phonons according to their dampings and group velocities. Optical phonons contribution are very broad, and rather appear as a quasi-constant background, while longitudinal acoustic phonons produce very small contributions when compared to others.



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