Experimental studies of structurally incommensurate crystal phases

The application of Raman spectroscopy for the investigation of phase transitions focused traditionally on the observation of soft modes in displacive systems. The present furthergoing study on displacive and order-disorder systems is based on the observation of systematic changes of the scattering profiles of hard modes during the phase transition. It reveals the temperature evolution of the order parameters, the role of order-parameter fluctuations and phonon density of states effects in model systems like improper ferroelastic Pb3(P1-x As x O4)2, lead diluted ferroelastic (Pb1-x Ba x )3(PO4)2, pure ferroelastic As2O5 and the relaxor ferroelectric Pb(Sc0.5Ta0.5)O3. Allied with supplementary experimental techniques hard-mode Raman spectroscopy (HMRS) is an ideal method for the investigation of order-parameter coupling effects and the characterization of structural phase transitions.

Hard mode Raman spectroscopy and its application to ferroelastic and ferroelectric phase transitions

An attempt is made to explain the first-order phase transition (180.4 degrees C) and the presence of an intermediate phase (180.4 degrees C-300 degrees C) between the para- and ferro-phases in lead phosphate, Pb3(PO4)2, by invoking the basic ideas of the three-dimensional renormalised Potts model. This involves the introduction of three order parameters with two different critical temperatures. A relaxational type flip mode is proposed as the driving soft mode. The abnormal behaviour of the spontaneous strain between 160 degrees C and 180 degrees C, as well as the anomalous behaviour of the elastic stiffness constants C11 and C22 during the phase transition, are explained.

https://iopscience.iop.org/article/10.1088/0022-3719/14/33/001/pdf

Potts model and phase transition in lead phosphate Pb3(PO4)2

2014 The existence of static and dynamic deformation in the intermediate phase between the high and low temperature phases (paraand ferroelastic) has been examined by high resolution neutron scattering, X-ray diffusion and Raman spectroscopy. The behaviour of the order parameter was investigated through the measurement of optical birefringence under shear stress. It was found that the structural deformation of the intermediate phase, as compared with the high temperature structure, is similar to that of the ferroelastic phase but with three nearly equivalent binary axes of the monoclinic unit cell. The spontaneous thermal switching between these three axes as a dynamical effect (flip-mode) is observed in Pb3(PO4)2. In Pb3(P1-xAsxO4)2 static deformations occur at temperatures just above the ferroelastic transition point and are superposed by flipping motion at higher temperatures. J. Physique 43 (1982) 1379-1388 SEPTEMBRE 1982, . Classification Physics Abstracts 64.70K

Reinvestigation of the stepwise character of the ferroelastic phase transition in lead phosphate-arsenate, Pb3(PO4) 2 -Pb3(AsO4)2

In the improper ferroelastic palmierite-type lead phosphate order parameter coupling with a defect induced conjugate field leads to the renormalization of the two different critical temperatures of three order parameter components {Q 3} and {Q 1 Q 2}. The influence of the lead dilution by barium on the ferroelastic domain pattern, the critical temperature of the ferroelastic transformation R m–C2/c and the development of the intermediate regime in (Pb1–x Ba x )3(PO4)2 is studied using optical birefringence measurements, Raman and infrared spectroscopy. At the ferroelastic transition temperature T c the orientational contribution of the three-states Potts model becomes critical. T c is reduced from 453 K (x = 0) to zero K at x⋍ 0.12. Modifications of the shape of zigzag needle domains as well as the angle between the monoclinic binary axis and the W walls along [031] with temperature and increasing Ba-content are reported. Above the ferroelastic transition point the component Q 3, which correspond...

Renormalization phenomena in Ba-diluted ferroelastic lead phosphate, (Pb1−xBax)3(PO4)2

All elastic stiffness constants have been determined at room temperature using Brillouin spectroscopy. Some of them and the spectral width of the corresponding Brillouin peaks show important variations around the transition temperature (Ti = -143°C) between prototypic and incommensurate phases. Below Ti, the anomalies associated with the acoustic phonons propagating in the (001) direction are explained assuming a linear coupling between deformations and an overdamped mode. This mode is equivalent to a Debye relaxation process characterized by a relaxation time τ0 = 2.6 10-12 s.K.

Brillouin scattering study of the incommensurate transition of K2SeO4

In the β phase (above 180°C) the basis of the crystal consists of one molecule of lead phosphate. The Pb ions and the gravity centres of the PO4 ions are on the ternary axis.

Raman effect of a and β (PO4)2Pb3

Neutron scattering study of Hg2 Cl2 confirms the hypothesis of the condensation of a transverse acoustical mode at an X point of the Brillouin zone. In neutron scattering spectra, the soft mode appears well separated from the central peak and we can show that its frequency ω∞ has a non zero saturation value at the transition. Raman results in the two phases are in agreement with the neutron scattering ones.

Neutron and raman scattering studies in Hg2C12

The anomalies of velocity and damping of the longitudinal acoustic phonon propagating along [001] are investigated at various scattering angles and under hydrostatic pressure for right angle scattering near the commensurate-incommensurate transition (Ti∽130K). They are explained on the basis of a coupling with the amplitude mode.

J. P. Benoit

Papers

Brillouin scattering study of the incommensurate transition of K2SeO4

Raman effect of a and β (PO4)2Pb3

Neutron and raman scattering studies in Hg2C12

Scattering angle and pressure dependences of brillouin spectra in K2SeO4