Process of Structural Phase Transitions

from soft phonon mode to embryonic fluctuation

A reminiscence of Gen Shirane at the time of his 65th birthday

by Y. Yamada

The study of structural phase transitions with neutron scattering has been one of the major subjects pursued consistently at BNL since Shirane initiated investigations in this field in the early 1960's.  Materials studied cover a wide range of categories including ferroelectrics, low-dimensional conductors, superconductors, etc.

In this lecture, however, we will focus our attention only to the two materials: SrTiO₃ and NiAl, the oldest and the newest materials, respectively, which Shirane pursued in the area of structural transition study. In fact, not only do these two materials span a quarter century history of his study, but also they seem to span the two extreme cases in physics of lattice instability as will be discussed below.

SrTiO₃: soft phonon mode

In 1965, Shirane first succeeded to prove the existence of the long-searched-for 'soft phonon mode' as the precursor of the phase transition in SrTiO3, which has opened up the new era in the study of phase transitions.

Since the characteristic frequency of a harmonic phonon should be temperature-independent, the temperature-dependent soft mode implies the existence of anharmonicity in the lattice potential.  Softening was understood simply in terms of a quasi-harmonic representation of the system obtained by renormalization of the anharmonic effects.

Later, more detailed investigations on SrTiO₃ showed some difficult aspects which were manifested in the form of a 'central peak' of the scattered neutron spectra. This was in fact the Pandora's box! All sorts of possibilities such as entropy fluctuations, thermal diffusion mode, impurity effect etc. have been discussed without any decisive conclusion.

Except for this point, SrTiO₃ is still holding the position of the textbook example to discuss the structural phase transition in terms of soft phonon mode concept.

NiAl: embryonic fluctuation

Recently, Shirane and coworkers carried out a very interesting neutron scattering study on NiAl alloy. Ni_1-xAl_x (x = 0.6) undergoes a martensitic phase transformation from bcc to a specific structure called '7R' at T_c = 80 K.

Above T_c, they observed 'soft TA phonon' with the wave vector q ≈ 1/7[110].  The softening is however quite incomplete, and the spectrum develops a strong central peak.  The diffraction pattern in the martensite phase shows anomalous features: Corresponding to the observed soft mode, there appear satellite reflections at m/7[110] (m = 1 ~ 6). However, these are not at the regular positions but show subtle shifts from the commensurate positions. At the same time, the profiles exhibit asymmetric broadening and sometimes even show splitting into double peak structure.

In collaboration with Shirane's group, we carried out an analysis of the intensity data as well as the anomalous shifts.  The study has revealed new aspects of structural phase transition, which is understood based on the new concept of 'embryonic fluctuation'.  An embryonic fluctuation is a sort of local fluctuation which locally produces a micro-region (embryo) of low temperature structure.  This fluctuation is in contrast to a phonon which is a non-local excitation extending throughout the system.

We consider that in the vicinity of 1st order structural phase transi-tions of various kinds (including the case of NiAl) there exist embryonic fluctuations excited randomly (both spatially and temporally) within the crystal.  If this view is correct, that is, if the embryonic fluctuation is a real entity, the features of the phase transition should be described in a completely different language (or concepts) from the conventional ones such as 'mode softening', 'divergence of the amplitude of the soft phonon', etc.  Instead, the key words to be discussed will be 'embryo size', 'embryo life time', 'embryo density' etc., and the phase transition itself will be viewed as a cooperative ordering of embryos due to embryo-embryo interaction'.

Last Modified: Wednesday, 26-Jan-2005 16:51:46 EST

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