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,
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
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
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
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
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. Ni1-xAlx (x = 0.6) undergoes a martensitic
phase transformation from bcc to a specific structure called '7R' at Tc
= 80 K.
Above Tc, they observed 'soft TA phonon' with the wave
vector q ≈ 1/7. 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 (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
Last Modified: Wednesday, 26-Jan-2005 16:51:46 EST