Anti-isostructural phases and anomalous thermoelasticity in In-based alloys:
Synchrotron x-ray diffraction experiments and unified phenomenological model
V. P. Dmitriev,
1
D. Chernyshov,
1
Y. E. Filinchuk,
1
and V. F. Degtyareva
2
1
Swiss-Norwegian Beam Lines at ESRF, Boîte Postale 220, 38043 Grenoble, France
2
Institute of Solid State Physics, RAS, Chernogolovka, Moscow District, 142432 Russia
Received 20 September 2006; revised manuscript received 23 November 2006; published 17 January 2007
A combined in situ high-temperature high-pressure synchrotron radiation diffraction study has been carried
out on In alloys with Cd, Pb, and Sn. Anti-isostructural phase transitions between structures with opposite signs
of tetragonal distortion, found earlier in In-Pb, have also been observed in In-Sn alloys. We show that negative
thermal expansion of In and some of the In alloys is a phase-dependent effect resulting from a competition
between spontaneous strain induced by a proper ferroelastic transformation and normal thermal expansion. A
unified phenomenological model has been worked out for structural phase transitions in In and its alloys.
DOI: 10.1103/PhysRevB.75.024111 PACS numbers: 61.50.Ks, 61.66.Dk, 64.70.-p, 71.20.Be
I. INTRODUCTION
The anomalous elastic properties of the IIIA-group metal
indium, and its crystal structure, unusual for metallic ele-
ments, give rise to intense studies, both experimental and
theoretical. Elemental indium has at ambient conditions a
body-centered tetragonal structure c / a
fct
1 with one
atom in a primitive unit cell Z
p
=1 or, equally, two atoms in
the Bravais cell. The close relation to the fcc structure makes
it more convenient to use a face-centered tetragonal fct
setting for body-centered tetragonal structures, which we do
hereafter. A contraction negative expansion occurs in In
along the fourfold axis and an expansion in the basal plane
with increasing temperature.
1
One might have expected the
tetragonal distortion to be removed by application of external
pressure. However, high-pressure studies of In revealed the
stability of the fct structure.
2,3
Moreover, it lowers the sym-
metry from tetragonal to orthorhombic at about 45 GPa.
4
By
contrast, alloying In with the IIA-group metal Cd x
Cd
5 at. % on the IVA-group metal Pb x
Pb
30 at. % not
only allows one to remove the tetragonal distortion of the
crystal lattice and stabilize the face-centered cubic fcc
structure,
5,6
but also switches the sign of the distortion and
stabilizes another tetragonal structure fct' with c / a
fct
1 15 x
Pb
30 at. % .
The rich and reliable experimental information accumu-
lated for In-based alloys has stimulated, in the last decade,
numerous theoretical works. Two approaches were devel-
oped in order to work out a unified model for In-based solid
solutions. One, going back to an idea by Goodenough,
7
fo-
cused on the interaction between the Brillouin zone bound-
ary planes and the Fermi surface for a review, see Ref. 8 and
references therein. The fitting of the Brillouin zone to the
Fermi sphere provides, in the corresponding model, minimi-
zation of the electron band structure energy for the structures
observed in In-based alloys. The other approach argues for
an electron-controlled structural competition between the
high-symmetry cubic and low-symmetry tetragonal struc-
tures. It was shown that the tetragonal distortion of the cubic
structure leads to an increased hybridization of the 5s and 5p
valence bands and, consequently, a gain of the band
energy.
9–11
Despite the complexity of the problem, both ap-
proaches successfully accounted for some of the alloy prop-
erties; however, many aspects of their temperature and pres-
sure behavior remain unclear so far. This is exemplified by In
itself: no mechanism has been suggested explaining its nega-
tive thermal expansion, and no approach has been elaborated
allowing understanding of the atypical behavior of the tetrag-
onal distortion in the compressed metal.
There is one more unexplored aspect of the phase transi-
tions occurring in In-based alloys—they are proper ferroelas-
tic transformations. This is allows one, by applying a rather
simple phenomenological formalism, to uncover the generic
features of phase stability and crystal lattice transformations.
This approach is symmetry based and, therefore, model-free.
Its important advantage consists as well in easy incorpora-
tion of different external variables, like pressure, concentra-
tion, or temperature, so that, for instance, the latter is not
restricted to T =0 K.
In this paper we show, using our recent as well as already
published experimental data, that the temperature-pressure-
concentration evolution of the crystal lattice of In-based al-
loys can be comprehensively accounted for in the framework
of a unified phenomenological theory on a symmetry basis
only. We show that the anomalous elastic effects in the alloys
are of a nonequilibrium nature and they are induced by the
same mechanism, which destabilizes the parent cubic struc-
ture.
II. EXPERIMENTAL METHODS
In situ high-temperature and high-pressure data were ob-
tained at the Swiss-Norwegian beamline BM1A of the Eu-
ropean Synchrotron Radiation Facility ESRF, Grenoble,
France. X-ray diffraction patterns were collected in angle-
dispersive geometry using an image plate detector
MAR345. The monochromatic beam at wavelength
=0.7112 or 0.7642 Å was slitted down to 70 70 m
2
. The
sample-to-detector distance and the tilt angles of the detector
were calibrated using Si and LaB
6
NIST standards. The two-
dimensional diffraction images were analyzed using the
ESRF FIT2D software,
12
yielding the one-dimensional inten-
sity vs diffraction angle.
Small chips from polycrystalline alloy lumps were studied
in an externally heated diamond-anvil cell DAC equipped
PHYSICAL REVIEW B 75, 024111 2007
1098-0121/2007/752/0241118 ©2007 The American Physical Society 024111-1