Superconductivity and crystallographic transitions of InBi under pressure

Article abstract of DOI:10.1088/0953-8984/10/33/003

Measurements of the superconducting transition temperature T_c of the compound InBi under pressures up to 40 GPa reveal three different regions corresponding to the observed structural transitions I-II-III from the initial phase I of InBi type (t P4) to phase II of β-Np type (t P4) and to a body-centred tetragonal phase III (t 12). Some similarities and distinct differences in the superconducting and structural behaviour of the III-V compound InBi in comparison with the isoelectronic group IV element Sn point to some differences in the possible mechanisms for the crystallographic transformations under pressure.

Full text of DOI:10.1088/0953-8984/10/33/003

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Superconductivity and crystallographic transitions of InBi under pressure
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1998 J. Phys.: Condens. Matter 10 7303
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J. Phys.: Condens. Matter 10 (1998) 7303–7308. Printed in the UK
PII: S0953-8984(98)93161-7
Superconductivity and crystallographic transitions of InBi
under pressure
V G Tissen†, V F Degtyareva†, M V Nefedova†, E G Ponyatovskii† and
W B Holzapfel‡§
†
Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka,
Moscow district, Russia
FB 6 Physik, Universit a¨ t-GH-Paderborn, 33095 Paderborn, Germany
‡
Received 2 April 1998, in final form 12 May 1998
Abstract. Measurements of the superconducting transition temperature Tc of the compound
InBi under pressures up to 40 GPa reveal three different regions corresponding to the observed
structural transitions I–II–III from the initial phase I of InBi type (tP 4) to phase II of β-Np type
(tP 4) and to a body-centred tetragonal phase III (tI2). Some similarities and distinct differences
in the superconducting and structural behaviour of the III–V compound InBi in comparison with
the isoelectronic group IV element Sn point to some differences in the possible mechanisms for
the crystallographic transformations under pressure.
1. Introduction
Group IV elements and isoelectronic III–V compounds are intensively studied
experimentally and theoretically because of the semiconductor-to-metal transition observed
on moving from lighter to heavier elements as well by increase of pressure. The lighter group
IV elements Si and Ge transform under pressure from a diamond type (cF8) semiconducting
structure to metallic phases of white tin type (tI4) and simple hexagonal (hP 1) structure
[1, 2]. III–V compounds with diamond-like structures of zinc blende or wurtzite type at
ambient pressure have high-pressure forms based on NaCl type, white tin type or simple
hexagonal structures with additional complexities such as orthorhombic distortions and
superlattices with or without effects of atomic ordering.
The heavier group IV element Sn does not transform under pressure to the simple
hexagonal structure but shows the different structural sequence [3]: grey tin (cF8) →
white tin (tI4) → tetragonal body centred (tI2) → cubic body centred (cI2). Some
similarity with this behaviour was observed recently in a high-pressure study on the heavier
III–V compound InBi [4]. Unlike the lighter III–V compounds, which are semiconductors
at ambient conditions, InBi forms a semimetallic compound with tetragonal structure of its
1
2
1
2
own type, tP 4, space group P4/nmm with In in the special position 2a (0 0 0;
0) and
1
2
1
2
Bi in 2c (0 z; 0 z¯) with z = 0.393 [5]. InBi is not superconducting at ambient pressure
above 0.5 K [6].
Structural transformations of InBi under pressure are expected to affect also other
physical properties. Especially, the behaviour of the superconducting transition temperature,
§
E-mail address for correspondence: holz we@physik.uni-paderborn.de.
0
953-8984/98/337303+06$19.50 ꢀc 1998 IOP Publishing Ltd
7303

7304
V G Tissen et al
Tc, in this compound seems to be interesting in comparison with high pressure studies of
superconductivity in Sn [7–9] from the point of view that some correlations between crystal
structures and superconducting properties of high-pressure phases had been established
earlier [10] showing a trend of increase in Tc with increasing packing density.
2. Experiment
The sample material was obtained by melting stoichiometric amounts of the pure elements
99.99%) in evacuated silica tubes with further thermobaric treatment as described
(
previously [11]. The structural studies were performed with diamond anvil cells [12]
and energy dispersive x-ray diffraction using synchrotron radiation at the beamline F3 of
HASYLAB/DESY [13, 14]. Either standard diamond anvils with flat faces of 600 µm
or bevelled faces of 300 µm diameter were used depending on the required maximum
pressure. The samples were mounted in the gasket hole of 100–200 µm diameter together
with ruby or gold as a pressure marker and mineral oil as pressure transmitting medium.
All the diffraction patterns are obtained at ambient temperature; however in one series the
◦
sample was heated at ∼17 GPa up to 240 C for 1 hour to reduce deviatoric stresses before
the measurements were performed. More details of the structural studies are described
elsewhere [4]. Specially adopted software [15] was used for the evaluation of the diffraction
spectra.
A diamond anvil cell made out of a nonmagnetic alloy was used in the high-pressure
study of the superconducting transition temperature on samples with typical dimensions of
3
8
0×80×30 µm . Anvils with 500 µm culet diameter were mounted in this case on sapphire
backing plates in order to decrease the inductive coupling between the metallic surroundings
and the coil system used for the ac susceptibility measurements. Gaskets were preindented
to 60 µm from an initial thickness of 300 µm. The sample and several small ruby chips
were loaded in the gasket hole of 150 µm diameter. The common methanol–ethanol mixture
in the ratio 4:1 served as pressure transmitting medium. The cell was cooled down to 1.4 K
in a liquid He cryostat. The temperature was measured by a Cu–Fe/Cu thermocouple with
an accuracy of ±0.2 K. The pressure was determined at room temperature by the ruby
fluorescence method using the nonlinear ruby scale [16] without any correction for thermal-
pressure shifts. The superconducting transition was detected by measuring the ac magnetic
susceptibility as a function of temperature during the heating cycle, thereby the pick-up
coil was positioned around the anvils and a reference coil was placed nearby. The two
coils were parts of an inductor bridge. After initial compensation the signal was detected
with a lock-in amplifier. All the other details of this methods have been described just
previously [17].
3. Results and discussion
Since the structures of the high-pressure phases InBi(II) and InBi(III) were determined just
recently [4], the structural transitions of InBi will be discussed here only with respect to
results on Tc of InBi under pressure.
As illustrated in figure 1, diffraction patterns of InBi show two transformations with
increasing pressure, one at ∼7 GPa and one at ∼20 GPa. The crystal structure of InBi(II)
is tetragonal with four atoms in the unit cell, tP4, space group P4/nmm. It is isostructural
with InBi(I), but with strong compression along the c-axis to c/a ≈ 0.60. Therefore, the
structure shows some similarity to β-Np, however, with its two different atomic species in

Transitions of InBi under pressure
7305
Figure 1. dhkl-values for InBi under pressure. Only two sets of data are shown for phase I
and data with phase mixture in the transition region from phase I to phase II are also omitted
for clarity. Indices for the tP 4 structure are given for both the phases I and II for the stronger
peaks. Phase III is indexed according to a tI2 structure. The inset illustrates structural relations
for the InBi(II)–(III) transition. Solid lines represent the structure of InBi(II, tP 4) with In in the
1
2
1
2
1
1
position 2a (000;
0) and Bi in 2c (0 z; 0z¯). At the transition to InBi (III, tI2) z increases
2
2
1
to reducing the cell to tI2 (dashed lines) with disordering of the atoms.
2
the two different positions: In in 2a (0 0 0, 1 0) and Bi in 2c (0 z, 0 z¯). This structure,
1
2
1
2
1
2
2
InBi(II), shows ‘compositional order’ (see inset to figure 1). The value of the parameter z
is determined from the intensity ratio of the (211) and (220) peaks, since this intensity ratio
is very sensitive to the value of z. As can be seen in figure 2, this small section of the
diffraction spectra demonstrates that the intensity of the (211) peak decreases with increasing
pressure. The free atomic parameter z for Bi changes from z = 0.326 at 3.1 GPa (observed
on decompression) to z = 0.5 at pressures above 20 GPa. At z = 0.5 the structure changes
to higher symmetry and can be described with a smaller unit cell containing only two
atoms. InBi(III) must be compositionally disordered, because no superstructure peaks for
atomic ordering in a primitive tetragonal cell (tP2) are observed. Therefore the structure
of InBi(III) is considered to be body-centred tetragonal (tI2) space group I4/mmm.
The structural transformation II–III seems to be continuous, as shown in figures 1
and 2. The c/a-ratio as function of pressure is shown in figure 3(a) for all the three phases
to illustrate the discontinuity at the I–II transition and the continuous changes in the II–III
transition, whereby the tP 4 assignment is used in this case also for InBi(III).
At ambient pressure, no Tc was observed in InBi above 1.4 K in accordance with the
previous work [6]. However, the small increase in pressure to 0.8 GPa results in a noticeable
superconducting signal which indicates that Tc is close to 1.4 K in this case. The width

7306
V G Tissen et al
Figure 2. Sections of energy dispersive x-ray diffraction spectra for InBi under pressure,
including the two principal peaks (211) and (220) of the tP 4 structure. ‘g’ represents a peak
◦
from the gasket (inconel) in the spectra taken with 2 = 4.943 . Patterns at 5.4 GPa and 3.1
GPa were obtained on decompression in another run without diffraction from the gasket with
◦
2
= 4.850 to illustrate the continuous decrease in the relative intensity of the (211) peak in
the whole range of pressures.
of the transition is about 0.2 K and does not change appreciably with increasing pressure.
The pressure dependence of the superconducting transition temperature Tc (the midpoint of
the susceptibility change) is displayed in figure 3(b), which demonstrates a quite different
Tc(P) behaviour in three different regions. At first, Tc increases steeply with increasing
pressure to about 6 GPa, then Tc(P) has only a small positive slope and above 15 GPa Tc
shows a strong decrease.
The pressures values for the anomalies in Tc are close to values where structural
transitions occur at room temperature. The small differences can be accounted for by
variations of the phase boundaries with temperature and by small differences between the
pressures measured at ambient temperature and the actual pressures at low temperature. In
any case, the three different regions on the Tc(P ) curve are clearly related to the three
different structures of InBi (I to III).
The drastic increase of Tc under pressure for InBi(I) represents an unusual behaviour in
comparison with normal metals but it correlates with the strong anisotropy of this structure:
the compressibility along c is an order of magnitude larger than along a, as shown also
earlier by precise measurements with neutron powder diffraction up to 2.6 GPa [18] and
confirmed by the recent high pressure x-ray study [4]. At P = 6.2 GPa the phase InBi(I) has
the lattice parameters a = 495.1 pm and c = 445.7 pm with c/a = 0.900 and extrapolation
of the data for phase II down to this pressure gives the lattice parameters a = 557.7 pm
and c = 335.4 pm with c/a = 0.601. At the I–II transition the axial ratio decreases thus by
3
2
3%, the c-axis decreases by 25%, the a-axis expands by 12.5% and the volume changes by
%. The sharp increase of Tc with pressure and the elastic anisotropy of InBi(I) correlate
with previously observed anomalies in resistivity and acoustic measurements, and had been
assigned to pressure induced electron changes [19].

Transitions of InBi under pressure
7307
Figure 3. Effect of pressure on InBi illustrating the boundaries between the phases I, II and III:
(
a) c/a-ratio for a common tP 4 unit cell (O from [17], other symbols—different runs from [4]).
Horizontal lines show lower and upper limits of c/a for phase III which are 0.644 and 0.675
for the tP 4 unit cell and 0.911 and 0.955 for the tI2 unit cell, respectively, as discussed in [4].
(b) Superconducting transition temperature Tc (two different runs). Dashed lines are guides to
the eye.
It is interesting to compare the structural and superconducting behaviour under pressure
for InBi with the isoelectronic group IV element Sn. The structural analogue of β-Sn(tI4)
is the β-Np-like structure of InBi(II, tP 4) because both structures are tetragonal with four
atoms in the unit cell and show nearly the same axial ratios. While the β-Sn structure has
space group I41/amd with one atomic position 4a (0 0 0, 0 1 ) which accommodates only
1
4
2
one atomic species, the β-Np-type structure with space group P4/nmm has two different
atomic positions to accommodate two different atomic species. Despite some resemblance
of the two structures, the behaviour of Tc for InBi(II) differs considerably from the one
of β-Sn, which shows a large decrease of Tc with increasing pressure [7, 8]. Furthermore,
the transformation to the Sn(tI2) structure is accompanied with a discontinuous increase
of Tc (figure 4), whereas the II–III transformation of InBi can be described as displacive
type with a continuous increase in the atomic parameter z from ∼0.33 to 0.5. At the value
1
2
z = , the symmetry changes from P4/nmm to P4/mmm (if ordered) or to I4/mmm
(if disordered). The absence of any discontinuous change in Tc at the II–III transition is
compatible with a (second order) displacive character for this transition. In addition, this
transformation seems to involve a change from atomic order to disorder due to a systematic
absence of the respective x-ray diffraction intensities for InBi(III). Therefore, InBi(III) is
an analogue of bct-Sn(tI2) and this is a second example of a tetragonally distorted body-
centred structure with an axial ratio in the range 0.91–0.96. Obviously, this similarity of
the pressure dependence of Tc for both InBi(III) and bct-Sn, as shown in figure 4, points
also to a close similarity in the electronic structure of both phases.

7308
V G Tissen et al
Figure 4. Dependence of Tc on atomic volume for InBi and for Sn. Dashed lines are guides to
the eye. Comparison of Tc against volume shows similarities for β-Sn and InBi(II)-β-Np type
at the lowest pressure (at nearly equal volumes), but significant difference in Tc behaviour on
compression. Further similarities can be noticed in the slopes of Tc(V ) for the tI2 phases of
both substances.
Acknowledgments
The authors wish to thank W Sievers and W Br o¨ ckling for experimental assistance. This
work was partially supported by the Russian Foundation for Basic Research through grants
96-15-96806 and 96-62-18545.
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