Crystal structure of InBi under pressure up to 75 GPa

Article abstract of DOI:10.1103/PhysRevB.57.4975

InBi is studied by energy-dispersive diffraction with synchrotron radiation in a diamond-anvil cell under pressure up to 75 GPa. Three phase transitions are observed from its initial tetragonal structure tP4 with c/a≈0.95 to another tP4 structure with c/a≈0.65 typical for the β-Np structure, than to a disordered tetragonal body-centered structure tI2, and finally some hints are obtained for a transition to a cubic body-centered structure cI2. All these transformations are reversible with large hysteresis. InBi(tI2), phase III, shows initially a steep increase in c/a from 0.91 to 0.94, in the pressure range from 20 to 30 GPa, and a nearly constant value of about 0.96 above 55 GPa. Hints for the possible stability of a new phase IV are noticed in the present experiments on decompression from 75 GPa as admixture of new lines to phase III giving strong indications for a first-order phase transition with large hysteresis. The origin of the tetragonal distortion and the transformation to a cubic phase are discussed from the point of view of nesting the Fermi sphere in the Brillouin zone.

Full text of DOI:10.1103/PhysRevB.57.4975

PHYSICAL REVIEW B
VOLUME 57, NUMBER 9
1 MARCH 1998-I
Crystal structure of InBi under pressure up to 75 GPa
V. F. Degtyareva
Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow district, 142432 Russia
M. Winzenick and W. B. Holzapfel
¨
FB 6 Physik, Universitat-GH-Paderborn, 33095 Paderborn, Germany
͑Received 1 July 1997͒
InBi is studied by energy-dispersive diffraction with synchrotron radiation in a diamond-anvil cell under
pressure up to 75 GPa. Three phase transitions are observed from its initial tetragonal structure tP4 with
c/aϷ0.95 to another tP4 structure with c/aϷ0.65 typical for the ␤-Np structure, than to a disordered tetrag-
onal body-centered structure tI2, and finally some hints are obtained for a transition to a cubic body-centered
structure cI2. All these transformations are reversible with large hysteresis. InBi(tI2), phase III, shows
initially a steep increase in c/a from 0.91 to 0.94, in the pressure range from 20 to 30 GPa, and a nearly
constant value of about 0.96 above 55 GPa. Hints for the possible stability of a new phase IV are noticed in the
present experiments on decompression from 75 GPa as admixture of new lines to phase III giving strong
indications for a first-order phase transition with large hysteresis. The origin of the tetragonal distortion and the
transformation to a cubic phase are discussed from the point of view of nesting the Fermi sphere in the
Brillouin zone. ͓S0163-1829͑98͒00110-6͔
INTRODUCTION
ing the present structural study on InBi in situ under pres-
sures up to 75 GPa.
Structural systematics for the group IV elements and for
the isoelectronic III-V compounds have been the subject of
many recent experimental and theoretical high-pressure stud-
ies. Besides the increase in coordination numbers and pack-
ing efficiency a general structural sequence is found for Si
and Ge of the type diamond-like(cF8)→␤-tin(tI4)
EXPERIMENTAL DETAILS
The present study was performed with diamond-anvil
cells25,26 and energy-dispersive x-ray diffraction ͑EDXD͒ us-
ing synchrotron radiation at the beamline F3 of
HASYLAB/DESY.27,28 The samples were mounted in gasket
holes 120 ␮m diameter or larger, together with ruby or gold
as pressure marker29,30 and mineral oil as the pressure trans-
mitting medium. The sample material was obtained by melt-
ing stoichiometric amounts of the pure elements ͑99.99%͒
subjected to thermobaric treatment, as described
previously.24 Small pieces from these samples were used for
four sets of experiments at room temperature. In two addi-
tional series the samples were heated in the diamond cell
under pressure up to 240 °C for 1–2 h to check for special
effects of kinetics, recrystallization, and order-disorder tran-
sitions. Specially adopted software31 was used for the evalu-
ation of the diffraction spectra.
→simple hexagonal(hP1)→hcp(hP2)/fcc(cF4)
exper-
imentally1–4 and in theoretical calculations.4–6
Isoelectronic III-V compounds display
a
similar
structural sequence under pressure: zinc blende(cF8)
→NaCl(cF8)/white tin type(tI4)→simple hexagon-
al(hP1). In addition to these rather simple structures also
more complicated structures with free atom position param-
eters are found.7–9 Besides disordered structures also struc-
tures with atomic ordering and large superlattices are
observed,10–13 and theoretical studies have been performed
for III-V compounds.14–18
However for the heavier III-V compound InBi experimen-
tal data were available up to now only for pressures below 3
GPa ͑Ref. 19͒ and a comparison with the heavier group IV
element tin with its structural sequence ␤-tin(tI4)
20,22
→bct(tI2)→bcc(cI2) ͑without hP1͒
leads to the ex-
RESULTS AND DISCUSSION
pectation of a special behavior also for InBi.
The diffraction spectra for the initial phase InBi͑I͒ were
strongly effected by texture. Nevertheless, the diffraction
spectra gave clear evidence for the formation of a new phase
II at pressures 7–8 GPa. The positions and intensities of the
corresponding diffraction peaks changed gradual after this
transition up to 20–22 GPa, where systematic changes in the
diffraction spectra signaled the occurrence of a new phase
III. Typical diffraction spectra of InBi in the three modifica-
tions are shown in Fig. 1. To reduce effects from stress and
texture, one sample was pressurized to 20 GPa and annealed
at this pressure for 2 h at 240 °C. The spectrum obtained at
20.1 GPa after cooling to room temperature corresponds to
pure InBi͑III͒. The spectra in Fig. 1 for 3.1 and 0 GPa were
At ambient conditions InBi forms a metallic compound
with tetragonal structure of its own type, tP4, space group
P4/nmm with In in the special position 2a (000;1/2 1/2 0)
¯
and Bi in 2c (0 1/2 z;1/2 0 z) with zϭ0.393, aϭ500.0 pm,
cϭ477.3 pm, and c/aϭ0.9546.23 Neutron powder diffrac-
tion up to 2.6 GPa ͑Ref. 19͒ showed only a large decrease in
c/a, but a complex structural behavior was observed later in
quenched InBi alloys after thermobaric treatment ͑P
р7 GPa, Tр300 °C͒.24 New phases were obtained in meta-
stable states ͑at Pϭ0 GPa, TϭϪ100 °C͒, some showing
simple hexagonal structure (hP1) and others more complex
structures which are not yet determined definitely, motivat-
0163-1829/98/57͑9͒/4975͑4͒/$15.00
57
4975
© 1998 The American Physical Society

4976
BRIEF REPORTS
57
TABLE I. Observed and calculated d spacings and integrated
intensities for the EDXD spectrum of InBi͑II, tP4͒ at 3.1 GPa. The
best fit gives aϭ566.5(1) pm and cϭ337.3(1) pm. Intensities are
calculated for zϭ0.33 and normalized to I(200). A sample thick-
ness of 40 ␮m was assumed.
(hkl)
dobs ͑pm͒
dcalc ͑pm͒
Iobs
Icalc
110
101
200
111
211
220
310
301
102
311
112
321
400
212
411
420
302
331
312
322
400.4
289.7
283.2
258.0
202.6
200.4
179.2
164.8
161.5
158.3
155.4
400.6
289.8
283.3
258.0
202.6
200.3
179.1
164.8
161.6
158.2
155.4
142.4
141.6
140.4
127.2
126.7
125.8
124.2
122.8
115.0
4
12
100
32
20
16
2
4
2
12
1
8
60
100
62
42
33
3
8
7
20
9
8
6
7
4
6
2
3
4
2
142.0
140.3
126.9
10
2
5
125.7
124.2
122.8
115.0
1
2
1
1
atoms in the positions ͑000͒ and (1/2 1/2 1/2). The fitting of
the observed diffraction peaks to this tetragonal cell is illus-
trated in Table II. Thereby the difference in the atomic num-
bers for In ͑49͒ and Bi ͑83͒ is large enough to cause some
‘‘difference’’ reflections for an ordered structure, however
there was no evidence for this atomic ordering in the spectra,
and therefore this new structure must be described as body-
centered tetragonal (tI2), which is the same structure as for
the high-pressure form of tin.
FIG. 1. EDXD spectra of InBi at different pressures measured
with ⍜ϭ4.85°. f and e denote fluorescence and escape peaks,
respectively. Diffraction lines of phases I and II are indexed accord-
ing to tP4 and phase III according to tI2.
obtained from the same sample on decompression and cor-
respond to InBi͑II͒ and InBi͑I͒, respectively. These spectra
illustrate the complete reversibility of these two transforma-
tions.
A structural assignment for the diffraction data of InBi͑II͒
is given in Fig. 1 and shown in more detail in Table I. Spe-
cial assignment software31 finds only this one solution with
four atoms in the unit cell according to a tetragonal primitive
metric tP4, which gives indeed a perfect matching for all the
observed and calculated line positions within the resolution
of the EDXD technique.
Figure 2 represents the change of the average atomic vol-
ume vs pressure for the three phases. The equation of state
͑EOS͒ for phase III is represented equally well by two dif-
TABLE II. Observed and calculated d spacings and integrated
intensities for the EDXD spectrum of disordered InBi͑III, tI2͒ at
20.1 GPa. The best fit gives aϭ371.3(1) pm and
c
ϭ342.3(1) pm. Intensities are normalized to I(101). A sample
thickness of 40 ␮m was assumed.
In fact, this metric represents only a sudden change in c/a
from ϳ0.91 to ϳ0.61 at the transition from phase I to II. If
one adopts the same space group P4/nmm for both phases
with In on the position 2a (000, 1/2 1/2 0) and Bi on 2c
(hkl)
dobs ͑pm͒
dcalc ͑pm͒
Iobs
Icalc
110
101
200
002
211
112
220
202
310
301
262.6
251.7
185.7
171.4
149.4
143.4
131.3
125.9
117.5
116.5
262.5
251.7
185.7
171.1
149.4
143.4
131.3
125.8
117.4
116.4
72
100
59
2
29
5
4
5
3
5
63
100
20
7
30
12
5
6
4
4
¯
(0 1/2 z;1/2 0 z ) one finds also reasonable agreement be-
tween observed and calculated intensities for the correspond-
ing pattern at 3.1 GPa with zϭ0.33. The decrease in the
intensity ratio I211 /I220 towards zero at higher pressures
points to an increase in z→0.5 and the ratio I211 /I220Ͼ1 at
3.1 GPa is only compatible with ordering of In on 2a and Bi
on 2c sites but not with the opposite assignment. On the
other hand, for zϭ1/2 this structure can be represented by a
smaller tetragonal unit cell with anewϭaold /& with its two

57
BRIEF REPORTS
4977
FIG. 2. Effect of pressure on the atomic volume for InBi.
Crosses: phase I ͑Ref. 19 and one data point from the present work
at 5 GPa͒. Triangles: phase II ͑three different runs͒. Diamonds and
circles: phase III. Squares: phase IV. Open symbols denote com-
pression and solid symbols decompression, respectively.
ferent EOS forms, however, with significantly different val-
ues for the commonly used free parameters: V0 for the ͑ex-
trapolated͒ volume at ambient pressure, K0 for the
corresponding bulk modulus, and KЈ0 for its pressure deriva-
tive. The second-order Birch equation32 results in V0
ϭ28.2(4)ϫ106 pm3, K0ϭ67(8) GPa, and K0Јϭ3.8(2),
whereas the more recently proposed form H12 ͑Ref. 30͒
gives V0ϭ27.98(2)ϫ106 pm3, K0ϭ74.7(3) GPa, and K0Ј
ϭ3.05(2) with significantly smaller standard deviations for
the strongly correlated parameter values.
FIG. 4. Effect of pressure on InBi and Au diffraction peaks in
EDXD spectra (⍜ϭ4.24°) showing the approach towards cubic
InBi͑IV͒ in the spectra numbered 3–23 and the reversal on further
decompression.
Changes in the axial ratio for the phases II and III with
pressure are shown in Fig. 3, which gives also the structural
relation between phases II(tP4) and III(tI2) assuming that
phase III is disordered. With increasing pressure c/a of
InBi(tI2) ͑phase III͒ shows at first a steeper increase and
later an almost constant value of about 0.960 up to the high-
FIG. 3. c/a ratios vs pressure for InBi͑II͒ ͑left-hand scale͒ and
for InBi͑III͒ ͑right-hand scale͒. The values 3/␲ and (3/␲)2 repre-
sent special cases of c/a ͑see text͒. c/aϭ1 corresponds to cubic
InBi͑IV͒. The shaded area represents a region of hysteresis for the
II-III phase transition. The inset illustrates structural relations for
the InBi͑II͒-͑III͒ transition. Solid lines represent the structure of
InBi(II, tP4) with In in the position 2a(0 0 0; 1/2 1/2 0) and Bi in
FIG. 5. Peak profiles fitted as doublet (110ϩ101)t at 71.2 GPa
and as triplet including (110)c and (110ϩ101)t at decompression.
The values for the halfwidths were fixed for all three peaks to the
values from well resolved spectra at lower pressures. To compen-
sate for the line shifts, the energies are scaled to different reference
values Er .
¯
2c(0 1/2 z; 1/2 0 z ). At the transition to InBi(III, tI2) z increases
to 1/2 reducing the cell to tI2 ͑dashed lines͒ with disordering of the
atoms.

4978
BRIEF REPORTS
57
est pressure of 75 GPa for the present study. However, on
decompression ͑Fig. 4͒ the (110)ϩ(101) doublet changes its
shape and a deconvolution gives strong hints for the admix-
ture of a third component ͑Fig. 5͒ corresponding to a ͑110͒
peak for a new cubic phase IV similar to the high-pressure
behavior of Sn.21 The admixture of this extra line for a new
phase InBi(cI2) ͑phase IV͒ increases at first on further de-
compression down to about 60 GPa ͑Fig. 5͒ before the cubic
component disappears around 50 GPa. From the number of
observed lines one would conclude that this new phase IV
would also show disorder with respect to the occupation of
the lattice sites by In or Bi atoms and the change in the
lattice parameters in the III-IV phase transition would corre-
spond to a volume change of less than 1% explaining to
some extend the sluggishness of the transition. Certainly, this
interpretation of the present spectra needs further support by
measurements at higher pressures, by pressure cycling
around the transition, and by measurements at higher tem-
peratures. Since however similar features of a tetragonal-to-
cubic transition with small volume change, discontinuity in
c/a, and phase coexistence over a substantial range of pres-
sure were previously observed for tin,21,33 and theoretical
high-pressure studies for tin34 indicate that the energy differ-
ence between these two phases is indeed very small over a
large range in pressure, it appears necessary to point out this
possible interpretation of the present spectra in the range
between 60 and 80 GPa.
The tetragonal distortions for the high-pressure phases of
both tin and InBi can be explained qualitatively within the
nearly-free-electron approach due to the additional lowering
in the crystal energy by the so-called band-structure terms. If
one considers for sp metals the Fermi sphere nesting in the
Brillouin zone of some noncubic structures, special values in
axial ratios for certain hexagonal and tetragonal structures
can be stabilized for specific values of the number of free
electrons per atom ne .35
For the cI2 structure with neϭ4 one finds that kF is
larger than the lattice parameter 2␲/a of the reciprocal lat-
tice and a distortion to tI2 is favored with an optimum value
of c/aϭ3/␲ϭ0.955. Simple geometric relations between kF
and reciprocal-lattice parameters of cubic and tetragonal
structures, for instance kF /(2␲/ac)ϭ(2␲/at)/kF , provide
another special value for the axial ratio: c/aϭ(3/␲)2
ϭ0.912. These values are very close to the experimentally
observed limits of c/a ratios for the tI2 phases of Sn ͑Refs.
21, 33͒ and InBi͑III͒ ͑see Fig. 3͒.
ACKNOWLEDGMENTS
The authors wish to thank G. Reiss and W. Sievers for
experimental assistance. V.D. acknowledges support from
DAAD.
1 S. K. Sikka, H. Olijnyk, and W. B. Holzapfel, Phys. Lett. 103A,
137 ͑1984͒.
͑1966͒.
21 H. Olijnyk and W. B. Holzapfel, J. Phys. ͑Paris͒ Colloq. 45, C8-
153 ͑1984͒.
2 J. Z. Hu and I. L. Spain, Solid State Commun. 51, 263 ͑1984͒.
3 S. I. Duclos, Y. K. Vohra, and A. L. Ruoff, Phys. Rev. Lett. 58,
775 ͑1987͒.
22 S. Desgreniers, Y. K. Vohra, and A. L. Ruoff, Phys. Rev. B 39,
10 359 ͑1989͒.
4 Y. K. Vohra, E. Brister, S. Desgreniers, A. L. Ruoff, K. L. Chang,
and M. L. Cohen, Phys. Rev. Lett. 56, 1944 ͑1986͒.
5 M. T. Yin and M. L. Cohen, Phys. Rev. B 26, 5668 ͑1982͒.
6 K. J. Chang and M. L. Cohen, Phys. Rev. B 30, 5376 ͑1984͒.
7 S. T. Weir, Y. K. Vohra, and A. L. Ruoff, Phys. Rev. B 36, 4543
͑1987͒.
23 Pearson’s Handbook of Crystallographic Data for Intermetallic
Phases, edited by P. Villars and L. D. Calvert ͑American Soci-
ety for Metals, Metals Park, OH, 1985͒.
24 V. F. Degtyareva, S. A. Ivakhnenko, E. G. Ponyatovskii, and V. I.
Rashchupkin, Fiz. Tverd. Tela ͑Leningrad͒ 24, 1350 ͑1982͒
͓Sov. Phys. Solid State 24, 770 ͑1982͔͒.
8 C. A. Vanderborgh, Y. K. Vohra, and A. L. Ruoff, Phys. Rev. B
40, 12 450 ͑1989͒.
25 K. Syassen and W. B. Holzapfel, Europhys. Conf. Abstr. 1A, 75
͑1975͒.
9 S. T. Weir, Y. K. Vohra, C. A. Vanderborgh, and A. L. Ruoff,
Phys. Rev. B 39, 1280 ͑1989͒.
26 W. B. Holzapfel, in High Pressure Chemistry, edited by H. Kelm
͑Reidel, Boston, 1978͒, p. 177.
W. A. Grosshans, E.-F. Dusing, and W. B. Holzapfel, High
10 R. J. Nelmes, M. I. McMahon, P. D. Hatton, J. Crain, and R. O.
Piltz, Phys. Rev. B 47, 35 ͑1993͒.
27
¨
Temp.-High Press. 16, 539 ͑1984͒.
11 M. I. McMahon, R. J. Nelmes, N. G. Wright, and D. R. Allan,
Phys. Rev. B 50, 13 047 ͑1994͒.
28 J. W. Otto, Nucl. Instrum. Methods Phys. Res. A 384, 552 ͑1997͒.
29 H. K. Mao, P. M. Bell, J. W. Shaner, and D. J. Steinberg, J. Appl.
Phys. 49, 32 ͑1978͒.
12 M. I. McMahon and R. J. Nelmes, J. Phys. Chem. Solids 56, 485
͑1995͒.
30 W. B. Holzapfel, Europhys. Lett. 16, 67 ͑1991͒; Rep. Prog. Phys.
59, 29 ͑1996͒.
13 R. J. Nelmes and M. I. McMahon, Phys. Rev. Lett. 74, 106
͑1995͒.
31 F. Porsch, EDXPOWDER-program for evaluation of EDXD spectra,
RTI, Paderborn, Germany, 1969.
14 S. B. Zhang and M. L. Cohen, Phys. Rev. B 35, 7604 ͑1987͒.
15 S. B. Zhang and M. L. Cohen, Phys. Rev. B 39, 1450 ͑1989͒.
16 G. Y. Guo, J. Crain, P. Blaha, and W. M. Temmerman, Phys.
Rev. B 47, 4841 ͑1993͒.
32 F. Birch, J. Geophys. Res. 83, 1257 ͑1978͒.
33 M. Liu and L. Liu, High Temp.-High Press. 18, 79 ͑1986͒.
34 J. L. Corkill, A. Garcia, and M. L. Cohen, Phys. Rev. B 43, 9251
͑1991͒.
17 A. Garcia and M. L. Cohen, Phys. Rev. B 47, 6751 ͑1993͒.
18 A. Mujica, R. J. Needs, and A. Munoz, Phys. Rev. B 52, 8881
͑1995͒.
19 J. D. Jorgensen and J. B. Clark, Phys. Rev. B 22, 6149 ͑1980͒.
20 J. D. Barnett, V. E. Bean, and H. T. Hall, J. Appl. Phys. 37, 875
35 V. F. Degtyareva, in Stability of Materials, Vol. 355 of NATO
Advanced Study Institute, Series B: Physics, edited by A. Gonis,
P. E. A. Turchi, and J. Kudrnovsky ͑Plenum, New York, 1996͒,
p. 465.