High-pressure elastic properties of gallium phosphide
Alain Polian
Physique des Milieux Condense´s, Universite´ Pierre et Marie Curie, B 77, 4 Place Jussieu, F-75252 Paris, Cedex 05, France
Marcos Grimsditch
Materials Science Division, Argonne National Laboratories, 9700 South Cass Avenue, Argonne, Illinois 60439
~Received 24 November 1998!
The pressure dependence of the elastic constants C
ij
of GaP have been measured up to 15 GPa in a diamond
anvil cell. Brillouin backscattering experiments along the principal crystallographic directions yielded four
combinations of elastic constants from which the three independent C
ij
were extracted. Above 15 GPa the
closure of the energy band gap prevents the detection of the signal. @S0163-1829~99!04827-4#
I. INTRODUCTION
Like many III-V semiconductors, gallium phosphide crys-
tallizes in the cubic zinc-blende structure ( F 4
¯
3 m space
group!. In this structure, the atoms are tetrahedrally bonded
to their nearest neighbors through covalent bonds. Under
pressure, the cubic phase is destabilized, and a transition to a
tetragonal metallic phase occurs. At room temperature, this
transition takes place in the 20-GPa range.
The properties of the zinc-blende phase as a function of
pressure have been studied by Raman scattering up to 13.5
GPa,
1–5
fundamental absorption,
6
refractive index
measurements,
7
and a combined x-ray diffraction-x-ray ab-
sorption spectroscopy experiment.
8
The transition to the me-
tallic phase was first observed in resistivity
measurements,
9,10
and then by x-ray diffraction.
11–13
The elastic properties were studied under hydrostatic and
uniaxial pressures up to about 0.14 GPa using ultrasonics.
14
From such a study, the second- and third-order elastic
moduli were deduced, and hence the bulk modulus B and its
pressure derivative B 8 .
In the present paper we present the pressure dependence
of the second-order elastic moduli of GaP up to 15 GPa
measured by Brillouin scattering in a diamond anvil cell.
Section II of this paper is devoted to a brief presentation
of the experimental techniques used, as well as to details of
the data analysis. The results obtained for GaP are presented
and discussed in Sec. III.
II. EXPERIMENT AND BACKGROUND
The Brillouin scattering technique has been extensively
described in the literature.
15,16
The 514.5-nm argon ion laser
line with a single longitudinal mode was used with an input
power of about 150 mW. In the present study, we used a 5
14 tandem Fabry-Perot interferometer. The diamond anvil
cell was of the Block-Piermarini type,
17
and hence all experi-
ments were restricted to the backscattering geometry. In this
geometry, the shift ~in cm
21
! of the scattered radiation is
given by
D s 52 n v / l c , ~1!
where n is the refractive index of the medium, l the wave-
length of the incident radiation ~in cm!, c the velocity of
light, and v the velocity of sound in the medium. Experi-
ments were performed with three different directions of pho-
non propagation: @100#, @110#, and @111#. Longitudinal
modes are observed for all three propagation directions,
18
additionally a transverse mode is also observed for the @111#
direction.
18
The combinations of elastic moduli involved in
these experiments are summarized in Table I. Argon was
used as a pressure transmitting medium in all our experi-
ments, and the pressure was measured from the shift of the
R
l
luminescence peak of a ruby microsphere, using the
quasihydrostatic scale.
19
In order to deduce the sound velocity from Eq. ~1!, it is
necessary to know the pressure dependence of the refractive
index. We used the determination of Ref. 7, i.e.,
n ~ l , P ! 5n ~ l ! 1
S
] n ~ l , P !
] P
D
l
P 1
S
]
2
n ~ l , P !
] P
2 D
l
P
2
, ~2!
TABLE I. Combination of elastic moduli involved in the vari-
ous propagation directions explored.
Propagation
direction Polarization Combination of elastic moduli
@100# L C
11
@110# L ( C
11
1C
12
12 C
44
)/2
@111# L ( C
11
12 C
12
14 C
44
)/3
@111# T ( C
11
2C
12
1C
44
)/3
TABLE II. Ambient condition elastic moduli and bulk modulus
~in GPa! obtained by different authors.
C
11
C
12
C
44
B Ref.
141.260.3 62.560.3 70.560.1 88.861 Weil ~Ref. 20!
141.4 64 70.3 89.8 Boyle ~Ref. 21!
141.163.8 62.662.5 70.361.2 88.866 Yamada ~Ref. 22!
145.1 61.1 71.6 89.1 Pesin ~Ref. 23!
137.5 59.4 72.2 85.4 Gehrlich ~Ref. 24!
140.5 62.0 70.3 88.1 Yogˇurtc¸u ~Ref. 14!
146.160.9 63.661.2 69.960.8 91.165 Present work
PHYSICAL REVIEW B 15 JULY 1999-I VOLUME 60, NUMBER 3
PRB 60 0163-1829/99/60~3!/1468~3!/$15.00 1468 ©1999 The American Physical Society