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