Sound Velocities And Elastic Properties Of Silicon Under High Pressures

Silicon has been intensively studied on its mechanical and electronic properties at ambient pressure and it has been widely used in semiconductor field.Upon compression,silicon metalizes and undergoes a series of phase transitions,and thus is considered as a representative elemental solid on pressure-induced phase transitions studies.Up to now,a great deal of studies of silicon about its phase transitions and crystal structures have been performed by X-ray diffraction technique.However,measurement of elastic parameters under high pressures is still a challenge.Only very a few works reported their abilities to study the elastic properties of silicon in low-pressure region.Measurement of sound velocity is an efficient way to probe intrinsic elastic properties of solid matter.In this paper,picosecond laser ultrosonics?PLU?technique combined DAC is used to study the sound velocities as well as elastic properties of silicon under high pressures.Silicon remains stable from 1 atm.to 9 GPa in a diamond cubic?Si-I?structure;for the primitive hexagonal structural silicon?Si-V?,it has been found to be stable and unique phase in the pressure range from 18 GPa to 38 GPa,after intermediate phase transitions from Si-I to Si-V.In this work,sound velocities and elastic properties of silicon have been studied between 0-9 GPa and 18-37 GPa.Firstly,we found that the starting silicon sample remains as single crystal till 9 GPa,and we measured the longitudinal sound velocities along<100>direction.Secondly,with the densities and bulk modulus of silicon under high pressure extracted from the well-known equation of state,the pressure-dependent elastic constants C₁₁ and C₁₂ have been deduced,then compared with our calculations and published experimental and theoretical results.For the Si-V phase,the sample could be regarded to be elastically isotropic due to the appearance of smaller randomly oriented grains after three phase transitions.We found that from 18 GPa to 27 GPa,the measured velocities correspond to the average sound velocity in Si-V.The corresponding shear modulus has thus been obtained.It is worth noting that,above 27 GPa,the measured velocities increase much faster and deviate from the theoretical V_L?avg?,but toward the maximum theoretical velocity in single crystalline Si-V?known to be along the c-axis?,which indicates that the developing texture was characterized by a growing number of grains which c-axis pointed into the propagation direction of the sound pulse,perpendicular to the diamond culet.We did not have a further discussion on data between 9-18 GPa,since two or more phases co-exist during the phase transition processes,under which circumstances we do not know the proportion of each phase,posing difficulties to the quantitative study of a certain phase.The picosecond laser ultrasonics is an advanced all-optical pump-probe technique which demonstrates irreplaceable advantages compared to other optical techniques like Brillouin light scattering and synchrotron–based X-ray diffraction techniques.And the high time resolution of PLU allows measurements on micron-size samples loaded in DAC.The combination of PLU and DAC demonstrate immense potentialities in condensed matter physics and geophysics.