High-Pressure Phase Transition And Multi-phase Equation Of State For Sn

Phase diagram and equation of state(EOS)are of great importance for the investigation on dynamic mechanical feature of materials,with which the change of materials state during dynamic progress might be possibly understood,simulated,and predicted.For Sn with typical multi-solid phase,there still is divergence on melting behavior at high pressure.EOS of multi-solid phase have not yet determined correctly.So,experimental and theoretical investigations to determine the phase boundary and EOS of multi-solid phase have been carried out in presented study.In this work,the porous Sn with two relatively low initial porosities and the solid Sn are experimentally investigated to obtain multiple experimental melting data on melting line.Inverse impact shock experiments were performed to measure the longitudinal sound velocity of Sn with porosities of 1.01 and 1.02.The transition points of the longitudinal sound velocities indicated that the Sn with different porosities shows different melting pressures,which are 49 GPa(porosity 1.01)and about 46 GPa(porosity 1.02),respectively.Additionally,the longitudinal sound velocities of solid Sn at pressures of 53.4 GPa and 60.1 GPa were measured.Combining the experimental data for solid and porous Sn,shock melting pressure was revised to about 58 GPa for solid Sn.And the liquid incipient pressure was found to be about 66 GPa.Based on the measured longitudinal sound velocities data,refined phase transition on Hugoniot curves were discussed.From the sound velocities of porous Sn,bcc phase transition was not observed along Hugoniot.From the velocity histories,state parameters of phase transition along release path were also obtained.Based on GRAY code,a three-phase(solid,liquid and vapor)EOS for metals,solid phase transition EOS modules were established.Parameters of each phase were determined independently.And each phase was calculated independently.Increment of internal energy at normal condition of the phase exist in high pressure area relative to that of the neighbor phase exist in low pressure area was considered.The increased internal energy and entropy were determined from the phase transition state parameters and the slope dP/dT of 300 k isotherm.The volume fraction of each phase in mix phase area was determined from input free parameter volume V and phase transition volume at the first and end point of phase transition area of each isotherm.The execution process of phase transition calculation was presented.And the basic EOS was verified by experimental data of Al and Pb.For Sn,four solid phase EOS were constructed.Parameters in EOS of each phase were restrained using the experimental data in this work and other references.Multi-solid phase diagram of Sn in the pressure range 0-160 GPa is given.The EOS was further verified by isentropic released data from experiments.Melting line determed in this article is consistent with the experimental data of R Briggs' published in 2017 from the static compression.It is worthy to point out that real track of ?-bcc and bcc-hcp phase boundaries still need to be determined by experimental data.