Softening of sound velocity and Hugoniot parameter measurement for shocked bismuth in the solid-liquid mixing pressure zone

Abstract

Polymorphic phase transformation and melting under shock wave loading are important for studying the material dynamic mechanical behavior and equation of state in condensed matter physics. In this paper, the accurate Hugoniot parameter and sound velocity of shocked pure bismuth (Bi) in a pressure range of 17.3-28.3 GPa are obtained by using flyer impact method and rarefaction overtaking technique, respectively, and the sound velocity softening trend in shock-induced melting zone and the melting kinetics of Bi are then analyzed. In each experiment, six Bi samples with different thickness values are affected by oxygen-free-high-conducticity copper flyer fired through power gun. Shock wave velocity and particle velocity in Bi are experimentally determined through measuring the impact velocity and shock wave time in the thickest sample by photon Doppler velocimetry (PDV) technique. The velocity profiles on each interface between Bi and lithium fluoride (LiF) window are measured by displacement interferometer system of any reflector (DISAR), and then the sound velocity of shocked Bi is determined using the rarefaction overtaking method. The analyses of our results show that the softening of sound velocity of Bi approximatively satisfies the linear relation of Cs=3.682-0.015 p in the solid-liquid coexistence zone, and the pressure zone of the solid-liquid coexistence phase is further affirmed to be in a range of 18-27.4 GPa. Additionally, the obtained Hugoniot data for Bi in this paper supply a gap in the pressure zone of solid-liquid mixing phase. The quadratic equation with the expression of Ds=0.401+ 3.879 up-0.876 up2 can better demonstrate the relation between shock wave velocity and particle velocity than a linear one when the particle velocity lies in a range of 0.5-1.0 km/s, and this non-linear property maybe has a relationship with the shock-induced melting of Bi. Finally, our wave profile measurement of the Bi/LiF interface shows peculiar ramp characteristics in the expected velocity plateau zone in the pressure zone of solid-liquid coexistence phase, which may be associated with both the nonhomogeneous melting kinetics and the long time scale of melting for bismuth.

Equation of State for Bismuth at High Energy Densities

“…The results of the calculation of the shock adiabats for bismuth samples of different initial densities are shown in Figures 2-4 in comparison with the available shock-wave data [55][56][57][58][59][60][61][62][64][65][66][67]]. An analysis of the figures allows one to conclude that the calculated shock adiabats are in good agreement with the experimental data in the entire studied region of states of the bcc and liquid phases of bismuth.…”

“…The shock compressibility of bismuth has been studied using traditional planar explosive systems [55][56][57][58][59][60][61][62][63][64][65][66][67][68] up to a pressure of 177 GPa. The use of hemispherical explosive systems [69,70] made it possible to obtain a pressure behind the shock wave front in this metal up to 385 GPa [56,61].…”

“…Such experiments on isentropic expansion of shock-compressed samples make it possible to study a wide range of states from highly-compressed and heated condensed matter to rarefied gas and plasma. ) and initial temperatures (T 0 ) at an initial normal pressure (P 0 = 0.1 MPa): solid lines-results of calculations using the present model (curve H0 corresponds to the initial state of the liquid phase at T 0 = 673 K and ρ 00 = 9.89 g/cm 3 ; curves H1 to H6 correspond to the initial state of the solid phase at room temperature and ρ 00 = 9.8, 6.62, 5.1, 5, 4 and 3.44 g/cm 3 ); markers-experimental data (I1- [55]; I2- [56]; I3- [57]; I4- [58]; I5-[59]; I6- [60]; J1 to J6- [61], ρ 00 = 9.8, 6.62, 5.1, 5, 4 and 3.44 g/cm 3 , respectively; K1- [62], T 0 = 88 K, solid; K2- [62], T 0 = 673 K, liquid; K3- [64]; K4- [65]; K5- [66]; K6- [67]). P c ) and shock loading of samples of different initial densities and initial temperatures at an initial normal pressure (H0 to H6): T1 and T2-data from static experiments at high pressure and room temperature for the bcc phase (T1- [53,54]; T2- [51,52]); the rest of the designations are the same as in Figure 2.…”

“…Figure 2. Shock adiabats of bismuth samples with different initial densities (ρ 00 ) and initial temperatures (T 0 ) at an initial normal pressure (P 0 = 0.1 MPa): solid lines-results of calculations using the present model (curve H0 corresponds to the initial state of the liquid phase at T 0 = 673 K and ρ 00 = 9.89 g/cm3 ; curves H1 to H6 correspond to the initial state of the solid phase at room temperature and ρ 00 = 9.8, 6.62, 5.1, 5, 4 and 3.44 g/cm 3 ); markers-experimental data (I1-[55]; I2-[56]; I3-[57]; I4-[58]; I5-[59]; I6-[60]; J1 to J6-[61], ρ 00 = 9.8, 6.62, 5.1, 5, 4 and 3.44 g/cm3 , respectively; K1-[62], T 0 = 88 K, solid; K2-[62], T 0 = 673 K, liquid; K3-[64]; K4-[65]; K5-[66]; K6-[67]). …”