Hugoniot and refractive indices of bromoform under shock compression

We investigate physical properties of bromoform (liquid CHBr3) including compressibility and refractive index under dynamic extreme conditions of shock compression. Planar shock experiments are conducted along with high-speed laser interferometry. Our experiments and previous results establish a linear shock velocity−particle velocity relation for particle velocities below 1.77 km/s, as well as the Hugoniot and isentropic compression curves up to ∼21 GPa. Shock-state refractive indices of CHBr3 up to 2.3 GPa or ∼26% compression, as a function of density, can be described with a linear relation and follows the Gladstone-Dale relation. The velocity corrections for laser interferometry measurements at 1550 nm are also obtained.


I. INTRODUCTION
Physical properties including compressibility and refractive index under extreme conditions (e.g., shock compression), are equally interesting for solids and liquids, but measurements on such properties of liquids are unproportionally rare, in particular for refractive index.The seminal work by Walsh and Rice 1 reported measurements on refractive indices of water and carbon tetrachloride under shock compression, which remain transparent at 310 GPa and up to 5 GPa, respectively.Using an immersed-foil technique and streak camera photography, Ahrens and Ruderman 2 determined refractive indices of shock-compressed glycerol (022 GPa), water (05.8GPa), ethanol (013.5 GPa), and hexane (04.1 GPa).Peterson and Rosenberg 3 used the same techniques to extend the measurements on glycerol to 41 GPa and on ethanol to 26 GPa.
][6][7][8][9][10] Elastic precursor decay, stress relaxation, and elasticplastic two wave structure in weakly shocked solid windows may complicate wave characteristics and interpretation of interferometry measurements, 11,12 while liquid windows are immune to such complications.In addition, liquid windows broaden the spectrum of impedance for impedance match purposes.
Bromoform (CHBr 3 ) is a transparent liquid with a high density of ρ 0 = 2.89 g/cm 3 under ambient conditions, and its shock properties have been firstly reported in Ref. 13.The Hugoniot data is measured from 3 to 24 GPa, and demonstrated that CHBr 3 remains transparent up to 24 GPa.CHBr 3 has been used as an optical analyzer in shock experiments. 14Sheffield 15 estimated that chemical reaction of CHBr 3 begins at a shock pressure about 10 GPa.While the Hugoniot measurements were made from 3 to 110 GPa, 13,[16][17][18][19] there are no Hugoniot data below 3 GPa, and refractive index measurements are essentially non-existent.Previous low pressure Hugoniot data also show a marked

II. EXPERIMENTAL
The CHBr 3 liquid sample has approximately a purity of 98%, and contains ∼2% ethanol as a stabilizer.Planar shock compression experiments are conducted on a single-stage gas gun with a bore diameter of 10 mm.Experimental setup is illustrated in Fig. 1.The CHBr 3 liquid is sealed in a stainless steel cell in diameter of ∼10 mm and depth of ∼1.8 mm.The sample box consists of a 50-µm thick Cu foil as a driver plate, a high density glass (HDG) anvil as a window, and a stainless steel spacer.A Cu flyer plate in diameter of ∼9.4 mm and ∼4.5 mm thick is attached to a polycarbonate sabot, and this projectile is accelerated to 0.10.55 km/s.The projectile speed ( ) is measured within 0.5% by an optical beam blocking system. 9pon projectile impact, shock waves are generated and propagate both forward and backward into the target and the flyer, respectively.The Cu foil driver/CHBr 3 interface velocity is monitored by a Doppler pin system (DPS) with a nanosecond resolution. 20,21A single-mode optical fiber is used as the DPS probe and collects reflected light carrying velocity information.Superposition of the Doppler-shifted light reflected from a moving interface with the reference light reflected from a static surface (window free surface or the fiber end surface) create interference fringes, and the beat frequency is proportional to the interface velocity.Optical signals are input to a fast infrared photoelectric detector, recorded by a digitizer data acquisition system with high bandwidth, and analyzed via fast Fourier transformation with a narrow sliding time window to deduce velocity histories (Fig. 2).
Shock waves reach the Cu foil/sample interface at time t 0 = 0, and the sample/HDG interface at t 1 (Fig. 2).The transit time for a shock traversing the sample is t 1 t 0 (Fig. 2), thus allowing for the determination of shock velocity U s .Given U s and , the true particle velocity u p in shocked bromoform is calculated with the impedance match method.For Cu, the initial density is ρ 0 = 8.93(5) g/cm 3 , and its U s u p relation is U s = 3.933 + 1.5u p in km/s. 13,22From the Hugoniot jump conditions, we also obtain shock state pressure, P = ρ 0 U s u p , and density, ρ = ρ 0 U s /(U s u p ), as well as specific volume V = ρ 1 .The corresponding apparent particle velocity, u a , directly measured with DPS at the Cu/sample interface, is not equivalent to the true particle velocity since a correction for the refractive index effect is necessary.Thus, our experiments also yield the velocity correction relation, u p u a , useful for shock experiments involving bromoform.Setchell 23 showed that under a steady shock state, the refractive index of a window material or a transparent sample is where n 0 is the refractive index at ambient conditions, which is depend weakly on wavelength in infrared region of the optical spectra and n 0 =1.5795 at the 1550 nm wavelength taken from Ref. 24.Given directly measured U s and u a , p from the impedance match, n at a given shock state is obtained.

III. RESULTS AND DISCUSSION
A of five shots are performed in the pressure range of 0.32.3GPa.A typical fringe pattern of DPS measurement is shown in Fig. 2(a) for shot BF03 (P = 0.63 GPa).A shock wave enters CHBr 3 sample at the moment t 0 = 0, and there is a burst of fringes with good signal-to-noise ratio.This feature lasts for the whole period of measurement, indicative of an excellent optical transparency  in shocked CHBr 3 under this experiment condition.Another burst of fringes with different frequencies occurs upon shock arrival at the sample-HDG interface at t 1 .The reduced data are displayed in Fig. 2(b).From such velocity histories and impedance match, we obtain the Hugoniot equation of state parameters, U s , u p , and thus P and V. u a is directly measured as the plateau value between t 0 and t 1 , and we then deduce n and the velocity correction relation.Figure 3 shows all the velocity history measurements, and the experimental results are summarized in Table I. Figure 4 shows the U s u p relation and P V compression curve from this work and previous studies. 13,17,19Our low-pressure measurements complement previous measurements at higher shock strengths.Previous U s u p measurements for u p < 1 km/s show a pronounced scatter, while our results show little scatter and fall between the two prior studies. 13,19A previous study 15 suggested shock-induced chemical reaction occurs at ∼10 GPa or u p < 1.2 km/s; however, it is not identifiable simply from the U s u p relation.On the other hand, high pressure results on the U s u p plot indicate a possible chemical decomposition of bromoform at u p > 1.77 km/s.Therefore, we perform linear fitting, U s = C 0 + su p , to our data and to all the available data, and both fits are almost identical: C 0 = 0.943(8) km/s, and s = 1.742(29) for u p < 1.77 km/s.The fitted value of C 0 is very close to the reported value of 0.931 km/s at the ambient condition. 13The corresponding compression curve mapped from the U s u p relation is shown in Fig. 4(b).Thus, our measurements along with previous results firmly establish the Hugoniot equation of state at u p < 1.77 km/s or P < 21 GPa.Assuming γ/V = γ 0 /V 0 , a Hugoniot compression curve can be reduced to an isentrope via 9,25 where η = u p /U s , γ is the Grüneisen parameter, and subscript 0 refers to the initial condition.γ 0 was previously obtained as 1.38. 26The measured P V Hugoniot data, the Hugoniot compression curve calculated from the U s u p relation (for P < 21 GPa), and the calculated isentropic compression curve, are plotted in Fig. 4(b).
The widely used the Birch-Murnaghan finite-strain equation of state (EOS) can be used to describe isothermal or isentropic compression curves, 27 and the Rose-Vinet universal EOS 28,29 is one of its modifications.We fit the isentropic compression curve in Fig. 4(b) using the Rose-Vinet EOS, where x = (V/V 0 ) 1/3 , and the fitting parameters K 0 and K 0 are the bulk modulus and its pressure derivative at zero pressure, respectively.K 0 can be obtained independently from ρ 0 and C 0 as ρ 0 C 2 0 = 2.50 GPa.With K 0 fixed, the fitting with Eq. (3) yields K 0 = 8.65(3).On the other hand, fitting K 0 and K 0 simultaneously leads to K 0 = 2.04(8) GPa and K 0 = 9.52 (16).Given the U s u p relation, shock-compression curve, and apparent particle velocities, the refractive indices at 1550 nm of shocked CHBr 3 are calculated with Eq. (1) (Table I), and plotted in Fig. 5 as a function of density.n(ρ) can be described with a linear function where the fitting parameters n 0 = 1.577 (5), and k = 0.216(8) cm 3 /g, given ρ 0 = 2.89 g/cm 3 .The fitted value of n 0 is in excellent agreement with that from independent measurement (1.5795). 24 addition, n 0 kρ 0 = 0.952 ∼ 1.Therefore, the refractive indices of shocked CHBr 3 appear to follow the Gladstone-Dale relation. 30or a practical purpose, it is necessary to establish a relationship between the true particle velocity of a given window and the apparent velocity measured with laser interferometry, i.e., the velocity correction.The true vs apparent particle velocity data of CHBr 3 at 1550 nm are plotted in Fig. 6, and fitted with a power law, u p = 1.067(3)u 1.024 (2) a . ( Here u p and u a are in km/s.

IV. CONCLUSION
We have performed planar shock compression experiments on bromoform to investigate its Hugoniot and refractive indices.Our experiments, along with previous results, establish a linear U s u p relation to a particle velocity of 1.77 km/s, as well as the Hugoniot and isentropic compression curves up to ∼21 GPa.Shock-state refractive indices of CHBr 3 up to 2.3 GPa or ∼26% compression can be described with n = 0.952(10) + 0.216(8)ρ at 1550 nm, which follows the Gladstone-Dale relation.The velocity corrections for laser interferometry measurements at 1550 nm are also obtained.

FIG. 3 .
FIG. 3. Apparent particle velocity histories of CHBr 3 shocked at different impact velocities as noted.Arrows indicate shock arrivals at the CHBr 3 /HDG interface.Dashed lines are a guide to the eyes.

FIG. 4 .
FIG. 4. (a) U s u p measurements on CHBr 3 .The dash-dot and solid lines denote linear fitting to our data, and to all available data for u p < 1.77 km/s, respectively.(b) The corresponding Hugoniot and isentropic compression curves.

TABLE I .
Summary of experimental results.Symbols h, , u a , U s , u p , ρ, P, and n denote sample thickness, impactor velocity, apparent particle velocity, shock velocity, true particle velocity, density, shock pressure and refractive index, respectively.Numbers in parentheses are uncertainties in the last one or two significant digits.