1

Features of Cerium Compressibility and Spall Strength in the () Phase–

Transformation Region under Explosive Loading

 V. I. Tarzhanov†, E. A. Kozlov†, Yu. N. Zuev†,

D.G.Pankratov†, I. V. Telichko†, A. N. Grachev†, D.M.Gorbachev†, A. V. Vorobyev†, Yu. S. Moreva†, E.V.Kakshina†, N. A. Tsepilov†, E. A. Shmakov†,

N.V.Ivanova†, M.A. Zocher ‡, G.T. Gray III ‡, F. Cherne ‡

  † FSUE “RFNC-VNIITF”, 456770, Russia, Snezhinsk, Chelyabinsk

region, P.O. Box 245; E-mail: V.I.Tarzhanov@vniitf.ru‡Los Alamos National Laboratory , Los-Alamos , USA  

  Joint Russian-American Conference on Advances in Materials Science,

August 31-September 3, 2009, Prague, Czech 

2

Introduction

Cerium is the material with very complicated phase diagram. Particularly in cerium, the process of isostructural (with retention of crystal lattice type) –-electronic phase transformation with uniquely high (20%) specific volume jump was experimentally discovered more than 50 years ago. Cerium is the only element in Mendeleev's table, in which presence of a critical point is established in the solid phase range, and namely both in the range of positive (compressive), and negative (tensile) stresses.

The objectives of this work are as follows:

– refinement of data on compressibility of high-purity cerium under its explosive loading in the range of the -- and -liquid phase transformations ;

– registration of wave profiles that demonstrate kinetics of high-rate deformation of cerium in the initial -phase and kinetics of the - - electron phase transformation;

– determination of spall strength of cerium in the test range of longitudinal stress.

3

b)a)

1–tested sample, 2–screen-cover, 3–slit aperture system (scan pattern) illuminated by explosive light source, 4–layer of plastic HE, which detonates in sliding mode, 5– PETN- or HMX-based HE layer,

which detonates in direction orthogonal to screen-cover surface.

Schematic diagrams of experiments on loading of wedge samples with (а) sliding or (b) normal detonation of HE layers

For investigation purposes, one used high-purity cerium (99.99%) with initial density of 6.75 g/cm3. Eight wedge samples of size 30406 mm3 with 1200 angle were made from special thermo-mechanically processed sheet blank with 6-mm thickness. The material had a single-phase initial structure and 100-μm size of equiaxed grains. The free surface of wedge samples was grinded, polished, and after the ionic cleaning, 10-μm thin cooper layer was applied to it by the vacuum-deposition technique; then this layer was polished up to the required mirror state.

4

Loading – normal detonation of plastic HE layer, hHE=5.0 mm.

Film scanning rate is 3.75 mm/μs.Optical lever: а) – 30.0 mm, b) – 130.0 mm (displacement screen lines are not defined).

1-1 – elastophase precursor, 2-2 –principle plastic wave.

a)

2

2

Time

b)

Time12

2 1

Streak camera records of experiment #638 and screen line tracing

Time profiles of free surface velocity for wedge samples and wave velocity in them were recorded by the photochronographic optical lever technique, which allows one to obtain in each experiment 5-10 analogous optical tracks with spatial and time resolution of 0.01 mm and 10 ns using SFR-2M streak camera. High spatial resolution was achieved through the application of the developed computer program «OL Tracing». The tracing algorithm is setting off the maximum on the photometric traverse profile of each track.

51, 2 – states on elastic and phase precursors, 3 – states on plastic wave. I, II, III – regions of single-wave, two-wave, and tree-wave configurations.

Wave velocities of propagation of axial stress amplitude values on fronts of the three-wave and single-wave configurations in cerium vs. particle velocities u

   Data on cerium compressibilityCerium compression curves presented in D,u- and σхх,V/V0-coordinates are typical for materials with phase

transformation and elastic behavior at low σхх.

The velocity of elastic precursor (EP) in cerium was 2.35±0.02 km/s. Maximum and minimum rates of phase precursor (PP) were equal to 2.1 and 1.7 km/s at хх

max =0.6 and 0.8 GPa with wedge thickness of х=2.2 and 4.6 mm.

The achieved minimum velocity of plastic wave was D3min =1.0 km/s (in laboratory coordinate system). In the

coordinate system associated with PP its velocity will come to 0.84 km/s. This velocity can be treated as an estimate of volume velocity of sound in heated and loose –phase formed on the width of plastic wave front.

Dotted lines in figure present the boundaries of cerium regions, in which the single-wave, two-wave elastoplastic configurations, as well as three-wave configurations correspondent to the region of the mixture of - and -phases should exist.

1

2 3

particle velocity u, km/s

wave velocity D, km/s

6

a) full measurement range, b) area A – enlarged.

Amplitude values of axial stress хх vs. relative specific volume V/V0

The curve of cerium compression in coordinates σхх,V/V0 in the region σхх< 1 GPa is convex upwards. Just this

convexity provides an increase in amplitudes of phase precursor as σхх is decreasing in the plastic wave. The best

separation between PP and plastic wave having similar wave velocities is achieved with the minimum loading amplitude realized in wedge samples on the maximum wedge thickness. PP is capable of maximum forward running and demonstration of its profile maximum.

The VNIITF data on high-purity cerium compressibility agree well with analogous laser-interferometric data obtained in Los-Alamos Laboratory for the metal of the same purity. Our data are characterized by a relatively small scatter of points. They agree well with the shock adiabat in the -region and with isentrope in the region of the mixed - and -phases from the multiphase equation of state for cerium, which was derived by V. M. Elkin, et al. using only static data.

The absence of specifics on the cerium-compression curve, which could be indicative of (α-ε) transformation, confirms the theoretic prediction that this curve has no intersection with the boundary of α- and ε-phases.

Experimental points at ххmax =14-16 GPa possibly lie near the boundary inside the cerium melting region on the

shock adiabat and this is indirectly evidenced by sharp falloff in intensity of the light reflected from the sample free-surface.

relative specific volume V/V0 relative specific volume V/V0

axial stress xx , GPaaxial stress xx , GPa

relative specific volume V/V0

7

Particle velocity profiles for cerium sample in elastoplastic precursor, exp. #638(a), #636(b)

All three-wave configurations recorded in experiments contain the principle plastic wave and the merging elastic and phase precursors characterized by smoothly growing stress. Particle velocity profiles obtained from tracings of streak records for free surface velocity W(t) bear information on kinetics of elastic precursor, as well as on kinetics of the (γ – α) transformation and relaxation of stresses in cerium).

The above curve - is approximation of the maximum states on the phase precursor. Numbers above curves show sample thickness in mm, the upper line of figures –

is amplitude хх in GPa.

8

It is obvious that elastic precursor profile smoothly grows up to its maximum parameters umax

EP = 6 m/s, σххEP = 0.1 GPa. In this work, absence of the two-wave

elastoplastic structure of compression in streak camera records is associated with low growth of stresses. In the predicted region II of this structure existence, the stress growth in the elastic precursor turns out to be lower than the optical lever method resolution even though the rate of the elastic precursor and plastic waves is almost the same and the run of the elastic wave is small. The merging of elastic and phase precursors is explained by kinetics slowness of stress growth in elastic precursor, as well as by the fact that their wave velocities are almost the same. But we succeeded in recording the separation of the elastic and phase precursors in the bottom range of stresses at σхх = 0.6 – 1.6 GPa and

wedge thickness of 3.5-5 mm. This separation is accompanied by extraction on the phase precursor tip of the shock front with σхх

max =0.4 GPa . The neighborhood of

this shock front is referred to as “X” wave. The reason for shock front extraction is the increase of the phase precursor amplitude and steepness.

9

1

1

2

3

2

Loading – sliding detonation of plastic HE from sample “tip”, hHE = 0.99 mm.

Scanning velocity on the film is 3.75 mm/μs. 1-1– elastoplastic precursor, 2-2 – primary plastic wave, 3 – «Х» wave.

1

12

3

2

Time

Streak camera records of experiment #646 and tracing of screen lines

10

Spall strength vs. gradient of negative stresses in spall plane

In the tested range of axial stresses, we determined the spall strength of cerium that

turned out to be rather low and variable in the range хх* = 0.2-0.4 GPa. The obtained

values of spall strength agree with the data of VNIIEF. Thickness of spall layers calculated from the streak camera records was 0.2-0.4 mm. The spall plates of the same thickness were found among the sample fragments recovered in the chamber. Figure illustrates existence of correlation between spall strength and the gradient of negative stress in the spall plane. The figure gives data of experiments with three types of loading devices and two types of HE.

11

1. The optical lever method was used to obtain new data on compressibility of high-purity cerium explosively loaded in the range σхх = 0.6–16 GPa with the high-rate

deformation occurring in the initial -phase, as well as in the range of “-” and “-liquid” phase transformations. These data are in a good agreement with the published results and have smaller experimental scatter. Theoretical absence of intersection between the shock adiabat and the line of -–phase equilibrium was experimentally confirmed. At хх=14–16 GPa, the optical lever method registered a sharp falloff in

intensity of the light reflected from the free surface of the sample. This falloff can be conditioned by the shock-wave melting of cerium.

2. Registered profiles of stress waves in wedge samples of high-purity cerium demonstrate existence of one common plastoelastic precursor before the plastic wave front at хх≤7GPA. Amplitude of this common complex increases up to 0.9-1 GPa with

the decrease of loading level down to 3-4 GPa. Separation of the -–phase and elastic precursors takes place at the bottom levels of loading (хх=2–3 ГПа) with the shock

front extracted at the phase precursor tip. 3. Spall strength of cerium determined from wave profiles for the velocity of sample free

surface is rather low, i.e. 0.2–0.4 GPa. It depends on the gradient of the longitudinal stress in the tensile region. Thickness of the first spall is 0.2-0.4 mm.

Conclusions

12

References 1.E. A. Kozlov, V. M. Elkin, A. V. Petrovtsev, et al. Behavior and properties of unalloyed high-purity cerium. Review of

experimental and theoretic information by phase diagram, thermodynamic and elastic properties, and phase transformations under shock loading, shear stresses, and wave profiles in cerium. RFNC-VNIITF Report, 2004, PS 04.9179.

2.V. M. Elkin, E. A. Kozlov, E. V. Kakshina, Yu. S. Moreva. Equation of state for cerium and features of its dynamic compression in --transition region, FMM, 2006, Vol. 101, Issue 2 [Phys. Met. and Metall.. (Engl. transl.), 2006, Vol. 101, No. 3, pp. 208–217]

3.L. V. Altshuler, A. A. Bakanova, I. P. Dudoladov. The effect of electronic structure on metal compressibility at high pressures. ZHTF, 1967, Vol. 53, Issue 6, P. 1967.

4.Carter W.J., Fritz J.N., Marsh S.P., and McQueen R.G., Hugoniot equation of state of the Lantanides. J. Chem. Phys. Solids, 1975, vol. 36, pp. 741-752.

5.M. N. Pavlovsky, V. V. Komissarov, A. R. Kutsar. Isomorphic phase transition of cerium under shock compresion. Fizika Gorenia i Vzryva (Physics of Combustion and Explosion, 1999, Vol. 35, No 1, P. 98-101.

6.M. V. Zhernokletov, A. E. Kovalev, V. V. Komissarov, M. G. Novikov, M. A. Zocher, F. J. Cherne, Measurement of sound velocities and Shear Strength of Cerium under Shock Compression, In Proceedings of Joint 21st AIRAPT and 45st EHPRG International Conference on High Pressure Science and Technology, G. G. N. Angilella, R. Pucci, F. Siringo (eds.), Catania, Italy, September 17-21, 2007, Abst. 0420, pp. 424-428

7.F. J. Cherne, P. A. Rigg, B. J.  Jensen, W. W.Anderson, G. N. Chesnut, D. B. Hayes, M. D. Knudson. Experimental Studies of Cerium. IX Khariton Talks March 12-16, 2007. Sarov, RFNC-VNIIEF, 2007.

8.V. M. Elkin, V. N. Mikhaylov, T. Yu. Mikhaylova. Multiphase (,,,liquid) equation of state and features of cerium shock compression. VIII International Workshop «Fundamental Plutonium Properties», September 8-12, 2008, Snezhinsk, Russia.

9.V. A. Borisenok, V. G. Simakov, V. A. Volgin, V. M. Belsky, M. V. Zhernokletov. Study of phase transitions in iron and cerium by PVDF gauge. Fizika Gorenia i Vzryva (Physics of Combustion and Explosion, 2007, Vol. 43, No 4, P. 121-126.

10.G. R.Fowles. J. Appl. Phys., 1961, V. 32, № 8, pp.1475-1487.11.E. A. Kozlov, A. K. Muzyra, R. H. Chinkova et al. Incipient spall in copper. Physics of Combustion and Explosion,

1984, Vol.20, P.123-126.12.Е. А. Kozlov. Shock Adiabat Features, Phase Transition Macrokinetics and Spall Fracture of Iron in Different Phase

States, HIGH PRESSURE RESEARCH, 1992, vol.10, pp.541-582.13.V.A.Pushkov, V.A.Ogorodnikov, S.V.Erunov, Crack Resistance and Spall Strength of Cerium at Dynamic Loading, IX

Khariton Talks, March 12-16, 2007, Sarov, RFNC-VNIIEF, 2007, p.232-233.