Gateway for:

Member Countries

The study into thermodynamic hydrogen isotope properties


The Study into Equation of State for Hydrogen Isotope Crystal Phase within Megabar Pressure Region

Tech Area / Field

  • PHY-SSP/Solid State Physics/Physics

8 Project completed

Registration date

Completion date

Senior Project Manager
Latynin K V

Leading Institute
VNIIEF, Russia, N. Novgorod reg., Sarov


  • Los Alamos National Laboratory, USA, NM, Los-Alamos\nLawrence Livermore National Laboratory / University of California, USA, CA, Livermore\nWashington State University / Institute for Shock Physics, USA, WA, Pullman\nLos Alamos National Laboratory / Hydrodynamic & X-Ray Physics, USA, NM, Los-Alamos\nSandia National Laboratories, USA, NM, Albuquerque

Project summary

The goal of the project is to determine parameters of equation of state (EOS) for hydrogen isotopes – protium and deuterium – in crystal state within a pressure region from 1 to 3-4 Mbar. It is assumed that the basic activity under the project will be a set of experiments. Each shot will determine pressure and simaltaneous density in hydrogen. The sample will be compressed isentropically up to a pressure of several megabar, using the ultra-high magnetic field.

The interest to equation of state for hydrogen results from two things: first, hydrogen isotopes are widely spread in the Universe, second, hydrogen is used for various applications. In addition hydrogen is predicted to have many unusual phases. Thus, in already classical work [1] it has been discussed for the first time if there is a possibility for transition of molecular crystal dielectric (hydrogen under low temperature and pressure) into an atomic crystal with metal conductance. The following experimental and theoretic investigations (see [2]) have discovered as minimum three phases of high-pressure hydrogen that differ by the crystal lattice type. Further, in [3] the idea of superconductivity of metal hydrogen (with high critical temperature) has been assumed. In articles [4] and [5] there have been discussed thermodynamic and kinetic properties of liquid metal phase that can be implemented under high pressures through zero fluctuation of nuclei. In [6] the team headed by Yu. Kagan has shown the possibility for metastable crystal of metal hydrogen to exist at zero pressure. Thus, the study into properties (in particular EOS) of crystal hydrogen high-density phases is still a very important and urgent issue.

In connection with aforementioned it is quite clear why many scientists experimented with hydrogen at the maximum possible experimentally available pressure. High-pressure physics has two main lines of investigations. The first is based on the method of material static compression in diamond anvil [7]. Uniform hydrostatic pressure in them increases very slowly along some isotherm (depending on compression tube environment temperature) reaching the value of several megabar [7]. Thus, the authors of [8-10] built low temperature (4 K and 77 K) and “room” isotherms for normal protium (n-H2) and normal deuterium (n-D2) up to pressure of about 300 kbar. However, the difficulty in determining of the investigated sample density, associated with a microscopic size of the sample, has not promoted the statistic method of EOS building beyond one Mbar. Besides, growth of pressure in hydrostatic devices has a natural limit – yield strength of anvil material (see e.g. [11]).

The second line combines various methods of dynamic compression. They handle with macroscopic size samples and are not limited by strength material properties of a compression chamber. The most frequent method is shock wave. It assumes that experimental points are built on Hugoniot adiabat of the sample [16]. Because of high gradient of particle velocity at a shock wave front the latter not only compresses, but also heats an initially solid sample up to its liquid state or high-density plasma. Here the thermal pressure constitutes a significant fraction of the full one. Thus, for example the temperature of liquid n-D2 compressed by the direct shock wave to pressures of 170 - 234 kbar and by the reflected wave to those of 525-865 kbar [13], proved to be considerably higher, than the fusion temperature corresponding to the same pressures calculated by any of fusion criteria [14]. Thus the shock wave method is not quite adequate for investigation of crystal material phase within the megabar pressure region.

One more dynamic method of the study into thermodynamic properties is quasiisentropic sample compression affected by gradually increasing outer pressure [15]. In this case the heat component of the full pressure will be significantly lower than its “cold” portion, and with a low initial crystal temperature its isentrope does not deviate considerably from the corresponding isotherm even under megabar pressures. The compressed sample remains in a crystal state. Its density and pressure can be determined by the methods similar to those that are applied in static. Thus, presently only the method of isentropic compression effectively determines EOS parameters of the material solid phase within the multimegabar pressure region, where the use of the static method is hampered by small sizes of the samples or anvil material properties. The shock wave method results in high heating of the sample and its transfer into a gaseous-liquid phase.

Isentropically compressed hydrogen has not been studied much. VNIIEF team has been working on compression of initially gaseous normal protium to the density 0.5-2 g/cm3 in a thick-walled cylindrical liner [16,17]. The analysis performed in [17] has shown that within the entire range of the densities studied hydrogen was either liquid or plasma. The employees from Livermore [18] with the help of magnetocumulative generator [19] compressed initially liquid n-H2 up to the density close to 1 g/cm3, measured gammagraphically same as in [16]. (A significant fault in the studies [16-18] was the fact that the pressure in the sample was not measured at the same time as the density, but was calculated using one-dimensional gas dynamic and MHD codes). Experimentalists from Kurchatov Institute used metallic z-pinch as a generator for compression normal polycrystal protium [20]. Hydrogen density and pressure was determined by x-ray pictures of the reference and investigated samples compressed at the same time. The highest pressure recorded in this work was not higher than 200 kbar. To reach megabar pressures in the sample investigated one should accelerate a heavier compressing tube having a larger initial diameter by significantly higher magnetic pressure.

That is why in our study into the properties of crystal protium and deuterium compressed isentropically up to megabar pressures under the effect of ultra-high magnetic field we assume to use metallic q-pinch as a pressure source: two cascade magnetic cumulative generator MC-1 [21,22] with a heavy metal compressing tube located coaxial within the uniform magnetic field portion. In case of easily compressed materials the tube wall first does not meet resistance against compression, then it is gradually accelerated by generator magnetic pressure, picks up significant kinetic energy before it starts to decelerate and stops affected by increased counterpressure of material inside the tube. The pressure amplitude inside the compressing tube can exceed several folds the maximum value of accelerating magnetic pressure and reach several megabar. A layer of frozen gas and a single or several layers of the reference material with the known isentrope (within the pressure range considered) is located coaxial inside the tube. Gas is frozen with the help of liquid helium in the cryostat several times used for the same purpose in activity related to conducting properties of high density condensed hydrogen [23]. During the experiment the compression tube central portion is x-rayed at the preliminary moment, when all the materials have the known initial density, and at one of the compression moments. Based on the radiographs of the tube and the samples inside it is possible to determine compression of the sample under investigation and the reference sample. Now with the knowledge of the initial densities of investigated and reference samples it is possible to determine their densities at this moment. Based on the reference sample density and on its known isentrope it is possible to determine pressure in it and, hence, in the studied sample (under condition that radial pressure gradients are little). In order to get more accurate value of the pressure it is necessary to choose as reference those materials that are mostly compressible and have EOS the mostly known within the required pressure range. Aluminum proves to be the best for this purpose within the pressure range > 1 Mbar. As a result of shock wave experiments much statistical data has been accumulated for aluminum and copper, corresponding to the range of “cold’ pressures measured by us [24,25]. To get more qualitative image it would be reasonable to locate between the reference and investigated samples a contrast material, i.e. a layer of material whose density and serial number (in Mendeleev’s table) are considerably higher than those of aluminum and hydrogen. It is desirable that the contrast material isentrope would be well known also, because in this case it is possible to find a thickness of compressed contrast layer thus, increasing the accuracy of determining the sample (investigated or reference) compression. Copper as a contrast material meets all these requirements.

In the experiments proposed there will be used a powerful gammagraphic machine [26], that can be used for getting a collimated horizontal g-radiation flux of high and uniform intensity. At a time it is possible to get two, sometimes three qualitative radiographs [27] in one and same shot. Exposure time for each of it does not exceed 80 nsec, thus boundary shift for the exposure time can be neglected.

In order to select the best values of the initial parameters for the experiment it is necessary to perform a set of preliminary calculations. Such parameters are for example, powering current amplitude, powering current frequency and compression tube initial sizes. Optimum choice of their values must result in the least radial pressure nonuniformities. Calculations are performed with the use of one-dimensional MHD code and quasi-two-dimensional hydrodynamic code improved and debugged by us [28, 29]. Based on MHD calculation results and using the applications program [30], it is possible to simulate the image of the calculated device.

We have accumulated huge experience (including experience within the contracts with LANL) on studying the properties of the materials compressed by ultra-high magnetic pressure. During a long time we have been studying compressibility and conductivity of isentropically compressed noble gases and hydrogen isotopes in a crystal state. Thus, we have discovered conducting properties in protium under P~1.5 Mbar [23] and in argon under P~2 Mbar [31]. We have studied dielectric properties of Teflon [32] and compressibility of such materials as quarts, graphite and aluminum [33].

Thus, VNIIEF method to determine density and pressure at the same time based on the sizes of the reference and investigated samples within the range of quasiuniform pressure can be used to build experimentally isentropic lines of solid hydrogen isotopes for the pressure from 3 to 4 Mbar, and in such a way to determine within the said range the parameters of elastic interaction curve for the materials under investigation. In its turn this will help to choose among theoretical models of EOS for hydrogen isotopes the most adequate or to propose a new one.

During the project activity we also assume the possibility to record continuously pressure with the help of barooptic [7] or baroresistive [34] phenomena.


1. Wigner E, Huntigton H.B. J. Chem. Phys. 3 764 (1935).

2. Mao H.K., Hemley R.J. Rev. Mod. Phys. 66 671 (1994).
3. Ashcroft N.W. Phys. Rev. Lett. 21 1748 (1968).
4. J. Oliva and N.W. Ashcroft Phys. Rev. B 23 6399 (1981).
5. J. Oliva and N.W. Ashcroft Phys. Rev. B 25 223 (1982).
6. E.G. Brovman, U. Kagan, A. Kholas ZhETF 61 2429 (1971).
7. Jayaraman Rev. Mod. Phys. 55 65 (1983).
8. J. van Straaten and I.F. Silvera Phys. Rev. B 37 1989 (1988).
9. V.P. Glazkov et al. Pisma v ZhETF 47 661 (1988).
10. R.J. Hemley et al Phys. Rev. B 42 6458 (1990).
11. S.J. Clark, G.J. Ackland, and J. Crain Phys. Rev. B 52 15035 (1995).
12. L. Altshuler UFN 85 198 (1965).
13. N.C. Holmes, M. Ross, and W.J. Nellis Phys. Rev. B 52 15835 (1995).
14. M. Kumari, N. Dass High Temp. High Pressures 22 406 (1990).
15. B.K. Godwal, S.K. Sikka and R. Chidambaram Phys. Rep. 102 122 (1983).
16. F. Grigoriev Pisma v ZhETF 16 286 (1972).
17. F. Grigoriev, S. Kormer,O. Mikhailova, A. Tolochko, V. Urlin ZhETF 69 743 (1975).
18. R.S. Hawke et al Phys.Earth Planet. Interiors 6 44 (1972).
19. H. Knoepfel Pulsed High Magnetic Fields. Amsterdam – London 1970
20. V. Matveev, I. Medvedev, V. Prut, P. Suslov, S. Shibaiev Pisma v ZhETF 39 219 (1984).
21. A.I. Pavlovski, In: Sverhsilnyie magnitnye polya./Pod redactsiyej V.M. Titiva, G.A. Shvetsova. M: Nauka, 1984, p. 19.
22. A.I. Pavlovski Priroda 1990 #8, p. 39.
23. A.I. Pavlovskii et al. In: MG-IV, Megagauses Technology and Pulsed Power Applications. 1986, p.255.
24. N.N. Kalitkin, L.V. Kuzmina. In: Udarnye volny I ekstremalnye sostoyaniya veshestva. M: Nauka, 2000, p.107.
25. L. Altshuler, S. Brusnikin, E. Kuzmenkov, ZhPMTF №1 134 (1987).
26. A.I. Pavlovski et al. DAN SSSR 160 68 (1965).
27. Y.P. Kuropatkin et al. In: BIM-M//11th IEEE Pulsed Power Conference. Digest of technical papers/ Eds. G.Cooperstein and I.Vitkovitsky. 1997, p.1663.
28. V.V. Aseeva et al. In: Megagaussnaya impulsnaya tekhnologiya i primeneniya/Pod red V.K. Chernysheva, V.D. Selemira, L.N. Plyaskevicha. Sarov, VNIIEF, 1997, p. 510.
29. V.V. Aseeva, G.V. Boriskov, and A.I. Panov. In: Abstracts of VIIIth International Conference on Megagauss Magnetic Field Generation and Related Topics. October 18-23, 1998. Tallahassee, Florida, USA, p. 167.
30. G.V. Boriskov et al. In: Abstracts of VIIIth International Conference on Megagauss Magnetic Field Generation and Related Topics. October 18-23, 1998. Tallahassee, Florida, USA, p. 174.
31. M.I. Dolotenko Megagaussnaya impulsnaya tekhnologiya i primeneniya/Pod red V.K. Chernysheva, V.D. Selemira, L.N. Plyaskevicha. Sarov, VNIIEF, 1997, p. 805
32. V.V. Aseeva et al. In: Abstracts of VIIIth Int. Conference on Megagauss Magnetic Field Generation and Related Topics. October 18-23, 1998. Tallahassee, Florida, USA, p. 168.
33. A.I. Pavlovskii et al. In: MG IV, Megagauses Fields and Pulsed Power Systems/Eds. V.M. Titov and G.A. Shvetsov. N.Y. Nova Science Publishers 1990, p.155.
34. G. Kannel. Primeneniye manganinovykh datchikov dlya izmereniya davleniy udarnogo szatiya kodensirovannykh sred. IHF AN SSSR, Chernogolovka, 1973. Dep.VINITI, 477-47, p.40.


The International Science and Technology Center (ISTC) is an intergovernmental organization connecting scientists from Kazakhstan, Armenia, Tajikistan, Kyrgyzstan, and Georgia with their peers and research organizations in the EU, Japan, Republic of Korea, Norway and the United States.


ISTC facilitates international science projects and assists the global scientific and business community to source and engage with CIS and Georgian institutes that develop or possess an excellence of scientific know-how.

Promotional Material

Значимы проект

See ISTC's new Promotional video view