Counterintuitive effects of isotopic doping on the phase diagram of H2–HD–D2 molecular alloy
- aKey Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, China;
- bCenter for High Pressure Science & Technology Advanced Research, Shanghai 201203, China;
- cUniversity of Science and Technology of China, Hefei 230026, China;
- dCentre for Science at Extreme Conditions, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom;
- eSchool of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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Contributed by Ho-Kwang Mao, April 9, 2020 (sent for review January 21, 2020; reviewed by Yuichi Akahama and Sandro Scandolo)

Significance
When hydrogen and deuterium are mixed, they form
Abstract
Molecular hydrogen forms the archetypical quantum solid. Its quantum nature is revealed by behavior which is classically impossible and by very strong isotope effects. Isotope effects between
Hydrogen and deuterium have unique and distinctive properties which set them aside from the rest of the periodic table. Hydrogen has the lowest nuclear mass, and
It is believed that the molecular hydrogens form the same series of phases if pressurized and/or cooled, although with measurably different phase boundaries. There are five experimentally described solid molecular phases in the pure isotopes (2⇓⇓⇓⇓⇓⇓⇓⇓⇓–12). In a qualitative description (13), phase I adopts a hexagonal close-packed arrangement of rotating molecules. Rotation at very low temperature is only possible due to quantum nuclear effects for which the rotational ground state has no zero-point energy. Phases II and III are typical molecular phases (2, 8), where symmetry breaking arises from quadrupole–quadrupole interactions [phase II (14)] or efficient packing of elongated molecules [phase III (13)]. Phases IV and V possess mixed molecular states with both strongly bound rotating and weakly bound molecules (4, 5, 15). The phase I(II)→III transition is density driven, resulting in a close to vertical phase line (quasi-isobaric) separating the two phases (2, 16, 17). Conversely, the I→II and III→IV(V) transformations are mostly temperature (entropy) driven, resulting in a flatter phase line (quasi-isothermal) separating the partially ordered phase II from the rotor phase I and the mixed-molecular phases IV(V) from phase III (4, 18). The situation is further complicated by the o-p distinction: due to the exchange symmetry,
Hydrogen deuteride has been studied less than the pure isotopes, and its spectroscopy is complicated by the localization of the vibrational modes. Pure HD was claimed to have a phase II with an unusual reentrant phase line at low temperatures (19, 20), and on further compression above ∼160 GPa, to transform to phase III (21). Recently, using Raman spectroscopy, phase IV was found in
Recently, we reported the behavior of the pure isotopes at low temperatures up to pressures of 210 GPa, characterizing the phase transition criteria between phases I, II, and III. These measurements suggested the existence of a phase II’ in
Here we study compressed hydrogen–deuterium mixtures at low temperatures. Remarkably, we find that the mixtures have a higher transformation pressure (equivalently, lower temperatures) to phases II and III than either
We studied three concentrations of mixtures: H:D = 40:60 (
Measurements were conducted through both isobaric cooling/heating cycles and isothermal compressions at low temperature (Fig. 1). We identify the phase changes using standard phase transformation criteria (2), namely, the appearance of new, sharp, low-frequency excitations and changes in the pressure/temperature dependence of the vibron frequencies.
The proposed low-temperature phase diagrams of three representative
Fig. 2 shows a representative temperature scan of the 75:25 mixture at 116 GPa. As the temperature is decreased below 75 K, both criteria are clearly observed in the Raman spectra: the appearance of new peaks (Fig. 2, Left) and a change in temperature dependence of the vibrational frequencies (Fig. 2, Right). It is significant that the changes in the frequencies of the H–H and H–D vibrons vs. temperature happen simultaneously and have the same shapes as observed in pure
(Left and Middle) Representative rotational, librational, and vibrational Raman spectra of a 75:25
Figs. 3 and 4 show the evolution of the low-frequency (librons) and vibrational parts (vibrons) of the Raman spectrum of three mixtures during the isothermal compression in the 7 to 200 GPa pressure regime. At low pressures, i.e., 7 to 20 GPa, the rotational part of the spectra could be described as the linear superposition of three independent isotopic molecules, although the rotational modes of HD are considerably broader than those of
Representative low-frequency Raman spectra of (Left) 40:60, (Middle) 50:50, and (Right) 75:25
Representative vibrational Raman spectra of (Left) 40:60, (Middle) 50:50, and (Right) 75:25
The vibrational modes can be assigned to three types of molecules; however, their frequencies are all higher in mixtures than in the pure isotopes (SI Appendix, Fig. S12). This is due to resonant coupling between the vibrations on identical molecules. In mixtures, most neighbors are of a different species; hence, there is vibrational decoupling, and the modes are more localized. The coupling has two effects: it shifts the mean frequency downward and creates dispersion. Since the Raman active mode has typically the lowest frequency in the phonon band, the dispersion lowers the Raman frequency further. By contrast, the IR active modes are nearer to the top of the band, so in IR the two effects tend to cancel out. In fact, the Raman vibrational frequencies of H–H, H–D, and D–D modes in mixtures are located at the range between Raman and infrared frequencies in the pure isotopes, as shown in SI Appendix, Fig. S13. This also shows the comparison of Raman vibrational frequencies of H–H mode calculated in the ideal mixing of the alloy and measured in our experiment with different concentrations.
There is an interesting feature shared by all concentrations: rapid decrease of the
When pressures above 100 GPa are reached, sharp low-frequency peaks emerge (Fig. 3; see 95, 110, and 105 GPa), and the spectra of the 40:60 and 50:50 concentrations start to closely resemble those of pure
The pressure needed to transform pure p-
One might expect isotopic mixtures to be intermediate between
The trapped kinetic energy in
Fig. 4 shows isotope effects in the transition to phase III: mixtures transform at higher pressures than the pure species. The transition to phase III is characterized by the splitting of the
The phase II to III transition occurs at pressures where the vibron frequency is significantly decreasing, presumably associated with increased bond length and the molecule becoming more elliptical. Thus, the packing efficiency of three-dimensional ellipsoids can be taken as the driving force for the transition (13). The electric dipole of HD is so small that dipole–dipole interactions contribute only μeV of energy. It is well known that polydispersity reduces the packing efficiency, so the thermodynamic density advantage of phase III is lower in mixtures, meaning that higher pressures are required to stabilize it.
By combining all of the P-T paths taken for the different concentrations, we are able to constrain the phase diagram of the H–D molecular alloys (Fig. 1) with o-p ratios characteristic of rapid cooling. Although the overall phase diagram(s) resemble the pure isotopes, there are some interesting and unusual features. All of the phase I to II transition pressures in mixtures of all concentrations are higher than those of pure isotopes. Logically, the phase boundaries of the mixtures is consistent with that of the predominant isotope; i.e., the 40:60 mixture boundary is at lowest pressure which is closest to that of pure
Surprisingly, the mixtures’ phase II to III transition boundaries do not lie between those of hydrogen and deuterium as one would expect but are shifted to higher pressures starting the transition at 163 GPa and completed by 191 GPa (SI Appendix, Fig. S12). Just like in case of phase I to phase II the doping stabilizes the lower-pressure phase (phase II in this case). It is interesting that phase II of the 50:50 molecular alloy appears to resist the transformation to phase III up to the highest pressures and covers a larger amount of P-T space.
We have also explored the phase III to IV boundary in the molecular alloys. The Raman spectra of the 50:50 mixture collected over a broad region of phase III (see the P-T paths taken in Fig. 1, Inset) indicate that phase III is stable up to 260 GPa in a broad temperature range, transforming to phase IV at temperatures above ∼250 K. A recent IR study (22) showed that above 160 GPa, pure HD dissociates and recombines forming a molecular mixture of
The strong S(1) peaks seen after rapid cooling prove that the nuclear spin state is trapped. In the case of
Methods
Samples of
Raman spectroscopy measurements were made using a custom-built microfocused Raman system (2). The excitation source was a 532-nm laser, and the laser power was between 10 and 50 mW, with collection times ranging between 3 and 30 s. For diamonds with culet size bigger than 100 μm and pressure below 50 GPa, the pressure was measured using ruby spheres and correlated with the frequency of the stressed diamond edge. For diamond with culet size smaller than 100 μm or pressure above 50 GPa the stressed diamond edge was used to estimate the pressure using the relationship from Akahama and Kawamura (27).
In the typical isothermal experiment the sample was cooled down within 1 to 2 h and then the Raman spectra were collected within 3 to 4 h upon pressure increase. In the typical isobaric experiment the target pressure would be reached at 300 K, the sample cooled within 1 to 2 h, and Raman spectra were measured upon warming. In our experiments the samples were not kept at very low temperatures (<50 K) for more than 5 to 6 h (see ref. 24 where normal hydrogen [deuterium] converted to the p-
Acknowledgments
This work was supported by research grants of National Science Foundation of China (11874361, 11404343, 51672279, 51727806, and 11774354), Chinese Academy of Sciences Innovation Fund (CXJJ-19-B08), Science Challenge Project (TZ201601), the Hefei Institutes of Physical Science Chinese Academy of Sciences Director’s Fund (YZJJ201705), and the European Research Council (Hecate).
Footnotes
- ↵1To whom correspondence may be addressed. Email: xiaodi{at}issp.ac.cn, maohk{at}hpstar.ac.cn, or e.gregoryanz{at}ed.ac.uk.
↵2Present address: School of Science, RMIT University, Melbourne, Victoria 3000, Australia.
Author contributions: X.-D.L. and E.G. designed research; X.-D.L., P.D.-S., R.T.H., H.-C.Z., W.X., J.B., and E.G. performed research; X.-D.L., P.D.-S., R.T.H., H.-K.M., and E.G. contributed new reagents/analytic tools; X.-D.L., P.D.-S., R.T.H., G.J.A., and E.G. analyzed data; H.-K.M. contributed to the discussion of results; and X.-D.L., G.J.A., and E.G. wrote the paper.
Reviewers: Y.A., University of Hyogo; and S.S., The Abdus Salam International Center for Theoretical Physics.
The authors declare no competing interest.
↵*Details of the para and ortho states and corresponding statistics are given in SI Appendix.
This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2001128117/-/DCSupplemental.
Published under the PNAS license.
References
- ↵
- ↵
- X. D. Liu,
- R. T. Howie,
- H. C. Zhang,
- X. J. Chen,
- E. Gregoryanz
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- I. B. Magdău,
- M. Marqués,
- B. Borgulya,
- G. J. Ackland
- ↵
- S. van de Bund,
- G. J. Ackland
- ↵
- ↵
- ↵
- ↵
- R. T. Howie,
- T. Scheler,
- C. L. Guillaume,
- E. Gregoryanz
- ↵
- ↵
- Y. Crespo,
- A. Laio,
- G. E. Santoro,
- E. Tosatti
- ↵
- ↵
- ↵
- X. D. Liu,
- R. T. Howie,
- H. C. Zhang,
- X. J. Chen,
- E. Gregoryanz
- ↵
- A. F. Goncharov,
- J. H. Eggert,
- I. I. Mazin,
- R. J. Hemley,
- H.-k. Mao
- ↵
- I. B. Magdău,
- G. J. Ackland
- ↵
- ↵
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