Helium-Iron Compounds at Terapascal Pressures

Helium-iron compounds at terapascal pressures

Bartomeu Monserrat,1, 2, ∗ Miguel Martinez-Canales,3, 4 Richard J. Needs,2 and Chris J. Pickard5, 6 1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA 2TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom 3Scottish Universities Physics Alliance, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom 4Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom 5Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom 6Advanced Institute for Materials Research, Tohoku University 2-1-1 Katahira, Aoba, Sendai, 980-8577, Japan (Dated: May 22, 2018) We investigate the binary phase diagram of helium and iron using ﬁrst-principles calculations. We ﬁnd that helium, which is a noble gas and inert at ambient conditions, forms stable crystalline compounds with iron at terapascal pressures. A FeHe compound becomes stable above 4 TPa, and a FeHe2 compound above 12 TPa. Melting is investigated using molecular dynamics simulations, and a superionic phase with sublattice melting of the helium atoms is predicted. We discuss the implications of our predicted helium-iron phase diagram for interiors of giant (exo)planets and white dwarf stars.

Matter under extreme compression exhibits rich and sequence it has been suggested that the cooling rate of unexpected behaviour, such as unconventional chem- white dwarf stars is slowed by their helium-rich atmo- istry [1,2], structure [3], and phases [4]. Inside planets spheres, and therefore current estimates of their ages and stars, electrons and nuclei are subject to extreme need to be revised. conditions of pressure and temperature, and the explo- Helium has two electrons in the closed-shell 1s state, ration of new physics and chemistry under these condi- and is chemically inert under ambient conditions. The tions is necessary for the study of astrophysical processes only known helium compounds are either metastable, in- + within the interior of the Earth [5–7], other planets [8,9], volving ionised species such as HeH2 [17]; or are formed or stars [10–12]. by weak van der Waals interactions, such as helium in- Static experiments using diamond anvil cells have side C60 [18]. Recently, a helium-sodium compound has reached pressures of 1 terapascal (TPa, 1 TPa = 107 been reported above pressures of about 0.1 TPa [19]. atmospheres) [13], well above those at the center of the Iron has one of the highest binding energies per nu- Earth but smaller than those found at the cores of gi- cleon (the highest is 62Ni) and is therefore also very abun- ant gas planets such as Jupiter and Saturn [14]. Higher dant [20]. It accounts for about 80% of the Earth’s core pressures can be explored with dynamic compression ex- mass [7], where it is found at pressures up to 0.35 TPa, periments, as exemplified by the recent report from a and it is responsible for the magnetic field surrounding team in the US National Ignition Facility that subjected the planet [21]. Iron is not expected to exhibit mag- diamond to pressures of 5 TPa [15, 16]. With high pres- netic order at TPa pressures, and it is predicted to occur sure experiments starting to investigate the realm of ter- in a series of closed-packed non-magnetic crystal struc- apascal physics and chemistry, theoretical predictions are tures [22]. Iron compounds with hydrogen, carbon, oxy- starting to emerge that reveal unexpected behaviour and gen, silicon, and sulfur have been investigated at pres- complexity under these conditions. sures of about 0.35 TPa due to their importance for the In this context, we use quantum mechanical calcula- composition of the Earth’s core [23]. tions to explore the phase diagram of helium and iron, In this work we investigate the possibility that, un- two of the most abundant elements in the Universe. der extreme compression, helium might form stable com- Helium nuclei formed in the early Universe during Big pounds with iron. The high abundances of helium and Bang nucleosynthesis, and the primordial 25% mass frac- iron make it crucial to understand the helium-iron phase tion of helium makes it the second most abundant ele- diagram for astrophysical modelling of the interiors of ment after hydrogen. In addition, thermonuclear reac- giant planets, including the increasing number of exo- tions within the interiors of stars fuse hydrogen to form planets being discovered [24], and iron-core white dwarf helium. Therefore, helium is found inside many astro- stars [25]. physical objects, from planets, to stars, to white dwarf Our strategy is to search for high-pressure compounds stars, and it plays a central role in their behaviour. For of helium and iron using first-principles quantum me- example, recent experimental and theoretical work has chanical density functional theory (DFT) methods as im- shown that helium metallises at TPa pressures [10–12], plemented in the castep code [26], and the ab initio which is higher than previously anticipated. As a con- random structure searching (AIRSS) method [27]. The 2

7 22 35 Fe 0 hcp fcc hcp bct/bcc

-1

4Cmcm 50 Fm-3m FeHe -2

toichiometry FeHe2

S (a) FeHe. (b) FeHe . 12Cmmm 47 I41/amd -3 2

hcp FIG. 2. Crystal structures of Cmcm FeHe and Cmmm FeHe2

He -4 Formation energy (eV/atom) at 10 TPa. Helium atoms are represented in blue, and iron 1 20 40 60 80 100 atoms in grey. Pressure (TPa)

FIG. 1. Pressure-composition phase diagram of the helium- in three distinct structures which have similar energies. iron system at the static lattice level. For FeHe, the Cmcm The first is an orthorhombic structure of space group structure is stable between 4 and 50 TPa, and the F m3m Cmmm with nine atoms in the primitive cell, which structure above 50 TPa. For FeHe2, the Cmmm structure is stable between 12 and 47 TPa, and above that pressure the forms around 12 TPa. The second has a space group of I4 /amd symmetry with six atoms in the primitive stable structure is I41/amd. The formation energy per atom, 1 calculated using ∆Gs = (Gs−(GHeNHe+GFeNFe))/(NHe+NFe) cell, and becomes the most stable FeHe2 structure above as described in the text, is indicated by the gradients and 47 TPa. The third has P 6/mmm space group and three approaches −4 eV/atom for both stoichiometries at 100 TPa. atoms in the primitive cell, but is not thermodynam- ically stable. Structure files for all of the helium-iron compounds are provided as Supplemental Material. stability of a compound s with respect to the constituent The helium-iron compounds that form at the lowest elements can be evaluated by calculating the Gibbs free pressures have the FeHe Cmcm and the FeHe2 Cmmm energy of formation per atom ∆Gs = (Gs − (GHeNHe + structures shown in Fig.2. The iron atoms form open GFeNFe))/(NHe + NFe), where Gs is the Gibbs free en- channels containing helium chains in the FeHe Cmcm ergy of the compound s, GA is the Gibbs free energy per structure (Fig. 2a). At 10 TPa, the minimum He-He atom of A, and NA is the number of A atoms in com- distance is 0.98 A,˚ the He-Fe distance is 1.16 A,˚ and pound s. The Gibbs free energy has contributions from the Fe-Fe distance is 1.47 A.˚ The volume per formula the electrons, which we calculate using DFT, and from unit in FeHe is 2.76 A˚3, compared to 0.50 A˚3 in hcp the quantum and thermal nuclear motion, which we cal- helium and 2.27 A˚3 in both hcp and fcc iron, which add culate using DFT within the harmonic approximation to- to a combined volume of 2.77 A˚3 per formula unit. In gether with the recently proposed nondiagonal supercell the FeHe2 Cmmm structure (Fig. 2b), the helium atoms approach [28] which greatly reduces the computational form hexagonal layers incorporated inside iron channels cost. that are wider than those present in FeHe. The minimum We show the static lattice phase diagram of the helium- He-He distance is 0.89 A˚ at 10 TPa, the He-Fe distance iron system in the pressure range 1–100 TPa in Fig.1. is 1.19 A,˚ and the Fe-Fe distance is larger at 1.54 A.˚ The 3 Helium is predicted to adopt the hexagonal closed-packed volume per formula unit in FeHe2 is 3.24 A˚ , which is (hcp) crystal structure at TPa pressures [11]. Iron ex- smaller than that of the elements (total of 3.27 A˚3). The hibits a sequence of phase transitions at TPa pressures, smaller volumes of the compounds favour their formation starting with the hcp structure which transforms to the under pressure via the enthalpy term in the Gibbs free face-centered cubic (fcc) structure in the range 7–22 TPa, energy. then it transforms back to the hcp structure up to pres- We next investigate the effects of temperature on the sures of 35 TPa, above which it transforms into the body- formation of helium-iron compounds upon increasing centered tetragonal (bct) structure, which approaches pressure. If the effects of nuclear motion are neglected, the body-centered cubic (bcc) structure with increasing FeHe forms at pressures above 4.1 TPa, and the inclu- pressure [22, 29]. sion of quantum and thermal nuclear motion lowers this The structure searches find several compounds of he- pressure to 2.7 TPa at 10, 000 K. FeHe2 only forms at lium and iron that are energetically competitive in the a higher pressure of about 12 TPa, and therefore we fo- TPa pressure range, and the most stable have stoichiome- cus on the FeHe compound to study the formation of tries FeHe and FeHe2 (see Fig.1). The FeHe stoichiom- helium-iron compounds under pressure. etry first forms at 4 TPa in a structure of orthorhombic We use ab initio molecular dynamics simulations in space group Cmcm containing 8 atoms in the primitive conjunction with the Z-method [30] to estimate the melt- cell, and at 50 TPa it transforms to a F m3m structure ing temperature of FeHe. These calculations are per- (rock-salt structure). The FeHe2 stoichiometry appears formed using the quantum espresso package [31], and 3

20 19, 000 K at 10 TPa. Fluid Our results suggest that the FeHe compound should form at the pressures accessible to dynamic compres- Superionic FeHe 16 sion experiments. Furthermore, the formation pressure of FeHe is predicted to be within the pressure range found at K) 3 the core of Jupiter, with a core-mantle boundary pressure 12 of 4.2 TPa and temperature of 20, 000 K, and at the highest pressures found at the centre of Saturn, with a core- mantle boundary pressure of 1 TPa [14, 36]. The interiors of exoplanets with masses similar or larger than that of 8 FeHe Fe+fluid He Jupiter will also be subject to pressures higher than those required to form FeHe. This raises the possibility that Temperature (10 helium is captured by iron within the interior of these 4 Fe+He planets, and potentially bound to other elements. The atmosphere of Saturn is indeed depleted of helium [37], and the capture of helium in compounds in its interior 2 4 6 8 10 could contribute to this phenomenon. This could also af- Pressure (TPa) fect the helium composition of the atmospheres of giant exoplanets. White dwarf stars are subject to more ex- FIG. 3. Helium-iron phase diagram. The solid lines indicate treme conditions, with helium-rich atmospheres subject formation lines, sublattice melting, and full melting. The sublattice melting of FeHe occurs at 15, 100 ± 1, 000 K at to tens of terapascals, and the interiors to even higher 5.38 TPa, and at 18, 200 ± 1, 000 K at 10.6 TPa, while the pressures. Due to cooling, white dwarf stars exhibit tem- full melting of FeHe occurs at 17, 600 ± 1, 000 K at 5.45 TPa, peratures in the range from only a few thousand Kelvin and at 19, 800 ± 1, 000 K at 10.65 TPa. The melting line of to hundreds of thousand of Kelvin [38], raising the pos- iron is taken from Ref. [35]. sibility that even the solid FeHe phases appear in these stars. The formation of helium compounds with other elements could alter the cooling rates of white dwarf stars, the details are provided in the Supplemental Material. which are largely determined by the atmospheric compo- The melting temperatures of helium and iron differ by sition, and as a consequence affect current estimates of thousands of degrees, suggesting that FeHe might exhibit their ages. Our results indicate that, in contrast to the superionicity, that is, sublattice melting of the helium inertness of helium at ambient pressure, accurate mod- component while the iron atoms oscillate around their els of the composition of planets and stars should treat crystallographic positions. Superionicity has been dis- helium as a compound-forming element. cussed before [32], for example in a lithium-based con- In conclusion, we have used first-principles methods ductor at ambient pressure [33], and in the melting of to study the binary phase diagram of helium and iron. ice and ammonia at extreme pressures [8]. Indeed, our We have found that compounds can form at pressures molecular dynamics simulations demonstrate that, upon of several TPa, suggesting that they might be found in- increasing temperature, the helium chains melt within side giant (exo)planets and white dwarf stars. We have the iron channels in FeHe before the iron channels them- also predicted that the most stable FeHe compound ex- selves melt. Interestingly, metallic superionic compounds hibits a superionic phase with sublattice melting of the are uncommon [34], and FeHe provides a nice platform helium atoms within a wide range of temperatures and to further investigate their properties. pressures. Overall, our results show that helium can form In Fig.3 we show the proposed phase diagram for the compounds at terapascal pressures. formation of helium-iron compounds under pressures up B.M. acknowledges Robinson College, Cambridge, and to 10 TPa. At low pressures, helium and iron do not mix. the Cambridge Philosophical Society for a Henslow Re- Below about 4, 000 K at 1 TPa and 6, 000 K at 3 TPa, search Fellowship. R.J.N. and C.J.P. acknowledge finan- both materials are found in the solid state, but helium cial support from the Engineering and Physical Sciences melts above this temperature. Iron only melts at much Research Council (EPSRC) of the UK [EP/J017639/1 higher temperatures, of the order of 15, 000 K [35]. Upon and EP/G007489/2]. C.J.P. is also supported by the increasing pressure, helium and iron form a FeHe com- Royal Society through a Royal Society Wolfson Research pound between 2 and 4 TPa, depending on the temper- Merit award. The calculations were performed on the ature. FeHe undergoes sublattice melting of the helium Cambridge High Performance Computing Service facil- atoms at temperatures between 13, 000 and 18, 000 K, de- ity and the Archer facility of the UK’s national high- pending on the pressure. The superionic phase is stable performance computing service (for which access was ob- in a wide temperature and pressure range, and melting tained via the UKCP consortium [EP/K014560/1 and is completed at around 17, 000 K at 4 TPa, and above EP/K013688/1]). 4

[16] Chris J. Pickard and Richard J. Needs, “High-pressure physics: Piling on the pressure,” Nature 511, 294 (2014). [17] T. R. Hogness and E. G. Lunn, “The ionization of hy- ∗ [email protected] drogen by electron impact as interpreted by positive ray [1] Chris J. Pickard, Miguel Martinez-Canales, and analysis,” Phys. Rev. 26, 44–55 (1925). Richard J. Needs, “Decomposition and terapascal phases [18] Martin Saunders, Hugo A. Jiménez-Vázquez,R. James of water ice,” Phys. Rev. Lett. 110, 245701 (2013). Cross, and Robert J. Poreda, “Stable compounds of he- [2] S. Ninet, F. Datchi, P. Dumas, M. Mezouar, G. Gar- lium and neon: He@C60 and Ne@C60,” Science 259, barino, A. Mafety, C. J. Pickard, R. J. Needs, and A. M. 1428–1430 (1993). Saitta, “Experimental and theoretical evidence for an [19] Xiao Dong, Artem R. Oganov, Alexander F. Goncharov, ionic crystal of ammonia at high pressure,” Phys. Rev. B Elissaios Stavrou, Sergey Lobanov, Gabriele Saleh, 89, 174103 (2014). Guang-Rui Qian, Qiang Zhu, Carlo Gatti, Volker L. De- [3] D. Kobyakov and C. J. Pethick, “Towards a metallurgy ringer, Richard Dronskowski, Xiang-Feng Zhou, Vitali B. of neutron star crusts,” Phys. Rev. Lett. 112, 112504 Prakapenka, Z. Konôpková,Ivan A. Popov, Alexander I. (2014). Boldyrev, and Hui-Tian Wang, “A stable compound of [4] A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Kseno- helium and sodium at high pressure,” Nat. Chem. 9, 440 fontov, and S. I. Shylin, “Conventional superconductiv- (2017). ity at 203 kelvin at high pressures in the sulfur hydride [20] E. Margaret Burbidge, G. R. Burbidge, William A. system,” Nature 525, 73 (2015). Fowler, and F. Hoyle, “Synthesis of the elements in [5] D. Alfè,M. J. Gillan, and G. D. Price, “The melting stars,” Rev. Mod. Phys. 29, 547–650 (1957). curve of iron at the pressures of the Earth’s core from ab [21] Bruce A. Buffett, “Earth’s core and the geodynamo,” initio calculations,” Nature 401, 462 (1999). Science 288, 2007–2012 (2000). [6] Monica Pozzo, Chris Davies, David Gubbins, and Dario [22] C. J. Pickard and R. J. Needs, “Stable phases of iron Alfè, “Thermal and electrical conductivity of iron at at terapascal pressures,” J. Phys. Condens. Matter 21, Earth’s core conditions,” Nature 485, 355 (2012). 452205 (2009). [7] Christopher Davies, Monica Pozzo, David Gubbins, and [23] Jean-Paul Poirier, “Light elements in the Earth’s outer Dario Alfè,“Constraints from material properties on the core: A critical review,” Phys. Earth Planet. Inter. 85, dynamics and evolution of Earth’s core,” Nature Geosci. 319 – 337 (1994). 8, 678 (2015). [24] Michel Mayor, Christophe Lovis, and Nuno C. San- [8] C. Cavazzoni, G. L. Chiarotti, S. Scandolo, E. Tosatti, tos, “Doppler spectroscopy as a path to the detection M. Bernasconi, and M. Parrinello, “Superionic and of Earth-like planets,” Nature 513, 328 (2014). metallic states of water and ammonia at giant planet con- [25] George C. Jordan IV, Hagai B. Perets, Robert T. Fisher, ditions,” Science 283, 44–46 (1999). and Daniel R. van Rossum, “Failed-detonation super- [9] Hugh F. Wilson, Michael L. Wong, and Burkhard Mil- novae: Subluminous low-velocity Ia supernovae and their itzer, “Superionic to superionic phase change in water: kicked remnant white dwarfs with iron-rich cores,” The Consequences for the interiors of Uranus and Neptune,” Astrophysical Journal Letters 761, L23 (2012). Phys. Rev. Lett. 110, 151102 (2013). [26] Stewart J. Clark, Matthew D. Segall, Chris J. Pickard, [10] S. A. Khairallah and B. Militzer, “First-principles studies Phil J. Hasnip, Matt I. J. Probert, Keith Refson, and of the metallization and the equation of state of solid Mike C. Payne, “First principles methods using castep,” helium,” Phys. Rev. Lett. 101, 106407 (2008). Z. Kristallogr. 220, 567 (2005). [11] Bartomeu Monserrat, N. D. Drummond, Chris J. [27] Chris J. Pickard and R. J. Needs, “Ab initio ran- Pickard, and R. J. Needs, “Electron-phonon coupling dom structure searching,” J. Phys. Condens. Matter 23, and the metallization of solid helium at terapascal pres- 053201 (2011). sures,” Phys. Rev. Lett. 112, 055504 (2014). [28] Jonathan H. Lloyd-Williams and Bartomeu Monserrat, [12] R. Stewart McWilliams, D. Allen Dalton, Zuzana “Lattice dynamics and electron-phonon coupling calcu- Konpkov, Mohammad F. Mahmood, and Alexander F. lations using nondiagonal supercells,” Phys. Rev. B 92, Goncharov, “Opacity and conductivity measurements in 184301 (2015). noble gases at conditions of planetary and stellar interi- [29] Lars Stixrude, “Structure of iron to 1 Gbar and 40 000 ors,” Proc. Natl. Acad. Sci. USA 112, 7925–7930 (2015). K,” Phys. Rev. Lett. 108, 055505 (2012). [13] Natalia Dubrovinskaia, Leonid Dubrovinsky, Natalia A. [30] A. B. Belonoshko, N. V. Skorodumova, A. Rosengren, Solopova, Artem Abakumov, Stuart Turner, Michael and B. Johansson, “Melting and critical superheating,” Hanfland, Elena Bykova, Maxim Bykov, Clemens Phys. Rev. B 73, 012201 (2006). Prescher, Vitali B. Prakapenka, Sylvain Petitgirard, Irina [31] Paolo Giannozzi, Stefano Baroni, Nicola Bonini, Mat- Chuvashova, Biliana Gasharova, Yves-Laurent Mathis, teo Calandra, Roberto Car, Carlo Cavazzoni, Davide Petr Ershov, Irina Snigireva, and Anatoly Snigirev, “Ter- Ceresoli, Guido L Chiarotti, Matteo Cococcioni, Ismaila apascal static pressure generation with ultrahigh yield Dabo, Andrea Dal Corso, Stefano de Gironcoli, Ste- strength nanodiamond,” Sci. Adv. 2 (2016). fano Fabris, Guido Fratesi, Ralph Gebauer, Uwe Ger- [14] W. B. Hubbard and B. Militzer, “A preliminary Jupiter stmann, Christos Gougoussis, Anton Kokalj, Michele model,” Astrophys. J. 820, 80 (2016). Lazzeri, Layla Martin-Samos, Nicola Marzari, Francesco [15] R. F. Smith, J. H. Eggert, R. Jeanloz, T. S. Duffy, D. G. Mauri, Riccardo Mazzarello, Stefano Paolini, Alfredo Braun, J. R. Patterson, R. E. Rudd, J. Biener, A. E. Pasquarello, Lorenzo Paulatto, Carlo Sbraccia, Sandro Lazicki, A. V. Hamza, J. Wang, T. Braun, L. X. Benedict, Scandolo, Gabriele Sclauzero, Ari P Seitsonen, Alexander P. M. Celliers, and G. W. Collins, “Ramp compression Smogunov, Paolo Umari, and Renata M Wentzcovitch, of diamond to five terapascals,” Nature 511, 330 (2014). “QUANTUM ESPRESSO: a modular and open-source 5

software project for quantum simulations of materials,” [35] G. Morard, J. Bouchet, D. Valencia, S. Mazevet, and J. Phys.: Condens. Matter 21, 395502 (2009). F. Guyot, “The melting curve of iron at extreme pres- [32] Stephen Hull, “Superionics: crystal structures and con- sures: Implications for planetary cores,” High Energy duction processes,” Rep. Prog. Phys. 67, 1233 (2004). Density Phys. 7, 141–144 (2011). [33] Noriaki Kamaya, Kenji Homma, Yuichiro Yamakawa, [36] N. Nettelmann, A. Becker, B. Holst, and R. Redmer, Masaaki Hirayama, Ryoji Kanno, Masao Yonemura, “Jupiter models with improved ab initio hydrogen equa- Takashi Kamiyama, Yuki Kato, Shigenori Hama, Koji tion of state (H-REOS.2),” Astrophys. J. 750, 52 (2012). Kawamoto, and Akio Mitsui, “A lithium superionic con- [37] D. J. Stevenson, “Saturn’s luminosity and magnetism,” ductor,” Nat. Mater. 10, 682 (2011). Science 208, 746–748 (1980). [34] Martin French, Thomas R. Mattsson, and Ronald Red- [38] Brad M.S. Hansen and James Liebert, “Cool white mer, “Diﬀusion and electrical conductivity in water at dwarfs,” Annu. Rev. Astron. Astrophys. 41, 465–515 ultrahigh pressures,” Phys. Rev. B 82, 174108 (2010). (2003).