The Mg-Si-O system is the major Earth and rocky planet-forming system. Here, through quantum variable-composition evolutionary structure explorations, we have discovered several unexpected stable binary and ternary compounds in the Mg-Si-O system. Besides the well-known SiO2 phases, we have found two extraordinary silicon oxides, SiO3 and SiO, which become stable at pressures above 0.51 TPa and 1.89 TPa, respectively. In the Mg-O system, we have found one new compound, MgO3, which becomes stable at 0.89 TPa. We find that not only the (MgO)x·(SiO2)y compounds, but also two (MgO3)x·(SiO3)y compounds, MgSi3O12 and MgSiO6, have stability fields above 2.41 TPa and 2.95 TPa, respectively. The highly oxidized MgSi3O12 can form in deep mantles of mega-Earths with masses above 20 M⊕ (M⊕:Earth’s mass). Furthermore, the dissociation pathways of pPv-MgSiO3 are also clarified, and found to be different at low and high temperatures. The low-temperature pathway is MgSiO3 ⇒ Mg2SiO4 + MgSi2O5 ⇒ SiO2 + Mg2SiO4 ⇒ MgO + SiO2, while the high-temperature pathway is MgSiO3 ⇒ Mg2SiO4 + MgSi2O5 ⇒ MgO + MgSi2O5 ⇒ MgO + SiO2. Present results are relevant for models of the internal structure of giant exoplanets, and for understanding the high-pressure behavior of materials.
Several astonishing discoveries have been recently achieved in planetary science, e.g, the discovery of super-Earth Gliese 832c1.This planet weighs at least 5 M⊕(M⊕ : Earth’s mass) and is the nearest candidate for habitable planet so far; a new type of planet, Kepler-10c, weighing 17 times as much as Earth, is also found to be a rocky planet2. Such a planet was previously believed to be impossible to form, because anything so heavy would grab hydrogen gas as it grew, and become a Jupiter-like gas giant. For now, this planet is the biggest rocky planet ever discovered, much bigger than previously discovered “super-Earths” (with masses 1 to 10 M⊕), making it a “mega-Earth” (with masses over 10 M⊕)2. These breakthroughs emphasize the importance of the exploration of internal structure and mineralogy of super-Earths and mega-Earths.
After the mysterious anomalies in the Earth’s D” layer have been at least partly explained by the discovery of the new mineral phase post-perovskite (pPv) MgSiO33,4, one wonders whether phase transitions exist in MgSiO3 under further compression, which is the key information to understand and model the internal structure of exoplanets. It was first reported that pPv-MgSiO3 will decompose into MgO and SiO25 under high pressure. However, with prediction of two new high-pressure silicates, MgSi2O56 and Mg2SiO47, the dissociation pathway of pPv-MgSiO3 became a complex three-step process at zero Kelvin: pPv-MgSiO3 first decomposes into Mg2SiO4 and MgSi2O5 at 0.77 TPa, then MgSi2O5 breaks down into Mg2SiO4 and SiO2 at 1.25 TPa, eventually Mg2SiO4 dissociates into MgO and SiO2 at 3.09 TPa. However, the effect of temperature on stability of Mg2SiO4 and MgSi2O5, which is extremely important in exoplanet mantles, has not been considered.
Recently, numerous counterintuitive compounds have been discovered under pressure. For instance, in Li-H system, besides “normal” LiH, new “counterintuitive” compounds LiH2, LiH6 and LiH8 are predicted to be stable under pressure8; moreover, experimental synthesis and characterization confirm the existence of unexpected Na-Cl compounds (such as Na3Cl and NaCl3)9; what’s more, magnesium oxide (MgO), one of the most abundant phases in the Earth’s mantle, was long believed to be the only binary compound in the Mg-O system. Nevertheless, two extraordinary compounds, MgO2 and Mg3O2 have been discovered to be stable above 116 GPa and 500 GPa, respectively10. These fascinating discoveries inspired us to explore possible stable binary and ternary compounds in the Mg-Si-O system.
In this work, we have performed comprehensive structure searches and investigations of the Mg-Si-O system in the pressure range 0.5–3 TPa. Due to the complexities of the ternary system, the Mg-Si, Si-O and Mg-O bounding binaries are discussed first. All of the ternary stable compounds (including the stable compounds discovered in this work) fall into the pseudo-binary MgO-SiO2 and MgO3-SiO3 joins. Hence, we discuss ternary compounds in these two pseudo-binary systems separately. Lattice dynamics calculations for all the investigated structures show no imaginary vibrational frequencies, suggesting their dynamical stability throughout the pressure ranges reported here.
Results and Discussions
Variable-composition structure searches using the USPEX code with up to 64 atoms in the unit cell at pressures ranging from 0.5 TPa to 3 TPa for the Mg-Si-O system have been carried out, identifying important low-energy structures that are likely to gain stability within this chemical system. Before we talk about binary and ternary compounds in the Mg-Si-O system, crystal structures of elemental Mg, Si and O should be clarified. For elemental Mg, several phase transitions are predicted in the pressure range 0.5–3 TPa. In excellent agreement with previous studies10,11, our calculations demonstrate that Mg adopts the fcc structure at 0.5 TPa, then it transforms into the simple hexagonal (sh) structure at 0.76 TPa; interestingly, when pressure increases to 1.07 TPa, it transforms into the simple cubic (sc, or α-Po) structure. Elemental Si adopts the fcc structure at 0.5 TPa, in agreement with literature12, but no phase transformation occurs in the pressure range of 0.5–3 TPa. Elemental O adopts a hexagonal hP8 structure at 0.5 TPa (Several similar structures are very close in enthalpy in the pressure range of 0.5 to 1.9 TPa. For more details, we refer to Ref. 13) and then transforms into the orthorhombic oC16 structure at 1.9 TPa, in good agreement with literature13.
Mg-Si binary system
Mg2Si is the only binary compound in the Mg-Si system at ambient pressure14. When pressure is increased above 0.5 TPa, Mg2Si remains the only stable binary compound in the Mg-Si system, until it decomposes into Mg and Si at 1.41 TPa (see Fig. S3a in Supplementary Materials). In this pressure range, it adopts the well-known AlB2-type structure (Fig. S1b).
Si-O binary system
Even though silicon monoxide SiO can exist in the gas phase15, no evidence shows that it can exist in the crystalline form, and the amorphous black solid form of silicon monoxide indeed is a mixture of amorphous silicon and silicon dioxide15. Therefore, silicon dioxide SiO2 is still the only known oxide in the Si-O system. In agreement with previous work16, pyrite-type SiO2 transforms into the Fe2P-type phase at 0.69 TPa. Nevertheless, if crystal structure exploration is carried out in the entire Si-O binary system, some unforeseeable structures are found. Figure 1a demonstrates the pressure-composition phase diagram of the Si-O system. A new oxide, SiO3, becomes thermodynamically stable at 0.51 TPa with the tI32 () structure. Interestingly, this tI32-SiO3 can further transform into the mP16 (P21/c) structure at 0.82 TPa. As illustrated in Fig. 1b,c, both structures can be constructed by SiO9 polyhedra (tricapped trigonal prisms), which is exactly the same coordination polyhedron as in Fe2P-type SiO216.
In order to further distinguish polyhedra in the two structures of SiO3, effective coordination numbers (ECoN)17 have been calculated. A large increase of the ECoN at the phase transition point from tI32 (ECoN = 7.48) to mP16 (ECoN = 8.05) phase can be observed in Fig. 1f, indicating that accommodation of increased coordination is the primary reason for the stability of mP16-SiO3 compared to tI32-SiO3. When pressure increases further, the ECoN of mP16-SiO3 reaches 8.5, equal to the mean value of the SiO9 polyhedron in Fe2P-SiO216. Perhaps surprisingly, the Si-O distances are in the range from 1.53 to 1.95 Å in tI32-SiO2 and 1.54 to 1.82 Å in mP16-SiO3 at 0.7 TPa, respectively. These distances are unexpectedly long under such a high pressure, and comparable to the values (1.6 Å) in silica and silicates at ambient pressure. This phenomenon is partly a consequence of geometry, since the typical bond-length must increase in order to accommodate the dramatic increase in Si-O coordination. Therefore, the relative Si-O bond length must necessarily increase with increasing coordination as the bonding polyhedra’s size expands to fill the space, a general phenomenon that is well-represented by a recently proposed coordinated hard sphere mixture model18. The same situation is also observed in Fe2P-SiO216, which indicates the tendency to form highly coordinated structures instead of shrinking the Si-O distances to lower the system energy.
When pressure is raised further, stable solid silicon monoxide appears in the Si-O system with the tP4 structure (P4/nmm) at 1.89 TPa, see Fig. 1d and Fig. S5c. SiO crystallizes in a layered structure with Si-Si-O-O stacking order. Each Si atom is coordinated by five O atoms and eight Si atoms. Therefore, SiO retains high coordination numbers, like SiO2 and SiO3, despite the drop of oxygen content.
SiO3 and SiO are both dynamically and thermodynamically stable, and it is still puzzling what stabilizes these exotic compounds. Based on classical chemical valence, only SiO2 can be expected. To unravel the nature of these new phases, their electronic structure and chemical bonding have been analyzed.
As tI32-SiO3 and mP16-SiO3 display similar charge transfer and chemical bonding features, mP16-SiO3 has been selected for the following discussion. In mP16-SiO3 at 1 TPa, the net Bader charge19,20 on Si is +3.42 e, indicating a very large degree (~85%) of charge transfer from Si to O atoms. Based on Bader analysis, two types of O atoms exist in the mP16-SiO3 structure (Fig.1d), the net charges on O1 and O2 are −1.63 e and −0.89 e, respectively. Therefore O1 attracts almost two electrons and attains a stable s2p6 electron configuration. Furthermore, the O-O bond distance between O2 atoms is 1.19 Å, the O-O bond distance for molecular crystal hP8-O2 at 1 TPa is 1.09 Å while the non-bonding O-O distances for MgSiO3 and SiO2 are in the range of 1.7 Å to 2.0 Å, which clearly indicates a covalent bond and the presence of a peroxide-ion [O-O]2−, fulfilling the octet rule. Electron Localization Function (ELF)21 of mP16-SiO3(Fig. S5b) confirms these conclusions: O2 atoms form peroxo-groups, while O1 atoms do not. SiO3 can be classified as a “peroxide oxide”, with a structural formula SiO[O2], just like the recently predicted Al4O7 and AlO222, in which O2− and [O2]2− ions are simultaneously present.
For tP4-SiO at 1.5 TPa, the net charge on Si is +1.83 e, and the net charge on O is −1.83 e. Thus, O atom attains a stable closed-shell electronic configuration. ELF distribution of tP4-SiO shows that besides accumulated electrons surrounding O atoms, we can also observe a strong interstitial electron localization in the Si4 tetrahedron as marked by letter A in Fig.1e. Considering the Si-Si distance (1.86 Å) is out of the range of core-core orbital overlap, the strong interstitial electron localization is due to the formation of multicenter covalent bonds between Si atoms. Each Si atom has four nearest such electron localization regions, each of which accumulates two valence electrons, indeed creating an octet and explaining why each Si atom can be stabilized with two valence electrons and why SiO adopts a Si-Si-O-O ordered layered structure.
Mg-O binary system
Besides MgO, two novel stochiometries MgO2 and Mg3O2 have recently been found to be stable under high pressure in the Mg-O system10. Intriguingly, if we further increase pressure, another extraordinary compound, tP8-MgO3 with symmetry, becomes thermodynamically stable at 0.89 TPa as shown in the pressure-composition phase diagram of the Mg-O system (Fig. 2a). Furthermore, Mg3O2 decomposes into MgO and Mg at 0.95 TPa, while MgO2 decomposes into MgO and MgO3 at 1.43 TPa, and above 1.43 TPa MgO3 and MgO are the only two stable magnesium oxides.
As shown in Fig. 2b, each Mg atom within MgO3 has 8 nearest O neighbors (O1 atoms) forming a cubic coordination (just as in B2-MgO) and 4 second nearest O neighbors (O2 atoms). Mg and O1 atoms form a distorted fluorite-type structure, empty voids of which are stuffed with O2 atoms. According to Bader analysis, in tP8-MgO3 at 1 TPa the net charge on Mg is +1.75 e, indicating the nearly complete transfer of valence electrons of Mg to O atoms. The net charges on O1 and O2 are −0.74 e and −0.18 e, respectively, while the Mg-O1 and Mg-O2 distances are 1.63 Å and 1.83 Å, respectively. Considering the O-O distance between O1 and O2 is 1.22 Å,and the O-O bond distance for molecular crystal hP8-O2 at 1 TPa is 1.09 Å while the non-bonding O-O distances for MgSiO3 and SiO2 are in the range of 1.7 Å to 2.0 Å, we can conclude that two O1 atoms and one O2 atoms form a bent singly bonded [O-O-O]2− group. From the ELF isosurface of tP8-MgO3 illustrated in Fig. 2c, we can also confirm the existence of [O-O-O]2−, with a significant electronic accumulation between O1 and O2 atoms. As far as we know, this type of trioxide group is found here for the first time.
Mg-Si-O ternary system
Phase diagrams of the Mg-Si-O ternary system in the pressure range 0.5–3 TPa, obtained through variable-composition crystal structure prediction for the ternary system, are shown in Fig. 3. In excellent agreement with previous works6,7, Mg2SiO4 and MgSi2O5 become thermodynamically stable under high pressure. We have also found two new stable ternary compounds, MgSiO6 and MgSi3O12. The MgO-SiO2and MgO3-SiO3pseudo-binaries contain numerous important stable compounds and are discussed in detail below.
MgO-SiO2 pseudo-binary system
In good agreement with previous works6,7, Mg2SiO4 with the tI28 (I2d) structure and MgSi2O5 with the mP32 (P21/c) structure become thermodynamically stable at 0.51TPa and 0.63 TPa, respectively, as shown in Fig. 4a. With increasing pressure, at zero Kelvin pPv-MgSiO3 decomposes into Mg2SiO4 and MgSi2O5 at 0.79 TPa, and then MgSi2O5 decomposes into Mg2SiO4 and SiO2 at 1.80 TPa. Mg2SiO4, the last ternary compound in the MgO-SiO2 pseudo-binary system, eventually decomposes into MgO and SiO2 at 2.3 TPa.
Temperature, another important factor affecting stability of minerals, should be considered when developing models of the internal structure of exoplanets. Here, thermodynamic properties of these phases were investigated within the quasiharmonic approximation (QHA), using the computed phonon spectra. Previous work suggests that the P-T conditions of interest are within the range of validity of the QHA5,23. The P-T phase diagram of MgSiO3, as shown in Fig. 4b, is determined by comparing finite-temperature Gibbs free energies of relevant phases and phase assemblages.
In order to evaluate the electronic entropy contribution, we have calculated the electronic structures and phonon dispersions of these newly reported compounds at finite temperatures (2 kK, 5 kK, 10 kK) within the Fermi-Dirac-smearing approach24. We have found that all the compounds discussed in Fig. 4b show very small electronic effects at these temperatures. For instance, for the decomposition reaction of MgSiO3 into Mg2SiO4 and MgSi2O5 under 0.75 TPa at 10 kK, the enthalpy changes by only 0.0006 eV/atom after taking electronic entropy into consideration, and the dP/dT slope of this reaction in Fig. 4b becomes more negative, but the change is so tiny that we can safely neglect the electronic entropy contribution. Other reactions in Fig. 4b show similar behavior. In order to further understand this question, we have calculated the band gaps of these compounds under different pressures as listed in Table S1 in the supplementary materials. We can observe that all the compounds discussed in Fig. 3d (MgO, SiO2, MgSiO3, Mg2SiO4, MgSi2O5) show wide band gaps, and the electronic structures and their phonon frequencies are not affected significantly by high temperature.
As shown in Fig. 4b, the dissociation pathways of pPv-MgSiO3 are different at high and low temperatures. At high temperatures (>6,610 K), MgSiO3 decomposes into Mg2SiO4 and MgSi2O5, followed by decomposition of Mg2SiO4 into MgO and MgSi2O5. The last stable ternary compound in the MgO-SiO2 pseudo-binary system is MgSi2O5, it eventually decomposes into MgO and SiO2 at relatively high temperature well within the P-T range of mega-Earth mantles. This decomposition pathway is most likely for giant exoplanets and has not been reported before. These phase transitions and reactions are expected to impact the dynamics of exoplanet interiors: as exothermic transformations (dP/dT > 0) generally enhance heat transfer through convection, while endothermic transformations (dP/dT < 0) decrease it25.As shown in Fig. 4b, decomposition of MgSi2O5 to Mg2SiO4 and SiO2 holds positive dP/dT slope, and should thus enhance convection, while all other transformations shown in Fig. 4b hold negative dP/dT slopes, partially inhibiting convection.
MgO3-SiO3 pseudo-binary system
MgSiO3, Mg2SiO4 and MgSi2O5 are traditional ordinary compounds satisfying the composition (MgO)x·(SiO2)y (x, y: positive integers).The discovery of novel compounds MgO3,SiO3 and SiO suggests that other compositions may appear in the ternary system. Excitingly, we have discovered two new stable magnesium silicates which belong to the MgO3-SiO3 pseudo-binary system.
As shown in Fig. 5a, MgSi3O12 with 64 atoms in the unit cell and cF64(Fm) structure becomes stable at 2.41 TPa. By increasing pressure further, another ternary compound, MgSiO6 (cP8, Pm) gains stability at 2.95 TPa. The two compounds share many similar structural features, as illustrated in Fig. 5b,c. Both are ordered cubic superstructures of the Cr3Si-type structure. Recently9 we have discovered a novel compound NaCl3 with the Cr3Si-type structure, and a related compound NaCl7. This structure is stable under pressure because of high density and high coordination numbers. Mg and Si atoms in MgSiO6 and MgSi3O12 are both icosahedrally coordinated (CN and ECoN = 12).
For these new ternary magnesium silicates, we need to clarify the nature of their stability. In both compounds, one can see infinite non-intersecting O-chains along the x, y and z axes. The O-O distances in cF64-MgSi3O12 are in the range 1.29–1.33 Å, which are much longer than in MgSiO6. Taking into account the O-O bond distance of oI16-O at 3 TPa is 1.10 Å, we can conclude that the O-O bonding in cF64-MgSi3O12 are much weaker than covalent single O-O bond. From Bader analysis, for cP8-MgSiO6 at 3 TPa, the net charge on Mg and Si are +1.59 e and +3.48 e, respectively, while the net charge on O is −0.85 e, indicating the nearly complete transfer of valence electrons of Mg and Si atoms to O atoms. For cF64-MgSi3O12 at 3 TPa, the net charges on Mg and Si are +1.6 e and +3.49 e, respectively, i.e. practically the same values as in cP8-MgSiO6, while the charge on O is −1.01 e, which is much higher than the value (−0.85e) of O atom in cP8-MgSiO6. The density of states of cF64-MgSi3O12 (Fig. 5d) shows that MgSi3O12 is a metal, with DOS near the Fermi level exhibiting features of a 1D-metal, which is consistent with the infinite non-intersecting O-chains in this structure. It is worth emphasizing that all the other oxides discussed in this work are insulators, which demonstrates the unique electronic structure of cF64-MgSi3O12.
By adopting Fermi-Dirac-smearing approach24, we have found that the electronic entropies of MgSiO6 and MgSi3O12 are much more significant and can’t be neglected. For instance, the enthalpy changes 0.10 eV/atom for MgSiO6 under 3.0 TPa at 10 kK after taking electronic entropy into account. MgSiO6 behaves more like a semi-conductor with band gap of 1.49 eV under 3.0 TPa, therefore bottom of the conduction band of MgSiO6 becomes populated and the phonon frequencies changes at high temperature. This effect is even larger for MgSi3O12 since MgSi3O12 is a metal, the enthalpy changes 0.11 eV/atom for MgSi3O12 under 2.0 TPa at 10 kK after taking electronic entropy into account. Here we have calculated the P-T phase diagram of MgSi3O12 with and without the Fermi-Dirac-smearing. As shown in Fig. 6, the reaction from MgO3 and SiO3 to MgSi3O12 is affected significantly by electronic entropy, and the phase boundary line shifts toward lower pressures. For Fig. 6, we can also observe that the stability of MgSi3O12 increases with increasing temperature. For O-rich exoplanets, MgSi3O12 are expected to exist at high temperature and pressure. It’s worth emphasizing that MgSiO6 is not stable below 3.0 TPa after considering zero-point energy, that’s why MgSiO6 cannot be observed in Fig. 6. Furthermore, for metallic and semiconducting compounds predicted in this work (MgSiO6, MgSi3O12), there is an intriguing possibility of their enhanced solubility in metallic iron-rich cores of exoplanets.
Using first-principles calculations and variable-composition evolutionary structure exploration in the Mg-Si-O system under exoplanet pressures, we have discovered numerous unexpected compounds. Two extraordinary compounds, SiO3 and SiO, have been found to become stable at pressures above 0.51 TPa and 1.89 TPa, respectively, in the Si-O system. Both tI32 and mP16 forms of SiO3 are peroxide oxides containing oxide O2− and peroxide [O2]2− ions, while strong electron localization in the Si4-tetrahedron plays the role of an additional anion to stabilize tP4-SiO. Besides two previously reported unusual compounds MgO2 and Mg3O2, we have found another extraordinary compound, hP8-MgO3, in the Mg-O system, which becomes thermodynamically stable at 0.89 TPa.
Taking temperature into consideration, two dissociation pathways of MgSiO3 are found at relatively low (<6.4 kK) and high (>6,6 kK) temperature are:
respectively. Interestingly, besides the well-known (MgO)x·(SiO2)y compounds, we have discovered two (MgO3)x·(SiO3)y compounds, MgSi3O12, MgSiO6, which can form at 2.41 TPa and 2.95 TPa, respectively, in the Mg-Si-O system. Surprisingly, MgSi3O12 is predicted to be a metallic oxide with 1D-metalicity while all other oxides discussed in this work are semiconductors or insulators.
As the dissociation pathway of pPv-MgSiO3 is clarified, the mineralogy and internal structure of planetary mantles can be understood much deeper. pPv-MgSiO3 can survive in super-Earths with masses smaller than 6 M⊕ as shown in Fig. 6b. Mg2SiO4 and MgSi2O5 can be found in the mantle of super-Earths with masses larger than 6 M⊕. Kepler-10c, 17 times heavier than Earth, would probably only have binary MgO and SiO2 near the CMB. For strongly oxidized planets, MgO3 and SiO3 can be expected to be found. The newly discovered MgO3, SiO3, MgSiO6, MgSi3O12 hold non-traditional stoichimetries, which fall off the MgO-SiO2 binary system. Given their thermodynamic stability, these new compounds must be included in future models of exoplanet mineralogy in order to better understand the role that they play in massive planetary structure and evolution. The highly-oxidized MgSi3O12 can be formed in the lowermost mantles of mega-Earths with masses above 20 M⊕, and even a metallic layer can exist. For O-rich planets, the extraordinary O-rich compounds MgO3, SiO3, MgSi3O12 and perhaps MgSiO6 can be important planet-forming minerals. They may also appear in gas giants, as a result of reaction between Mg-silicate solid core and H2O-rich fluid mantle. In future, the consideration of other important elements (e.g., Fe, Al), will likely reveal additional important high-pressure phases with similarly strange stoichiometries.
Further models of the internal structures of exoplanets must take these findings into account. Phase transitions and reactions predicted here will have a profound effect not only on the internal structure, but also on dynamical processes in planets. Exothermic reactions (with positive Clapeyron slope dP/dT in Fig. 4b) enhance convection, endothermic ones slow down or stop it, and a metallic layer can affect the planetary magnetic field25,26. Structure, dynamics and chemistry of planetary interiors may be much more complex and surprising than previously thought.
Searches for stable compounds and structures were performed using the variable-composition evolutionary algorithm, as implemented in the USPEX code27,28,29,30,31 merged with first-principles calculations within the framework of density functional theory (the Vienna Ab initio Simulation Package VASP)32,33 for the calculation of the total energies, structure relaxation, and computing their electronic structures. The electronic structure and force calculations at finite temperatures were implemented within the Fermi-Dirac-smearing approach24. The most significant feature of USPEX we used in this work is the capability of optimizing the composition and crystal structures simultaneously - as opposed to the more usual structure predictions at fixed chemical composition. The compositional search space is described via chemical building blocks. The whole range of compositions of interest is initially sampled randomly and sparsely. To ensure the child structures are within the desired area of compositional space, the chemistry-preserving constraints in the variation operators are lifted and replaced by the block correction scheme. A special “chemical transmutation” is introduced to reinforce the search efficiency. Stable compositions are determined using the convex hull construction: a compound is thermodynamically stable if the enthalpy of its decomposition into any other compounds is positive. For first-principles calculations we employed the all-electron projector augmented wave(PAW) method34 and the generalized gradient approximation35 for the exchange-correlation energy, along with a plane-wave cutoff energy of 800 eV and dense uniform Γ-centred k-point meshes with a reciprocal space resolution of 2π × 0.03 Å−1. The PAW potentials have [He] cores for all atoms, with radii 1.25, 1.4 and 1.15 a.u. for Mg, Si and O, respectively, which can guarantee no core overlap even at the highest pressures studied here. In addition, phonon dispersions throughout the Brillouin zone were derived using the finite-displacement approach as implemented in the Phonopy code36. Thermodynamic properties of these phases were investigated using their phonon spectra within the quasiharmonic approximation (QHA).
How to cite this article: Niu, H. et al. Prediction of novel stable compounds in the Mg-Si-O system under exoplanet pressures. Sci. Rep. 5, 18347; doi: 10.1038/srep18347 (2015).
We are grateful for support from the Government of the Russian Federation (No. 14.A12.31.0003), US National Science Foundation (EAR-1114313, DMR-1231586) and DARPA (No. W31P4Q1310005), from the “Hundred Talents Project” of Chinese Academy of Sciences, from NSFC of China (Grand Number: 51074151), as well as Beijing Supercomputing Center of CAS (including its Shenyang branch).
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