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The discovery of superconductivity in CaC6 with a critical temperature (Tc) of 11.5 K reignites much interest in exploring high-temperature superconductivity in graphite intercalation compounds (GICs). Here we identify a GIC NaC4, discovered by ab initio evolutionary structure search, as a superconductor with a computed Tc of 41.2 K at 5 GPa. This value is eight times higher than that of the synthesized GIC NaC2 and possesses the highest Tc among available GICs. The remarkable superconductivity of GIC NaC4 mainly arises from the coupling of {\pi} electrons in graphene with the low-frequency vibrations involving both Na and C atoms. These findings suggest that Na-GICs may hold great promise as high-Tc superconductors., Comment: 4 figures

Located at crystal voids, interstitial anion electrons (IAEs) have diverse topologies, which may be tuned to achieve new properties. Elucidating the role of IAEs in electron-phonon coupling (EPC), and using it to design new electride superconductors, leads to the current prediction of superconducting Li8Au at high pressure. We suggest that the occurence of high-temperature superconductivity in electrides requires high-symmetry structures with hydrogen-like cages, an electron acceptor element to balance charges, and isolated IAEs coupled with medium-frequency vibrations. The uniquely designed Li8Au electride has a NaCl-type (B1) lattice, with atomic Au and cubic Li8 cages as bases. Isolated IAEs are formed at the cage centers, with extra charges taken up by Au. These octahedrally coordinated IAEs have a p-orbital-like attribute and are strongly coupled with atomic vibrations in the Li8 cages. The strong EPC in Li8Au results in a calculated Tc of 73.1 K at 250 GPa, which is the highest Tc reported to date for all the electrides. A slight substitutional Pt doping can enhance the Tc of Li8Au to exceed liquid nitrogen temperature., Comment: 7 Pages, 3 Figures

Large-area single-crystal surface structures were successfully prepared on Cu(111) substrate with boron deposition, which is critical for prospective applications. However, the proposed borophene structures do not match the scanning tunneling microscopy (STM) results very well, while the proposed copper boride is at odds with the traditional knowledge that ordered copper-rich borides normally do not exist due to small difference in electronegativity and large difference in atomic size. To clarify the controversy and elucidate the formation mechanism of the unexpected copper boride, we conducted systematic STM, X-ray photoelectron spectroscopy and angle-resolved photoemission spectroscopy investigations, confirming the synthesis of two-dimensional copper boride rather than borophene on Cu(111) after boron deposition under ultrahigh vacuum. First-principles calculations with defective surface models further indicate that boron atoms tend to react with Cu atoms near terrace edges or defects, which in turn shapes the intermediate structures of copper boride and leads to the formation of stable Cu-B monolayer via large-scale surface reconstruction eventually., Comment: 15 pages, 4 figures

The intrinsic ferromagnetic (FM) axion insulators and Weyl semimetals (WSMs) with only single pair of Weyl points have drawn intensive attention but so far remain rare and elusive in real materials. Here, we propose a new class of Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$-B (\emph{X}=Ge, Sn, or Pb; \emph{B}=Sb or Bi; \emph{T}=Se or Te) family that is the stable structural form of this system. We find that the Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$-B family has not only the intrinsic FM axion insulators MnGe$_{2}$Bi$_{2}$Te$_{6}$-B, MnSn$_{2}$Bi$_{2}$Te$_{6}$-B, and MnPb$_{2}$Bi$_{2}$Te$_{6}$-B, but also the intrinsic WSM MnSn$_{2}$Sb$_{2}$Te$_{6}$-B with only a single pair of Weyl points. Thus, the Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$-B family can provide an ideal platform to explore the exotic topological magnetoelectric effect and the intrinsic properties related to Weyl points., Comment: 6 pages, 5 figures

Helium (He) is the most inert noble gas at ambient conditions. It adopts a hexagonal close packed structure (P63/mmc) and remains in the insulating phase up to 32 TPa. In contrast, lithium (Li) is one of the most reactive metals at zero pressure, while its cubic high-pressure phase (Fd-3m) is a weak metallic electride above 475 GPa. Strikingly, a stable compound of Li5He2 (R-3m) was formed by mixing Fd-3m Li with P63/mmc He above 700 GPa. The presence of helium promotes the lattice transformation from Fd-3m Li to Pm-3m Li, and tuns the three-dimensional distributed interstitial electrons into the mixture of zero- and two-dimensional anionic electrons. This significantly increases the degree of metallization at the Fermi level, consequently, the coupling of conductive anionic electrons with the Li-dominated vibrations is the key factor to the formation of superconducting electride Li5He2 with a transition temperature up to 26 K, dynamically stable to pressures down to 210 GPa., Comment: 5 pages, 3 figures

The origin of water on the Earth is a long-standing mystery, requiring a comprehensive search for hydrous compounds, stable at conditions of the deep Earth and made of Earth-abundant elements. Previous studies usually focused on the current range of pressure-temperature conditions in the Earth's mantle and ignored a possible difference in the past, such as the stage of the core-mantle separation. Here, using ab initio evolutionary structure prediction, we find that only two magnesium hydrosilicate phases are stable at megabar pressures, $\alpha$-Mg$_2$SiO$_5$H$_2$ and $\beta$-Mg$_2$SiO$_5$H$_2$, stable at 262-338 GPa and >338 GPa,respectively (all these pressures now lie within the Earth's iron core). Both are superionic conductors with quasi-one-dimensional proton diffusion at relevant conditions. In the first 30 million years of Earth's history, before the Earth's core was formed, these must have existed in the Earth, hosting much of Earth's water. As dense iron alloys segregated to form the Earth's core, Mg$_2$SiO$_5$H$_2$ phases decomposed and released water. Thus, now-extinct Mg$_2$SiO$_5$H$_2$ phases have likely contributed in a major way to the evolution of our planet.

The 8-Pmmn borophene, a boron analogue of graphene, hosts tilted and anisotropic massless Dirac fermion quasiparticles owing to the presence of the distorted graphene-like sublattice. First-principles calculations show that the stacked 8-Pmmn borophene is transformed into the fused three-dimensional borophene under pressure, being accompanied by the partially bond-breaking and bond-reforming. Strikingly, the fused 8-Pmmn borophene inherits the Dirac band dispersion resulting in an unusual semimetal-semimetal transition. A simple tight-binding model derived from graphene qualitatively reveals the underlying physics due to the maximum preservation of graphene-like substructure after the phase transition, which contrasts greatly to the transformation of graphite into diamond associated with the semimetal-insulator transition., Comment: 6 pages, 4 figures

Search for new high-temperature superconductors and insight into their superconducting mechanism are of fundamental importance in condensed matter physics. The discovery of near-room temperature superconductivity at more than a million atmospheres ushers in a new era for superconductors. However, the critical task of identifying materials with comparable superconductivity at near or ambient pressure remains. Carbon materials can always lead to intriguing surprises due to their structural diversity and electronic adjustability. Insulating diamond upon doping or external stimuli has achieved superconducting state. Thus, it still has a great opportunity to find superconducting ones with higher transition temperature (Tc). Here, we report an intrinsic superconducting graphite-diamond hybrid through first-principles calculations, whose atomic-resolution structural characteristics have been experimentally determined recently. The predicted Tc is approximated at 39 K at ambient pressure, and strain energizing can further boost Tc to 42 K. The strong electron-phonon coupling associated with the out-of-plane vibration of carbon atoms at the junction plays a dominant role in the superconducting transition. Our work demonstrates the great potential of such carbon materials as high-Tc superconductors, which will definitely attract extensive research., Comment: 11 pages, 3 figures

First-principles calculations reveal that sodium boride (NaB3) undergoes a phase transition from a tetragonal P4/mbm phase to an orthorhombic Pbam phase at about 16 GPa, accompanied by counterintuitive lattice expansion along the crystallographic a-axis. This unusual compression behavior is identified as negative linear compressibility (NLC), which is dominantly attributed to the symmetry-breaking of boron framework. Meanwhile, the P4/mbm and Pbam phases form superionic conductors after undergoing a peculiar swap state at high temperature. Specifically, under warm conditions the Na cation pairs exhibit a rare local exchange (or rotation) behavior, which may be originated from the asymmetric energy barriers of different diffusion paths. The study of NaB3 compound sheds new light on a material with the combination of NLC and ion transportation at extreme conditions., Comment: 5 figures

Carbon is likely the most fascinating element of the periodic table because of the diversity of its allotropes stemming from its variable (sp, sp2, and sp3) bonding motifs. Exploration of new forms of carbon has been an eternal theme of contemporary scientific research. Here we report on novel amorphous carbon phases containing high fraction of sp3 bonded atoms recovered after compressing fullerene C60 to previously unexplored high pressure and temperature. The synthesized carbons are the hardest and strongest amorphous materials known to date, capable of scratching diamond crystal and approaching its strength which is evidenced by complimentary mechanical tests. Photoluminescence and absorption spectra of the materials demonstrate they are semiconductors with tunable bandgaps in the range of 1.5-2.2 eV, comparable to that of amorphous silicon. A remarkable combination of the outstanding mechanical and electronic properties makes this class of amorphous carbons an excellent candidate for photovoltaic applications demanding ultrahigh strength and wear resistance., Comment: 40 pages, 17 figures

The energy landscape of helium-nitrogen mixtures is explored by ab initio evolutionary searches, which predicted several stable helium-nitrogen compounds in the pressure range from 25 to 100 GPa. In particular, the monoclinic structure of HeN$_{22}$ consists of neutral He atoms, partially ionic dimers N$_{2}$$^{\delta-}$, and lantern-like cages N$_{20}$$^{\delta+}$. The presence of helium not only greatly enhances structural diversity of nitrogen solids, but also tremendously lowers the formation pressure of nitrogen salt. The unique nitrogen framework of (HeN$_{20}$)$^{\delta+}$N$_{2}$$^{\delta-}$ may be quenchable to ambient pressure even after removing helium. The estimated energy density of N$_{20}$$^{\delta+}$N$_{2}$$^{\delta-}$ (10.44 kJ/g) is $\sim$2.4 times larger than that of trinitrotoluene (TNT), indicating a very promising high-energy-density material., Comment: 6 pages, 4 figures

Boron forms compounds with nearly all metals, with notable exception of copper and other group IB and IIB elements. Here, we report an unexpected discovery of ordered copper boride grown epitaxially on Cu(111) under ultrahigh vacuum. Scanning tunneling microscopy experiments combined with ab initio evolutionary structure prediction reveal a remarkably complex structure of 2D-Cu8B14. Strong intra-layer p-d hybridization and a large amount of charge transfer between Cu and B atoms are the key factors for the emergence of copper boride. This makes the discovered material unique and opens up the possibility of synthesizing ordered low-dimensional structures in similar immiscible systems., Comment: 19 pages

A computation methodology based on ab initio evolutionary algorithms and the spin-polarized density functional theory was developed to predict two-dimensional (2D) magnetic materials. Its application to a model system borophene reveals an unexpected rich magnetism and polymorphism. A stable borophene with nonzero thickness was an antiferromagnetic (AFM) semiconductor from first-principles calculations, which can be further turned into a half metal by finite electron doping. In this borophene, the buckling and coupling among three atomic layers are not only responsible for the magnetism, but also result in an out-of-plane negative Poissons ratios under uniaxial tension, making it the first elemental material possessing auxetic and magnetic properties simultaneously., Comment: 8 pages, 8 figures

"What is the difference between space and time?" is an ancient question that remains a matter of intense debate. In Newtonian mechanics time is absolute, while in Einstein's theory of relativity time and space combine into Minkowski spacetime. Here, we firstly propose Minkowski fermions in 2+1 dimensional Minkowski spacetime which have two space-like and one time-like momentum axes. These quasiparticles can be further classified as Klein-Gordon fermions and Dirac-Minkowski fermions according to the linearly and quadratically dispersing excitations. Realization of Dirac-Minkowski quasiparticles requires systems with particular topological nodal-line band degeneracies, such as hyperbolic nodal lines or coplanar band crossings. With the help of first-principles calculations we find that novel massless Dirac-Minkowski fermions are realized in a metastable bulk boron allotrope, Pnnm-B16.

We simulate boron on Pb(110) surface by using ab initio evolutionary methodology. Interestingly, the two-dimensional (2D) Dirac Pmmn boron can be formed because of good lattice matching. Unexpectedly, by increasing the thickness of 2D boron, a three-bonded graphene-like structure (P2_1/c boron) was revealed to possess double anisotropic Dirac cones. It is 20 meV/atom lower in energy than the Pmmn structure, indicating the most stable 2D boron with particular Dirac cones. The puckered structure of P2_1/c boron results in the peculiar Dirac cones, as well as substantial mechanical anisotropy. The calculated Young's modulus is 320 GPa.nm along zigzag direction, which is comparable with graphene., Comment: 6 pages, 5 figures

Boron suboxide B6O, the hardest known oxide, has an R-3m crystal structure ({\alpha}-B6O) that can be described as an oxygen-intercalated structure of {\alpha}-boron, or, equivalently, as a cubic close packing of B12 icosahedra with two oxygen atoms occupying all octahedral voids in it. Here we show a new ground state of this compound at ambient conditions, Cmcm-B6O (\b{eta}-B6O), which in all quantum-mechanical treatments that we tested (GGA, LDA, and hybrid functional HSE06) comes out to be slightly but consistently more stable. Increasing pressure and temperature further stabilize it with respect to the known {\alpha}-B6O structure. \b{eta}-B6O also has a slightly higher hardness and may be synthesized using different experimental protocols. We suggest that \b{eta}-B6O is present in mixture with {\alpha}-B6O, and its presence accounts for previously unexplained bands in the experimental Raman spectrum., Comment: 12 pages

Very recently, two-dimensional(2D) boron sheets (borophene) with rectangular structure has been grown successfully on single crystal Ag(111) substrates.The fabricated boroprene is predicted to have unusual mechanical properties. We performed first-principle calculations to investigate the mechanical properties of the monolayer borophene, including ideal tensile strength and critical strain. It was found that monolayer borophene can withstand stress up to 20.26 N/m and 12.98 N/m in a and b directions, respectively.However, its critical strain was found to be small. In a direction, the critical value is only 8%, which, to the best of our knowledge, is the lowest among all studied 2D materials.Our numerical results show that the tensile strain applied in b direction enhances the bucking height of borophene resulting in an out-of-plane negative Poisson's ratio, which makes the boron sheet show superior mechanical flexibility along b direction.The failure mechanism and phonon instability of monolayer borophene were also explored.

With the motivation of discovering high-temperature superconductors, evolutionary algorithm is employed to search for all stable compounds in the Sn-H system. In addition to the traditional SnH$_4$, new hydrides SnH$_8$, SnH$_{12}$ and SnH$_{14}$ are found to be thermodynamically stable at high pressure. Dynamical stability and superconductivity of tin-hydrides are systematically investigated. I$\bar{4}$m2-SnH$_8$, C2/m-SnH$_{12}$ and C2/m-SnH$_{14}$ exhibit higher superconducting transition temperatures of 81, 93 and 97 K compared to the traditional compound SnH$_4$ with T$_c$ of 52 K at 200 GPa. An interesting bent H$_3^-$ in I$\bar{4}$m2-SnH$_8$ and novel liner H$_4^-$ in C2/m-SnH$_{12}$ are observed. All the new tin-hydrides remain metallic over their predicted range of stability. The intermediate-frequency wagging and bending vibrations have more contribution to electron-phonon coupling parameter than high-frequency stretching vibrations of H$_2$ and H$_3$., Comment: 8 pages, 4 figures

We predict a two-dimensional (2D) antiferromagnetic (AFM) boron (designated as M-boron) by using ab initio evolutionary methodology. M-boron is entirely composed of B20 clusters in a hexagonal arrangement. Most strikingly, the highest valence band of M-boron is isolated, strongly localized, and quite flat, which induces spin polarization on each cap of the B20 cluster. This flat band originates from the unpaired electrons of the capping atoms, and is responsible for magnetism. M-boron is thermodynamically metastable and is the first cluster-based 2D magnetic material in the elemental boron system., Comment: 6 pages, 5 figures

Silicene, an analogue of graphene, was so far predicted to be the only two-dimensional silicon (2D-Si) with massless Dirac fermions. Here we predict a brand new 2D-Si Dirac semimetal, which we name siliconeet [silik'ni:t]. Unexpectedly, it has a much lower energy than silicene and robust direction-dependent Dirac cones with Fermi velocities comparable to those in graphene. Remarkably, its peculiar structure based on pentagonal rings and fivefold coordination plays a critical role in the novel electronic properties. Taking spin-orbit coupling into account, siliconeet can also be recognized as a 2D-topological insulator with a larger nontrivial band gap than silicene., Comment: 5 pages

Nitrogen oxides are textbook class of molecular compounds, with extensive industrial applications. Nitrogen and oxygen are also among the most abundant elements in the universe. We explore the N-O system at 0 K and up to 500 GPa though ab initio evolutionary simulations. Results show that two phase transformations of stable molecular NO2 exist at 7 and 64 GPa, and followed by decomposition of NO2 at 91 GPa. All of the NO+NO3- structures are found to be metastable at T=0 K, so experimentally reported ionic NO+NO3- is either metastable or stabilized by temperature. Upon increasing pressure, N2O5 transforms from P-1 to C2/c structure at 51 GPa. NO becomes thermodynamically stable at 198 GPa. This polymeric phase is superconducting (Tc = 2.0 K) and contains a -N-N- backbone.

Using systematic evolutionary structure searching we propose a new carbon allotrope, phagraphene, standing for penta-hexa-hepta-graphene, because the structure is composed of 5-6-7 carbon rings. This two-dimensional (2D) carbon structure is lower in energy than most of the predicted 2D carbon allotropes due to its sp2-hybridization and density of atomic packing comparable to graphene. More interestingly, the electronic structure of phagraphene has distorted Dirac cones. The direction-dependent cones are further proved to be robust against external strain with tunable Fermi velocities., Comment: 5 pages, 3 figures

A previously unknown thermodynamically stable high-pressure phase of BeF$_{2}$ has been predicted using the evolutionary algorithm USPEX. This phase occurs in the pressure range 18-27 GPa. Its structure has $C2/c$ space group symmetry and contains 18 atoms in the primitive unit cell. Given the analogy between BeF$_{2}$ and SiO$_{2}$, silica phases have been investigated as well, but the new phase has not been observed to be thermodynamically stable for this system. However, it is found to be metastable and to have comparable energy to the known metastable phases of SiO$_{2}$, suggesting a possibility of its synthesis., Comment: 6 pages, 7 figures

Abundant evidence has shown the emergence of exotic chemical phenomena under pressure, including the formation of unexpected compounds and strange crystal structures. In many cases, there is no convincing explanation for these phenomena and there are virtually no chemical rules or models capable of predicting or even rationalizing these phenomena. Here we calculate, as a function of pressure, two central chemical properties of atoms, electronegativity and chemical hardness, which can be seen as the first and second-order chemical potentials. Mulliken electronegativity, which equals minus the chemical potential of the electron relative to the vacuum, is appropriately modified - instead of taking the vacuum (impossible under high pressure), we take the homogeneous electron gas as reference. We find that for most elements, chemical hardness and electronegativity decrease with pressure, consistent with pressure-induced metallization. Furthermore, we discover that pressure-induced s-d orbital transfer makes Ni, Pd and Pt "pseudo-noble-gas" atoms with a closed d-shell configuration, and the elements preceding them (Fe and especially Co, Rh, Ir) electron acceptors, while the elements right after them (Cu, Ag, Zn, Cd, for example) become highly electropositive. We show the explicative and predictive power of our electronegativity and chemical hardness scales under pressure.

We report on a novel reconstruction of the alpha-boron (111) surface, discovered using an ab initio evolution structure search, and reveal that it has an unexpected neat structure and much lower surface energy than the recently proposed (111)-I_R,(a) surface. For this reconstruction, every single interstitial boron atom forms bridges with the unique polar-covalent bonds between neighboring B_12 icosahedra, which perfectly meet the electron counting rule and are responsible for the reconstruction-induced metal-semiconductor transition. The peculiar charge transfer between the interstitial atoms and the icosahedra plays an important role in stabilizing the surface., Comment: xfzhou@nankai.edu.cn;zxf888@163.com

Helium is generally understood to be chemically inert and this is due to its extremely stable closed-shell electronic configuration, zero electron affinity and an unsurpassed ionization potential. It is not known to form thermodynamically stable compounds, except a few inclusion compounds. Here, using the ab initio evolutionary algorithm USPEX and subsequent high-pressure synthesis in a diamond anvil cell, we report the discovery of a thermodynamically stable compound of helium and sodium, Na2He, which has a fluorite-type structure and is stable at pressures >113 GPa. We show that the presence of He atoms causes strong electron localization and makes this material insulating. This phase is an electride, with electron pairs localized in interstices, forming eight-centre two-electron bonds within empty Na8 cubes. We also predict the existence of Na2HeO with a similar structure at pressures above 15 GPa.

It has been widely accepted that planar boron structures, composed of triangular and hexagonal motifs are the most stable two dimensional (2D) phases and likely precursors for boron nanostructures. Here we predict, based on ab initio evolutionary structure search, novel 2D boron structure with non-zero thickness, which is considerably, by 50 meV/atom lower in energy than the recently proposed alpha-sheet structure and its analogues. In particular, this phase is identified for the first time to have a distorted Dirac cone, after graphene and silicene the third elemental material with massless Dirac fermions. The buckling and coupling between the two sublattices not only enhance the energetic stability, but also are the key factors for the emergence of the distorted Dirac cone., Comment: 5 pages and 4 figures; xfzhou@nankai.edu.cn

The energy landscape of Mg(BH4)2 under pressure is explored by ab initio evolutionary calculations. Two new tetragonal structures, with space groups P-4 and I41/acd are predicted to be lower in enthalpy, by 15.4 kJ/mol and 21.2 kJ/mol, respectively, than the earlier proposed P42nm phase. We have simulated X-ray diffraction (XRD) spectra, lattice dynamics, and equations of state (EOS) of these phases. The density, volume contraction, bulk modulus, and the simulated XRD patterns of I41/acd and P-4 structures are in excellent agreement with the experimental results., Comment: xfzhou@nankai.edu.cn

The high-pressure phase transitions of B1-structured stoichiometric transition metal carbides (TMCs, TM=Ti, Zr, Hf, V, Nb, and Ta) were systematically investigated using ab initio calculations. These carbides underwent universal phase transitions along two novel phase-transition routes, namely, B1\rightarrowdistorted TlI (TlI')\rightarrowTlI and/or B1\rightarrowdistorted TiB (TiB')\rightarrowTiB, when subjected to pressures. The two routes can coexist possibly because of the tiny enthalpy differences between the new phases under corresponding pressures. Four new phases result from atomic slips of the B1-structured parent phases under pressure. After completely releasing the pressure, taking TiC as a representative of TMCs, only its new TlI'-type phase is mechanically and dynamically stable, and may be recovered., Comment: fhcl@ysu.edu.cn

The physical mechanisms behind the reduction of the bulk modulus of a high-pressure cubic TiO2 phase are confirmed by first-principles calculations. An unusual and abrupt change occurs in the dependence of energy on pressure at 43 GPa, indicating a pressure-induced phase transition from columbite TiO2 to a newly-identified modified fluorite TiO2 with a Pca21 symmetry. Oxygen atom displacement in Pca21 TiO2 unexpectedly reduces the bulk modulus by 34% relative to fluorite TiO2. This discovering provides a direct evidence for understanding the compressive properties of such groups of homologous materials, Comment: htwang@nankai.edu.cn or xfzhou@nankai.edu.cn

A body-centered tetragonal carbon (bct-Carbon) allotrope has been predicted to be a transparent carbon polymorph obtained under pressure. The structural transition pathways from graphite to diamond, M-Carbon, and bct-Carbon are simulated and the lowest activation barrier is found for the graphite-bct transition. Furthermore, bct-Carbon has higher shear strength than diamond due to its perpendicular graphene-like structure. Our results provide a possible explanation for the formation of a transparent carbon allotrope via the cold compression of graphite. We also verify that this allotrope is hard enough to crack diamond., Comment: htwang@nankai.edu.cn or xfzhou@nankai.edu.cn

Based on the fact that both hardness and vibrational Raman spectrum depend on the intrinsic property of chemical bonds, we propose a new theoretical model for predicting hardness of a covalent crystal. The quantitative relationship between hardness and vibrational Raman frequencies deduced from the typical zincblende covalent crystals is validated to be also applicable for the complex multicomponent crystals. This model enables us to nondestructively and indirectly characterize the hardness of novel superhard materials synthesized under ultra-high pressure condition with the in situ Raman spectrum measurement., Comment: 11 pages, 2 figures. Any other comments will be greatly appreciated