Exotic stable calcium carbides: theory and experiment

It is well known that pressure causes profound changes in the properties of atoms and chemical bonding, leading to the formation of many unusual materials. Here we systematically explore all stable calcium carbides at pressures from ambient to 100 GPa using variable-composition evolutionary structure predictions. We find that Ca5C2, Ca2C, Ca3C2, CaC, Ca2C3, and CaC2 have stability fields on the phase diagram. Among these, Ca2C and Ca2C3 are successfully synthesized for the first time via high-pressure experiments with excellent structural correspondence to theoretical predictions. Of particular significance are the base-centered monoclinic phase (space group C2/m) of Ca2C, a quasi-two-dimensional metal with layers of negatively charged calcium atoms, and the primitive monoclinic phase (space group P21/c) of CaC with zigzag C4 groups. Interestingly, strong interstitial charge localization is found in the structure of R-3m-Ca5C2 with semimetallic behaviour.


Results
Convex hull. We have used the ab initio evolutionary algorithm USPEX 1,8,20 , which can simultaneously find stable stoichiometries and the corresponding structures in multicomponent systems, to explore stable Ca-C compounds and their structures. In these calculations, all stoichiometries were allowed (with the constraint that the total number of atoms in the unit cell be below 16 atoms), and calculations were performed at 10 GPa, 20 GPa, 40 GPa, 80 GPa, and 100 GPa. The pressure-composition phase diagram of the Ca-C system is given in Fig. 1 a, in which the convex hull was 5 obtained from the calculated enthalpies of the most stable structures for each composition at a given pressure. Thermodynamically, the convex hull at a given pressure connects the phases that are stable against decomposition into other binaries or the elements.

b and Fig. 2).
For all the newly predicted structures, calculated phonon dispersion relations confirmed their dynamical stability. Surprisingly, our theoretical calculations show that the known phases of CaC 2 and CaC 6 are thermodynamically metastable at normal conditions (see Fig. 1 a); CaC 2 is thermodynamically stable only above 21 GPa, and CaC 6 does not have a thermodynamic stability field (BaC 6 is thermodynamically stable in the Ba-C system at 1 atm. 23 ). We also explored metastable phases of Ca 2 C and CaC at lower pressure. The most stable low-pressure phase obtained for Ca 2 C has C2/m symmetry and that of CaC has Immm symmetry. The dynamical stability of these two thermodynamically metastable phases was confirmed via phonon calculations.
In order to analyze these predicted structures, we recall that the C-C bond length depends on the bond order and at 1 atm these lengths are 1.20 Å for the triple C-C bond, 1.33 Å for double bond, and 1.54 Å for single C-C bond. The carbon 6 patterns predicted for calcium carbides, based on calculations presented in this work, are plotted in Figure 3. Combining this knowledge with the results of Bader analysis, we unravel very diverse chemistry. From the results of Bader analysis, one can clearly see the correlation between the charge and volume: negatively charged calcium atoms occupy significantly greater volume. Also we observe the decrease of C-C bond order from triple to double to single bonds as pressure increases. Note, however, that at pressures up to 100 GPa, the most carbon-rich stable compound is CaC 2 . We consider the predicted phases in order of increasing carbon content.
Ca 5 C 2 . The stable structure of Ca 5 C 2 has R-3m symmetry. It is a semimetal and is thermodynamically stable at pressures ranging from 58 GPa to at least 100 GPa. This phase has novel structural features: it can be described as consisting of alternating CaC 2 layers (where Ca is octahedrally coordinated by C atoms) and layers with composition Ca 4 . The electron localization function (ELF) distribution in Ca 5 C 2 shows strong charge transfer from Ca to C. Non-nuclear charge density maxima are located in the Ca 4 layer as plotted in Fig. 5 24 . However, no theoretical or experimental information has been reported on the methanide Ca 2 C 25 .
According to our calculations, Ca 2 C is thermodynamically stable above 15 GPa (space group Pnma (Z=4)). For Pnma-Ca 2 C we observe the largest negative charge of 7 carbon atoms among all these phases: -2.321. In this semiconducting phase with band gap of 0.64 eV at 14 GPa, C atoms are isolated and one can represent this compound as a carbide with an idealized charge transfer scheme (Ca 2+ ) 2 C 4adhering to the Zintl concept. Metallic metastable C2/m-Ca 2 C has a unique structure, consisting of alternating layers of stoichiometry Ca 2 (C 2 ) and Ca 2 (two kinds of calcium atoms play distinctly different roles, see Fig. 6 a), and these layers have net charges of +0.582 and -0.582, respectively. What is unusual is that the Ca-layer is negatively charged, i.e., it is a reservoir of electrons. To further analyze this phenomenon, it is instructive to look first at the Ca 2 (C 2 ) layer. This C 2 -group can be represented as having a triple C-C bond and its ideal charge is -2 (Bader charge is -1.892), and if each Ca had the ideal charge of +2, the total charge of the Ca 2 (C 2 ) layer would be +2, and two electrons would be transferred to the Ca 2 layer. In reality, the C-C bond here has a somewhat lower order (C-C distance is 1.28 Å at 5 GPa) and therefore takes more electrons from One can expect that the electrons in the Ca-layer are very loosely bound and the work function of this compound can be expected to be extremely low. The density of states of metastable C2/m phase of Ca 2 C reveals a remarkable step-like feature near the bottom of the valence band, followed by a nearly constant density of states (see Fig. 6 b), presenting an example of a quasi-two-dimensional electronic structure as observed 8 in Li-Be alloys 26 . The calculated Fermi surface of C2/m-Ca 2 C at 3 GPa holds a hollow square cylinder-like Fermi surface along the Γ-V direction (i.e., reciprocal lattice basis vector b 3 direction) in the Brillouin zone, signaling quasi-two-dimensional electronic properties (see Fig. 6 c). CaC. Metallic CaC has two thermodynamically stable phases below 100 GPa. At 14 GPa, the metastable orthorhombic Immm structure transforms into a monoclinic P2 1 /c structure (stable thermodynamically above 26 GPa, favored over a wide pressure range of 14-57.5 GPa), followed by a thermodynamic stable Imma structure. P2 1 /c-CaC is very interesting because its structural formula Ca 4 (C 4 ) contains a unique and hitherto unknown zigzag C 4 -group, with C-C distances between 1.48-1.50 Å at 14 GPa, indicating bond orders between 1 and 2 and ideal charges of about -2.5 for the end C atoms (Bader charge -1.447) and about -1 for the central C atoms (Bader charge -0.905). Imma-CaC has infinite zigzag chains of C atoms (C-C bond length of 9 1.55 Å at 57.5 GPa, indicating a weakened single bond) in the y-axis direction. The structural formula of metastable Immm-CaC is Ca 2 (C 2 ), and with a doubly bonded C 2 -group (C-C distance 1.33 Å at 7.1 GPa) that has an ideal charge of -4 (Bader charge -2.340), it exactly balances the ideal charge of two Ca atoms. All three phases of CaC beautifully conform to the trend of increasing polymerization of the C-sublattice with increasing pressure. the calculated bulk modulus B 0 of C2/m-Ca 2 C 3 is about 89 GPa, which is higher than that of CaC 2 (50 GPa). At ~40 GPa, the metallic C2/c structure transforms into a metastable P-1 structure (metal), which dominates the pressure range between 40-65 GPa. At higher pressures, a metallic metastable Imma structure is stable and contains zigzag carbon chains (Figs. 3 and 4). We searched at much higher pressures for 3D-polymeric carbon frameworks in Ca 2 C 3 , but found none at pressures up to at least 300 GPa. For comparison, in CaC 2 we have found that graphene sheets predicted in the high-pressure phase can be stable up to at least 1 TPa 15 .
For Ca 2 C 3 , the carbon arrangement changes from isolated C 3 to carbon chains to 10 ribbons (Fig. 3). The structure of C2/m-Ca 2 C 3 can be described as Ca 2 layers linked together by nearly linear symmetric C 3 groups with double C-C bonds (C-C distances Imma-Ca 2 C 3 has a very interesting structure with extended 1D-ribbons of carbon atoms cut from the graphene layer. Bond lengths in this ribbon are 1.50-1.52 Å at 70 GPa, slightly longer than in graphene and indicating predominantly single bonds.
Electronic structure calculations show that both P-1 and Imma phases of Ca 2 C 3 are metals. Based on Allen and Dynes modified equation 29 , we have checked for superconductivity in these phases at 34 GPa and 65 GPa, respectively, and found 11 none.
CaC 2 . CaC 2 is thermodynamically stable above 21 GPa (see Fig. 1 Fig. 1 a). It is very unexpected, but the above numbers fully confirm this conclusion, that the well-known and industrially produced compound CaC 2 is metastable at ambient conditions, while the so far never seen compound Ca 2 C 3 is actually stable. This could be either due to kinetics, or due to conditions of synthesis. In addition to our previous result 15 , we found a new phase with P-1 symmetry, which contains infinite carbon chains with five-membered rings (C-C distance is between 1.442-1.507 Å at 20 GPa (see Fig. 3 i), signaling single or double bonds), and is the lowest enthalpy structure over a wide pressure range from 7.5 GPa to 37 GPa (thermodynamically stable from 21 GPa to 37 GPa, see Fig. 4).
With further application of pressure, metallic P-1-CaC 2 transforms into metallic At pressures above ~22 GPa, a second carbide phase (Pnma-Ca 2 C) was synthesized upon laser heating. This same phase was reproducibly formed both from elemental Ca+C mixtures and from samples containing C2/m-Ca 2 C 3 , indicating disproportionation of Ca 2 C 3 into a more stable carbide phase above ~22 GPa. Figure 7 shows experimental PXRD data at 24 GPa with a = 6.122 (1)

Discussion
We find that the carbon sublattice within all predicted carbide phases has close correlation with the Ca:C ratio (see Fig. 2). With increasing carbon content, isolated carbon atoms are polymerized, in turn, into C 2 dumbbells, C 3 and C 4 groups, chains, ribbons and graphene sheets (see Figs. 4). The polymeric carbon structures reveal an expected trend when comparing to the structural chemistry of the heavier congeners of the 4 th main group elements in Zintl phases (alkali or alkaline-earth silicides, germanides, and stannides) 16,32 . Yet in spite of certain similarities to silicides, calcium carbides differ from them due to distinct bonding features. Combining present analysis and our previous results 15,16,19 , one can conclude that for the Ca-C system, one can cover sp to sp 2 to sp 2 +sp 3 to sp 3 hybridizations of carbon as pressure 14 increases. This pressure-induced structural evolution of carbon was also found in other alkali metal or alkaline-earth metal carbides 16,19,23 . Together with our previous results for CaC 2 15 and CaC 6 19 , it is clear that a three-dimensional network of carbon in CaC x can be formed when x is greater than 2, (from sheets to three-dimensional frameworks to Ca-C phase separation with slabs of diamond at high C content), consistent also with the behavior of the metastable CaC 4 compound found in our structural searches. On the other hand, the structural features of carbon-rich compounds 19 can be extended to alkali-metal or alkaline-earth metal congeners of the group four elements, which allows one to fabricate a variety of the 3D framework structures of the group four elements by removing metal sublattices. The unexpected mechanical 19,33 or electronic characteristics 34 uncovered in these 3D framework structures pave the way to novel materials.
In summary, we have produced the first complete pressure-composition phase diagram for CaC x compounds at pressures up to 100 GPa and demonstrated the experimental synthesis of two previously unknown compounds (Ca 2 C 3 and Ca 2 C), validating part of our predicted phase diagram. Contrary to normal ionic compounds, there is no "dominant" compound stable in this whole pressure range. The well-known CaC 2 and CaC 6 were found to be metastable at normal conditions; CaC 2 is stable only above 21 GPa, and CaC 6 is never thermodynamically stable, while hitherto unreported Ca 2 C 3 is actually thermodynamically stable at ambient pressure.
Bader analysis unravels very diverse chemistry: the decrease of C-C bond order from triple to double to single bonds at increasing pressure; a negatively charged metal 15 layer in calcium-rich Ca 2 C compound; a hitherto unknown bent linear C 4 group in the Pressure was estimated using the Ne equation of state 41 and/or with a ruby gauge 42