Investigation of exotic stable calcium carbides using theory and experiment

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Received 13 Nov 2014 | Accepted 18 Mar 2015 | Published 11 May 2015 DOI: 10.1038/ncomms7974 OPEN
## Investigation of exotic stable calcium carbides using theory and experiment

Yan-Ling Li 1, Sheng-Nan Wang 2, Artem R. Oganov 2,3,4,5, Huiyang Gou 6, Jesse S. Smith 7 & Timothy A. Strobel 6

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 using the USPEX code. 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 is the base-centred 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 semi-metallic
behaviour.

1 Laboratory for Quantum Design of Functional Materials, School of Physics and Electronic Engineering, Jiangsu Normal University, 221116 Xuzhou, China.
2 Department of Geosciences, State University of New York, Stony Brook, New York 11794–2100, USA. 3 Center for Materials by Design, Institute for
Advanced Computational Science, State University of New York, Stony Brook, New York 11794-2100, USA. 4 Moscow Institute of Physics and Technology, 9
Institutskiy lane, Dolgoprudny city, Moscow Region 141700, Russia. 5 Northwestern Polytechnical University, Xi’an 710072, China. 6 Geophysical Laboratory,
Carnegie Institution of Washington, Washington, District of Columbia 20015, USA. 7 High Pressure Collaborative Access Team, Geophysical Laboratory,
Carnegie Institution of Washington, Argonne, Illinois 60439, USA. Correspondence and requests for materials should be addressed to Y.-L.L.
[(email:ylli@jsnu.edu.cn)](mailto:ylli@jsnu.edu.cn) or to A.R.O. (email: [artem.oganov@stonybrook.edu)](mailto:artem.oganov@stonybrook.edu) or to T.A.S. (email: [tstrobel@carnegiescience.edu).](mailto:tstrobel@carnegiescience.edu)

nexpected chemical reactions can happen under extreme
conditions, with emergence of rich phase diagrams and
materials possessing intriguing properties. Recently, by
# U
combining variable-composition structure prediction methods
with first-principles total energy calculations 1, pressurecomposition (P-x) phase diagrams were predicted for such
binary systems as Mg-O (ref. 2) and Na-Cl (ref. 3). In both
cases, the predicted unexpected compounds have been
successfully synthesized 3,4 . Elemental carbon and calcium both
exhibit rich diversity of stable and metastable phases under
pressure 5–7 . Compressed calcium shows unique structural and
electronic properties and exhibits the highest recorded
superconducting critical temperature among pure elements 8 .
For carbon, only graphite and diamond are experimentally
known as thermodynamically stable solids (graphite is thermodynamically stable at ambient condition and diamond under high
pressure), although numerous metastable phases are known. For
example, by applying pressure to graphite at low temperatures, a
new superhard carbon allotrope was found, and its properties
match those of one of the theoretically predicted structures (Mcarbon) 9–12 . For the Ca-C system, the well-known Ca carbides
include CaC2 and CaC6, whose high-pressure behaviours have
been studied experimentally 13–15 and by ab initio calculations 16–
20. An interesting structural evolution has been uncovered under
pressure: carbon atoms polymerize from dumbbells to onedimensional (1D) chains to ribbons to two-dimensional (2D)
graphene sheets in compressed CaC2 (ref. 16) and from graphite
sheets to a mixed sp 2 –sp 3 structure in CaC6 (ref. 20). In addition,
superconductivity was predicted in metallic high-pressure phases
of CaC2 with critical temperatures comparable to those observed
in CaC6 (ref. 16).

Here, using variable-composition structure prediction code
USPEX 1,9,21, the pressure-composition phase diagram of the
Ca-C system was explored in order to fully understand the
structural diversity and evolution of the C–C bonding types
under high pressure. This resulted in five newly predicted
stable stoichiometries (Ca5C2, Ca2C, Ca3C2, CaC and Ca2C3)
with diverse carbon arrangements: isolated atoms in Ca2C,
hitherto unknown zigzag tetramers in CaC, and ribbons
consisting of five-membered rings in CaC2. Two phases (Ca2C
and Ca2C3) were confirmed experimentally via in situ
synchrotron powder X-ray diffraction (PXRD) measurements.
Most surprising is that the low-pressure phase (monoclinic C2/m
structure) of Ca2C exhibits quasi-2D metallic behaviour and
contains negatively charged calcium atoms. In addition, strong
interstitial electron localization was found in the newly predicted
R-3m phase of Ca5C2, just as in compressed elements Li (ref. 22),
Na (ref. 23) and Ca (ref. 6), as well as in the compound Mg3O2
(ref. 2).

Results
Convex hull. We have used the ab initio evolutionary algorithm
USPEX 1,9,21, 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, 20, 40,
80 and 100 GPa. The pressure-composition phase diagram
of the Ca-C system is given in Fig. 1a, in which the convex
hull was 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.

C / (Ca+C) ratio

0.0 0.2

0.0

–0.2

–0.4

–0.6

–0.8

5:2

0.4

0.6

0.8 1.0

0 GPa
30 GPa
60 GPa

1:6

0.7

0.6

0.5

0.4

0.3

2:1 3:2 1:1 2:3 1:2

Stoichiometry

( _C_ 2/ _m_ ) ( _Cmcm_ )
( _P_ -1) CaC2( _Immm_ )

_(Imma)_

( _C_ 2/ _m_ )

( _Immm_ )

( _C_ 2/ _c_ ) Ca2C3( _P_ -1)

CaC( _P2_ 1/ _c_ ) _(Imma)_

( _P4/mbm_ ) Ca3C2 ( _C_ 2/ _c_ )

( _C2/m_ )

Ca2C ( _Pnma_ )

Ca5C2( _R-_ 3 _m_ )

0 20 40 60 80

Pressure (GPa)

100

Figure 1 | Stability of new calcium carbides. (a) Convex hull diagram for
the Ca-C system at selected pressures. At a given pressure, the compounds
located on the convex hull are thermodynamic stable. (b) Pressurecomposition phase diagram of the Ca-C system. Thick solid lines represent
thermodynamically stable phases and dashed lines represent metastable
phases (Red lines represent metal and blue semiconductor).

Thermodynamically stable or metastable phases. Using variable-composition evolutionary searches, we found that Ca5C2,
Ca2C, Ca3C2, CaC, Ca2C3 and CaC2 have thermodynamic stability fields on the phase diagram: Ca2C3, stable from 0 to 28 GPa;
Ca5C2, stable above 58 GPa; Ca2C, stable above 14 GPa; Ca3C2,
stable from B50 GPa; CaC, stable above 26 GPa; and CaC2, stable
above 21 GPa (see Figs 1b and 2). All crystallographic parameters
are listed in Supplementary Table 1. For all the newly predicted
structures, calculated phonon dispersion relations confirmed
their dynamical stability (see Supplementary Figs 1–5 and
Supplementary Note 1). Surprisingly, our theoretical calculations
show that the known phases of CaC2 and CaC6 are thermodynamically metastable at normal conditions (see Fig. 1a); CaC2
is thermodynamically stable only above 21 GPa, and CaC6 does
not have a thermodynamic stability field (BaC6 is thermodynamically stable in the Ba-C system at 1 atm (ref. 24)). We also
explored metastable phases of Ca2C and CaC at lower pressure.
The most stable low-pressure phase obtained for Ca2C 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 (Supplementary Figs 6 and 7).

c
b

a
b a c a

b
a

b c a

a ab b c

a b

Figure 2 | The predicted crystal structures of stable Ca-C compounds. (a) Thermodynamically stable Pnma structure of Ca2C. (b) The metastable
low pressure P4/mbm structure of Ca3C2. (c) Thermodynamiclly stable high pressure C2/c structure of Ca3C2. (d) Thermodynamically stable
P21/c structure of CaC. (e) Thermodynamically stable high pressure Imma structure of CaC. (f) Ca2C3 crystallizes in C2/m structure at pressures up to
28 GPa. (g) Thermodynamically metastable C2/c structure of Ca2C3. (h) Thermodynamically metastable P-1 structure of Ca2C3. (i) Thermodynamically
metastable high pressure Imma of Ca2C3. (j) Thermodynamically stable P-1 structure of CaC2. (k) Thermodynamically stable Immm structure of CaC2.
The blue and brown spheres represent calcium and carbon atoms, respectively.

In order to analyse 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 patterns predicted
for calcium carbides, on the basis of calculations presented in this
work, are plotted in Fig. 3. The carbon patterns together with
their pressure range of existence in calcium carbides are
summarized in Fig. 4 and in Supplementary Table 2. Combining
this knowledge with the results of Bader analysis (see
Supplementary Table 1), we unravel very diverse chemistry.
From the results of the Bader analysis, one can clearly see the
correlation between the charge and volume: negatively charged
calcium atoms occupy significantly greater volume. In addition,

we observe the decrease in C–C bond order from triple to double
to single bonds as pressure increases. Note, however, that at
pressures up to 100 GPa, the carbon-richest stable compound is
CaC2. Below we consider the predicted phases in order of
increasing carbon content.

Ca5C2. The stable structure of Ca5C2 has a R-3m symmetry. It is a
semi-metal (see Supplementary Fig. 8) and is thermodynamically
stable at pressures ranging from 58 GPa to at least 100 GPa (see
Fig. 4). This phase has novel structural features: it can be
described as consisting of alternating CaC2 layers (where Ca is
octahedrally coordinated by C atoms) and layers with

1.338
1.500

1.468

1.549
1.428

1.478

1.471

1.501

1.453
1.394

1.475
1.525

1.448

1.505 1.504

1.474

1.503

1.442

1.507
1.474

1.515 1.515

1.504 1.504

1.501
1.501

Figure 3 | Carbon patterns in the Ca-C system. (a) The isolated carbon anions in the Pnma structure of Ca2C. (b) Carbon dimers observed in the C2/m
structure of Ca2C, P4/mbm and C2/c structures of Ca3C2, Immm structure of CaC, and C2/m or C2/c structures of CaC2. (c) The carbon trimer occurs in
the C2/m structure of Ca2C3 at zero pressure. (d) Zigzag C4 groups observed in P21/c structure of CaC at 20 GPa. (e) Zigzag carbon chains in the Imma
structure of CaC at 58 GPa. (f) Carbon chains with two types of carbon-carbon bondings in C2/c structure of Ca2C3 at 34.5 GPa. (g) Carbon chains with
four types of carbon-carbon bongdings in P-1 structure of Ca2C3 at 40 GPa. (h) Armchair carbon chains in the Cmcm structure of CaC2 at 4 GPa. (i) Carbon
stripes in the P-1 structure of CaC2 at 20 GPa. (j) Carbon ribbons in the Immm structure of CaC2 at 10 GPa. (k) Carbon ribbons in the Imma structure of
Ca2C3 at 65 GPa. Bond lengths (in Å) are given. The inequivalent C1, C2, C3, and C4 (occupying different Wyckoff positions in the unit cell, see
Supplementary Table 1) are shown by red, blue, yellow, and grey spheres, respectively.

CaC2 Stripes Ribbons

_P-_ 1, Metal _Immm_, Metal

C 3 trimers

Ca2C3

_C_ 2 _/m_, Semiconductor

CaC Tetramers Chains

_P_ 21 _/c_, Metal _Imma_, Metal

Ca3C2 C 2 dumbbells
_C_ 2 _/c_, Metal, Pseudogap

Ca2C

Isolated C anions

_Pnma_, Semiconductor

Ca5C2

Isolated C anions

_R-_ 3 _m_, Semimetal

0 20 40 60 80

Pressure (GPa)

100

Figure 4 | Carbon arrangement with increasing carbon content. Only
thermodynamically stable phases are shown (For metastable phases, see
Supplementary Table 2). Additionally, the conducting properties are shown.

composition Ca4. The electron localization function distribution
in Ca5C2 shows strong charge transfer from Ca to C. Non-nuclear
charge density maxima are located in the Ca4 layer as plotted in

Fig. 5 (electron localization function ¼ 0.75 at 60 GPa). Bader
charges are þ 1.039 for Ca1, þ 0.823 for Ca2, þ 0.973 for Ca3
and - 0.459 for the interstitial electron density maximum.

Ca2C. Known alkali earth methanides include well-know Be2C
(Fm-3m, Z ¼ 4) and Mg2C (antifluorite) recently synthesized by
Kurakevych et al. 25 However, no theoretical or experimental
information has been reported on the methanide Ca2C (ref. 26).
According to our calculations, Ca2C is thermodynamically stable
above 15 GPa (space group Pnma (Z ¼ 4)). For Pnma-Ca2C we
observe the largest negative charge of carbon atoms among all
these phases: - 2.321. In this semiconducting phase with band
gap of 0.64 eV at 14 GPa (see Supplementary Fig. 9), C atoms are
isolated and one can represent this compound as a carbide with
an idealized charge transfer scheme (Ca 2 þ )2C 4 � adhering to the
Zintl concept. Metallic metastable C2/m-Ca2C has a unique
structure, consisting of alternating layers of stoichiometry
Ca2(C2) and Ca2 (two kinds of calcium atoms play distinctly
different roles, see Fig. 6 a), and these layers have net charges of

þ 0.582 and - 0.582, respectively (see Supplementary Table 1).
What is unusual is that the Ca layer is negatively charged, that is,
it is a reservoir of electrons. To further analyse this phenomenon,
it is instructive to look first at the Ca2(C2) layer. This C2 group

Ca2C2 layer

Ca2 layer

Figure 5 | Electron localization function (ELF) of R-3 m-Ca5C2 at 60 GPa.
The isosurface ELF ¼ 0.75 is shown. The observed interstitial electron
charge accumulation shows that Ca5C2 with R-3 m symmetry is an
electride.

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 þ 2, the total charge of the Ca2(C2) layer would be

þ 2, and two electrons would be transferred to the Ca2 layer (see
Supplementary Table 1). 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 Ca atoms, leaving less for the
Ca2 layer, but not changing the picture qualitatively. To our
knowledge, this is the first example of negatively charged metal
atoms in a compound with more electronegative atoms. Note the
enormous difference of Bader volumes of the positively and
negatively charged Ca atoms (16.570 versus 41.901 Å 3 ). 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 the metastable C2/m phase
of Ca2C reveals a remarkable step-like feature near the bottom of
the valence band, followed by a nearly constant density of states
(see Fig. 6b), presenting an example of a quasi-2D electronic
structure as observed in Li–Be alloys 27 . The calculated Fermi
surface of C2/m-Ca2C at 3 GPa has a hollow square cylinder-like
Fermi shape along the G-V direction (that is, reciprocal lattice
basis vector b3 direction) in the Brillouin zone (BZ), signalling
quasi-2D electronic properties (see Fig. 6c).

Ca3C2. For Ca3C2, no thermodynamically stable phase exists
below 50 GPa. A metastable P4/mbm (Z ¼ 2) phase, favoured in
the pressure range from 5 to 30 GPa, transforms into a C2/c
(Z ¼ 4) structure at 30 GPa, which is thermodynamically stable
above 50 GPa. The structure of P4/mbm-Ca3C2 contains doubly
bonded C2 groups (C–C distance 1.39 Å at 20 GPa), with an ideal
charge - 4, that is, accepting four electrons from calcium atoms,
leaving two electrons per formula to form Ca–Ca bonds in this
metallic compound. Metallic C2/c-Ca3C2 with a pseudogap at the
Fermi level (see Supplementary Fig. 10) has singly bonded C2
groups (C–C bond length 1.51 Å at 38.7 GPa), which have ideal
charge - 6, exactly balanced by three Ca atoms in the formula.

CaC. Metallic CaC has two thermodynamically stable phases
below 100 GPa. At 14 GPa, the metastable orthorhombic Immm
structure transforms into a monoclinic P21/c structure (stable
thermodynamically above 26 GPa, favoured over a wide pressure
range of 14–57.5 GPa), followed by a thermodynamically stable
Imma structure. P21/c-CaC is very interesting because its structural formula Ca4(C4) contains a unique and hitherto unknown
zigzag C4 group, with C–C distances between 1.48 and 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).

0
–6 –4 –2 0 2

E-Ef (eV)

- V

Figure 6 | Structural and electronic property of C2/m phase of Ca2C at
3 GPa. (a) The top view of C2/m structure along the y axis shows a clearly
layered structure. (b)Total electronic density of states (DOS). (c) Fermi
surface of the C2/m structure. The indication of a quasi-two-dimensional
metal in total DOS is confirmed by the hollow square prismatic cylinder-like
Fermi surface.

Imma-CaC has infinite zigzag chains of C atoms (C–C bond
length of 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 Ca2(C2), and with a doubly bonded C2 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.

Ca2C3. The structure of Mg2C3 (space group Pnnm, Z ¼ 2), the
only known alkaline-earth metal allylenide with C3 4 � anions 26,

Signature of

2D metal

was considered when searching for stable phases of Ca2C3. Total
energy calculations exclude the possibility of the ambientpressure Mg2C3-type structure. The semiconducting C2/m
structure (band gap of 1.06 eV at 10 GPa, see Supplementary
Fig. 11) is instead the most stable one below 34.5 GPa
(thermodynamically stable from 0 to 28 GPa), followed by
metastable C2/c structure. By fitting energy versus volume data
to the third-order Birch–Murnaghan equation of state 28, the
calculated bulk modulus B0 of C2/m-Ca2C3 is B89 GPa, which is
higher than that of CaC2 (50 GPa). At B40 GPa, the metallic C2/c
structure transforms into a metastable P-1 structure (metal),
which dominates the pressure range between 40 and 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
Ca2C3, but found none at pressures up to at least 300 GPa. For
comparison, in CaC2 we have found that graphene sheets
predicted in the high-pressure phase can be stable up to at least
1 TPa (ref. 16).
For Ca2C3, the carbon arrangement changes from isolated C3
to carbon chains to ribbons (Fig. 3). The structure of C2/m-Ca2C3
can be described as Ca2 layers linked together by nearly linear
symmetric C3 groups with double C–C bonds (C–C distances
1.32 Å at 18.1 GPa). With this configuration, the total charge of
the C3 group should be - 4 (Bader charge - 2.692), exactly
compensating the charge of two Ca atoms in the formula (see
Supplementary Table 1). Central carbon atoms in the C3 group in
this valence scheme should be neutral, and yet turn out to have a
large negative Bader charge of - 0.738, whereas the end atoms,
whose idealized charge is - 2, develop a lower Bader charge
( � 0.977). This discrepancy is explained by the effects of Ca
atoms, which form significant bonds with the central carbon
atom in the C3 group and transfer some electronic charge to
them. Most recently, some of us reported the prediction and
synthesis of b-Mg2C3 (ref. 29), which is isostructural with our
C2/m-Ca2C3 reported here. The structure of C2/c-Ca2C3 (C–C
distances 1.43–1.47 Å at 34.5 GPa) has an idealized charge
transfer scheme Ca2 4 þ C3 4 � . In this metallic phase, C atoms are
polymerized into infinite chains with nearly closed six-member
rings running through channels of Ca host lattice. P-1-Ca2C3
features a complicated extended 1D ribbon of carbon atoms with
nearly single C–C bonds (lengths 1.47–1.50 Å at 40 GPa).

Imma-Ca2C3 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 Ca2C3 are metals. On the basis of Allen and Dynes
modified equation 30, we have checked for superconductivity in
these phases at 34 and 65 GPa, respectively, and found none.

CaC2. CaC2 is thermodynamically stable above 21 GPa (see
Fig. 1a). The lower-pressure phases C2/m and Cmcm reported
previously 16 are metastable, which could be unravelled by
calculating enthalpy of formation (DHf) at lower pressure.
Considering that graphite is the ground state of carbon at zero
pressure, we performed additional calculations where the van der
Waals interaction is accounted for by using the optPBE-van der
Waals functional 31 . At zero pressure, the calculated DHf
( � 0.17 eV per atom) of CaC2 is close to the experimental
standard DHf ( � 0.21 eV per atom at 298 K and 1 atm (ref. 32))
but higher than that ( � 0.27 eV) of Ca2C3, confirming the
thermodynamic metastability of CaC2 under ambient conditions
(see Fig. 1a). It is very unexpected, but the above numbers fully
confirm this conclusion, that the well-known and industrially
produced compound CaC2 is metastable under ambient

conditions, while the so far never seen compound Ca2C3 is
actually stable. This could be either due to kinetics, or due to
high-temperature conditions of synthesis. In addition to our
previous result 16, we found a new phase with the P-1 symmetry,
which contains infinite carbon chains with five-membered rings
(C–C distance is between 1.442 and 1.507 Å at 20 GPa (see
Fig. 3i), signalling single or double bonds), and is the lowest
enthalpy structure over a wide pressure range from 7.5 to 37 GPa
(thermodynamically stable from 21 to 37 GPa, see Fig. 4 and
Supplementary Fig. 12). With further application of pressure,
metallic P-1-CaC2 transforms into metallic Immm-CaC2 (ref. 16),
in which carbon atoms are polymerized to form quasi-1D ribbons
(see Figs 2–3).

Experiments. In order to confirm theoretical structure predictions, we performed synthesis under high-pressure/high-temperature conditions. Diamond anvil cells were loaded with both
calcium- and carbon-rich Ca þ C mixtures, compressed to pressures up to 25 GPa, heated to temperatures up to B2,000 K and
probed in situ using synchrotron PXRD. Under these pressure
conditions, the formation of Immm-CaC2, C2/m-Ca2C3 and
Pnma-Ca2C may be expected on the basis of thermodynamic
stabilities, as these phases are the only stable ones that appear on
the convex hull up to 25 GPa (see Fig. 1); indeed, two of these
three structures were observed experimentally.

When samples were compressed above B10 GPa and heated to
B2,000 K, mixtures of elemental glassy carbon and face-centred
cubic (fcc) Ca transformed into a new low-symmetry phase. After
comparison with density functional theory (DFT) structure
predictions, PXRD reflections originating from this phase were
readily indexed to the monoclinic C2/m-Ca2C3 structure with
excellent agreement between experiment and theory (see
Supplementary Table 3). Figure 7 shows experimental PXRD
data obtained at 17 GPa with a ¼ 5.169(4) Å, b ¼ 4.994(3) Å,
c ¼ 6.322(3) Å and b ¼ 128.53(3)�, which compares with
a ¼ 5.151 Å, b ¼ 4.962 Å, c ¼ 6.306 Å and b ¼ 128.81� for the
theoretical structure relaxed at 18 GPa. This sample was
decompressed in steps of B2 GPa to obtain lattice parameters
as a function of pressure (see Fig. 8). Theoretical lattice
parameters show an average absolute deviation of 0.3% from
experiment over the entire pressure range, and the C2/m-Ca2C3
phase was recoverable to ambient pressure, but was found to be
air/moisture-sensitive. The experimental P–V data were fit to a
second-order Birch–Murnaghan equation of state with B0 ¼ 84(2)
GPa, in good agreement with theoretical predictions (89 GPa).

At pressures above B22 GPa, a second carbide phase (PnmaCa2C) was synthesized upon laser heating. This same phase was
reproducibly formed both from elemental Ca þ C mixtures and
from samples containing C2/m-Ca2C3, indicating disproportionation of Ca2C3 into a more stable carbide phase when pressure is
raised above B22 GPa, i.e. above its predicted stability field.
Figure 7 shows experimental PXRD data at 24 GPa with
a ¼ 6.122(1) Å, b ¼ 4.004(1) Å, c ¼ 7.223(1) Å, which compares
with a ¼ 6.044 Å, b ¼ 3.977 Å, c ¼ 7.265 Å for DFT calculations at
the same pressure (see Supplementary Table 4). Calculated lattice
parameters show an average absolute deviation of 0.5% from
experimental values between 25 and 5 GPa (see Fig. 8), which was
the lowest pressure obtained due to failure of a diamond anvil.
Fitting the P–V data to a second-order Birch–Murnaghan
equation of state yields B0 ¼ 53(4) GPa.

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

5.4

5.2

5.0

6.6

6.4

6.2

129

127

150

140

130

120

_Pnma_ -Ca2C

DFT

EXP

_C_ 2 _/m_ -Ca2C3

DFT

_C_ 2 _/m_ -Ca2C3 _Pnma_ -Ca2C

6.7

6.4

6.1

4.4

4.2

4.0

7.9

7.6

7.3

240

220

200

180

160

0 10 20 0 10 20 30

24(1) GPa

17.1(9) GPa

Ca Ca
Ca Ca

EXP

Pressure (GPa)

6 8 10 12 14 16 18

2θ (degrees) _�_ =0.406626 Å

Figure 7 | PXRD patterns for experimentally observed Ca-C phases.
(a) Pnma-Ca2C synthesized at 24 GPa (wRp ¼ 1.5%, Rp ¼ 0.9%).
(b) C2/m-Ca2C3 synthesized at 17 GPa (wRp ¼ 2.0%, Rp ¼ 0.9%).
Experimental data (points) are compared with full-profile refinements using
the Le Bail method (blue lines), with differences (red lines). Simulated
powder patterns using atomic positions derived from DFT-optimized
structures are shown for intensity comparison (green lines). Positions of
reflections of Ca2C (a) or Ca2C3 (b), Ca, Ne and a third carbide phase (see
Supplementary Note 2) are indicated by black, green, blue and red tick
marks, respectively.

polymerized, in turn, into C2 dumbbells, C3 and C4 groups,
chains, ribbons and graphene sheets (see Fig. 4 and
Supplementary Table 2). The polymeric carbon structures reveal
an expected trend when comparing with the structural chemistry
of the heavier congeners of group IV elements in Zintl phases
(alkali or alkaline-earth silicides, germanides and stannides) 17,33 .
Yet in spite of certain similarities to silicides, calcium carbides
differ from them because of distinct bonding features. Combining
present analysis and our previous results 16,17,20, one can conclude
that for the Ca-C system, one can cover sp to sp 2 to sp 2 þ sp 3 to
sp 3 hybridizations of carbon as pressure increases. This pressureinduced structural evolution of carbon was also found in other
alkali metal or alkaline-earth metal carbides 17,20,24 . Together with
our previous results for CaC2 (ref. 16) and CaC6 (ref. 20), it is
clear that a 3D network of carbon in CaCx can be formed when x
is greater than 2 (from sheets to 3D frameworks to Ca-C phase
separation with slabs of diamond at high C content), consistent
also with the behaviour of the metastable CaC4 compound found
in our structural searches. On the other hand, the structural
features of carbon-rich compounds 20 can be extended to
alkali-metal or alkaline-earth metal congeners of the group-IV
elements, which allows one to fabricate a variety of the 3D
framework structures of the group-IV elements by removing
metal sublattices. The unexpected mechanical 20,34 or electronic
characteristics 35 uncovered in these 3D framework structures
pave the way to novel materials.

Figure 8 | Lattice parameters and unit cell volumes for Ca-C phases.
Experimental parameters (points) are compared with DFT predictions
(dashed lines) for both C2/m-Ca2C3 (a) and Pnma-Ca2C (b).
Experimentally-derived equations of state for both phases are shown as
solid lines in the lower panels.

In summary, we have produced the first complete pressurecomposition phase diagram for CaCx compounds at pressures up
to 100 GPa and demonstrated the experimental synthesis of two
previously unknown compounds (Ca2C3 and Ca2C), 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 CaC2 and CaC6 were
found to be metastable at normal conditions; CaC2 is stable only
above 21 GPa, and CaC6 is never thermodynamically stable, while
hitherto unreported Ca2C3 is actually thermodynamically stable
at ambient pressure. Bader analysis unravels very diverse
chemistry: the decrease in C–C bond order from triple to double
to single bonds at increasing pressure; a negatively charged metal
layer in calcium-rich Ca2C compound; a hitherto unknown bent
linear C4 group in the P21/c phase of CaC; C ribbons being
present in carbon-rich compounds. The C2/m-Ca2C phase
provides a fresh and very attractive example of a 2D metal,
presenting the only known example of a compound where a metal
atom (Ca) develops a negative Bader charge in presence of a more
electronegative atom (C). Such unusual compounds are likely to
find potential applications if synthesized in sufficiently large
quantities. While powerful computational methods, such as
USPEX, are capable of reliably predicting these exotic compounds, simple theoretical models capable of anticipating them
are yet to be developed.

Methods
Structure search and theoretical calculations. Searches for stable structures of
the Ca-C system under compression were carried out using the evolutionary
algorithm USPEX in combination with the VASP code 36 on the basis of DFT
within the generalized gradient approximation with the exchange-correlation
functional of Perdew, Burke and Ernzerhof 37, employing the projector-augmented
wave 38 method [He] and [Ne] cores for C and Ca atoms, respectively. For carbon, a
‘hard’ PAW potential was used in search for stable structures. For the crystal
structure searches, we used a plane-wave basis set cutoff of 700 eV and performed
the BZ integrations using uniform Gamma-centred k-point meshes. The most

interesting structures were further relaxed at a higher level of accuracy with a basis
set cutoff of 1,000 eV and a k-point grid of spacing 2p � 0.018 Å � 1 . Iterative
relaxation of atomic positions was stopped when all forces were smaller than
0.001 eV Å � 1 . For compounds predicted via variable-composition searches, we researched their stable structures using fixed-composition calculations, with two,
three and four formula units per unit cell. For Ca2C3, some evolutionary
calculations were also performed under the pressure of 30, 50, 80, 120, 160, 240 and
300 GPa with two or four chemical formula units per unit cell so as to discern the
possibility of 3D network carbon.

The enthalpy of formation per atom of CanCm is defined as
DHf(CanCm) ¼ [H(CanCm)-nH(Ca)-mH(C)]/(n þ m), where all enthalpies H are
given at the same pressure and zero temperature. At a given pressure, the calcium
carbides located on the convex hull are thermodynamically stable against
decomposition to any other binaries or the elements, while the compounds above
the convex hull are meta-stable.

The Bader analysis was performed for exploring chemical bonding and local
electrons 39 . To get a converged charge density, the plane wave kinetic energy cutoff
of 1,000 eV and Monkhorst-Pack k-point meshes with the reciprocal space
resolution of 2p � 0.02 Å � 1 were used for all the structures. A series of FFT grids
to accurately reproduce the correct total core charge were tested by increasing
parameters NG(X,Y,Z)F to 1.5, 2 and 2.5 times the default one.

The lattice dynamics and superconducting properties of Ca2C3 were calculated
by the Quantum ESPRESSO package 40 using Vanderbilt-type ultrasoft
pseudopotentials with cutoff energies of 50 and 500 Ry for the wave functions and
the charge density, respectively. The electronic BZ integration in the phonon
calculation was based on a 12 � 12 � 12 of Monkhorst-Pack k-point meshes. The
dynamical matrix was computed on the basis of a 6 � 6 � 6 mesh of phonon wave
vectors. The electron–phonon coupling was convergent with a finer grid of
48 � 48 � 48 k points and a Gaussian smearing of 0.01 Ry. For other compounds,
phonon calculations were performed using the Phonopy code 41 . The Fermi surface
of C2/m-Ca2C at 3 GPa was calculated using Quantum Espresso and 16 � 16 � 8 of
Monkhorst-Pack k-point mesh.

Experiment. Reagents for experimental studies consisted of commercial calcium
metal (Sigma-Aldrich, dendritic pieces, 99.99%) and glassy carbon (Sigma-Aldrich,
2–12 mm, 99.95%). The carbon powder was degasified for 12 h at B200 �C in a
vacuum oven and then sealed under Ar. Diamond anvil cell syntheses (up to
25 GPa and 2,000 K with in situ PXRD) were performed at High Pressure
Collaborative Access Team (HPCAT), sector 16, of the Advanced photon Source. A
small amount of carbon powder and Ca metal shavings were pressed in thin layers
within a rhenium gasket in a diamond anvil cell equipped with 400-mm culet
diamonds inside of an inert Ar glovebox (O2o1 p.p.m.; H2Oo1 p.p.m.). It was not
possible to control the precise Ca:C ratio; however, compositions were estimated to
range between 0.333rCa:Cr3, on the basis of the volume of material loaded into
the diamond cell. Samples were sealed inside the glovebox without pressure
medium or loaded with Ne to improve thermal isolation from diamonds and quasihydrostatic conditions for subsequent diffraction measurements. Pressure was
estimated using the Ne equation of state 42 and/or with a ruby gauge 43 . To generate
high temperatures, samples were heated on both sides using infrared fibre lasers. In
some cases two or three heating cycles were performed, with X-ray diffraction
patterns collected before, during and after laser heating. During laser heating,
temperatures from each side of the sample were estimated by collecting emitted
thermal radiation, correcting for the optical system response and fitting the spectral
data to Planck’s equation. Angle-dispersive PXRD patterns were collected using a
mar345 detector (marXperts GmbH, Norderstedt, Germany) image plate calibrated
with a CeO2 standard. Patterns were integrated using FIT2D (ref. 44) and phase
recognition and indexing were performed using PowderCell and CheckCell
programmes 45 . While observed PXRD intensities were in good agreement with
DFT-derived structural models, observed powder statistics were not suitable for
Rietveld refinements. Full profile refinements were performed using the Le Bail
intensity extraction method, as implemented in GSAS 46 with EXPGUI 47 (see
Supplementary Figs 13–15 and Supplementary Note 2 for additional details).

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Acknowledgements
Y.-L.L. acknowledges support from the NSFC (11347007), Qing Lan Project and the
Priority Academic Program Development of Jiangsu Higher Education Institutions
(PAPD). A.R.O. and S.-N.W. thank the National Science Foundation (EAR-1114313,
DMR-1231586), DARPA (Grants No. W31P4Q1210008 and No. W31P4Q1310005), the
Government of Russian Federation (No. 14.A12.31.0003) for financial support and the
Foreign Talents Introduction and Academic Exchange Program (No. B08040). Calculations were performed on XSEDE facilities and on the cluster of the Center for Functional
Nanomaterials, Brookhaven National Laboratory, which is supported by the DOE-BES
under contract no. DE-AC02-98CH10086. Experimental efforts were supported by
DARPA under grant No. W31P4Q1310005. Portions of this work were performed at
HPCAT (Sector 16), Advanced Photon Source, Argonne National Laboratory. HPCAT
operations are supported by DOE-NNSA under Award No. DE-NA0001974 and

DOE-BES under Award No. DE-FG02-99ER45775, with partial instrumentation funding
by NSF. The Advanced Photon Source is a US Department of Energy (DOE) Office of
Science User Facility operated for the DOE Office of Science by Argonne National
Laboratory under Contract No. DE-AC02-06CH11357.

Author contributions
Y.-L.L. and A.R.O. designed the research. T.A.S. designed the experiments. Y.-L.L.,
A.R.O. and S.-N.W. performed calculations. H.G., J.S.S. and T.A.S. performed the
experimental studies. All authors analysed the data and contributed to write the paper.

Additional information
Supplementary Information accompanies this paper at [http://www.nature.com/](http://www.nature.com/naturecommunications)
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Competing financial interests: The authors declare no competing financial interests.

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How to cite this article: Li, Y. L. et al. Investigation of exotic stable calcium carbides
using theory and experiment. Nat. Commun. 6:6974 doi: 10.1038/ncomms7974 (2015).

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