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Journal of Materials ScienceFull Set - Includes `Journal of MaterialsScience Letters' ISSN 0022-2461Volume 49Number 7 J Mater Sci (2014) 49:2723-2733DOI 10.1007/s10853-013-7973-6
First-principles computational designand synthesis of hybrid carbon–siliconclathrates
Kwai S. Chan, Michael A. Miller, WuweiLiang, Carol Ellis-Terrell & Xihong Peng
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First-principles computational design and synthesis of hybridcarbon–silicon clathrates
Kwai S. Chan • Michael A. Miller • Wuwei Liang •
Carol Ellis-Terrell • Xihong Peng
Received: 24 August 2013 / Accepted: 16 December 2013 / Published online: 9 January 2014
� Springer Science+Business Media New York 2014
Abstract Type I and Type II silicon clathrates (Si46 and
Si136), which can be considered as analogs of carbon ful-
lerene materials, are composed with face-sharing Si20, Si24,
and Si28 cages linked through sp3-covalent bonds. Besides
silicon clathrates, theoretical computations have shown that
both Type I carbon clathrate (C46) and Type II carbon
clathrate (C136) may exist as metastable phases under high
pressures. However, the energies of formation for the Type I
and Type II carbon clathrates are extremely high and neither
Type I nor Type II carbon clathrates have been synthesized.
The objective of this investigation was to develop Type I
hybrid carbon–silicon clathrates by substituting atoms on the
silicon clathrate framework with C atoms. A first-principles
computational approach was first utilized to design the
framework structure and to identify appropriate guest atoms
that are amenable to the formation of hybrid carbon–silicon
clathrate compounds. A new class of Type I clathrates based
on the carbon–silicon system was discovered as potential
candidates. Some of the promising candidate clathrates were
synthesized using an industrial arc-melting technique. The
yield and stability of these newly discovered clathrates were
evaluated. In addition, the electronic properties of selected
clathrate materials were predicted using first-principles
computations, which showed profound influences of the
electronic properties by C atom substitution on the Si
framework and insertion of guest atoms into the cage
structure.
Introduction
Silicon clathrates have received considerable attention due
to their unique structure and their potential as thermo-
electric (TE) [1–7], magnetic [3], superconducting [3, 8–
10], energy-storage [11–14], and hard materials [3, 15].
Their properties are derived from their cage structure and
the interactions between the cage frame-work and guest
atoms residing within the cage cavities [3, 16–18]. Silicon
clathrates can be considered as analogs of carbon fullerene
materials and are composed with face-sharing Si20, Si24,
and Si28 cages linked through sp3-covalent bonds [16].
Various types of clathrates have been classified based on
the arrangement of the cage structure [3, 16–18]. Type I
clathrates are of the form MxSi46, and Type II clathrates are
of the form MxSi136, where M is the guest atom, and x is
the number of guest atoms. The structure of Type I clath-
rates is depicted in Fig. 1. Both Type I and II clathrates of
silicon and germanium alloys are attractive TE materials,
because they can be engineered as nearly ideal phonon
glass-electron crystals [19], which scatter phonons but do
not interrupt electron conduction.
Theoretical computations have shown that both Type I
carbon clathrate (C46) and Type II carbon clathrate (C136)
may exist as metastable phases under high pressures [20–
22]. The cage structure of Type I carbon clathrate, C46, is
similar to that of Si46 shown in Fig. 1. Insertion of guest
atoms such as Li, Na, or Ba into the cage structures has
been predicted to be feasible under high pressures. How-
ever, the energies of formation for the Type I and Type II
K. S. Chan (&) � M. A. Miller � W. Liang � C. Ellis-Terrell
Southwest Research Institute, San Antonio, TX 78238, USA
e-mail: [email protected]
Present Address:
W. Liang
Math Works, 3 Apple Hill Drive, Natick, MA 01760, USA
X. Peng
School of Letters and Sciences, Arizona State University, Mesa,
AZ 85212, USA
123
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DOI 10.1007/s10853-013-7973-6
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carbon clathrates are extremely high, and neither Type I
nor Type II carbon clathrates have been synthesized.
The performance metric for thermoelectric devices
(TEDs) is the conversion efficiency figure of merit,
ZT = S2rT/j (where S = Seebeck coefficient, r = elec-
trical conductivity, T = temperature, and j = thermal
conductivity). The ZT value for current TE materials such
as Bi2Te3 and PbTe is about 1 (0.7–1.2), which is less than
the desired value of 3–4 for the development of highly
energy efficient TEDs [1, 2]. To date, the value of ZT for
various Type I and Type II silicon clathrates and germa-
nium clathrates ranges from 0.01 to 1.35 [7], which is
comparable to state-of-the-art TE materials but is well
below a ZT value of 3–4 required, for example, in high
efficiency TE generation for harvesting waste heat from
industrial and automotive sources [1, 2]. To increase the
figure of merit, the Seebeck coefficient and the electric
conductivity must be enhanced, and the thermal conduc-
tivity of the silicon clathrates must be further reduced.
Recent research reported in the literature [23] indicated that
the Seebeck coefficient of a germanium clathrate can be
increased by using a confining pressure, which also
increases the electrical conductivity. A threefold increase
of the ZT value from 0.35 to 0.75 was reported by Meng
et al. [23]. Therefore, the challenge is to achieve a larger
improvement in the thermal power and ZT value at ambient
pressure in silicon-based or germanium-based clathrates.
Theoretical analysis has identified that the increase of TE
performance by pressure is the result of a rapid increase or
fluctuation of electronic conductivity with a small increase
of energy of the cage structure near the conduction band [23,
24]. Furthermore, the performance enhancement achieved
by mechanically induced pressure [23] may be simulated
using chemically induced pressure by substituting atoms on
the cage framework with atoms of a smaller size to contract
the cage structure, or by inserting smaller guest atoms within
the cage structure to induce contractive interactions between
the guest atoms and the framework (or both). So far, only
limited work [25] has been done to substitute the framework
or guest atoms of Si- or Ge-based clathrates using small-
sized atoms, because the potential benefits of small-sized
atoms on TE performance have not been recognized. Most
of the prior studies in the literature [1–3, 5–8, 19] have been
directed toward inserting large-sized atoms into the cage
structure by either direct synthesis or arc melting, the two
common methods for making Si- or Ge-based clathrates.
Thus, there are gaps in the existing database and potential
benefits to be reaped by investigating the influence of small-
sized atom substitution and insertion on the TE performance
of silicon clathrates.
The main objective of this investigation was to develop
novel silicon clathrate materials for energy harvesting and
storage applications by substituting the framework and
guest atoms of clathrate structures with small-sized atoms.
A first-principles computational approach was first utilized
to identify appropriate small-sized atoms that were ame-
nable to the formation of new silicon-based clathrate
compounds. A new class of Type I clathrates based on the
carbon–silicon framework was discovered as potential
candidates. Some of the promising candidate clathrate
systems were fabricated using an industrial arc-melting
technique under argon partial pressure (sub-atmospheric).
The yield and stability of these newly discovered clathrates
were evaluated. In addition, the electronic properties and
bulk modulus of selected clathrate materials were predicted
using first-principles computations, which showed pro-
found influences of the electronic properties by small-sized
atom substitution on the framework and insertion into the
cage structure. Because resources for making the new
clathrate materials in large quantities were limited, exper-
imental measurements of the electronic or mechanical
properties of the new clathrate materials for validation of
the predicted electronic properties were not evaluated in
this study.
First-principles computational modeling
Type I clathrate structure
The structure of Type I intermetallic clathrates is shown in
Fig. 1, which shows that it is comprised a framework of X
atoms forming a 3D cage structure. Type I silicon clathrate,
Si46, consists of crystalline Si with a regular arrangement
of 20-atom and 24-atom cages fused together through 5
atom pentagonal rings. It has a simple cubic structure with
a lattice parameter of 10.335 A and 46 Si atoms per unit
Fig. 1 Schematics of the cage structure of Type I intermetallic
clathrate. The clathrate framework is shown in orange. The frame-
work atoms include C, Si, Ge, or Sn. Substitution atoms (in blue) on
the framework can include Al, N, and among others, Cu. Guest atoms
are alkaline and alkaline-earth metals. They can reside in six large
cages (green, 6d sites) or in two small cages (maroon, 2a sites).
Modified from Rogl [1, 2] (Color figure online)
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cell [26, 27]. The crystal structure of the Si46 clathrate
belongs to the Space group Pm�3n and Space Group
Number 223 [26, 27]. Some of the framework atoms of a
Type I clathrate can be substituted by atom M. The empty
space within the cage structure can serve as host sites for
guest atoms A. There are two small cages that can host two
guest atoms (2a sites), and there are six large cages that can
host six atoms (6d sites) without a significant effect on the
unit cell volume. Type I clathrates can be described by the
formula: AxMyX46-y [1–3], where A represents the guest
atoms, and x is the number of guest atoms. M represents the
substitution atoms on the framework, y is the number of the
substitution atoms, and X represents the framework atoms.
Representative framework, substitution, and guest atoms
are listed in Fig. 1.
First-principles computational methods
An ab initio molecular dynamics code based on the Car-
Parrinello molecular dynamics (CPMD) method [28, 29]
was utilized to investigate theoretically and systematically
the effects of small-atom substitution on the framework
and insertion into the empty space inside the cage structure
on the energy formation and lattice constant of selected
intermetallic clathrate compounds. The CPMD code [28] is
a plane wave implementation of density functional theory
(DFT) [29]. It uses an approximation frozen-core approach
that only the chemically active valence electrons are dealt
with explicitly, and the inert core electrons are considered
frozen together with the nuclei as rigid non-polarizable ion
cores. It is capable of both first-principles wave-function
optimization (static calculation) and ab initio molecular
dynamics calculations. The PBE functional [30] and pro-
jector-augmented wave (PAW) [31, 32] potentials were
used along with the plane wave basis sets for the geometry
optimization and self-consistent total energy calculations.
The energy cutoff for the plane wave basis set was
2041 eV. The convergence criterion for energy was set at
1 9 10-7. Reciprocal space was sampled using 3 9 3 9 3
Monkhorst–Pack meshes centered at Gamma. The number
of k-points was 64 (4 9 4 9 4). The energy and equilib-
rium lattice constant of a unit cell at ground state (0 K)
were computed by calculating the energies for unit cells
with different lattice constants by performing wave-func-
tion optimization and atom relaxation with CPMD. A high-
order (e.g., 4th-order) polynomial was fitted to the energy
points. The equilibrium lattice constant was determined by
finding the lattice constant corresponding to the minimum
energy on the polynomial curve.
To validate the CPMD computations, another first-prin-
ciples DFT code VASP [33] was used to calculate the energy
of formation, optimal lattice constants of the hybrid carbon–
silicon clathrates, as well as the electronic structures such as
band structure and density of state (DOS) of several selected
materials. The PBE functional [30] and PAW [31, 32]
potentials were used along with the plane wave basis sets for
the geometry optimization and self-consistent total energy
calculations. The energy cutoff for the plane wave basis set
was 400 eV. The convergence criteria for energy and forces
were set to be 0.01 and 0.1 meV, respectively. Si 3s3p, C
2s2p, Ba 5s5p6s, Li 1s2s, Na 2p3s, K 3s3p4s, Mg 2p3s, and
Ca 3p4s electrons were treated as valence electrons. Reci-
procal space was sampled using 3 9 3 9 3 Monkhorst–
Pack meshes centered at Gamma. To predict the optimized
lattice constants for the hybrid clathrates, we performed the
settings in VASP so that not only the ion positions were
relaxed, but also the volume of the unit cell was optimized.
The final lattice constant obtained from the optimized vol-
ume was further crosschecked so that the pressure in all three
x, y, and z directions were minimal.
The formation energies were calculated by subtracting
the total energies of the elements from the energy of the
structure, then dividing by the total number of atoms. For
example, the formation energy, DEform, for AxCySi46-y was
calculated using the equation given by
DEform ¼E AxCySi46�y
� �� xE Að Þ� yE Cð Þ� 46� yð ÞE Sið Þ
xþ 46;
ð1Þ
where E AxCySi46�y
� �, E(Si), E(C), and E(A) are the
energies per atom for the compound, Si, C (diamond), and
A metal, respectively.
Hybrid carbon–silicon clathrates
A series of Type I hybrid carbon–silicon compounds was
designed by substituting some of the Si atoms on the Si46
framework with C atoms. First-principles computations
based on the CPMD code indicate that the silicon atoms on
the Si46 framework can be partially substituted by carbon
atoms to form a hybrid silicon–carbon clathrate, which can
be represented by the chemical formula CySi46-y. Fig-
ure 2a shows a representation of the Type I CySi46-y
clathrates. Furthermore, guest atoms can be inserted into
the cage structure to stabilize the hybrid silicon carbon
clathrate by reducing the energy of formation to form a
class of new hybrid silicon and carbon clathrates, repre-
sented as AxCySi46-y. These hybrid structures do not exist
in nature and, thus, represent a novel structure of matter
neither known in the open literature nor covered in existing
patents on clathrate compounds. Figure 2b shows a struc-
tural representation of the Type I AxCySi46-y clathrate
compounds. The computed values of the energy change of
J Mater Sci (2014) 49:2723–2733 2725
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formation per atom for selected Ba8CySi46-y, C46, C40Si6,
and C23Si23 are compared with those for Si46 and Ba8Si46
in Fig. 3. The positive values for the energy of formation at
the minima of the energy change curves indicate that these
Ba8CySi46-y clathrate compounds are metastable.
The influence of guest atoms on the stability of hybrid
carbon–silicon clathrates was further investigated by
inserting guest atoms A such as Li, K, Na, and Ba into the
cage structure. Results of the energy calculation for this
series of Type I clathrates are summarized in Fig. 4. The
AxC6Si40 clathrates are of interest, because the values of
the energy of formation are only slightly positive and less
than 0.3 eV. In addition, the lattice parameter can be
reduced upon judicious selection of the guest atoms.
Variants of the AxCySi46-y clathrates are AxE8-xCyAlzSi46-y-z with two types of guest atoms (A and E), where A
and E are guest atoms, and C and Al are substitution atoms
on the Si framework. Al substitution of the Si framework
was considered because a previous study [34] reported that
Al-substituted Si clathrates were stable compounds that
could be synthesized by conventional vacuum arc-melting
techniques. Figure 4 presents the results in a plot of energy
change versus lattice parameters for Al and C substitution
on the framework with Ba, Li, and K guest atoms. Com-
pared to the Si46, Al substitution resulted in a slight
expansion of the framework as the equilibrium lattice,
represented by the minimum point of the DE versus lattice
parameter curve, is shifted to a larger value for the lattice
parameter, while C substitution produced the opposite
effect on the lattice parameter. Ba, K, and Li insertion
stabilize the C-, and Al-substituted framework as the
energy change is reduced to negative values. At the same
time, the equilibrium lattice constant and the framework
Fig. 2 Cage structure of Type I
carbon–silicon clathrate,
CySi46-y, a without guest atoms
and b with x number of guest
atoms A resided within the cage
Lattice Parameter, A
6 8 10 12
E, e
V/a
tom
0
1
2
3
o
BaxCySi46-y
Ba8C23Si23
Ba8Si46
Ba8C6Si40
Si46
C23Si23
C46
C40Si6
Fig. 3 Energy changes curves for selected Type I clathrate com-
pounds of Ba8CySi46-y, C46, C40Si6, and C23Si23 compared against
those of Si46 and Ba8Si46Lattice Parameter, A
8 9 10 11 12 13
E, e
V/a
tom
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
o
AxE8-xCyAlzSi46-y-z
Li8C6Al10Si30
Ba8C6Si40
Ba2Li6C6Al10Si30
K2Li6C6Al10Si30
Ba8C23Si23
C6Si40
Li8C6Si40
Ba2Li6C6Si40
K2Li6C6Si40
C23Si23
Fig. 4 Computed energy curves for various C-substituted Type I
silicon clathrate frameworks with and without Li, Na, K, and Ba guest
atoms
2726 J Mater Sci (2014) 49:2723–2733
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size can be decreased, as shown in Fig. 4, for
Li8C6Al10Si30 and Ba2Li6C6Al10Si30.
The CPMD results were utilized to establish a correla-
tion between the energy of formation and the lattice
parameter for carbon-substituted silicon clathrates,
AxCySi46-y, with guest atoms, A, which are alkaline metals
such as Li, Na, K, and Ba. The correlation, shown in Fig. 5,
indicates that the alkaline guest atoms generally lower the
energy formation but increase the lattice constant of the
carbon-substituted silicon clathrates. Without exception, all
of the carbon-substitute silicon clathrates exhibit positive
values of energy of formation, meaning that these inter-
metallic compounds are metastable.
To validate the CPMD computations, energies of for-
mation for the same series of intermetallic clathrates were
computed using VASP [33]. A comparison of these two
sets of energy of formation computations for AxCySi46-y is
presented in Fig. 6. Generally there is good agreement
between the CPMD and VASP computations, as shown in
Fig. 6. Small discrepancies between VASP and CPMD
computations for C40Si6 are shown due to slight differences
in the relaxed atom positions.
Synthesis of novel clathrate materials
Based on the first-principles computational results of the
energy of formation, several candidate alloyed clathrate
materials were selected for syntheses by a vacuum arc-
melting method. Table 1 provides a list of the candidate
series and the elemental or alloy components constituting
the admixture of starting materials. Silicon (99 %,\10 lm
size), silicon carbide (99 %, 325 mesh), and aluminum
(99.98 %, 325 mesh) powders were obtained from Noah
Technology (San Antonio, TX). Barium (99.2*,\0.8 % Sr,
in pieces) and graphite (100 %) were obtained from Alfa
Aesar (Ward Hill, MA). Lithium silicide (99.9 %, 160
mesh) was obtained from LTS Chem (Orangeburg, NY),
and sodium silicide (unknown purity) was obtained from
Signa Chem (New York, NY). With the exception of bar-
ium metal, ball-milling techniques and inert (i.e., glove
box) process methods were first used to pulverize each of
the starting materials into fine powders so that they could
then be homogeneously mixed together at the appropriate
stoichiometric ratios as indicated in Table 1. Barium-con-
taining compositions were mixed using barium spherical
ingots, instead of the powder form, because conventional
ball-milling techniques employed in this work are not
energetic enough to overcome the shear modulus of barium
metal. After thoroughly mixing the fine powders (plus
ingots where applicable), each admixed composition was
individually packaged in a stainless steel tubular container
and sealed with Swagelok fittings before removing it from
the argon-filled glove box. All six packaged compositions
were then shipped to Sophisticated Alloys, Inc. (Butler,
PA) for vacuum arc-melting in an industrial vacuum arc-
melter. The arc-melting process was conducted in an argon
atmosphere under a sub-atmospheric pressure.
Syntheses of six candidate clathrate compounds were
attempted. The target compound and the produced mate-
rials are summarized in Table 2. As a trial, two admixed
compositions were selected for synthesis to test the process
parameters and hardware of the arc melter: (1)
Na2Li6Al10C6Si30 and (2) Li8Al10C6Si30. The PXRD pat-
tern measured for Li8Al10C6Si30 indicates that the arc-
melted material contained Si, SiC, and AlLiSi, but no
evidence of Li8Al10C6Si30 Type I clathrate. Similar results
were obtained for Na2Li6Al10C6Si30. A summary of the
target compounds and the actual products is presented in
Table 2.
Lattice Parameter, A
6 7 8 9 10 11 12
En
erg
y o
f F
orm
atio
n, e
V/a
tom
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
C46
C23Si23
Ba8C23Si23
Na8C23Si23
K8C6Si40
Li8C6Si40
Ba8C6Si40Si46
Ba8Si46
Ba8C20Si26
Trend Line AxCySi46-y
C40Si6
o
CPMD
K2Li6C6Si40
Ba2Li6C6Si40
Li8CySi46-y
Fig. 5 Energy formation computed via CPMD for various interme-
tallic clathrates based on the AxCySi46-y compositions with the hybrid
CySi46-y framework
Lattice Parameter, A
6 7 8 9 10 11 12
En
erg
y o
f F
orm
atio
n, e
V/a
tom
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
C40Si6
C23Si23
C6Si40C46
AxCySi46-y
CPMDVASP
o
C32Si14
Trend Line Ba8Si46
Ba8C6Si40Si46
Na8C23Si23
Li8C6Si40
K8C6Si40
C42Si4
C12Si34
C26Si20
C20Si26
Ba8C23Si23
Ca8C6Si40
Fig. 6 Comparison of CPMD and VASP computations of the energy
of formation for various intermetallic clathrates based on the
AxCySi46-y compositions with the hybrid CySi46-y framework
J Mater Sci (2014) 49:2723–2733 2727
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2728 J Mater Sci (2014) 49:2723–2733
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The third composition selected for arc-melting was
Ba8C6Si40. Selection of Ba8C6Si40 was based on first-
principles computational results, which indicate a very
small positive energy of formation. A small value of
positive energy of formation indicates that the compound is
metastable, but the energy input required for its formation
is small enough that fabrication by arc-melting may be
feasible. XRD data of the arc-melted product based on
Composition (3) resulted in BaSi2, Si, and graphite, but no
evidence of Ba8C6Si40 with the Type I clathrate structure.
The presence of graphite in the product form suggested that
graphite may be too stable to react with Si to form the
C6Si40 Type I clathrate structure with a comparatively
higher energy state.
The fourth composition selected for arc-melting was
Ba8C20Si26. Selection of Ba8C20Si26 was based on the fact
that it could be synthesized using SiC as the starting
material instead of graphite. Admixture of Ba, Si, and SiC
was arc-melted to make this compound. XRD data of the
arc-melted product based on Composition (4) are presented
in Fig. 7, which indicates the presence of Ba, SiC, BaSi2,
and Si in the arc-melted product. There are, however, extra
XRD peaks in the spectra that do not belong to Ba, Si,
BaSi2, and Si that require additional analysis for compound
identification. Further analysis of the XRD results was
carried out by subtracting the SiC and Si peaks from the
Ba8C20Si26 spectra. The remaining peaks are then com-
pared with the theoretical XRD spectra for Type I clathrate
structure for Ba8C6Si40 and Ba8C23Si23 as well as those for
Ba and BaxSi46. Although the structure of BaxSi46 (x = 2,
6, or 8) [35] is similar to that of Ba8C20Si26, BaxSi46 is not
expected to be present in the arc-melt product, since
BaxSi46 cannot be synthesized by arc-melting [36, 37], but
requires high-temperature (800 �C) and high- pressure
(1–5 GPa) synthesis in a multianvil press [36] or via redox
reactions of a precursor phase [37]. A comparison of the
experimental and theoretical XRD peaks is presented in
Fig. 8. The theoretical peaks for Ba8C6Si40, Ba8C23Si23,
and Ba8Si46 were computed using the optimized Type I
clathrate structures from CPMD and the crystal structure
XRD analysis software called Diamond [38]. The XRD
peaks of Ba2Si46 and Ba6Si46, which were computed using
the lattice constants from the literature [35], are similar to
those of Ba8Si46 and are not shown in Fig. 8 for clarity
purposes. The comparison indicates that a Type I clathrate
compound is present in the arc-melted Ba8C20Si26 product.
The crystal structure of this clathrate compound matches
those of Ba8C6Si40 and Ba8C23Si23 based on the charac-
teristic peaks at 2h of 18�, 21�, 30�, and 32�. In contrast,
the XRD peaks of the arc-melt product do not match well
with those of Ba8Si46. On this basis, the Type I clathrate in
the arc-melt product may be those of Ba8C6Si40,
Ba8C20C26, or Ba8C23C23, but not BaxSi46.
Some of the as-synthesized Ba8C20Si26 materials were
ball-milled into finer powders and subsequently charac-
terized by XRD. Figure 9 presents the XRD peaks
observed in the ball-milled materials, which indicate the
presence of Ba, BaSi2, SiC, and Si peaks in the ball-milled
powders. The characteristic peaks of Type I clathrate at 2hof 18�, 21�, 30�, and 32� have all disappeared and been
replaced by those of BaSi2 in the ball-milled materials.
The results indicate that the Type I clathrate material in
the as-synthesized Ba8C20Si26 is metastable, and it can be
made to transform to BaSi2 by ball-milling. This finding is
consistent with first-principles computations in Fig. 4
which shows that Ba8C6Si40, Ba8C20Si26, and Ba8C23Si23
are metastable compounds with positive energies of
Table 2 Summary of targeted compounds and actual compounds produced by arc-melting
Composition Target compound Actual compounds produced Type I clathrate Yield (%)
1 Na2Li6Al10C6Si30 None (all sublimed except Si) No 0
2 Li8Al10C6Si30 Si, SiC, and AlLiSi No 0
3 Ba8C6Si40 BaSi2, Si, and graphite No 0
4 Ba8C20Si26 Ba, SiC, BaSi2, Si, and Ba8C20Si26 Yes (Ba8C20Si26) 39
5 Ba8C6Si40 Ba, SiC, BaSi2, Si, and Ba8C6Si40 Yes (Ba8C6Si40) 26
6 Ba8C23Si23 Ba, SiC, BaSi2, Si, and Ba8C23Si23 Yes (Ba8C23Si23) 16
2θ15 20 25 30 35 40 45 50
No
rmal
ized
Inte
nsi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2Non-Milled Ba8C20Si26
BaBaSi2SiCSi
Fig. 7 PXRD patterns measured for Composition (4) subsequent to
arc-melting of powdered admixture of Ba, SiC, and Si (d-Si)
J Mater Sci (2014) 49:2723–2733 2729
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formation. Among the three compounds, Ba8C6Si40 has the
lowest energy of formation, followed by Ba8C20Si26 and
Ba8C23Si23. The finding that Ba8C20Si26 could be synthe-
sized by arc-melting using SiC as the starting material
suggests that the arc-melting technique may also be suc-
cessful for the synthesis of Ba8C6Si40 and possibly
Ba8C23Si23.
Following the successful syntheses of Ba8C20Si26 by
vacuum arc-melting, the same method was utilized to
synthesize two additional carbon-substituted silicon clath-
rate materials, Ba8C6Si40 and Ba8C23Si23, which are shown
as Compositions 5 and 6 in Table 2. The XRD patterns for
Ba8C6Si40 and Ba8C23Si23 are presented in Fig. 10a, b,
respectively. In both cases, the XRD powder patterns show
the peaks for the Type I silicon clathrate among those for
BaSi2, SiC, and Ba. The yield of individual carbon-
substituted silicon clathrates produced by the vacuum arc-
melting technique was estimated from the XRD integra-
tions for each structure, and the results are presented in
Table 2. The yield ranges from 16 to 39 %, which are
somewhat low and need further improvement. Further-
more, ball milling of the as-synthesized materials caused
transformation of the Type I clathrate materials to BaSi2indicating that both Ba8C6Si40 and Ba8C23Si23 are
metastable.
Electronic properties
The electronic band structure and DOS for A8C6Si40,
where A = Li, Na, K, Mg, Ca, and Ba, were computed
using VASP [33]. Figure 11a, b, c compares the band
structures and DOSs of Si46, C6Si40, and Ba8C6Si40,
respectively. The DFT predicts a band gap of 1.31 eV for
Si46. The band gap is reduced to 0.44 eV for C6Si40 when 6
2θ15 20 25 30 35 40 45 50
No
rmal
ized
Inte
nsi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Non-Milled Ba8C20Si26
Predicted Ba8C6Si40
Predicted Ba8C23Si23
BaBaSi2Ba8Si46
Fig. 8 PXRD patterns measured for Ba8C20Si26 minus those of SiC
and Si compared with those of Ba, and the theoretical spectra of
Ba8Si46, Ba8C6Si40 and Ba8C23Si23 with the Type I clathrate structure
2θ15 20 25 30 35 40 45 50
No
rmal
ized
Inte
nsi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Ball Milled Ba8C20Si26
BaBaSi2SiCSi
Fig. 9 PXRD patterns measured for ball-milled Ba8C20Si26 after arc-
melting of powdered admixture of Ba, SiC, and Si(d-Si), which is
Composition (4). The disappearance of the XRD peaks at 2h of 18�,
21�, 30�, and 32� indicates that the Type I clathrate compound was
metastable and transformed to BaSi2 during ball-milling
2θ
No
rmal
ized
Inte
nsi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Non-Milled Ba8C6Si40
Predicted Ba8C6Si40
SiCBaBaSi2Si
15 20 25 30 35 40 45 50
(a)
2θ15 20 25 30 35 40 45 50
No
rmal
ized
Inte
nsi
ty
0.0
0.2
0.4
0.6
0.8
1.0
1.2Non-Milled Ba8C23Si23
Predicted Ba8C23Si23
SiCBaBaSi2Si
(b)
Fig. 10 PXRD pattern of non-milled Ba8CySi40-y powders compared
with those of Ba, Si, SiC, BaSi2, and the theoretical spectra of
Ba8CySi40-y with the Type I clathrate structure: a Ba8C6Si40 and
b Ba8C23Si23
2730 J Mater Sci (2014) 49:2723–2733
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Si atoms are substituted by 6 C on the framework. Insertion
of Ba atoms inside the framework as guest atoms close up
the band gap completely.
For the systems considered, insertion of Li, Na, K, Ca,
Mg, and Ba guest atoms into the C6Si40 cage structure
closes up the band gap of the material. Carbon substitution
and small guest-atom insertion such as Li and Na also
reduce the lattice constant, as summarized in Table 3.
Discussion
The results of this investigation demonstrated that first-
principles DFT computational method can be an effective
method for designing and evaluating new clathrate com-
pounds. In particular, substitution of Si atoms on the Si46
framework by C atoms is a viable means of designing new
carbon-substituted silicon clathrates. First-principles
computation also demonstrated that the cage structure of
Type I carbon–silicon framework can be inserted with
guest atoms of various atomic sizes including small atoms
such as Li and large atoms such as Ba. Both Li and Ba
insertion have been shown to lower the energy of formation
for hybrid carbon–silicon clathrates, providing a new
pathway for synthesizing these metastable alloyed carbon
clathrates. Type I silicon clathrates can be viewed as full-
erences, intercalation compounds, or Zintl phases [16–18].
As Zintl phases, the electronic structure of Type I silicon
clathrates can be predicted from the Zintl concept [17, 18].
According to this concept, each alkali metal guest atom is
an electron donor and transfers its valence electron to the Si
framework to become a cation. Each Si atom on the
framework is bonded to four other Si atoms and is, there-
fore, neutral. Thus, Type I Si clathrates with alkaline guest
atoms with ideal stoichiometry (8 guest atoms to 46 Si
atoms on the framework) should be a conductor because of
the eight extra electrons per formula from the eight alkaline
metals inside the cage [17]. The substitution of carbon
atoms on the Si framework to form a hybrid-silicon
framework is predicted to reduce the band gap. Further-
more, the insertion of alkaline or alkaline-earth metal guest
atoms into the hybrid carbon–silicon framework is pre-
dicted to close up the band gap, which is consistent with
the Zintl concept. However, experimental measurements of
electronic properties have shown that Type I clathrate
phases can be diamagnetic and semiconducting, instead of
metallic due to the presence of vacancies on the framework
[17]. Therefore, the prediction of closed up band gaps
shown in Table 3 for various AxCySi46-y Type I clathrates
needs to be validated by experimental studies in the future.
0-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Γ X M R Γ M
(a) Si46
Ene
rgy
(eV
)
DOS-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Γ X M R Γ M
(b) C6Si
40
Ene
rgy
(eV
)
DOS-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
Γ X M R Γ M
(c) Ba8C
6Si
40
Ene
rgy
(eV
)
DOS
Fig. 11 The DFT predicted band structure for a Si46, b C6Si40, and c Ba8C6Si40. The Fermi level is set at zero
Table 3 The DFT predicted lattice constants and band gaps for
various AxCySi46-y
Compounds Lattice constant (A) Band gap (eV)
Si46 10.23 1.31
C6Si46 9.63 0.44
Li8C6Si40 9.84 0 (closed up)
Na8C6Si40 9.70 0 (closed up)
K8C6Si40 10.08 0 (closed up)
Mg8C6Si40 9.80 0 (closed up)
Ca8C6Si40 9.99 0 (closed up)
Ba8C6Si40 10.28 0 (closed up)
J Mater Sci (2014) 49:2723–2733 2731
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Some of the predictions of the first-principles compu-
tations have been confirmed by successful syntheses of
Type I clathrates such as Ba8C6Si40, Ba8C20Si26, and
Ba8C23Si23 using a vacuum arc-melting method. The as-
synthesized products, however, contain mixtures of the
targeted compounds and starting materials. Thus, both the
yield and the purity of the arc-melting synthesis method
need further improvements. Even though the yield of pure
product was somewhat low (16–39 %), successful synthe-
sis of Ba8C6Si40, Ba8C20Si26, and Ba8C23Si23 represents a
significant accomplishment as these compounds, which are
synthesized for the first time, do not exist in nature.
The energy of formation for C46 is similar to that of
Ba8C6Si40, Ba8C20Si26, and Ba8C23Si23. The success in
synthesizing Ba8C6Si40, Ba8C20Si26, and Ba8C23Si23 by arc-
melting appears to be related to the use of SiC in the
admixture of starting compounds for these clathrates. It is
thought that SiC is of a higher energy state that, upon energy
input from the arc-melting process, overcomes the energy
barrier of reaction and allows the metastable carbon–silicon
clathrate compounds to form. In addition, the absence of C
or graphite peaks in the XRD patterns, the metastable nature
of the synthesized compounds, and the position of the XRD
peaks all support the notion that the synthesized compounds
are Ba8C6Si40, Ba8C20Si26, and Ba8C23Si23, and not variants
of Ba8Si46. In contrast, using graphite in the starting
admixtures to synthesize the carbon–silicon clathrate com-
pounds has led to failure, probably because graphite is too
stable to overcome the energy barrier associated with
metastable Ba8C6Si40, Ba8C20Si26, or Ba8C23Si23 for the
reaction to proceed. This finding is consistent with a pre-
vious study that showed Ba8Si46 cannot be synthesized by
arc-melting of elemental powders but must be synthesized
under high temperatures and high pressure conditions [36].
The yield and purity of the hybrid carbon–silicon clathrates
formed by the arc-melting synthesis method are still quite
low, because the processing parameters have not been
optimized. Future work is needed to optimize the processing
conditions and improve the product quality. Additional
work is also needed to identify the positions of the carbon
atoms in the hybrid carbon–silicon framework.
Conclusions
A new class of Type I silicon and carbon clathrates with
hybrid silicon and carbon atoms on the framework of the
cage structure and guest atoms A inside the cage structure
has been discovered wherein the composition of this series
of clathrates is qualitatively represented by the formula
AxCySi46-y, with 1 B y B 45 and A = Li, Na, K, and Ba,
which are capable of occupying the empty spaces inside the
large cages of the clathrate structure. These materials can
be formed, albeit in low yield and purity, by arc-melting
admixtures of A, SiC, and Si under a partial pressure of Ar
(in vacuo). The resultant clathrate products are metastable
as indicated by their positive energies of formation, which
were determined from first-principles computations at the
level of CPMD and DFT methods. The metastable phase
state of these hybrid clathrate materials was validated
experimentally by demonstrating that they revert to the
more stable compound (BaSi2) upon subjecting them to
mechanical forces (i.e., ball milling) under moderate
conditions.
First-principles computations further show that the
energy of formation for an ensemble of framework-atom
substitutions and guest atoms trends toward negative values
(i.e., thermodynamic stability) with increasing lattice con-
stant of the Type I clathrate structure. Substituting silicon
framework atoms with carbon along this trend lowers and
eventually eliminates the band gap, thus increasing their
electrical conductivity. Overall, it is found that the phase
stability, mechanical, and electrical properties of these
novel hybrid clathrates can be engineered at will with
judicious choice of framework atom substitution and guest
atom.
Acknowledgements This work was supported by The Internal
Research Program of Southwest Research Institute (KSC, MAM, WL,
and C E-T) and Faculty Scholarship Award from the School of Letters
and Sciences (XP) at Arizona State University (ASU). We
acknowledge the Texas Advanced Computing Center of the TerraGrid
Network and the Extreme Science and Engineering Discovery Envi-
ronment (XSEDE) High Performance Computing Facilities for pro-
viding the computational resources for the CPMD calculations. We
also acknowledge the ASU Advanced Computing Center for pro-
viding computational resources on Saguaro Cluster for the VASP
calculations. Clerical assistance by Ms. L. Salas, SwRI, in the prep-
aration of this manuscript is acknowledged.
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