1 23

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

1 23

Your article is protected by copyright and all

rights are held exclusively by Springer Science

+Business Media New York. This e-offprint is

for personal use only and shall not be self-

archived in electronic repositories. If you wish

to self-archive your article, please use the

accepted manuscript version for posting on

your own website. You may further deposit

the accepted manuscript version in any

repository, provided it is only made publicly

available 12 months after official publication

or later and provided acknowledgement is

given to the original source of publication

and a link is inserted to the published article

on Springer's website. The link must be

accompanied by the following text: "The final

publication is available at link.springer.com”.

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: kchan@swri.edu

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

J Mater Sci (2014) 49:2723–2733

DOI 10.1007/s10853-013-7973-6

Author's personal copy

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)

2724 J Mater Sci (2014) 49:2723–2733

123

Author's personal copy

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

123

Author's personal copy

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

123

Author's personal copy

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

123

Author's personal copy

Ta

ble

1C

and

idat

eco

mp

osi

tio

ns

and

elem

enta

lo

ral

loy

star

tin

gco

mp

on

ents

for

hy

bri

dca

rbo

n–

sili

con

clat

hra

tesy

nth

esis

by

vac

uu

mar

cm

elti

ng

Co

mp

osi

tio

nT

arg

etcl

ath

rate

com

po

un

d

d(g

/cc)

FW

(g/m

ol)

Ba

3.5

1

13

7.3

27

NaS

i 21

.70

76

.95

28

5

LiA

l

1.5

6

33

.92

25

4

LiS

i 22

.00

63

.11

2

g-C

2.2

3

12

.01

07

d-S

i

2.3

2

28

.08

55

Al

2.7

0

26

.98

15

4

SiC

3.2

1

40

.09

62

B4C

2.5

2

55

.25

47

B6S

i

2.4

0

92

.95

15

To

tal

(g/m

ol)

Bat

ch(g

)

Est

imat

ed

den

sity

(g/c

c)

Est

imat

ed

vo

lum

e(c

c)

1N

a 2L

i 6A

l 10C

6S

i 30

Ato

mra

tio

22

46

18

8

Wei

gh

t(g

)0

.00

15

3.9

16

7.8

52

52

.45

72

.06

50

5.5

42

15

.85

0.0

00

.00

0.0

01

26

7.6

52

.20

Bat

ch0

.00

24

.28

10

.70

39

.83

11

.37

79

.76

34

.06

0.0

00

.00

0.0

02

00

.00

90

.91

2L

i 8A

l 10C

6S

i 30

Ato

mra

tio

86

14

10

Wei

gh

t(g

)0

.00

0.0

00

.00

50

4.9

07

2.0

63

93

.20

26

9.8

20

.00

0.0

00

.00

12

39

.97

2.2

7

Bat

ch0

.00

0.0

00

.00

81

.44

11

.62

63

.42

43

.52

0.0

00

.00

0.0

02

00

.00

88

.22

3B

a 6C

6S

i 40

Ato

mra

tio

86

40

Wei

gh

t(g

)1

09

8.6

20

.00

0.0

00

.00

72

.06

11

23

.42

0.0

00

.00

0.0

00

.00

22

94

.10

2.8

9

Bat

ch9

5.7

80

.00

0.0

00

.00

6.2

89

7.9

40

.00

0.0

00

.00

0.0

02

00

.00

69

.27

4B

a 8C

20S

i 26

Ato

mra

tio

86

20

Wei

gh

t(g

)1

09

8.6

20

.00

0.0

00

.00

0.0

01

68

.51

0.0

08

01

.92

0.0

00

.00

20

69

.05

3.3

0

Bat

ch1

06

.20

0.0

00

.00

0.0

00

.00

16

.29

0.0

07

7.5

20

.00

0.0

02

00

.00

60

.66

5B

a 8C

6S

i 40

Ato

mra

tio

83

46

Wei

gh

t(g

)1

09

8.6

20

.00

0.0

00

.00

0.0

09

54

.91

0.0

02

40

.58

0.0

00

.00

22

94

.10

2.9

8

Bat

ch4

7.8

90

.00

0.0

00

.00

0.0

04

1.6

20

.00

10

.49

0.0

00

.00

10

0.0

03

3.5

2

6B

a 8C

23S

i 23

Ato

mra

tio

82

3

Wei

gh

t(g

)1

09

8.6

20

.00

0.0

00

.00

0.0

00

.00

0.0

09

22

.21

0.0

00

.00

20

20

.83

3.3

7

Bat

ch5

4.3

60

.00

0.0

00

.00

0.0

00

.00

0.0

04

5.6

40

.00

0.0

01

00

.00

29

.65

2728 J Mater Sci (2014) 49:2723–2733

123

Author's personal copy

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

123

Author's personal copy

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

123

Author's personal copy

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

123

Author's personal copy

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.

References

1. Rogl P (2006) Intermetallic clathrates: a challenge for thermo-

electric. Institute of Physical Chemistry, University of Vienna,

Vienna

2. Rogl P (2005) Formation of clathrates, in thermoelectrics. In:

Proceedings of the 24th International Conference on Thermo-

electrics, pp 440–445

3. San-Miguel A, Toulemonde P (2005) High-pressure properties of

group IV clathrates. High Press Res 25(3):159–185

4. Connetable D (2007) Structural and electronic properties of

p-doped silicon clathrates. Phys Rev B 75(125202):1–10

5. Nolas GS, Slack GA (2001) Thermoelectric clathrates. Am Sci

89:136–141

6. Beckman M, Nolas GS (2008) Inorganic clathrate-II materials of

group 14: synthetic routes and physical properties. J Mater Chem

18:842–851

7. Saramat A, Svensson G, Palmqvist AEC et al (2006) Large

thermoelectric figure of merit at high temperature in czochralski-

grown clathrate Ba8Ga16Ge30. J Appl Phys 99(023708):1–5

2732 J Mater Sci (2014) 49:2723–2733

123

Author's personal copy

8. Kawaji H, Horie H-O, Yamanaka S, Ishikawa M (1995) Super-

conductivity in the silicon clathrate compound (Na, Ba)xSi46.

Phys Rev Lett 74:1427–1429

9. Yamanaka S (2010) Silicon clathrates and carbon analogs: high

pressure synthesis, structure, and superconductivity. Dalton Trans

39:1901–1915

10. Li Y, Garcia J, Chen N et al (2013) Superconductivity in Al-

substituted Ba8Si46 clathrates. J Appl Phy 113(203908):1–6

11. Chan KS, Chan CK, Liang W (2012) Silicon clathrate anodes for

lithium-ion batteries, United States Patent Application Publica-

tion, US 0021283 A1

12. Langer T, Dupke S, Trill H et al (2012) Electrochemical lithiation

of silicon clathrate-II. J Electrochem Soc 159(8):A1318–A1322

13. Yang J, Tse JS (2013) Silicon clathrates as anode materials for

lithium ion batteries? J Mater Chem A 1:7782–7789

14. Wagner NA, Raghaven, R, Zhaoe R et al (2013) Electrochemical

cycling of sodium-filled silicon clathrate, CHEMELECTRO-

CHEM (published on-line). doi:10.1002/celc.201300104

15. San-Miguel A, Melinon P, Blase X et al (2002) A new class of

low compressibility materials: clathrates of silicon and related

materials. High Press Res 22:539–544

16. Pouchard M, Cros C, Hagenmuller P, Reny E et al (2002) A brief

overview on low sodium content silicides: are they mainly

clathrates, fullerenes, intercalation compounds or Zintl phases?

Solid State Sci 4(5):723–729

17. Bobev S, Sevov SC (2000) Clathrates of group 14 with alkali

metals: an exploration. J Solid State Chem Acad Press

153:92–105

18. Shevelkov AV, Kovnir K (2011) Zintl Clathrates. Struc Bond

139:97–142

19. Nolas GS, Slacjk GA, Schujman SB (1966) Semiconductor

clathrates: a phonon glass electron crystal material with potential

for thermoelectric applications. In: Tritt TM (ed) Semiconductors

and Semimetals, chap 6, vol 69. Academic Press, San Diego,

pp 255–300

20. Perottoni CA, da Jornada JAH (2001) The carbon analogues of

type-I silicon clathrates. J Phys Condens Matter 13:5981–5998

21. Wang J-T, Chen C, Wang D-S, Mizuseki H, Kawazoe Y (2010)

Phase stability of carbon clathrates at high pressure. J Appl Phys

107(063507):1–4

22. Rey N, Munoz A, Rodrıquez-Hernandez P, San-Miguel A (2008)

First-principles study of lithium-doped carbon clathrates under

pressure. J Phys Condens Matter 20:215218–215224

23. Meng JF, Shekar VC, Badding JV, Nolas GS (2001) Threefold

enhancement of the thermoelectric figure of merit for pressure

tuned Sr8Ga16Ge30. J Appl Phys 89:1730–1733

24. Blake NP, Latturner S, Bryan JD, Stucky GD, Metiu H (2001)

Band structure and thermoelectric properties of the clathrates

Ba8Ga16Ge30, Sr8Ga16Ge30, Ba8Ga16Si30, and Ba8In16Sn30.

J Chem Phys 115:8060–8073

25. Jung W, Lorincz J, Ramlau R, Borrmann H et al (2007) K7B7Si39,

a borosilicide with the clathrate I structure. Angewandte Chem

46:6725–6728

26. Adams GB, O’Keeffe M, Kemkov AA, Sankey OF, Huang Y-M

(1994) Wide-band-gap Si in open fourfold-coordinated clathrate

structures. Phys Rev B 49:8053–8084

27. Melinon P, Keghelian P, Perez A, Champagnon B et al (1999)

Phonon density of states of silicon clathrates: characteristic width

narrowing effect with respect to the diamond phase. Phys Rev B

59:10099–10103

28. Car R, Parrinello M (2008) Molecular dynamics: an ab initio

electronic structure and molecular dynamics program, Version

3.13.1, The CPMD Consortium, June 27, 2008. http://www.cpmd.

org. Accessed 4 Jan 2014

29. Car R, Parrinello M (1985) Unified approach for molecular

dynamics and density functional theory. Phys Rev Lett

55(22):2471

30. Perdew P, Burke K, Ernzerhof M (1996) Generalized gradient

approximation made simple. Phys Rev Lett 77(18):3865–3868

31. Blochl PE (1994) Projected augmented-wave method. Phys Rev

B 50(24):17953–17979

32. Kresse G, Joubert D (1999) From ultra soft pseudo potentials to

projector augmented-wave method. Phys Rev B 59(3):1758–1775

33. Kresse G, Marsman M, Furthmuller J (2012) Vienna ab initio

simulation package—VASP the guide. Universitat Wien, Wien

34. Tsujii N, Roudebush JH, Zevalkink A et al (2011) Phase stability

and chemical composition dependence of the thermoelectric

properties of the type-1 clathrate Ba8A1xSi46-x (8 B x B 15).

J Solid State Chem 184(5):1293–1303

35. Kitano A, Moriguchi K, Yonemura M, Munetoh S, Shintani A

(2001) Structural properties and thermodynamic stability of Ba-

doped silicon type-I clathrates synthesized under high pressure.

Phys Rev B 64(045206):1–9

36. Yamanaka S, Enishi E, Fukuoka H, Yasukawa M (2000) High-

pressure synthesis of a new silicon clathrate superconductor,

Ba8Si46. Inorg Chem 39:56–58

37. Liang Y, Bohme B, Reibold M, Schnelle W, Schwarz U, Bait-

inger M (2011) Synthesis of the clathrate-1 phase Ba8-xSi46 via

redox reactions. Inorg Chem 50:4523–4528

38. Diamond Version 3.2 (2013) Crystal Impact, Bonn, Germany

J Mater Sci (2014) 49:2723–2733 2733

123

Author's personal copy