Paper D28:0010: March APS Meeting, Pittsburgh, PA, March 16, 2009
Effects of Si on the Electronic
Properties of the Clathrates
A8Ga16SixGe30-x (A = Ba, Sr)
Emmanuel N. Nenghabi* and Charles W. Myles
*Deceased
For more details: See
Emmanuel N. Nenghabi and Charles W. Myles, Phys. Rev, B 77, 205203 (2008)
What are Clathrates?
• Crystalline phases based on Group IV elements
• Group IV atoms are 4-fold coordinated in sp3 bonding
configurations, but with distorted bond angles.
 A distribution of bond angles.
Lattices have hexagonal & pentagonal rings, fused together with
sp3 bonds to form large, open “cages” of Group IV atoms.
Cages of 20, 24 & 28 atoms.
• Meta-stable, high energy phases of Group IV elements.
• Applications: Thermoelectric materials & devices.
• Not found naturally. Must be lab synthesized.
Clathrate Types
• Type I: Formula: X8E46 (simple cubic lattice)
• Type II: Formula: X8Y16E136 (face centred cubic lattice)
X,Y = alkali metal or alkaline earth atoms, E = group IV atom
“Building Blocks”
24 atom cages 
28 atom cages 
dodecahedra (D)
hexakaidecahedra (H)
20 atom cages 
tetrakaidecahedra (T)
Type I: cage ratio: 6 D’s to 2 T’s
E46 sc lattice
Type II: cage ratio 16 T’s to 8 H’s
E136 fcc lattice
Why Ba8Ga16SixGe30-x & Sr8Ga16SixGe30-x?
• Some of these have been lab synthesized & have also been
found to have promising thermoelectric properties
J. Martin, S. Erickson, G.S. Nolas, P. Alboni, T.M. Tritt, & J. Yang
J. Appl. Phys. 99, 044903 (2006)
First Principles Calculations
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•
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VASP (Vienna ab-initio Simulation Package)
Many e- effects: Generalized Gradient Approximation (GGA).
Exchange Correlation: the Perdew-Wang Functional
Vanderbilt ultrasoft Pseudopotentials
Plane Wave Basis Set
Structural Parameters and
Equation of State Parameters
(from fits of GGA results to Birch-Murnaghan Equation of State)
E0  Minimum binding energy
K  Equilibrium bulk modulus
V0  Volume at minimum energy
K´  (dK/dP)  Pressure derivative of K
(We also have calculated results for other x than the ones shown)
Discussion: From this table, we obtain several predictions:
• Unit cell volume strongly depends on Si concentration x.
(We also calculated results for other x than those in the table)
• Cell volume decreases as x goes through the sequence:
Ba8Ga16Ge30, Ba8Ga16Si5Ge25, & Ba8Ga16Si5Ge15.
• Similar trend for the Sr-containing clathrates.
– Expected, because bonds between a Group III atom & a Group IV atom
are longer than those between 2 Group IV atoms. Might also be a reason
for our predicted increased stability of the material as x increases.
• Binding energies E0 for Ba8Ga16SixGe30-x & Sr8Ga16SixGe30-x
decrease by ~5.6% & ~5.7% as x changes 0  15.
• Bulk modulus K increases with increasing x.
 Larger Si concentration x, means a “harder” material.
• Sr-containing clathrates have smaller lattice constants than Ba-containing
materials. Consistent with Sr being a “smaller” atom than Ba
• Where data are available, predicted & experimental lattice constants are
within ~2% of each other.
Band Structures
Recall that the GGA doesn’t give correct band gaps!
 Ba8Ga16SixGe30-x
Sr8Ga16SixGe30-x 
Energy Band Gap Trend With x
GGA doesn’t give correct band gaps, but trend the with x should be ok
Band gap in Ba8Ga16SixGe30-x
decreases with x
Band gap in Sr8Ga16SixGe30-x
decreases with x
Discussion
From this table, we obtain several predictions:
Ba8Ga16SixGe30-x
• The GGA gap of Ba8Ga16Ge30 is ~ 0.55 eV & is reduced to
~ 0.42 eV for Ba8Ga16Si15Ge15. We also calculated bands for
x = 3, 8, & 12. For all values of x considered, the band gap slowly
decreases as x increases.
– Contrast to type-II Si-Ge clathrate alloys, for which others find that the
gap increases with increasing Si concentration.
Sr8Ga16SixGe30-x
• Contrast to Ba8Ga16SixGe30-x: The GGA gap of Sr8Ga16SixGe30-x
slowly increases with increasing x. Changes from ~0.18 eV in
Sr8Ga16Ge30 to ~0.48 eV in Sr8Ga16Si15Ge15.
Qualitative Comparison of Ba8Ga16SixGe30-x & Sr8Ga16SixGe30-x
• Blake et. al., for Sr- & Ba-containing Ge-based clathrates,
proposed an explanation of different behavior of band gaps in
the 2 material types:
– Sr is “smaller” than Ba. So, it can move further away from cage
center than Ba. Leads to more anisotropic guest-framework
interactions in the Sr-containing materials than in those with Ba.
• Our calculations show that the dependence of the lower
conduction bands on x is different in the 2 materials.
– In the Sr-containing materials, lower conduction bands are
flatter in the X-M region of the Brillouin zone than in the Bacontaining materials. This due to the Ba & Sr guests, which
donate electrons to the anti-bonding states of the host. Ba is
“larger” than Sr, so it can more easily donate electrons to the host.
Projected Electronic State Densities
• Substitutional Si & Ga in
the Ge lattice plus the Ba
or Sr guests in the cages
modify states near valence
band maxima &
conduction band minima
Illustrated here 
in the Projected DOS
for the Si s & p orbitals in
Ba8Ga16Si5Ge25
Clearly, contributions to the DOS
of the s orbitals near the conduction
band bottom are very small
compared to those of the p orbitals.
Total Electronic Densities of States
• Total DOS calculations for both material types find a
small gap in the valence band at energy ~ −0.7 eV.
– For other clathrate materials, others have found a similar
gap in the valence band at similar energies.
– This gap has been associated with five ring patterns of the Ge
or Si atoms. These rings may lead to a significant angular
distortion of the tetrahedrally bonded framework atoms which
causes them to play an important role in producing this gap.
– In a self-consistent plane-wave calculation, one typically can’t
easily calculate a value for the valence band maximum on an
absolute scale, so the energy at which this gap occurs may not
be quantitatively correct.
Conclusions
• We hope that our predicted structural & electronic
properties for the clathrate alloys Ba8Ga16SixGe30-x ,
Sr8Ga16SixGe30-x will lead to investigations of the
thermoelectric properties of these interesting
materials.
• We also hope that these investigations will provide
information about which of these materials will be
useful in the search for better thermoelectric
materials.