1. Effects of Si on the Electronic Properties of the Clathrates
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, (2008)

2. 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.

3. X,Y = alkali metal or alkaline earth atoms, E = group IV atom
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  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

4. 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, (2006)
First Principles Calculations
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

5. (We also have calculated results for other x than the ones shown)
Structural Parameters and Equation of State Parameters (from fits of GGA results to Birch-Murnaghan Equation of State)
E0  Minimum binding energy V0  Volume at minimum energy
K  Equilibrium bulk modulus K´  (dK/dP)  Pressure derivative of K
(We also have calculated results for other x than the ones shown)

6. 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.

7. Band Structures Sr8Ga16SixGe30-x   Ba8Ga16SixGe30-x
Recall that the GGA doesn’t give correct band gaps!
 Ba8Ga16SixGe30-x
Sr8Ga16SixGe30-x 

8. 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

9. From this table, we obtain several predictions:
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.

10. 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 Ba-containing 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.

11. 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.

12. 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.

13. 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.