Paper D28:0010 : March APS Meeting, Pittsburgh, PA, March 16, 2009

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.

• 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

Clathrate Types

“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’sE46 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• 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 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)

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

Ba8Ga16SixGe30-x

Sr8Ga16SixGe30-x

Recall that the GGA doesn’t give correct band gaps!

Energy Band Gap Trend With xGGA 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

DiscussionFrom 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 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.

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.