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

1. Effects of Si on the Electronic Properties of the Clathrates A8Ga16SixGe30-x (A = Ba, Sr) Paper D28:0010:March APS Meeting, Pittsburgh, PA, March 16, 2009 Emmanuel N. Nenghabi* and Charles W. Myles *Deceased For more details: See Emmanuel N. Nenghabi and Charles W. Myles,Phys. Rev, B77, 205203 (2008)

2. What are Clathrates? • Crystallinephases based on Group IV elements • Group IV atoms are 4-fold coordinated insp3 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 ofGroup IVelements. • Applications: Thermoelectric materials & devices. • Not found naturally. Must be lab synthesized.

3. 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: 6D’s to 2 T’s E46 sc lattice Type II: cage ratio 16 T’s to 8 H’s E136fcc lattice

4. WhyBa8Ga16SixGe30-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

5. 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 xgoes 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 xchanges 0 15. • Bulk modulus Kincreases 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 Recall that theGGA 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. Discussion From this table, we obtain several predictions: Ba8Ga16SixGe30-x • The GGA gap of Ba8Ga16Ge30is ~ 0.55 eV & is reduced to ~ 0.42 eV for Ba8Ga16Si15Ge15. We also calculated bands for x= 3, 8, & 12. For all values of xconsidered, 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 Comparisonof 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: • Sris “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 xis different in the 2 materials. • In the Sr-containing materials, lower conduction bands are flatter in the X-Mregion 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” thanSr, 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 theProjected DOS for theSis&porbitals in Ba8Ga16Si5Ge25  Clearly, contributions to the DOS of the s orbitals near the conduction band bottom are very small compared to those of the porbitals.

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.