1. Clathrate Semiconductors
Recall introductory lectures:
Relatively new area
Part of my research while on sabbatical at Arizona State U. in Spring, 2000.
New crystalline phases of group IV elements: Si, Ge, Sn.
Pure elemental phases have not been made. Always compounds, usually compounds with groups I and II elements (Na, K, Cs, Ba).
Interesting properties (possible applications as thermoelectrics).
Crystal structures briefly again, then bandstructures.

2. Clathrate Semiconductors (Si; could be any group IV element)
Open, cage-like structures, with large “cages” of Si atoms.
All Si atoms tetrahedrally (4-fold) coordinated, with sp3 covalent bonds.
Hexagonal (6 atom) and pentagonal (5 atom) rings, fused together with sp3 covalent bonds to form “cages”.
Cages of size 20, 24, and 28 Si atoms!

3. Clathrates (Si; could be any group IV element)
Si46 (46 atoms/ cubic unit cell)
Two, 20 atom cages combined with six, 24 atom cages, fused through 5 atom pentagonal rings.
Overall crystal structure is simple cubic.
Si136 (136 atoms/cubic unit cell)
Sixteen, 20 atom cages combined with eight, 28 atom cages, fused through 5 atom pentagonal rings.
Overall crystal structure is face centered cubic.

4. Si clathrates (Could be any group IV element)

5. Si46 clathrates (Could be any group IV element)

6. Si136 clathrates (Could be any group IV element)

7. Clathrates (Any group IV element)
Not found in nature! Synthesized in the lab, mainly by solid state chemists, using complicated chemical reactions.
Normally in pure form. Usually have impurities (“guests”) encapsulated inside the cages.
Guests: group I atoms (alkali metals: Li, Na, K, Cs, Rb) or group II atoms (alkaline earth metals: Be, Mg, Ca, Sr, Ba)

8. Si46 clathrates (with guest impurities)

9. Ge and Sn clathrates
Among materials of interest are germanium (Ge) and tin (Sn) clathrates.
Possible use as thermoelectric materials.

10. Clathrate Bandstructure Calculations Highly computational!
Start with guessed lattice geometry (atomic configuration, including interatomic distances & bond angles).
One electron Hamiltonian H + many electron effects obtained using the Local Density Approximation (LDA).
One electron potential is approximated using pseudopotential method.

11. Clathrate Bandstructures Highly computational!
Interatomic forces act to relax lattice to equilibrium configuration (distances, angles). Done by using of Schrdinger Eq. for interacting electrons & Newton’s 2nd Law motion for atoms!
At relaxed lattice configuration (“optimized geometry”) use one electron Hamiltonian + many electron corrections to solve Schrdinger Eq. for bandstructures Ek.

12. Clathrate Bandstructures Highly computational!
Bandstructures Ek.
Let
NB =Number of bands
Ne = number of electrons / atom NA = number of atoms / unit cell
 NB = Ne x NA
For clathrates
Ne = 4 valence electrons.
 If NA = 46, NB = 184!
 If NA = 136, NB = 544! (actually only 136, if take fcc unit cell where NA = 34).

13. Ge Clathrate Bandstructures
From J.J. Dong & O.F. Sankey J. Phys. Condensed Matter, (1999).

14. Sn46 Clathrate Bandstructures
C.W. Myles, J.J. Dong & O.F. Sankey, unpublished.

15. Sn136 Clathrate Bandstructures
C.W. Myles, J.J. Dong & O.F. Sankey, unpublished.

16. Cs8Ga8Sn38 Clathrate Bandstructures
C.W. Myles, J.J. Dong & O.F. Sankey, unpublished.