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Effects of Si on the Electronic Properties of the Clathrates A 8 Ga 16 Si x Ge 30-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 - PowerPoint PPT Presentation
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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.