Effects of Si on the Vibrational and Thermal Properties of the Clathrates

A8Ga16SixGe30-x (A = Ba, Sr)

For more details: See

Emmanuel N. Nenghabi and Charles W. Myles, Phys. Rev, B 78, 195202 (2008)

Charles W. Myles and Emmanuel N. Nenghabi*

*Deceased

Paper D28:0011: March APS Meeting, Pittsburgh, PA, March 16, 2009

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

Ba8Ga16SixGe30-x Sr8Ga16SixGe30-x

These show: An up-shift in the optic modes as x increases.Largest for the optic modes, in which bond-stretching modes are important.

In Ba8Ga16SixGe30-x:

The highest optic modes are 253, 334, 373 cm−1 for x = 0,5, 15.

In Sr8Ga16SixGe30-x :

These are 327, 350, 428 cm−1 for x = 0,5, 15.

Phonon Dispersion Relations

The phonon modes show:

An up-shift in the optic modes as x increases.

Explanation: Ge substitution by Ga & Si strengthens bonds. Calculated lattice constants a show that a in Ba compounds is larger than in the Sr materials because the Ba atomic mass is larger than Sr’s. So, a larger strain effect occurs when Ba is in the cages than if Sr is in them.

Also: Because the Si atom is “smaller” than Ba, Sr, Ge, & Ga atoms, the lattice constant a decreases as x increases. The nearest-neighbor bond distances in Ba8Ga16SixGe30-x range from 2.53–2.63 Å. In Sr8Ga16SixGe30-x these range from 2.44–2.62 Å. Shorter bonds strengthen the structures, resulting in larger force constants.

Vibrational State Densities (VDOS) • The VDOS increases at the bottom of the optic

band, just above the acoustic modes.– Eigenvector analysis shows that these

additional modes are from the Sr & Ba guests.

• The VDOS is higher for x = 5 than for x = 0 & higher for x = 15 than for x = 5.

• The optic modes compress the acoustic bandwidth. For x = 0,5,15, the tops of the acoustic bands in Ba8Ga16SixGe30-x are at 33, 36, 30 cm-1. In Sr8Ga16SixGe30-x, these are at 40, 42, 33 cm-1 for x = 0, 5, 15.

• The acoustic bandwidths are reduced (in comparison to that of pristine Ge46) by ~16%–40%, depending on the value of x.

Uiso ~ (kBT)/φ

φ = Calculated force constant

for Ba, Sr vibrations.• Results for the Ba, Sr in 20 atom cages & in 24 atom cages are both shown.

• Uiso values for Sr are larger than for Ba. In qualitative agreement with experiments by

Bentien et al. in Ba8Ga16Ge30, Ba8Ga16Si30, Ba8In16Ge30, Sr8Ga16Ge30.

• Because of the Sr small atom in

comparison to Ba, the Sr atoms are more off-centered in the cages than Ba, which leads to a larger ADP.

Mean Square Atomic Displacement Parameters (ADP)

x = 5

x = 15

Heat Capacity, Cv, Entropy S, Helmholtz Free Energy F

• Of course, because of their low frequencies of vibration, the Ba guests contribute little to these properties.

• As can be seen, the dependence on the Si composition x is also very small for each of these properties.

• Similar calculations for Sr8Ga16SixGe30-x for these properties show that the Ba-containing materials are thermodynamically more stable than the Sr-containing materials.

Cv S F

Thermal Properties: Cv, S, F for Ba8Ga16SixGe30-x

Conclusions• We hope that our predicted vibrational and thermal

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.