Paper D28:0011: March APS Meeting, Pittsburgh, PA, March 16, 2009
Effects of Si on the Vibrational and
Thermal Properties of the Clathrates
A8Ga16SixGe30-x (A = Ba, Sr)
Charles W. Myles and Emmanuel N. Nenghabi*
*Deceased
For more details: See
Emmanuel N. Nenghabi and Charles W. Myles, Phys. Rev, B 78, 195202 (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.
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: 6 D’s to 2 T’s
E46 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
Phonon Dispersion Relations
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.
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 cm1. In Sr Ga Si Ge
-1
8
16 x
30-x, these are at 40, 42, 33 cm 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.
Mean Square Atomic Displacement Parameters (ADP)
Uiso ~ (kBT)/φ
φ = Calculated force constant
for Ba, Sr vibrations.
• Results for the Ba, Sr in 20 atom
x=5
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.
x = 15
Thermal Properties: Cv, S, F for Ba8Ga16SixGe30-x
Cv
S
F
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.
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.