Clathrate Colloquium, 2005

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Paper D280011 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)
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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.

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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 Ds to 2 Ts E46 sc
lattice Type II cage ratio 16 Ts to 8 Hs
E136 fcc lattice
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• 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

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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.
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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 Srs.
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 2.532.63 Å. In
Sr8Ga16SixGe30-x these range from 2.442.62 Å.
Shorter bonds strengthen the structures,
resulting in larger force constants.

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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 1640,
  depending on the value of x.

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Mean Square Atomic Displacement Parameters (ADP)

• Uiso (kBT)/f
• f 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.

x 5

x 15
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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.

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• 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.