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

Paper D28:0011 : March APS Meeting, Pittsburgh, PA, March 16, 2009. Effects of Si on the Vibrational and Thermal Properties of the Clathrates A 8 Ga 16 Si x Ge 30-x (A = Ba, Sr). Charles W. Myles and Emmanuel N. Nenghabi * * Deceased. For more details: See

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

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  1. 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, B78, 195202 (2008)

  2. What are Clathrates? • Crystallinephases based on Group IV elements • Group IV atoms are 4-fold coordinated insp3 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.

  3. 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: 6D’s to 2 T’s E46 sc lattice Type II: cage ratio 16 T’s to 8 H’s E136fcc lattice

  4. WhyBa8Ga16SixGe30-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

  5. 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.

  6. 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 theSi 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.

  7. 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-1for 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.

  8. Mean Square Atomic Displacement Parameters (ADP) Uiso ~ (kBT)/φ φ =Calculated force constant forBa, Srvibrations. • Results for the Ba, Sr in 20 atom cages & in 24 atom cages are both shown. • Uisovalues 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

  9. 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.

  10. 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.

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