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In Search of Microscopic Evidence of Negative Thermal Expansion in Fullerenes

In Search of Microscopic Evidence of Negative Thermal Expansion in Fullerenes. S. Brown , J. Cao, and J. L. Musfeldt University of Tennessee N. Dragoe Universit´e Paris-Sud F. Cimpoesu Institute of Physical Chemistry, Romania R. J. Cross Yale University.

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In Search of Microscopic Evidence of Negative Thermal Expansion in Fullerenes

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  1. In Search of Microscopic Evidence of Negative Thermal Expansion in Fullerenes S. Brown, J. Cao, and J. L. Musfeldt University of Tennessee N. Dragoe Universit´e Paris-Sud F. Cimpoesu Institute of Physical Chemistry, Romania R. J. Cross Yale University

  2. Negative Thermal Expansion : ZrW2O8 Lattice Constant Gruneisen Parameter Thermal volumetric expansion coefficient  ≈ - 0.9 10-5 K-1 Ernst et al., Nature, 396,147 (1998) Sm2.72C60 and Graphite exhibit Negative Thermal Expansion Lattice expands at low temperature – Bulk effect

  3. Recent Prediction on Molecular Level NTE Our Goal: Search for microscopic evidence of NTE at molecular level. We know that : • T (K) a (Å) • 14.154 • 14.111 • 14.052 • 5 14.040 -110-5 K-1 Bulk Effect - Normal Kwon et al., PRL, 92, 015901 (2004)

  4. Microscopic Picture of Molecular Level Negative Thermal Expansion Endohedral High Pressure Low Temperature Larger Relaxed Ball Modes Soften Larger Ball Softer Vibrational Frequencies

  5. Review of Group Theory Point group Ih Ten Raman active modes2 Ag + 8 Hg Four infrared active modes4 T1u Normal Coordinate Analysis[1] fcc lattice % Radial % Tangential A1g (1) 100 A1g(2) 100 T1u (1) 93.5 6.5 T1u(2) 66.6 33.4 Our Focus T1u (1) 527 cm-1 [2] 1Stanton & Newton, J. Phys. Chem., 92, 2141 (1988) 2http://www.public.asu.edu/~cosmen/

  6. Endohedral Fullerene Inert atoms or molecules inside fullerene cage Synthesis : High pressure, Temperature Condition Separation: High-Performance Liquid Chromatography Cage size effects due to guest host interaction

  7. Our Experiments • C60 and Kr@C60 in polyethylene matrix • Suitable for FIR Transmittance measurements • BRUKER IFS 113V • Frequency range 20 – 700 cm-1 • Temperature range 4.2 - 300 K • Resolution – 0.1 cm-1

  8. Infrared Spectra of C60 and Kr@C60 C60 Kr@C60 Unusual Mode Softening by 0.5 cm-1 T1u(1) Mode Softens @ Low Temperature

  9. Temperature Dependent Behavior MP2 level calculation optimizes the cage of Kr@C60 as contracted ball Cage Radius R ∆Kr@C60-C60≈ 2 cm-1 C60 3.5499 Å Kr@C60 3.5489 Å ∆RKr@C60-C60≈ - 110-3 Å

  10. Kr Extended X-Ray Absorption Fine Structure (EXAFS) Data on Kr@C60 Cage Radius 3.537 Å 300 K 3.540 Å 77 K Ball is Larger @ Low Temperature Thermal Expansion Coefficient  ≈ - 10-5 K-1 Ito et al., J. Phys. Chem. B, 108, 3191 (2004)

  11. Microscopic vs. Macroscopic Behavior Lattice Parameter EXAFS • Low temperature behavior • Cage expands • - Molecular effect • Lattice contracts • - Bulk effect Raman Infrared Temperature (K) Loosdrecht et al. , PRL (1992) Hamanaka et al. , J. Phys.: Condens. Matter (1995)

  12. Pressure Dependence of Vibrational Spectra Lattice Parameter Vibrational modes soften with increasing P below 0.4 GPa /P ≈ - 12 • /P < 0 • Hg(3), Hg(4), T1u(1) • Consisted with • “relaxed ball” • Lattice is compressed • as P increases Snoke et al.,PRB (1992) Meletov et al., Phys. Stat. Sol. (b) (1996)

  13. Volumetric Expansion Coefficient Isothermal Compressibility Mode Grüneisen Parameter Thermal expansion will be positive or negative depending upon Grüneisen Parameter i

  14. Mode Grüneisen Parameter (0-0.4 GPa) for C60 Many Negative Grüneisen Parameters

  15. Mode Specific Heat Calculation • Total No. of • Intramolecular Vibrational Modes 46 • Raman and Infrared Active Mode 14 Thermal Expansion Coefficient Specific Heat - No. of phonon /branch of frequency Area under the DOS plot Gompf et al., J. Superconductivity (1994)

  16. Microscopic Picture Endohedral Harder, Smaller Ball Higher Vibrational Frequency Due to change in potential and weak guest-host interaction High Pressure Low Temperature Larger Relaxed Ball Modes Soften Larger Ball Softer Vibrational Frequencies

  17. What We Learned • Measured variable temperature infrared spectra of C60 and Kr@C60 • T1u(1) mode softens throughout the temperature range under investigation • Previous variable temperature Raman and EXAFS, variable pressure Raman consistent • Consistent with predictions forMolecular Negative Thermal Expansion Acknowledgments Division of Materials Research, NSF

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