1. 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 In Search of Microscopic Evidence of Negative Thermal Expansion in Fullerenes

2. Negative Thermal Expansion : ZrW 2 O 8 Ernst et al., Nature, 396,147 (1998) Lattice Constant Gruneisen Parameter Thermal volumetric expansion coefficient  ≈ - 0.9  10 -5 K -1 Lattice expands at low temperature – Bulk effect Sm 2.72 C 60 and Graphite exhibit Negative Thermal Expansion

3. Recent Prediction on Molecular Level NTE Kwon et al., PRL, 92, 015901 (2004)  -1  10 -5 K -1 Our Goal: Search for microscopic evidence of NTE at molecular level. T (K) a (Å) 300 14.154 240 14.111 110 14.052 5 14.040 We know that : Bulk Effect - Normal

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

5. Review of Group Theory Ten Raman active modes 2 A g + 8 H g Four infrared active modes 4 T 1u Point group I h T 1u (1) 527 cm -1 A 1g (1) 100 A 1g (2) 100 T 1u (1) 93.5 6.5 T 1u (2) 66.6 33.4 % Radial % Tangential Our Focus Normal Coordinate Analysis [1] 1 Stanton & Newton, J. Phys. Chem., 92, 2141 (1988) [2] fcc lattice 2 http://www.public.asu.edu/~cosmen/

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

7. Our Experiments  C 60 and Kr@C 60 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 C 60 and Kr@C 60 C 60 T 1u (1) Mode Softens @ Low Temperature Unusual Mode Softening by 0.5 cm -1 Kr@C 60

9. Temperature Dependent Behavior MP2 level calculation optimizes the cage of Kr@C 60 as contracted ball C 60 3.5499 Å Kr@C 60 3.5489 Å Cage Radius R ∆R Kr@C 60 -C 60 ≈ - 1  10 -3 Å ∆  Kr@C 60 -C 60 ≈ 2 cm -1

10. Kr Extended X-Ray Absorption Fine Structure (EXAFS) Data on Kr@C 60 Ito et al., J. Phys. Chem. B, 108, 3191 (2004) Cage Radius 3.537 Å 300 K 3.540 Å 77 K Ball is Larger @ Low Temperature Thermal Expansion Coefficient  ≈ - 10 -5 K -1

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

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

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

14. Mode Grüneisen Parameter (0-0.4 GPa) for C 60 NegativeGrüneisen Parameters Many

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

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

17. What We Learned  Measured variable temperature infrared spectra of C 60 and Kr@C 60  T 1u (1) mode softens throughout the temperature range under investigation  Previous variable temperature Raman and EXAFS, variable pressure Raman consistent  Consistent with predictions for Molecular Negative Thermal Expansion Acknowledgments Division of Materials Research, NSF