S. Brown, J. Cao, and J. L. MusfeldtUniversity of Tennessee

N. DragoeUniversit´e Paris-Sud

F. CimpoesuInstitute of Physical Chemistry, Romania

R. J. CrossYale University

In Search of Microscopic Evidence of

Negative Thermal Expansion in Fullerenes

Negative Thermal Expansion : ZrW2O8

Ernst et al., Nature, 396,147 (1998)

Latt

ice

Con

stan

t

Gruneisen P

arameter

Thermal volumetric expansion coefficient

≈ - 0.9 10-5 K-1

Lattice expands at low temperature – Bulk effect

Sm2.72C60 and Graphite exhibit Negative Thermal Expansion

Recent Prediction on Molecular Level NTE

Kwon et al., PRL, 92, 015901 (2004)

-110-5 K-1

Our Goal: Search for microscopic evidence of NTE at molecular level.

T (K) a (Å)300 14.154301 14.111302 14.052 5 14.040

We know that :

Bulk Effect - Normal

Microscopic Picture of Molecular Level Negative Thermal

Expansion

High Pressure Low Temperature

Endohedral

Larger BallSofter Vibrational Frequencies

Larger Relaxed BallModes Soften

Review of Group Theory

Ten Raman active modes 2 Ag

+ 8 Hg

Four infrared active modes 4 T1u

Point group Ih

T1u (1) 527 cm-1

A1g (1) 100

A1g(2) 100

T1u (1) 93.5 6.5

T1u(2) 66.6 33.4

% Radial % Tangential

Our Focus

Normal Coordinate Analysis[1]

1Stanton & Newton, J. Phys. Chem., 92, 2141 (1988)

[2]

fcc lattice

2http://www.public.asu.edu/~cosmen/

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

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

Infrared Spectra of C60 and Kr@C60

C60

T1u(1) Mode Softens @ Low Temperature

Unusual Mode Softening by 0.5 cm-1

Kr@C60

Temperature Dependent Behavior

MP2 level calculation optimizes the cage of Kr@C60 as contracted ball

C60 3.5499 Å Kr@C60 3.5489 Å

Cage Radius R

∆RKr@C60-C60≈ - 110-3 Å

∆Kr@C60-C60 ≈ 2 cm-1

Kr Extended X-Ray Absorption Fine Structure (EXAFS) Data on Kr@C60

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

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

Infr

ared

Ram

anE

XA

FS

Temperature (K)

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 Hg(3), Hg(4), T1u(1) • Consisted with “relaxed ball”• Lattice is compressed as P increases

/P ≈ - 12

Lattice Parameter

Volumetric Expansion Coefficient

Pi

Tii

1

iciV

T

Thermal expansion will be positive or negative

depending upon Grüneisen Parameter i

Mode Grüneisen Parameter

TIsothermal Compressibility

dT

dV

V

1

Mode Grüneisen Parameter (0-0.4 GPa) for C60

Negative GrüneisenParameters

Many

Mode Specific Heat Calculation

Gompf et al., J. Superconductivity (1994)

Thermal Expansion Coefficient

Specific Heat iciV

T

iiV cpC 4

1

ip - No. of phonon /branch of frequency

•Total No. of Intramolecular Vibrational Modes 46•Raman and Infrared Active Mode 14

Area under the DOS plot

Microscopic Picture

Endohedral

High Pressure Low Temperature

Harder, Smaller BallHigher Vibrational FrequencyDue to change in potential and weak guest-host interaction

Larger BallSofter Vibrational Frequencies

Larger Relaxed BallModes Soften

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 for Molecular Negative Thermal Expansion

AcknowledgmentsDivision of Materials Research, NSF