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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
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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
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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
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Microscopic Picture of Molecular Level Negative Thermal
Expansion
High Pressure Low Temperature
Endohedral
Larger BallSofter Vibrational Frequencies
Larger Relaxed BallModes Soften
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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/
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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
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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
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Infrared Spectra of C60 and Kr@C60
C60
T1u(1) Mode Softens @ Low Temperature
Unusual Mode Softening by 0.5 cm-1
Kr@C60
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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
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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
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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)
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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
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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
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Mode Grüneisen Parameter (0-0.4 GPa) for C60
Negative GrüneisenParameters
Many
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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
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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
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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