Negative Thermal Expansion
November 11, 2011
The vast majority of
materials expand when heated, an effect known as
thermal expansion. Thermal expansion causes major problems in the manufacture of useful articles. Unless thermal expansion is taken into account during
design,
camera lenses will
defocus, and parts carefully fit at room temperature will
fracture as the temperature is increased.
The linear thermal expansion of materials is quantified by the
thermal expansion coefficient, which generally goes by the symbol, alpha (α),
α = (1/L)(∂L/∂T)
for which
L is the gauge length,
T is the
temperature, and the dimensions are usually (1/°C). The following table lists the thermal expansion coefficient at
room temperature (20°C) for a variety of materials.
You can see from the table that
hydrogen-bonded liquids (ethanol and water) have a large thermal expansion; and also why mercury was popular in the past for
thermometers. It's
intuitively easy to see why thermal expansion should exist. Temperature is simply the
vibration of atoms, and the vibrational energy will act against the
bonding forces that hold
atoms together. An end consequence of this is the eventual
vaporization of materials into a
gas.
That's why
negative thermal expansion (NTE) is so unusual. A few isolated examples of NTE were discovered over the years, one of which is
water between
freezing and 3.984°C.[1] There are so many unusual things about water, that even this brief excursion into NTE didn't raise too many eyebrows.
Silicon exhibits NTE in a temperature range of 18 - 120
K.
Hope that some utility can be gained from NTE began in 2004 with the discovery of NTE in an
oxide of
zirconium and
tungsten,
cubic zirconium tungstate, ZrW
2O
8.[2-3] Unlike water, where the temperature range for NTE is very limited, or silicon, where the temperatures are too low to be really useful, zirconium tungstate exhibits NTE from almost
absolute zero to 775 °C. Analogs of this material in which
hafnium substitutes for zirconium, and
molybdenum substitutes for tungsten, also exhibit NTE.
In 2010,
scandium fluoride (ScF
3), a material with a different
crystal structure, was discovered to have an NTE as large as -14 ppm/°C at temperatures from 60-110 K.[4] Its NTE increases to become equivalent to that of zirconium tungstate at room temperature, and the thermal expansion finally becomes positive above 1100 K.[4]
The crystal structure of scandium fluoride.
Drawing by author, rendered with Inkscape)
A research team from the
Department of Applied Physics and Materials Science of the
California Institute of Technology (Pasadena, California), and the
Neutron Scattering Science Division of
Oak Ridge National Laboratory (Oak Ridge, Tennessee), has just performed a study to elucidate the mechanism of scandium fluoride's NTE.[5-8] The study was somewhat enabled by the simple lattice structure of the scandium fluoride crystal, as shown in the above figure. The neutron scattering at the Oak Ridge National Laboratory
Spallation Neutron Source allowed measurement of the atomic vibrations.[7]
The neutron scattering revealed that all of the atomic resonances remained roughly constant as the temperature was changed, except for one that shifted to higher
frequency, an indication of increased bonding force.[6] What apparently happens is that the fluorine atoms are vibrating in a direction transverse to the linear chains of scandium-fluorine-scandium atoms. This is apparently the root cause of the negative thermal expansion.[7]
Principle of negative thermal expansion in scandium fluoride. The fluorine atoms vibrate in a transverse direction to the scandium atoms to pull them together. Drawing by author, rendered with Inkscape.
One curious finding is that the
restoring force of the fluorine vibration is a function of the fourth power of the
displacement. This quartic oscillation is unlike the quadratic (second power) oscillation that's found in atomic vibrations and
harmonic oscillators.[7] Says
Brent Fultz, study coauthor and Professor of Materials Science and Applied Physics at Caltech, "A nearly pure quantum quartic oscillator has never been seen in atom vibrations in crystals."[7]
The research team speculates that quartic oscillator materials may also be good
thermal insulating materials. NTE materials can be combined with other materials to produce zero expansion materials, at least over a small temperature range. Such materials would be useful in optics, but also things as mundane as
dental restoration.[6]
References:
- Martin Chaplin, Water Structure and Science - Explanation of the Density Anomalies of Water.
- Jason N. Hancock, Chandra Turpen, Zack Schlesinger, Glen R. Kowach and Arthur P. Ramirez, "Unusual Low-Energy Phonon Dynamics in the Negative Thermal Expansion Compound ZrW2O8," Phys. Rev. Lett., vol. 93, no. 22 (November 22, 2004), Document No. 225501
- David Lindley, "Bake, Shake, and Shrink," Physical Review Focus, vol. 14, no. 21 (November 22, 2004).
- Benjamin K. Greve, Kenneth L. Martin, Peter L. Lee, Peter J. Chupas, Karena W. Chapman and Angus P. Wilkinson, "Pronounced Negative Thermal Expansion from a Simple Structure: Cubic ScF3," J. Am. Chem. Soc., vol. 132, no. 44 (November 10, 2010), pp 15496-15498
- Chen W. Li, Xiaoli Tang, J. A. Muñoz, J. B. Keith, S. J. Tracy, D. L. Abernathy, and B. Fultz, "Structural Relationship between Negative Thermal Expansion and Quartic Anharmonicity of Cubic ScF3," Phys. Rev. Lett., vol. 107, no. 19 (November 4, 2011), Document No. 195504.
- Michael Schirber, "New Vibration in Material That Shrinks When Heated," Physics (APS), vol. 4, no. 90 (November 4, 2011).
- Marcus Woo, "An Incredible Shrinking Material," California Institute of Technology Press Release, November 4, 2011.
- Cal Tech, "An Incredible Shrinking Material," YouTube Video, November 4, 2011.
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