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Thermal Optics
January 18, 2013
One of the more interesting principles of
material mechanics is the concept of critical
flaw size. This was first developed by the
aeronautical engineer,
Alan Griffith.[1] Griffith noticed that the
real strength of materials was considerably less than the strength predicted by
chemical bonds, and his
experiments on
freshly-drawn glass fibers showed that fibers of very small
diameter fail at high applied
tensile stress.
Griffith realized that perfectly formed materials have high
fracture strength, and the small flaws extant in real materials are responsible for their low fracture strength. In his experiments, Griffith modified his tensile specimens by adding his own, larger flaw, a notch at the surface. This led to what's now known as
Griffith's criterion, that the product of the stress at fracture and the square root of the notch length is nearly a constant, at least for
brittle materials; viz.,
σf√a ≈ C
where
σf is the
stress at
fracture,
a is the notch length, and
C is a constant. Griffith's explanation for such behavior was that opening a crack forms two new surfaces and a creation of
surface energy. In that case, he was able to write an equation for the constant,
C,
C = √(2Eγ/π)
where
E is
Young's modulus and gamma (γ) is the surface energy
density. The equation works well for brittle materials, such as
glass, and it's been
modified for
plastic materials. The equation reduces to the
rule that a material will be resistant to fracture at a specified stress level if all its flaws are smaller than a critical flaw size. Of course, rules are made to be broken. As you can imagine, there have been big advances in the hundred years of fracture mechanics since Griffith.
Label for "Fractured," a 45-RPM record by Bill Haley and His Comets (1953).
As can be seen from the label, this was the B-side of the record. A-sides of records were the presumed "hits," and the B-side was usually a throwaway. The Elvis Presley record containing Don't Be Cruel and Hound Dog is a notable exception to this rule.
(Photograph by Waylon, via Wikimedia Commons)
Griffith's criterion is an example of the idea that the
microstructure of a material is as important to its
physical properties as its
chemical composition.
Nanotechnology now gives us the ability to create devices with novel physical properties. One recent example of this is the
research in
thermal optics ongoing in
MIT's Department of Materials Science and Engineering by
Martin Maldovan.[2-3]
Maldovan's thermal optics are different from optics designed to work on
infrared light. One example of such conventional thermal optics would be the
heat mirror, which was much more useful in the days before
energy-efficient light sources when intense light was needed without the attendant heat. As its name implies, a heat mirror reflects heat, more specifically, unwanted infrared radiation, back to its source. Such mirrors are actually
dichroic filters designed to pass the proper
wavelengths and
reflect all others.
Sound, like light, is also a
wave, and it can be manipulated with analogs of optical components. One experiment I did as an
undergraduate physics major was using a
lens-shaped bag containing
argon or
carbon dioxide to
focus sound waves from a
loudspeaker. This worked because the
density of argon and carbon dioxide are larger than that of
air (at
atmospheric pressure and 0
°C, 1.784
g/
L and 1.977 g/L
vs 1.2922 g/L). Since sound wavelengths are large, the bag needed to be about a
meter in diameter.
The preceding example was for sound waves in air. Sound is also present in
solids; and, just as light waves can be modeled as
particles called
photons, sound waves in solids are modeled as particles called
phonons. In solids, phonons transport heat, so manipulating phonons allows manipulation of heat. In a
previous article (Sound and Heat, August 23, 2011), I reviewed how nanoscale layers can reduce the
thermal conductivity of a material.
Alternating layers of different
acoustic impedance cause a
reflection of phonons because of
impedance discontinuities, and this inhibits heat transmission. In one experiment, a layered structure of
tungsten and
alumina in which the layers were just a few
nanometers thick had a thermal conductivity of just 0.6
watt/meter/kelvin.[4]
The wavelengths of natural sound in air are large, but they can be a lot smaller in a solid. This means that the structures needed for phonon manipulation must be small, as in the example of the alumina and tungsten layers above. The approach that Maldovan proposes is to first reduce the
frequency of the phonons that carry the heat to increase their wavelength and make it easier to build thermal-optics. This is important, since these frequencies are in the
terahertz range.[2]
These "hypersonic heat" phonons, as Maldovan calls them, are created in
silicon containing
germanium nanoparticles of specific size.[2] Alternatively, the layered approach, as I describe above, can also be used. Using such techniques, about 40% of the heat can be converted into a directed beam in a narrow range of phonon frequencies, from 100-300 gigahertz.[2]
Having nearly
monochromatic light allows phonon manipulation using acoustic analogs of
photonic crystals, which Maldovan calls "thermocrystals."[2] Using thermocrystals, it might be possible to create thermal
diodes that allow heat to pass in just one direction. One application would be as a means to make more energy-efficient buildings.[2] Maldovan's research is published in a recent issue of
Physical Review Letters.[3]
References:
- A.A. Griffith, A. A. (1921), "The phenomena of rupture and flow in solids," Philosophical Transactions of the Royal Society of London, vol. A221 (1921), pp. 163–198. Available here, also.
- David L. Chandler, "How to treat heat like light," MIT News Office Press Release, January 11, 2013.
- Martin Maldovan, "Narrow Low-Frequency Spectrum and Heat Management by Thermocrystals," Phys. Rev. Lett., vol. 110, no. 2 (January 11, 2013), Document No. 025902 (5 pages).
- R. M. Costescu, D. G. Cahill, F. H. Fabreguette, Z. A. Sechrist and S. M. George, "Ultra-Low Thermal Conductivity in W/Al2O3 Nanolaminates," Science, vol. 303, no. 5660 (February 13, 2004), pp. 989-990.
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