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. 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.
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.
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.
These "hypersonic heat" phonons, as Maldovan calls them, are created in silicon containing germanium nanoparticles of specific size. 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.
Having nearly monochromatic light allows phonon manipulation using acoustic analogs of photonic crystals, which Maldovan calls "thermocrystals." 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. Maldovan's research is published in a recent issue of Physical Review Letters.
- 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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