Thermal conductivity (continuous line) and linear thermal expansion coefficient (dash-dotted line) of silicon Refs. 30 and 31 the two temperatures (about 18 and ) where the thermal expansion coefficient vanishes, as well as the peak of the thermal conductivity at low temperature, are apparent in the plot in the small box.
Specific heat of silicon (Refs. 23 and 27).
Amplitude of the linear thermoelastic loss angle in a silicon fiber, computed using Eq. (2) and Ref. 23. Ideally, at the two temperatures where the thermal expansion coefficient vanishes is null. The expected temperature dependence of the thermoelastic peak frequency in a diam. silicon fiber is also shown. The frequency increase at low temperature should contribute to reduce the thermoelastic dissipation in the suspension.
Expected thermoelastic peaks at room temperature in fibers ( in diameter) made of C85 steel (solid curve), Ref. 10 sapphire (dashed curve) Ref. 23, fused silica (dotted curve) Refs. 10 and 23, and Silicon (dash-dotted curve) Ref. 23.
Schematic diagram for the -PD growth apparatus (hot zone part).
Image of a fiber during the growth process.
Grown Si single-crystal fibers in diameter and 17 and long.
The simulated second mode of a long fiber. In the expanded segment the stress distribution is also visible.
a) Measured loss angle of a (free length) fiber, with an average diameter of . The stars represent the thermoelastic contribution as predicted by the model described in the text; (b) measured loss angle for the same fiber after the etching process; the average diameter is now , while the free length is .
Measured values of for a long fiber after the etching process. The average diameter is .
Values of for a fiber with a roughly elliptical section.
Relative frequency variation vs temperature. For the three modes indicated in the figure all the frequency values have been recorded; for the other modes a subset of measurements has been performed.
Relative Young’s modulus variation vs temperature. The three straight lines show the extrapolation, below room temperature, of Young’s modulus behavior reported in Ref. 23 for the three crystal orientations: dashed line, dotted line, and dash-dotted line. The solid line is the fit of the model in Eq. (10) to the experimental data.
Temperature dependence of the mode vs temperature. The superimposed curve represents the expected loss angle due to thermoelastic dissipation in a silicon fiber having an average diameter of about .
Measured parameters for two different Si fibers.
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