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First characterization of silicon crystalline fibers produced with the -pulling technique for future gravitational wave detectors
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Image of FIG. 1.
FIG. 1.

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.

Image of FIG. 2.
FIG. 2.

Specific heat of silicon (Refs. 23 and 27).

Image of FIG. 3.
FIG. 3.

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.

Image of FIG. 4.
FIG. 4.

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.

Image of FIG. 5.
FIG. 5.

Schematic diagram for the -PD growth apparatus (hot zone part).

Image of FIG. 6.
FIG. 6.

Image of a fiber during the growth process.

Image of FIG. 7.
FIG. 7.

Grown Si single-crystal fibers in diameter and 17 and long.

Image of FIG. 8.
FIG. 8.

The simulated second mode of a long fiber. In the expanded segment the stress distribution is also visible.

Image of FIG. 9.
FIG. 9.

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 .

Image of FIG. 10.
FIG. 10.

Measured values of for a long fiber after the etching process. The average diameter is .

Image of FIG. 11.
FIG. 11.

Values of for a fiber with a roughly elliptical section.

Image of FIG. 12.
FIG. 12.

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.

Image of FIG. 13.
FIG. 13.

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.

Image of FIG. 14.
FIG. 14.

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 .


Generic image for table
Table I.

Measured parameters for two different Si fibers.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: First characterization of silicon crystalline fibers produced with the μ-pulling technique for future gravitational wave detectors