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Piezoelectric-based apparatus for strain tuning
4. J. Cao, E. Ertekin, V. Srinivasan, W. Fan, S. Huang, H. Zheng, J. W. L. Yim, D. R. Khanal, D. F. Ogletree, J. C. Grossman, and J. Wu, Nature Nanotechnol. 4, 732 (2009).
14.Pch 150/5 × 5/2, Piezomechanik GmbH.
16.Vishay Micro-Measurements EK-06-250PD-10C/DP. We took the gauge constant, the rate of change of gauge resistance against variation in the gauge's length, to be temperature-independent. Vishay Micro-Measurements Tech Note TN-504-1 (“Strain gauge thermal output and gauge factor variation with temperature”) indicates that the gauge constant for the Karma Alloy used in our gauges increases, with a linear temperature dependence, by 1.0% from 24 °C to −73 °C. Extrapolating to 0 K, the gauge constant would be ∼3% larger than at room temperature.
17.The response rates of the stacks were determined below 80 (200) V at room temperature (4 K), where the response was nearly linear with applied voltage.
19.Physik Instrumente GmbH, “Piezo Material Data.”
20.The Physik Instrument piezo materials datasheet indicates a coefficient of thermal expansion for various PZT formulations of −4 to −6 × 10−6/K, along the poling direction. The thermal contraction of most materials is much diminished below ∼77 K, so multiplying this coefficient by a ∼200 K temperature range yields an expansion of 0.08%–0.12% from room to cryogenic temperatures.
21.Both Refs. 6,13 report that much less strain is transmitted from the stack to the sample at higher temperatures, 300 K for the former and above ∼100 K for the latter, than at low temperatures, suggesting significant plastic deformation of the epoxy at higher temperatures. This may hinder measurements at higher temperatures, but could have the benefit of relieving thermal strains.
23. C. W. Hicks, D. O. Brodsky, E. A. Yelland, A. S. Gibbs, J. A. N. Bruin, K. Nishimura, S. Yonezawa, Y. Maeno, and A. P. Mackenzie, Science 344, 283 (2014).
24.With a Young's modulus of ∼200 GPa, the spring constant for straining the sample lengthwise will be Ewt/L ∼ 2 × 106 N/m, taking wt ∼ 0.01 mm2 and L ∼ 1 mm. The least stiff part of the apparatus is the bridge, which can be viewed approximately as two S-bending cantilevers 6 mm wide, 2.5 mm thick, and 9 mm long, yielding a spring constant of 14 × 106 N/m.
26. M. Euler, Mem. Acad. Sci. Berlin 13, 252 (1757).
27.The Young's modulus E for loads along x applies when the sample is free to expand and contract, following the Poisson's ratios, along y and z. If the sample is a thin plate, its strain along y may be constrained to be nearly zero, in which case should be used instead of E. For realistic materials, this will not be vastly different from E.
28. C. E. Ojeda, E. J. Oakes, J. R. Hill, D. Aldi, and G. A. Forsberg, “Temperature effects on adhesive bond strengths and modulus for commonly used spacecraft structural adhesives,” Jet Propulsion Laboratory (Pasadena, CA, USA), technical report.
30.Emerson and Cumings Stycast® 2850FT data sheet.
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We report the design and construction of piezoelectric-based apparatus for applying continuously tuneable compressive and tensile strains to test samples. It can be used across a wide temperature range, including cryogenic temperatures. The achievable strain is large, so far up to 0.23% at cryogenic temperatures. The apparatus is compact and compatible with a wide variety of experimental probes. In addition, we present a method for mounting high-aspect-ratio samples in order to achieve high strain homogeneity.
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