Contactless Conductivity Measurement: Difference between revisions
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v_p & = 4\pi G\chi _0 a^2 lfH_0\\ | v_p & = 4\pi G\chi _0 a^2 lfH_0\\ | ||
v_q & = \frac{1}{4} \pi \mu _0 G \sigma a^4 l f^2 H_0 | v_q & = \frac{1}{4} \pi \mu _0 G \sigma a^4 l f^2 H_0 | ||
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</div> | </div> | ||
where <math>v_p</math> is the real part of the induced voltage and <math>v_q</math> is the imaginary part. <math>\chi _0</math>, <math>\mu _0</math>, <math>\sigma</math>, <math>a</math>,<math>G</math>, <math>l</math> are the susceptibility, permeability, conductivity, radius, geometric coefficient and length of the cylindrical sample. <math>f</math>, <math>H_0</math> are the frequency and strength of the primary coil magnetic field. | where <math>v_p</math> is the real part of the induced voltage and <math>v_q</math> is the imaginary part. <math>\chi _0</math>, <math>\mu _0</math>, <math>\sigma</math>, <math>a</math>,<math>G</math>, <math>l</math> are the susceptibility, permeability, conductivity, radius, geometric coefficient and length of the cylindrical sample. <math>f</math>, <math>H_0</math> are the frequency and strength of the primary coil magnetic field. Some parameters can be reduced or cancelled out when we divide the two voltages and the equation we eventually use is | ||
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"> | |||
<math> | |||
\begin{alignat}{2} | |||
\sigma & = \dfrac{v_q}{v_p} \dfrac{16\chi _0}{\mu _0 a^2 f} | |||
\end{alignat} | |||
</math> | |||
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==To do list== | ==To do list== | ||
Revision as of 03:37, 29 April 2022
Introduction
In our Spintronics Lab, when we want to analyze a sample, conductivity or resistivity as a electrical property is almost always necessary. Normally, we use a Voltmeter or standard four probes method to take a measurement. However, surface preparation and contamination have great effects on the electrical properties of the samples. Thus, a contactless technic would be a better way to carry out the conductivity measurement. When we were doing the ac magnetic susceptibility measurement, we learn from literature that there is connection between the electrical conductivity and the ac magnetic susceptibility. We would like to build the set up from the literature, take a measurement on the conductivity of our metal sample and compare it with the result from standard four probes measurement.
Theory
The mechanism for the contactless conductivity measurement is identical to the effective magnetic susceptibility measurement. Basically, the sample is inserted into a primary coil and a secondary coil. An ac current passes through the primary windings will induce magnetic field. The sample responds to the magnetic field and eddy current will be induced within the sample. Then, EMF will be induced in the secondary coil due to not only the driving magnetic field of the primary coil, but also the magnetic field of the currents induced in the sample. Two magnetic fields are 90 degrees out of phase so that the real part and imaginary part of the resultant voltage will be separately related to the ac magnetic susceptibility and the conductivity. When calculating the conductivity from voltage, there are two different approaches introduced by Ishida et al.[1] and Iñiguez et al.[2]. The first approach uses susceptibility to express the magnetic flux penetrating the sample which gives us the final expressions
where is the real part of the induced voltage and is the imaginary part. , , , ,, are the susceptibility, permeability, conductivity, radius, geometric coefficient and length of the cylindrical sample. , are the frequency and strength of the primary coil magnetic field. Some parameters can be reduced or cancelled out when we divide the two voltages and the equation we eventually use is
To do list
Prepare the samples
Prepare the coils
Build the experimental set up
Measure
Graph and Report
Sample Preparation
Experiment Set up
Data Analysis
Conclusion
Team Members
Chen Guohao, Jiang Luwen
Lab Location
Spintronics and Magnetic Materials Lab
References
- ↑ Ishida, T., Monden, K., & Nakada, I. (1986). Electrodeless method for the measurement of ionic conductivity of RbAg4I5. Review of Scientific Instruments, 57(12), 3081-3084. https://doi.org/10.1063/1.1138995
- ↑ Iñiguez, J., & Raposo, V. (2007). Measurement of conductivity in metals: A simple laboratory experiment on induced currents. European Journal of Physics, 28(6), 1125-1129. https://doi.org/10.1088/0143-0807/28/6/009
Bean, C. P., DeBlois, R. W., & Nesbitt, L. B. (1959). Eddy‐Current method for measuring the resistivity of metals. Journal of Applied Physics, 30(12), 1976-1980. https://doi.org/10.1063/1.1735100
Crowley, J. D., & Rabson, T. A. (1976). Contactless method of measuring resistivity. Review of Scientific Instruments, 47(6), 712-715. https://doi.org/10.1063/1.1134714
Oike, H., Miyagawa, K., Kanoda, K., Taniguchi, H., & Murata, K. (2009). Contactless conductivity measurements on the organic conductor, κ-(ET)4Hg2.89Br8, under pressure. Physica. B, Condensed Matter, 404(3-4), 376-378. https://doi.org/10.1016/j.physb.2008.11.023
Kraftmakher, Y. A. (1991). Measurement of electrical resistivity via the effective magnetic susceptibility. Measurement Science & Technology, 2(3), 253-256. https://doi.org/10.1088/0957-0233/2/3/011
Bauhofer, W. (1977). Continuous, contactless measurement of the temperature-dependent electrical resistivity of metals. Journal of Physics. E, Scientific Instruments, 10(12), 1212-1214. https://doi.org/10.1088/0022-3735/10/12/003