Magnetoresistance in Bismuth – Experimental Investigations (Part 2 – The Thrilling Conclusion)

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By Timothy Raney…Bald Engineer Guy with Glasses

Note: Read the first exciting installment here.

Magnet #3 Modification and Calibration
To increase Magnet #3 flux density, I machined two O-1 alloy steel pole piece inserts to reduce the magnet’s gap width from 11.8mm to ~3mm. Each insert disc was ~4.46mm thick and 19mm in diameter. Subsequent measurements indicated the flux exceeded the gaussmeter’s range – its indicator needle stopped abruptly at 9.6kG, close to the scale’s 10kG maximum. Therefore, the 9.6kG value was used as the maximum flux (Bmax) until better instrumentation was available. Ambient temperature was 26OC. The calibration was necessary to verify the flux value before conducting this experiment. However, given the gaussmeter limitations, the “assumed” 9.6kG Bmax was not necessarily the true value. This situation is a good example of an approximation with a high degree of uncertainty. Magnet calibration instrumentation and procedures are shown in the Addendum.

Bismuth Specimen#4 ΔR Measurements
The purpose of this experiment was to measure the resistance of bismuth specimen #4. Magnet#3 was used for these trials with the Wheatstone bridge. Experimental set-up as shown in the figure below. In trial #1, Ri was 0.049Ω and Rf was 0.064Ω. The ΔR was 0.015W. In trial #2, there was no measurable ΔR. The observations were made ~30-minutes apart.

Bismuth Specimen #4 Long-term Resistance
The purpose of this experiment was to determine if the specimen’s long-term resistance was constant within a B field. Resistance measurements were recorded over a 23-day period with the Wheatstone bridge. Magnet #3’s flux was now 14.13kG after measuring it with a better higher-range gaussmeter calibrated to NIST-traceable standards. In this case, with a Ri of 0.049Ω, the ΔR was ~0.015Ω in a 14.13kG B field. See Table-1. Thus, it appeared specimen resistance remains relatively constant over time, except for an expected slight increase (+0.001W) at higher ambient temperatures.

ΔR Measurements – Ammeter and Voltmeter Method[1]
This experiment’s intent was to measure ΔR for specimen #4 using the ammeter and voltmeter method. See figures 9a and 9b. Apparatus included a 1.5V battery, lab stand and clamp; a single pole-single throw (SPST) switch, a DC voltmeter (1.5V full-scale), DC ammeter (30mA, center zero) and a decade resistance box (Shallcross, Mfg., Co.). Magnet #1 was used to provide a 9.4kG flux. Given the schematic diagram in figure 9a, the open-circuit potential was 1.63V. The total circuit resistance (RT) was 163kW at 27.5OC. Specimen #4 shown as RX. A 130kW ballast resistor (not shown) was used to limit the current through bismuth specimen. It and the decade resistance box provided a suitable current for the selected ammeter. No observable meter deflections occurred with specimen#4 in the 9.4kG flux. Under these conditions, the specimen did not exhibit a detectable ΔR.

ΔR Measurements of Specimen #4 with New Digital Multimeter
The purpose of this experiment was to measure specimen #4’s ΔR with a new BK Precision® digital multimeter (DMM). This DMM was designed to measure low resistance values (<1Ω) to within +/- 0.1%. Items used in this experiment included lab stand, jack and clamps. Magnet #3 provided a 14.13kG B field. The primary instrument used for these DR measurements was the DMM (#5491A). Specimen #4’s Ri was 0.090W. This Ri differed notably from earlier measurements (0.049Ω). This difference was attributed to using an instrument better suited for milliohm-range measurements. The Rf was 0.11Ω. The DR was then 0.02Ω. Interestingly, specimen resistance did vary over several minutes. Rf then appeared to stabilize at 0.09Ω to 0.10Ω in the 14.13kG flux at ~27OC. Thus, the magnetoresistive effect in this specimen was actually marginal and inconsistent.

Specimen#4 was then re-oriented so its long axis was perpendicular to the flux and just outside the poles. Its resistance dropped to ~0.07Ω in a 2.6kG B field. This anomaly was perhaps due in part to experimental error. I did not attempt to investigate it further. However, with a more accurate means to make resistance measurements, the ΔR due to a strong transverse B field was observable.  Though the ΔR was only ~0.01 to 0.02Ω at 14.13kG. This minimal change indicated a simple bismuth strip was not an effective sensor for a gaussmeter with a practical measurement range. What a difference good instrumentation makes.

ΔR Measurements of Specimen #3 with New Digital Multimeter
As above, I repeated the earlier experiments, but with better instrumentation. All equipment was the same as the preceding experiment. Bismuth specimen #3’s Ri was 0.07Ω and its Rf was 0.10Ω. The ΔR was then 0.03Ω. The Ri varied over a 20-minute period and appeared to stabilize at 0.09Ω in the 14.13kG B field at ~27OC. The observed magnetoresistance was again marginal. See Figures 10 and 11.

Conclusion
The purpose of these experiments was to explore magnetoresistance as exhibited by elemental bismuth when exposed to a high magnetic flux. It was also hoped results would support development of a gaussmeter based on a simple bismuth strip. Allied tasks performed in conjunction with these experiments included learning various measurement methods, developing techniques for bismuth specimen fabrication and magnet calibration. Other tasks included building the components needed to modify apparatus or improve its functioning. Unfortunately, these experimental results do not support development of a gaussmeter based on a simple bismuth strip as a sensor. Nor was this approach a satisfactory means of quantifying magnetic fields within a practical measurement range, i.e., arbitrarily 1kG to 15kG. The observed ΔR values were minimal (0.02Ω) considering the high flux densities employed – up to ~14kG. See Table-2 for a summary covering most of the experiments described herein.

Additional experiments along this line of investigation include designing a magnet with a high B field configured to influence a bismuth wire along its entire length. Other approaches could include configuring the sample as a pancake spiral[2] or other shapes or preparing a specimen by vacuum sputtering bismuth onto a glass substrate. This latter approach would yield a specimen with a higher resistance. However, these experiments did verify one could observe magnetoresistance in bismuth when the specimen was placed in a sufficiently strong B field. Thus, the transverse magnetoresistance effect was likely demonstrated to a minimal extent with relatively crude apparatus. Once again, in the immortal words of Professor Julius Sumner Miller, “No Experiment is a failure!”


Addendum – Magnet Calibration
This information summarizes the procedures for calibrating the magnets employed in these experiments. As a representative example, we will discuss Magnet#1 calibration briefly. The first step was to ensure the gaussmeter was showing accurate flux values by measuring the B field of a calibration magnet. Afterwards, the magnet’s gap was adjusted to a given width. The gaussmeter’s sensor probe was then positioned within the gap’s geometric center and fixed securely in place. Lastly, a test was conducted to measure the magnetic flux for a given gap width. In this case, a ~3mm gap was the smallest width that could accommodate the gaussmeter probe. The graph below plots the DB as a function of magnet gap width. The data shows the inverse relationship between magnetic flux and gap width. Accurate gap spacing was done with non-magnetic brass shim stock spacers. These spacers were first inserted into the gap and the  pole pieces adjusted accordingly.  Thus, this data characterized a particular magnet’s performance based on the distance (gap) between the pole pieces.

Footnotes:

[1] E. Hausmann, Swoope’s Lessons in Electricity (17th Ed), D. Van Nostrand Company, Inc., New York, 1926, pg. 280.

[2] L.B. Loeb, Fundamentals of Electricity and Magnetism (2nd Ed.), John Wiley & Sons, Inc., New York, 1938, pg. 309.

References:

[1]    R.G. Lerner and G.L. Trigg (Eds.), Encyclopedia of Physics (2nd Ed.), VCH Publishers, Inc., New York, 1991. See W.A. Reed - Magnetoresistance.

[2]    L.B. Loeb, Fundamentals of Electricity and Magnetism (2nd Ed.), John Wiley & Sons, Inc., New York, 1938.

[3]    W.M. Haynes and D.R. Lide (Eds.), CRC Handbook of Chemistry and Physics (92nd Ed.), CRC Press - Taylor & Francis Group, Boca Raton, FL, 2011.

[4]    R.G. Lerner and G.L. Trigg, pg. 421. See D.J. Sellmyer and C.M. Hurd - Galvanomagnetic and Related Effects.

[5]    S. Chikazumi (S.H. Charap, trans.), Physics of Magnetism, John Wiley & Sons, Inc., New York, 1964.

[6]    L.S. Lerner, Physics for Scientists & Engineers, Jones & Bartlett Publishers, Inc., Sudbury, MA, 1996.

[7]    R.G. Lerner and G.L. Trigg. See Sellmyer & Hurd.

[8]    L.R. Moskowitz, Permanent Magnet Design and Application Handbook, Cahners Books International, Inc., Boston, MA, 1976.

[9]    M.B. Stout, Basic Electrical Measurements, Prentice-Hall, Inc., New York, 1950.

[10] V. Karapetoff and B.C. Dennison, Experimental Electrical Engineering and Manual for Electrical Testing (vol. I - 4th Ed.), John Wiley & Sons, Inc., New York, 1933.

[11] Ibid, Stout.

[12] Ibid, Karapetoff and Dennison.

[13] E. Hausmann, Swoope’s Lessons in Electricity (17th Ed), D. Van Nostrand Company, Inc., New York, 1926.

[14] L.B. Loeb, Fundamentals of Electricity and Magnetism (2nd Ed.), John Wiley & Sons, Inc., New York, 1938.

End Notes

Transverse magnetoresistance is a subordinate effect under galvanomagnetic effects. R = (r) L/A. Where R is the resistance in ohms (W); L = length (cm or m); A = cross-sectional area and “r” is the resistivity expressed in ohm-meters (or ohm-centimeters). See Sellmyer and Hurd - galvanomagnetic effects) and Reed – Magnetoresistance in R.G. Lerner and G.L. Trigg [1] above.

Microscopic view of electrical resistance in a metallic conductor. See figure 27-11 in L.S. Lerner [6] above.

For Wheatstone bridge accuracy limits when measuring resistances under 1W, see M.B. Stout [9] above.

Using the Wheatstone Bridge. Expedient method and accuracy limits of using a Wheatstone bridge to measure resistances under 1W. See Karapetoff and Dennison [10] above.

See Keithley Instruments, Inc., Low Level Measurements (4th Ed.), Cleveland, OH, 1993 for valuable guidance on making low level electrical measurements.

Ammeter and voltmeter method for measuring resistance. See E. Hausmann [13] above.

Bismuth properties. Atomic number is 83, atomic weight is 208.9804 and its melting point is 271.4OC. See Haynes and Lide [3] above. Bulk resistivity (r) = 1.19 X 10-4W-cm (18OC) or 1.19 X 10-6W-meters). See Gray, D. E. (Coordinating Editor), American Institute of Physics Handbook (2nd Ed.), McGraw-Hill Book Company, Inc., 1963, pg. 9-38, Table 9d-1.


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2 Responses to Magnetoresistance in Bismuth – Experimental Investigations (Part 2 – The Thrilling Conclusion)

  1. Dave says:

    Excellent article!

    One consideration that should be taken into account is that Bismuth is also extremely diamagnetic. Thus, a sample may tend to exclude some of the magnetic field. I’m not real sure how this would be measured, though.

    As for Bismuth’s diamagnetism, a lump of it suspended on a long thread will swing away from a magnet placed near it; The effect is slight, but noticeable, not nearly as strong as the Meissner effect in superconductors, nor even as much as for pyrolytic Graphite, but definitely noticeable.

    http://en.wikipedia.org/wiki/Diamagnetism#History
    http://en.wikipedia.org/wiki/Meissner_effect

    Also, I’ve done some magnetic field measurements with the Allegro Hall Effect sensors (e.g., A1321, although I’m told it has been superseded by more recent parts).

    Dave

    • TIM RANEY says:

      Dave – Good points. Given my earlier work with bismuth’s diamagnetic properties, your comment is thought-provoking. Given some conjecture, the magnetic flux density and sample’s geometry, one would suspect a minimal affect on the measurements. However, I don’t know that as fact. I will give it further thought. Thanks very much for your interest!

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