Electrical resistivity measurements of metals often use the four-wire method, where data acquisition alternates between temperature and voltage. The temperature and voltage values are similar and manual selection of each set of measurements is time consuming.

Electrical resistivity of materials is a basic property that is measured and used in a large variety of studies. In one type of study, electrical resistivity data are used to calculate thermal conductivity and interior heat flow of terrestrial-type bodies. The electrical resistivity of a sample is often obtained using the four-wire method as it reduces the contribution of the electrodes that is present in the two-wire method. The four-wire method is used in the cooling of industrial devices [

The four-wire method incorporates a polarity switch and a mode switch, and results in a pattern of alternating values of temperature (emf) and voltage in a single column when acquired by a single voltmeter. A complete measurement produces a pattern similar to the following: temperature emf before voltage measurement (T_{b}), positive voltage drop with polarity in one direction (V^{+}), negative voltage drop with polarity in opposite direction (V), temperature emf after voltage measurement (T_{a}). The order of V^{+} and V^{–} may be alternated depending on the position of the polarity switch. At the University of Western Ontario, in the High-Pressure High-Temperature Laboratory, a programmable Keysight B2961 power supply is used to provide a constant direct test current of 0.2 A while data are acquired by a programmable Keysight 34470A meter operating at 20 Hz and 1 µV resolution. The selection of temperature and voltage values is typically done manually, and, to our knowledge, no software available in the literature is capable of automatically processing the temperature and voltage signals.

The application ^{+} and V^{–} selections are averaged to give the voltage drop (V), while T_{b} and T_{a} selections are averaged to give the temperature (T). The voltage drop and current (I) are then used to calculate the electrical resistance (R) of the sample using Ohm’s law:

The electrical resistivity is then calculated using Pouillet’s law:

where

where T is temperature and L_{o} is the theoretical Sommerfeld value (L_{o} = 2.44∙10^{–8} W∙Ω∙K^{–2}) of the Lorenz number. The error in temperature measurement corresponds to the standard deviation of the data points of each temperature section. The error in ρ is obtained by error propagation using the uncertainties in sample geometry and standard deviation of the voltage measurements. Similarly, the error in k corresponds to the propagation of the error in ρ.

The main page of _{b}, V^{+}, V^{–}, and T_{a} data alternate within the first column of the file (see

First, the intervals of negative values are labelled as voltage measurements (V_{total}). This temporary selection is displayed in _{b} V^{+} V^{–} T_{a} is considered and T_{b} and T_{a} are temporarily identified. To satisfy this scenario, the difference between T_{b} and V_{total} must be smaller than the difference between T_{a} and V_{total} considering that the part of V_{total} closer to T_{b} would be V^{+} and that closer to T_{a} would be V^{–} (and V^{–} < V^{+}). ^{+} is temporarily defined as the first trend in V_{total}. In the second scenario, the pattern T_{b} V^{–} V^{+} T_{a} is considered, and a similar loop is applied to identify the intervals where the difference between T_{b} and V_{total} is larger than that of T_{a} and V_{total}. Here, the part of V_{total} closer to T_{b} would be V^{–} and that closer to T_{a} would be V^{+}. Another analysis of the first scenario identifies the stable intervals on the main increasing trend right before V^{+} as T_{b}, and that right after V^{–} as T_{a}. In other words, fluctuations, or noise, between temperature and voltage measurements are automatically ignored. A similar analysis of the second scenario identifies the stable intervals on the main increasing trend right before V^{–} as T_{b} and that right after V^{+} as T_{a}. The corresponding indexes (x-axis) and data (y-axis) for each selection are combined into variables for T_{b}, V^{–}, V^{+}, and T_{a}. The ‘Outliers Degrees of Freedom’ parameter evaluates the differences between the trends of V^{–} and V^{+} and identifies data points outside of these trends as outliers. A larger degree of freedom will include more data points in the final variables for V^{–} and V^{+}, while a smaller degree of freedom will ignore more data points. The value 20 seems to be the best fit for this parameter, although it can be adjusted by the user. In other words, fluctuations of 20 times and more are defined as outliers. The final selection is displayed in ^{–1}K^{–1}) and error in k (Wm^{–1}K^{–1}) (see

^{–1}K^{–1}) and error in k (Wm^{–1}K^{–1}).

The script architecture is summarized in

Flowchart summarizing the script architecture. The chart should be read following the blue ribbon.

Examples of running the software are displayed in

Users may choose to download

Tested in Matlab R2021a, likely to work in earlier versions also.

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The application

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The application is designed on MATLAB App Designer. MATLAB is a registered trademark of The MathWorks, Inc.

This work was supported by funds to R.A.S. from the Natural Sciences and Engineering Research Council of Canada [grant number 2018-05021] and the Canada Foundation for Innovation [project number 11860].

The authors have no competing interests to declare.