“Laboratory” Exercise
Carefully read the notes on DC and AC Impedance Measurements included with this notice.
You are provided with 2 Excel data files. The first contains two worksheets containing dc conductivity data as a function of temperature for 2 samples (A & B). The second contains 4 worksheets of ac impedance data as a function of measurement frequency for a sample at 4 different temperatures (100, 200, 3000 and 400oC).
A. dc Measurements
1. Plot the data for the two samples as an Arrhenius plot [ln(conductivity) vs 1/T]. Remember to use values of temperature in Kelvin. [3]
2. For sample A, calculate the activation energy, Ea, from the slope of the graph. You will need to multiply the slope by the Boltzmann constant (kB = 1.38 x 10-23) and divide by the charge on the electron (e=1.6 x10-19) to produce an answer in eV. [3]
3. Comment on the form of the plot for sample B. Try to estimate the activation energy/energies ? [4]
B. ac Impedance Measurements
1. For each of the four data sets, produce a Cole-Cole plot (i.e. -Z’’ vs Z’ ). [3]
2. From the plots estimate the dc resistance at each of the 4 temperatures and construct an Arrhenius plot to estimate an activation energy for dc conduction in eV. [3]
3. For each of the 4 data sets, plot spectra of -Z’’ vs log(frequency) and M’’ vs log(frequency). [3]
4. From the Z’’ spectra estimate the relaxation frequency for each temperature and plot the data as an Arrhenius plot of ln(relaxation frequency) vs 1/T; estimate an activation energy. [3]
5. Comment on why the form of the M’’ spectra is different from that of the Z’’ spectra. [3]
If you use the Trendline function in Excel to calculate the slopes of your Arrhenius plots, be sure that the result that Excel provides has a sufficient number of decimal places to give an accurate answer. Current versions of Excel should be OK, but in older versions you may need to adjust the default number of decimal places that it uses to report the result.
Provide your answers in a Word or pdf file. Fully illustrate your answer by pasting all the plots into the file and submit it via the submission box in the “Submit My Work” section in Minerva by 23.59 on 30 April 2025.