The electrical resistivity of potassium below 4.2 K

Abstract

The electrical resistivity of potassium has been measured between 1.2 and 4.2 K for samples with various amounts of impurity, and also for samples which have been deformed and then progressively annealed. After allowing for departures for Matthiessen’s rule (M.r.) an estimate of the ‘ideal’ resistivity can be made: the logarithmic temperature derivative rises from 5.6 at 4.2 K and passes through a maximum of 9.0 at 2.1 K. The Bloch T 5 region does not extend above 1.8 K and does not contribute more than ρ = 20 x 10 -15 T 5 Ω cm to the total ideal resistivity ; at 4 K this T 5 contribution is only about 15% of the total ideal resistivity. The rest of the ideal resistivity between 1.8 and 4.2 K shows an exponential form, as expected from the freezing out of umklapp processes with a characteristic temperature of about 23 K. The measurements agree with recent calculations of Rice & Sham (1970) within about a factor of 2 over a range of 10 5 in resistivity, but they do not allow a clear choice to be made between the different forms of pseudopotential that were discussed. The deviations from M.r. for point defects in potassium appear to be accurately proportional to the ideal resistivity between 2 and 4.2 K, i.e. over a range of 300 in ideal resistivity. The magnitude of the deviations is consistent with galvanomagnetic data analysed according to the two-band model, and it implies that a small group of electrons, about 6% of the total, differs in relaxation time from the rest by a factor of about 3. However, the form of the deviations from M.r. does not seem to be compatible with the two-band model. Dislocations in potassium give a small but characteristic extra deviation from M.r. which may be correlated with umklapp scattering. No evidence was found for the momentum-non-conserving processes which have recently been suggested by Campbell, Caplin & Rizzuto (1971) to be very important in aluminium.