On the anharmonic, multi-phonon, Debye-Waller contributions to the phonon-limited resistivity of metals : applications to Na and K

The anharmonic, multi-phonon (MP), and Oebye-Waller factor (OW) contributions to the phonon limited resistivity (;0) of metals derived by Shukla and Muller (1979) by the doubletime temperature dependent Green function method have been numerically evaluated for Na and K in the high temperature limit. The anharmonic contributions arise from the cubic and quartic shift of phonons (CS, QS), and phonon width (W) and the interference term (1). The QS, MP and OW contributions to I' are also derived by the matrix element method and the results are in agreement with those of Shukla and Muller (1979). In the high temperature limit, the contributions to;O from each of the above mentioned terms are of the type BT2 For numerical calculations suitable expressions are derived for the anharmonic contributions to ~ in terms of the third and fourth rank tensors obtained by the Ewald procedure. The numerical calculation of the contributions to;O from the OW, MP term and the QS have been done exactly and from the CS, Wand I terms only approximately in the partial and total Einstein approximations (PEA, TEA), using a first principle approach (Shukla and Taylor (1976)). The results obtained indicate that there is a strong pairwise cancellation between the: OW and MP terms, the QS and CS and the Wand I terms. The sum total of these contributions to;O for Na and K amounts to 4 to 11% and 2 to 7%, respectively, in the PEA while in the TEA they amount to 3 to 7% and 1 to 4%, respectively, in the temperature range.

The effects of moisture, cation concentration, temperature, density and composition of soils on their electrical resistivity

The effects. of moisture, cation concentration, dens ity , temper~ t ure and grai n si ze on the electrical resistivity of so il s are examined using laboratory prepared soils. An i nexpen si ve method for preparing soils of different compositions was developed by mixing various size fractions i n the laboratory. Moisture and cation c oncentration are related to soil resistivity by powe r functions, whereas soil resistiv ity and temperature, density, Yo gravel, sand , sil t, and clay are related by exponential functions . A total of 1066 cases (8528 data) from all the experiments were used in a step-wise multiple linear r egression to determine the effect of each variable on soil resistivity. Six variables out of the eight variables studied account for 92.57/. of the total variance in so il resistivity with a correlation coefficient of 0.96. The other two variables (silt and gravel) did not increase the · variance. Moisture content was found to be - the most important Yo clay. variable- affecting s oil res istivi ty followed by These two variables account for 90.81Yo of the total variance in soil resistivity with a correlation ~oefficient ·.of 0 . 95. Based on these results an equation to ' ~~ed{ ct soil r esist ivi ty using moisture and Yo clay is developed . To t est the predicted equation, resistivity measurements were made on natural soils both in s i tu a nd i n the laboratory. The data show that field and laboratory measurements are comparable. The predicted regression line c losely coinciqes with resistivity data from area A and area B soils ~clayey and silty~clayey sands). Resistivity data and the predicted regression line in the case of c layey soils (clays> 40%) do not coincide, especially a t l ess than 15% moisture. The regression equation overestimates the resistivity of so i l s from area C and underestimates for area D soils. Laboratory prepared high clay soils give similar trends. The deviations are probably caused by heterogeneous distribution of mo i sture and difference in the type o f cl ays present in these soils.