Anisotropy of the Residual Resistivity of Tin with Sb, In, Zn, and Cd Impurities, and the Ideal Resistivities and Deviations from Matthiessen's Rule at 77 and 273°K

We have calculated the electrical resistivity of several dilute aluminum based alloys for which experimental data exist on the deviation from Matthiessen's rule(DMR). We take account of the anisotropy in the ideal (pure metal) scattering and its modification on adding impurities. This is a major source of DMR. In addition, we compute the effect of inelastic impurity scattering, interference between impurity and ideal scattering, Debye–Waller factors, and also the effect of mass changes on the alloy resistivity. While some of these mechanisms for DMR can be of importance under specific conditions, they should be included only after the major effect of anisotropy in the ideal scattering has been properly treated.

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Determination of the Ideal Resistivity and of the Deviation from Matthiessen's Rule in Silver

Canadian Journal of Physics ◽

10.1139/p73-213 ◽

1973 ◽

Vol 51 (15) ◽

pp. 1602-1618 ◽

Cited By ~ 26

Author(s):

J. F. Kos

Keyword(s):

Electrical Resistivity ◽

Temperature Dependence ◽

Additional Term ◽

Precise Determination ◽

One Step ◽

Matthiessen's Rule ◽

Matthiessen’S Rule ◽

Umklapp Scattering ◽

The Ideal

Measurements of the temperature dependence of the electrical resistivity of strained and annealed samples of very pure Ag between 1.4 and 295 °K have permitted the unambiguous and precise determination of the ideal resistivity ρi and of the deviation from Matthiessen's rule ρM. Between 12 and 23 °K, ρi varies as[Formula: see text]and has been attributed to normal and umklapp scattering. Below 10 °K an additional term with a T3.86 ± 0.08 behavior appears and is attributed to one-step umklapp scattering. For samples with [Formula: see text], [Formula: see text] over the entire temperature range. Below 10 °K the variation of ρM with temperature and with defect concentration is described in terms of the theory of phonon-assisted defect scattering proposed by Klemens.

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Matthiessen's rule

AccessScience ◽

10.1036/1097-8542.410800 ◽

2015 ◽

Keyword(s):

Matthiessen's Rule ◽

Matthiessen’S Rule

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Phonon residual resistance of pure crystals

International Journal of Modern Physics B ◽

10.1142/s0217979215502069 ◽

2015 ◽

Vol 29 (29) ◽

pp. 1550206

Author(s):

A. I. Agafonov

Keyword(s):

Electric Field ◽

Constant Electric Field ◽

Finite Thickness ◽

Mean Free Path ◽

Residual Resistivity ◽

Boltzmann Transport ◽

Residual Resistance ◽

Temperature Resistance ◽

Electron Mean Free Path ◽

The Ideal

In this paper, using the Boltzmann transport equation, we study the zero temperature resistance of perfect metallic crystals of a finite thickness d along which a weak constant electric field E is applied. This resistance, hereinafter referred to as the phonon residual resistance, is caused by the inelastic scattering of electrons heated by the electric field, with emission of long-wave acoustic phonons and is proportional to [Formula: see text]. Consideration is carried out for Cu, Ag and Au perfect crystals with the thickness of about 1 cm, in the fields of the order of 1 mV/cm. Following the Matthiessen rule, the resistance of the pure crystals, the thicknesses of which are much larger than the electron mean free path is represented as the sum of both the impurity and phonon residual resistances. The condition on the thickness and field is found at which the low-temperature resistance of pure crystals does not depend on their purity and is determined by the phonon residual resistivity of the ideal crystals. The calculations are performed for Cu with a purity of at least 99.9999%.

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Validity of Matthiessen's Rule for Cold-worked Wires

Australian Journal of Physics ◽

10.1071/ph530116 ◽

1953 ◽

Vol 6 (1) ◽

pp. 116 ◽

Cited By ~ 13

Author(s):

W Boas ◽

JF Nicholas

Keyword(s):

Electrical Resistivity ◽

Characteristic Temperature ◽

Wire Drawing ◽

Metals And Alloys ◽

Nickel Copper ◽

Aluminium Bronze ◽

Cold Worked ◽

Matthiessen's Rule ◽

Matthiessen’S Rule

Matthiessen's rule has been tested by, determining the slopes of the electrical resistivity-temperature curves for wires of eight common metals and alloys in various states of deformation by wire-drawing. The results show that the slope is independent of deformation, i.e. the rule is true, to within 0�5 per cent. for nickel, copper (two purities), iron, and 80/20 brass, and to within 1 per cent. for aluminium. However, for 75/25 brass and an aluminium bronze, deformations corresponding to logarithmic strains of 2�3 decrease the slopes by 1 and 3 per cent. respectively. As an explanation of this behaviour, it is suggested that deformation causes an increase in the characteristic temperature.

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