Deviations of Matthiessen's rule in some PdAu alloys

The low temperature electrical resistivity of Pd_1?cAu_c alloys (c = 0.1, 0.22, 0.38, 0.69, 0.82 and 1.1 at.%) have been studied in detail between 1.5 and 300 K. Deviations from Matthiessen's rule (DMR) have been analysed on the basis of a two-band model, and the agreement is found to be reasonably good. The parameter λ was found to decrease monotonically with temperature, and no anomalous maximum was observed as with earlier studies of $\text{Pd}$Ti. The variation of β shows a weak temperature dependence. The limitations of the model are also discussed.     

Breakdown of Matthiessen's rule in high purity aluminum based alloys

Deviations from Matthiessen's rule were measured for dilute alloys of Al with Mg. The concentration of the alloyed elements varied from 0.03 to 1.0 at.%. The results were compared with other experimental results and discussed with respect to the relevant theoretical models.     

On the cyclotron resonance width of an electron impurity system in two dimensions

Using the proper connected diagram expansion which incorporates the quasi-particle effect naturally we calculated the cyclotron resonance width γ in the extreme quantum limit.(a) γ ∝n

$\text{1}\text{2}$

_s B

$\text{1}\text{2}$

for a short range interaction, and (b) γ = π

$\text{1}\text{2}$

ze² κ^-1 <?crossed h.c.h;^-1 n

$\text{1}\text{2}$

_s for Coulomb interaction, are obtained. The field (B) and concentration (n_s)-dependence is in satisfactory agreement with experimental data. The variation γ = (γ²₁ + γ²₂ + …)

$\text{1}\text{2}$

of Matthiessen's rule γ = γ₁ + γ₂ + …, holds when there exist scattering centers of different kinds in the system.     

Electrical deviations from Matthiessen's rule in A Ag:Au alloy

Electrical resistivity of Ag:0.29 at % Au alloy has been measured and explained theoretically with the aim of understanding the deviations from Matthiessen's rule. The anisotropy in the electron-phonon interaction, the recoil of the impurity, mass-changes, nearest neighbour radial and angular force-constant-changes and Debye-Waller factors have been taken into consideration.     

Theory of cyclotron resonance lineshape for an electron-impurity system in two dimensions

Using the proper connected diagram expansion which incorporates the quasi-particle effect in a natural manner, we calculated the cyclotron resonance width Γ and frequency shift Δ in the extreme quantum limit, (a) Δ = 0 for any form of interaction potential, (b) Γ ∝ n_I^{$\text{1}\text{2}$}B^{$\text{1}\text{2}$} for a short range interaction, and (c) $\text{Γ = π}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{ze}{}^2\text{k}{}^{\mathrm{?1}}\text{n}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{I}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ for the unscreened Coulomb interaction, are obtained in the weak coupling approximation. The result (a) and the field (B)- and concentration (n_I)-dependence in case (b) are in satisfactory agreement with experimental data on the Si space-charge layers at the surface carrier densities higher than 1 × 10¹²cm^-2 and at liquid helium temperatures, where the main source of relaxation is thought to arise from a short-range interaction.     

Critical scattering and low temperature deviations from Matthiessen's rule in the resistivity of antiferromagnetic ErZn12

Critical effects in the spin disorder resistivity of the metallic antiferromagnet ErZn₁₂ have been observed. The ordering temperature of 2.77 ± 0.01 K is low enough for there to be no phonon contribution to the resistivity present. Below this temperature, the temperature derivative of the resistivity is described best by a divergence of a logarithmic form; above it, a divergence either of the type ($\text{T-T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ or of logarithmic form is consistent within experimental error. Possible deviations from Matthiessen's Rule have been observed above the ordering temperature; they are proportional to the estimated phonon resistivity at low temperature, and vary as T³ at higher temperature.     

Nonlinear superposition rule for Abel's equation

A nonlinear superposition rule for Abel's cubic differential equation involving four particular solutions can be replaced by a superposition rule involving only two particular solutions. Chiellini's restrictions on the particular solutions are found to be satisfied.     

Turbiner’s conjecture in three dimensions

We prove a modified version of Turbiner’s conjecture in three dimensions and we give a counter-example to the original conjecture. The Lie algebraic Schrödinger operators corresponding to flat metrics of a certain restricted type are shown to separate partially in Cartesian or cylindrical or spherical coordinates.     

On the physical basis for Urbach's rule

The low-energy tail of the E 6 a exciton in GeS obeys Urbach's rule, with Urbach parameters σ₀ = 1.45 ± 0.05, and $\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{= 8.7 ± 0.6 meV}$. The energy ?ω_p corresponds to a previously measured rigid-layer vibrational mode which has no associated electric field. This finding is inconsistent with Dow and Redfield's unified theory of Urbach and exponential absorption edges. Our results are consistent with Sumi and Toyazawa's theory of Urbach edges, and with Fivaz and Mooser's model for electron-phonon interactions in layered compounds.     

Theory of cyclotron resonance width for electrons inelastically scattered by phonons

The cyclotron resonance width for a semiconductor under extreme high fields is calculated with the assumptions that electrons are scattered by acoustic phonons inelastically. The numerical results are in very good agreement with the recent experiments on Ge by Miura et al. (T ～ 300 K, B ～ 97 tesla). The energy-dependent widths arising from the relaxation processes with absorption and emission of a phonon show quite distinctive behaviors at low electron energies. At extreme low temperatures when few phonons are present, the width arising from the zero-point motion of the lattice is finite but very small. The charged-impurity scattering with the density as low as 10¹² cm^?3 numerically dominate the width due to the electron-phonon interaction below 10 K. The present theory supplements the previous work by Suzuki et al. where the elastic-scattering and high-temperature approximation were used.     

Canonical quantization of polyakov's string in arbitrary dimensions

Last year Polyakov discovered the important role the trace anomaly plays in the relativistic string theory. This result means that one has to add counter terms to the string lagrangian

$\text{L}\text{=}\text{L}{}_{\mathrm{<mtext>string</mtext>}}\text{+C}\text{L}{}_1\text{,}$

, where $\text{L}$₁ contains a cosmological term and a term from the trace anomaly. In the conformal gauge we have

$\text{L}{}_1\text{=}\text{L}{}_{\mathrm{<mtext>Liouville</mtext>}}\text{.}$

. We give a conventional GGRT treatment of this modified lagrangian for the bosonic string. Under the assumption that the exact quantization of Liouville's equation does not yield any additional anomalies, we show that relativistic invariance requires the constant C to be $\text{C =}\text{26 ? D}\text{48π}$, in agreement with Polyakov's result. For D < 26 the string acquires longitudinal modes, and our calculations show explicitly how the longitudinal component of the string receives the degrees of freedom from the Liouville variable. Under the boundary conditions yielding the lowest value of the classical Liouville hamiltonian, the mass spectrum starts with a tachyon $\text{m}{}^2\text{= ?}\text{1}\text{α′}$, independent of D. The lowest-lying longitudinal excitation is $\text{m}{}^2\text{=}\text{1}\text{α′}$. These results are semiclassical. It is shown that an exact quantization of Liouville's equation could remove the tachyon state when D < 26.     

Hume-Rothery's 15% rule and the pseudo-alloy-atom model

The total binding energies of Na, K, Rb, Cs and their mutual binary alloys were calculated by the pseudo alloy atom model. From the calculated values of heat of solution, Hume-Rothery's so-called 15% rule on the atomic size factors of primary solid solutions was justified.     

The absorption edges of GeS and Urbach's rule

The low-energy absorption tail of the E∥a exciton in GeS obeys Urbach's rule over at least three orders of magnitude in absorption coefficient for 4.2 ? T ? 240 K. The E∥b polarization (for which no exciton is observed) does not obey Urbach's rule. The E∥a Urbach edge is caused by interactions between the excitons and a 8.7 meV rigid-layer vibrational mode. Our results are consistent with Sumi and Toyazawa's theory of the Urbach edge, and inconsistent with the models of Dow, Redfield and Skettrup. The absorption edge of GeS is confirmed as a direct edge.     

Electron-dislocation scattering and negative deviations from matthiessen's rule

It is shown that the negative deviations from Matthiessen's rule observed recently for the electrical resistivity of Al and of Ag can be explained quantitatively by including the effect of anisotropic electron-dislocation scattering.     

A computation of Adler's β sum rule

We try to check Adler's β sum rule for q² = μ². The integral of β can be divided into two parts: a first part which, if q² = μ², involves only an integral of the experimental πN cross section, and a second one which is a priori of order μ² compared to the first. This second term can be approximated by an explicit calculation of the $\text{N}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext><mtext>3</mtext><mtext>2</mtext>}}{}^1$ contribution in the framework of Adler's model for the $\text{ν}\text{N}\text{→ μ}\text{N}{}^1$ reactions. The sum rule is not too well balanced and different hypotheses are presented to explain the defect.     

On backflow in two and three dimensions

The interaction between the backflow patterns generated by two slowly-moving impurities in an arbitrary liquid is examined in both three- and two-dimensional systems. It is concluded that this interaction becomes more important as the dimensionality is reduced.     

Breakdown of Kohler's rule in Indium at low temperatures

Precise measurements of the transverse magnetoresistivity of pure samples of Indium between 3.4° and 7.8°K show that Kohler's rule is not strictly valid. Deviations from Kohler's rule occur even when the analysis is restricted to data obtained for a single sample in small magnetic fields.