Deviations from Matthiessen’s rule in high purity copper

Acta physica Academiae Scientiarum Hungaricae - Iron impurities in the ppm range caused by the rolling process of highest purity foils are used to study the deviation from Matthiessen’s rule....     

Deviations from Matthiessen's rule in aluminum alloys

Deviations from Matthiessen's rule were measured for dilute alloys of aluminum with gold. The concentration of the alloyed element varied from 0.05 to 0.25 at.%. The results were interpreted on two-band model as due to different anisotropies of the relaxation times associated with different scattering processes.     

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.     

Deviations from Matthiessen's rule at low temperatures: An experimental comparison between various metallic alloy systems

The low temperature electrical resistivity data on Al, Cu, Au, Ag, Pt, Mg, Sn, Zn, In and Ga are reviewed with particular emphasis on the variation of the phonon contribution with the magnitude of the impurity resistivity. A comparison is made within the various alloys having the same base metals, and also between the different solvents, by developing a phenomenological fitting formula for the deviations from Matthiessen's rule. The derived phenomenological parameters show a strong similarity for all metals. The limits imposed on this type of comparison by the uncertainty of data obtained on different samples and in different laboratories are discussed.

An updating of the references given in an earlier review in this journal by Bass (1972) is also included.     

Deviations from hydrodynamics on the nanoscale

This study has examined the decay of an instantaneously imposed heat pulse on an equilibrium model of a dense fluid. The spatial extent of the initial pulse is quite small, of the order of 100 cubic nanometres; the amount of energy added to the system is only 5% of the total system kinetic energy. This small pulse decays quite rapidly, within several picoseconds, but the decay proceeds more slowly than predicted by the hydrodynamic equations. During the first picosecond of the decay, the kinetic energy is not equipartitioned, and a rapid process of energy transfer from kinetic energy to potential energy via interparticle interactions takes place. A new transport theory is developed that includes the ‘pre-hydrodynamic’ stage of evolution of non-equilibrium systems. Formally exact expressions for the local density, velocity, and kinetic energy (temperature) fields are developed in terms of Green's functions that depend on dynamic quantities, such as the mean-square displacement, averaged over the ensemble of initial states. No partial differential equations are involved.     

Deviations from Matthiessen's Rule

We present a comprehensive review of the subject of Deviations from Matthiessens's Rule, including a historical survey and detailed critical evaluations of both theory and experimental data. We discuss deviations occurring: in substitutional alloys (both magnetic and non-magnetic); after quenching; after radiation damage; after plastic deformation; and in thin samples. The only topic omitted is that of anomalous negative deviations occurring at low temperatures (e.g. the Kondo effect).     

Deviations from the Stefan Boltzmann law at low temperatures

The total radiation energy in a cavity is studied in the limit of small volume and temperature. The validity of refined high-temperature expansions is examined. For the cube-shaped cavity with edge lengthL complete results covering the range 0≦LT<∞ are presented.     

Deviations from LTE in a stellar atmosphere

Deviations from LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient b is smaller than unity when the radiative cross section α_ν grows with frequency ν faster than ν²; b exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of α_ν. Overpopulation (b > 1) always implies that the kinetic temperature in the statistical equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.     

Deviations from the critical state model observed in niobium

The values of the critical current density of niobium slabs, measured with the help of trapezoidal ac magnetic fields are not in agreement with the critical state model. Extensions of this model are suggested to explain the observed deviation.     

Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form

We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott(HPS) form.These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector.The perturbing matrix is assumed to be purely imaginary(thus maximally T-violating) and to have a strength in energy scale no greater(but perhaps smaller) than the muon mass.As we shall show,it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O((mμ/mτ)2) ≈ 3.5 × 10?3 from their HPS values.Assuming that(mμ/mτ)2 can be neglected,we derive two simple constraints on the four parameters θ12,θ23,θ31,and δ of the mapping matrix.These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix.We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β;any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.     

Deviations from Fick's law in Lorentz gases

We have calculated the self-dynamic structure factorF(k,t) for tagged particle motion in hopping Lorentz gases. We find evidence that, even at long times, the probability distribution function for the displacement of the particles is highly non-Gaussian. At very small values of the wave vector this manifests itself as the divergence of the Burnett coefficient (the fourth moment of the distribution never approaching a value characteristic of a Gaussian). At somewhat larger wave vectors we find thatF(k,t) decays algebraically, rather than exponentially as one would expect for a Gaussian. The precise form of this power-law decay depends on the nature of the scatterers making up the Lorentz gas. We find different power-law exponents for scatterers which exclude certain sites and scatterers which do not.     

Deviations from exponential decay in quantum mechanics

The usual quantum mechanical explanation of exponential decay is not exact. The approximations made lead to an average lifetime which can also be obtained directly using Fermi's Golden Rule. The question whether or not quantum mechanical decay is always exponential was recently raised again in connection with the possible decay of the proton. In this paper we derive a new criterion for the length of the non-exponential decay era. A formalism for general quantum systems is used to derive an exact expression for the survival probability in terms of a spectral density function. This expression is used for numerical studies. We find that in general, for short times, the decay is not exponential. In some cases a quadratic law is followed instead.     

Deviations from two-dimensionality in classical adsorbed films

The statistical mechanical theory of adsorption is presented as an expansion about the two-dimensional approximation. Two corrections to the latter are additive in the perturbation limit. One contribution, arising from the lateral variation of the substrate potential, has been previously evaluated. The second correction term is due to the particles' mutual interaction when their separation vector is not parallel to the surface. The latter is expressed in terms of the radial distribution function. Its contribution to the deviation from two-dimensionality is shown to be comparable to the first term for the case of a Lennard-Jones model.     

Deviations from two-dimensionality in submonolayer adsorbed films

The effects of deviations from co-planarity on the thermodynamic properties of submonolayer adsorbed films are discussed by using van der Waals type theory. According to the proposed approach, the free energy of the reference hard core fluid is approximated by the free energy of a suitably defined two-dimensional mixture of hard disks.