Deviation From Matthiessen's Rule Research Articles

Disorder-enhanced effective masses and deviations from Matthiessen's rule in PdCoO2 thin films

The observation of hydrodynamic transport in the metallic delafossite PdCoO$_2$ has increased interest in this family of highly conductive oxides, but experimental studies so far have mostly been confined to bulk crystals. In this work, the development of high-quality thin films of PdCoO$_2$ has enabled a thorough study of the conductivity as a function of film thickness using both dc transport and time-domain THz spectroscopy. With increasing film thickness from 12 nm to 102 nm, the residual resistivity decreases and we observe a large deviation from Matthiessen's rule (DMR) in the temperature dependence of the resistivity. We find that the complex THz conductivity is well fit by a single Drude term. We fit the data to extract the spectral weight and scattering rate simultaneously. The temperature dependence of the Drude scattering rate is found to be nearly independent of the residual resistivity and cannot be the primary mechanism for the observed DMR. Rather, we observe large changes in the spectral weight as a function of disorder, changing by a factor of 1.5 from the most disordered to least disordered films. We believe this corresponds to a mass enhancement of $\geq 2$ times the value of the bulk effective mass which increases with residual disorder. This suggests that the mechanism behind the DMR observed in dc resistivity is primarily driven by changes in the electron mass. We discuss the possible origins of this behavior including the possibility of disorder-enhanced electron-phonon scattering, which can be systematically tuned by film thickness.

等温時効温度と銅添加に伴うＡｌ‐１％Ｍｇ２Ｓｉ合金でのマティーセン経験式の変化

Writing resistivity ratio ρ300/ρ77 as R and according to a linear relation between resistivity at 77 K, ρ77, and 1/(R−1) deduced from the Matthiessen's rule, the measured values of ρD77 using density method size factor have been plotted versus 1/(R−1). This diagram called as Matthiessen plot (MP) was very useful to detect errors in ρ measurements. Straight lines obtained by regression of the MP as ρD77=α/(R−1)+β were called as Matthiessen empirical relations (MER) . Other than the gradient α of the MER, a gradient α*=ρ77(R−1) of straight lines binding each plots and origin of the MP was induced. Using ρD77 and R data formerly measured in Al–1.0%Mg2Si– (0~0.7%) Cu alloys, variations in the two gradients with isothermal aging temperature and Cu addition were investigated. At all aging temperatures, the α was lower than the ideal value, 25.13 nΩ m for Al base solid solution without deviation from Matthiessen's Rule (DMR). The α decreased with lowering aging temperature from 473 K to room temperature and amount of Cu. A good linear relation was observed between α and β changed by aging temperature and Cu addition. The α* calculated from concentration of solutes in solution- treated and quenched state was decreased with the addition of Cu having negative DMR. The α* was increased by agings at and above 448 K, whereas decreased by room temperature aging. The α* increase by high temperature aging can be explained by overestimation of size factor due to high- resistivity precipitates decreasing the effective cross section for electric current. Assuming a large negative DMR of clusters or G.P. zones, the decrease in α* with room temperature aging can be understood.

The Deviation from Matthiessen's Rule at 4.2 K in Dilute Copper-Gold-Germanium Alloys

The deviation from Matthiessen's rule (DMR) of dilute copper-gold-germanium alloys was measured at 4.2, 77 and 273 K. The low-field Hall coefficient of binary Cu-Au and Cu-Ge alloys was also measured at 4.2 K to determine anisotropy parameters for the explanation of the DMR in the ternary alloys. In order to control the shape factor of the ternary samples the germanium content was brought into binary Cu-Au samples by vapour deposition and diffusion annealing. The limitation of the usual two-group model for the investigated alloys is shown and a more accurate three-group model is presented. Especially the DMR at 4.2 K of the ternary samples in the range 20-30 nΩ cm (as well as the DMR at 273 K) can be substantiated by the low-field Hall coefficient and by the anisotropy of scattering rates obtained from the de Haas-van Alphen effect for the binary alloys.

Theelectrical dislocation resistivity and the deviation fromMatthiessen's rule of deformed high-purity aluminium

The experimental dislocation resistivity of rolled samples of99.9999% pure aluminium was investigated in the temperature rangefrom 4.2 K to 300 K. The minimum in the deviation from Matthiessen'srule (DMR) below 40 K and the step height of the DMR from 4.2 K to300 K can be explained by anisotropic scattering in terms of athree-group or a two-group model. The physical relevance of thefitted anisotropy parameters for electron-dislocation (Ad)and electron-phonon scattering (Ap) can be better seen inthe two-group model. The variation of Ad and Apwith dislocation density is similar to that for the noble metals,whereby Ap at low temperatures is much more anisotropic foraluminium. The change of Ap with increasing dislocationdensity for T⩽50 K can be understood if anisotropic small-anglescattering at local phonon modes originating from the dislocationsis taken into account. This anisotropy could arise, as the Burgersvectors of the dislocations are oriented mainly in [011] directions.

Ａｌ‐ＴｉおよびＡｌ‐Ｚｒ合金固溶体の比抵抗の溶質濃度および測定温度依存性

Trace amounts of titanium and zirconium are often added to commercial aluminium alloys. Using the high purity Al–Ti and Al–Zr dilute binary alloys with 5 to 6 different compositions, the contributions per unit concentration of the solutes to resistivity, Δρ, are determined at 77 K and 300 K. The Δρ of solute Ti at 77 K and 300 K, ΔρTi77 and ΔρTi300, are 31.5 and 31.8 nΩm·mass%−1 respectively, showing small deviation from Matthiessen's rule (DMR). The solute Zr gives ΔρZr77 and ΔρZr300 as 19.7 and 18.2 nΩ·mass%−1 respectively, showing a negative DMR. The difference between ΔρTi and ΔρZr expressed per at% is less than 15% of the absolute values, which is roughly consistent with the Linde's law. Temperature of heat treatments (TH) vs resistivity diagrams (TH–ρ diagrams), calculated from present Δρ values and the temperature dependence of equilibrium solid solubilities, show the effect of Ti on the resistivity increase is extremely larger than that of Zr especially when heat treated at higher temperatures.

Electron - phonon scattering in noble metals containing dislocations

In the limit of small deformation (true strain ) it is possible to derive from curves of the deviation from Matthiessen's rule (DMR) for samples containing dislocations the anisotropy parameter of electron - phonon scattering as a function of temperature. In this case the fitted -curves for copper and silver samples based on the two-group model (TGM) are in excellent agreement with the theoretical calculation of Hasegawa and Kasuya. In contrast -curves derived from low-field Hall effect data within the (uncorrected) TGM are not directly suitable for DMR calculations due to the different averaging of relaxation times for the conductivity and the Hall effect. For understanding DMR curves with the two-group model is insufficient. Up to about 0.2 of normalized DMR seems to result from a DMR between small- and large-angle scattering.

Electrical dislocation resistivity and anisotropic scattering in high‐purity copper single crystals

AbstractThe experimental dislocation resistivity (or the deviation from Matthiessen's rule (DMR)) at 4.2 and 77 K of several single slip and multislip crystals was investigated. Additionally low‐field Hall effect measurements at 4.2K using a dc SQUID picovoltmeter were performed in order to study the anisotropy of electron–dislocation and electron‐impurity scattering directly. It is shown that oxygen annealing applied to increase the “electrical purity” of the crystals does not change the character of the scattering behaviour. The anisotropy parameters Adis for electron–dislocation scattering derived within the two‐group model are in good agreement with recent results for high‐purity polycrystals.

高濃度Ｍｇ‐Ａｌ二元固溶体の比抵抗の組成依存性と温度依存性

Electrical resistivity of Mg-Al binary alloys containing up to 14.2%Al has been measured at 77K and 300K. Resistivity of alloys containing up to 9.69%Al, which give perfect solid solution after appropriate solution treatments, shows a good linear relation with a function g(X) = X (1-2.86X) of aluminium atomic fraction X deduced by an empirical correction of Nordheim's rule. The resistivity at 300K and 77K can be expressed as, 44<ρMg-Al300/nΩm=_??_1.966×103X(1-2.86X)+44.73_??_± 1.2<1755<ρMg-Al77/nΩm=_??_2.095×103X(1-2.86X)+5.46_??_± 1.0<142.From gradients Δρg(X) of these linear relations, ηMg = Δρ300/Δρ77 is determined to be 0.938 and the deviation from Matthiessen's rule (DMR) is negative in agreement with previous reports on alloys up to 2.8%Al. Relation between R = ρ300/ρ77 and ρ77 corrected with the DMR is obtained as5<ρMg-Al77/nΩm=_??_39.53/(R-0.938)+0.175_??_± 1.0<142for change in concentration of solute aluminium in Mg-Al solid solution.dρ/dT measured between 280K and 308K decreases with aluminum concentration, which also coincides with the negative DMR of solute aluminum. The R of two (α + β) phase specimens shows a tendency to increase with volume fraction of β (Mg17Al12) phase.

３．８％以下のＭｇを含むＡｌ‐Ｍｇ固溶体のマチーセン則経験式

The relations between the ratio of resistance measured at two different temperatures and the resistivity are induced for general solid solutions showing deviation from Matthiessen's Rule (DMR) through dependences of resistivity on concentration and on temperature. The contribution to resistivity per unit concentration (Δρ) of Mg has been experimentally determined at 77 and 300K. The Δρ is larger at higher temperature and the DMR is slightly positive. After a correction about DMR, the empirical relation between the resistance ratio (R=ρ(300)/ρ(77)) and the resistivity at 77K (ρ(77)) has been obtained as2.3<ρ(77)/nΩm=[25.15/(R-1.054)]-0.028<23in the solution treated state. Comparing the Matthiessen empirical relation of cold rolled specimens to that of annealed specimens, the DMR of dislocation in aluminum is estimated to be negative.

Formation and Decomposition of Mn&amp;ndash;N Dipoles during Quench-Ageing in Fe&amp;ndash;Mn&amp;ndash;N Alloys

The formation and decomposition of Mn-N dipoles in extra low carbon steels have been investigated during ageing at several temperatures between 523 and 623 K by means of measurements of the electrical resistivity and its deviation from Matthiessen's rule (DMR). The amount of nitrogen atoms which contributed to the precipitation of nitride during ageing by the decomposition of quenched-in Mn-N dipoles, x, and the amount of single nitrogen atoms in solid solution which contributed to the precipitation, y, were calculated from the changes in the electrical resistivity and DMR during ageing

Deviation from Matthiessen's rule at high temperatures: Theoretical interpretation

Theoretical interpretation is given for the deviation from Matthiessen's rule (DMR) at high temperatures on dilute alloy systems Au in Cu, Cu in Au, and Ni in Cu, and Cu, Ag, and Ge in Al, measured with the use of the new experimental techniques developed by Fujita and others. The measured deviation from this rule, $\ensuremath{\Delta}(c, T)$, can be fitted to curves of $Y+AT$ ($Y\ensuremath{\approx}0$), where $T$ is the absolute temperature, and the numerical constant $A(Y)$ can be calculated using a standard lowest-order (higher-order) variational scheme. $Y$ is always positive and gives a measure of the anisotropy of the scattering at high temperatures. For most of the Al-based and noble-metal-based dilute alloys, $Y$ is small and the anisotropy scattering is unimportant. The proportionality factor $A$ has been evaluated, within the standard variational formalism, using an atomistic model calculation for the electron-phonon spectral function. It is shown that the leading contribution to the high-temperature DMR is due to the change in the phonon spectral function $F(\ensuremath{\omega})$ for Cu in Al, Ge in Al, Cu in Au, and Au in Cu alloys, while it comes from the change in the electron-phonon coupling function ${\ensuremath{\alpha}}_{\mathrm{tr}}^{2}(\ensuremath{\omega})$ (electron-mass-enhancement parameter ${\ensuremath{\lambda}}_{\mathrm{tr}}$) for the Ag in Al alloy.

Deviations from Matthiessen's Rule on the Surface Scattering in Aluminum

The electrical resistivity of aluminum strips has been measured for various thickness (0.02-1.48 mm) and over a temperature (1.5-60 K). The results show the deviation from Matthiessen's rule (DMR) Δ s ( T ) on the surface scattering. The surface reflection parameter p is determined to be nearly zero from the temperature at which the maximum of Δ s ( T ) appears. The DMR Δ s ( T ) shows different profiles from DMR on the impurity scattering. The comparison of the present data with Husstad-Lothe theory shows that the effect of small angle electron-phonon scattering is small on the surface scattering. The present experiments can be explained by a term of the surface resistivity ρ s ( T ) (=ρ s (0)+ Δ s ( T )) deduced from Fuchs-Sondheimer theory. It is thus concluded that DMR Δ s ( T ) mainly arises from the spatial variation of the electron distribution function.

Deviations from Matthiessen's Rule of the Electrical Resistivity Due to Dislocations in Gold

The electrical resistivity due to dislocations in gold has been measured in the temperature range between liquid helium temperature and 300 K. The deviation from Matthiessen's rule (DMR) of the dislocation resistivity is different from that of the impurity resistivity in the temperature dependence and the residual resistivity dependence. DMR of the dislocation resistivity cannot be explained by the mechanism due to an anisotropic electron distribution function. Other two mechanisms due to phonon localized modes associated with dislocations and to electron levels localized near dislocations, are considered. In conclusion DMR of the dislocation resistivity is explained fairly well by a model of electron localized levels associated with dislocations.

Deviation from matthiessen's rule of dilute Al-alloys computed by 4-OPW approximation

Deviation from Matthiessen's rule (DMR) for five Al based alloys (AlAg, AlMg, AlZn, AlGa and AlGe) are calculated at 20, 50, and at 100 K by 4-OPW approximation. The published data of electron-phonon relaxation time and those of electron-impurity relaxation time are used. The Caplin-Rizzuto plots of calculated DMR agree with experimental data at lower temperature. At higher temperature it is suggested that interference effect of the two scattering agents must be taken into account to get better agreement.

Deviation from Matthiessen's rule at high temperatures: Ag in Al

The deviation from Matthiessen's rule (DMR) has been investigated for Ag in Al for concentrations ranging between 0.002 and 0.2 at.%, and at temperatures close to the melting point. Results show that the impurity resistivity decreases gradually with increasing temperature and impurity concentration, reaching to 80 approximately 90% of the values at 0K. The author's results, in conjunction with previous data at lower temperatures, establish the general feature of DMR in the entire temperature range.

High-temperature deviation from Matthiessen's rule in InCd alloys

High-precision resistivity data are obtained for InCd alloys in the range up to 3at% Cd and for temperatures between 50 and 300K. The deviation from Matthiessen's rule (DMR) shows a broad maximum around 150K. Above about 200K the DMR is linear with respect to temperature. A correlation between DMR and the electron-phonon interaction is suggested in this temperature range.

The resistivity of Cu and CuMn and CuCr alloys: Kondo effect and deviations from Matthiessen's rule

We have measured the resistivity (1–300 K) of Cu and CuMn and CuCr alloys (10–200 ppm). The data on pure Cu were compared with the Bloch-Gruneisen formula. The impurity contribution (ϱalloy − ϱCu) contains a Kondo term and a deviation from Matthiessen's rule (DMR). The Kondo contribution was analyzed in terms of a modified Hamann-Fischer expression, yielding a good fit to our data with parameters in agreement with expectation. The DMR results in CuCr and CuMn are similar to the DMR reported in nonmagnetic Cu alloys. A phenomenological expression was derived which accounts for the observed concentration and temperature dependences.

Charge Transport in Dilute Aluminum Alloys

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.