Thermo-electricity at low temperatures. IX. The transition metals as solute and solvent

1962 ◽  
Vol 266 (1325) ◽  
pp. 161-184 ◽  
Keyword(s):  
Experimental Data ◽  
Transition Metals ◽  
Low Temperatures ◽  
Transition Element ◽  
Present Theory ◽  
Parent Metal ◽  
Transition Elements ◽  
Thermo Electric ◽  
Conduction Electrons ◽  
Spin Dependent Scattering

Transition metals (in particular Cr, Mn, Fe, Co and Ni) present as solutes give rise to highly anomalous thermo-electric powers and unusual resistive behaviour at very low temperatures. Following an outline of the theories which have been proposed to account for this behaviour, experimental data are presented on alloys of gold as parent metal with transition element solutes down to very low temperatures, and the results compared broadly with the conclusions of present theory. It is generally believed that the fundamental origin of the anomalous thermo-electric behaviour lies in the spin-dependent scattering of conduction electrons by the magnetic solute ions. Experimental data are also presented of the thermo-electric behaviour down to very low temperatures of alloys of the transition metals Pd and Pt with both transition elements and non-transition elements as solutes.

Thermo-electricity at low temperatures III. The absolute scale of thermo-electric power: a critical discussion of the present scale at low temperatures and preliminary measurements towards its redetermination

1955 ◽  
Vol 231 (1187) ◽  
pp. 534-544 ◽  
Keyword(s):  
Electric Power ◽  
Low Temperatures ◽  
Alkali Metals ◽  
Present Theory ◽  
Critical Discussion ◽  
Electric Force ◽  
Thermo Electric ◽  
Absolute Scale ◽  
The Absolute

In order to compare exactly the present theory of thermo-electric power in metals with the behaviour of the simple alkali metals, particularly sodium, at low temperatures, it is necessary to know the absolute thermo-electric, power of one single conductor. There has been only one such determination of an absolute scale of thermo-electric power, and this was derived 23 years ago as the outcome of measurements which had been made primarily for other purposes. As measurements of the thermo-electric force of the alkali metals at low temperatures have recently become available, it is appropriate now to review critically the experimental basis of that scale. In view of new experimental evidence on the behaviour of the thermo-electric power of superconductors just above the transition point which has appeared in the last few years, it appears that a redetermination of the scale is necessary, at least at low temperatures. In this paper the present absolute scale of thermo-electric force is critically discussed particularly in relation to preliminary measurements towards its redetermination.

The relaxation time of conduction electrons in the noble met

1963 ◽  
Vol 275 (1361) ◽  
pp. 209-217 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Relaxation Time ◽  
Boltzmann Equation ◽  
Fermi Surface ◽  
Low Temperatures ◽  
Lattice Vibrations ◽  
Thermo Electric ◽  
Multiply Connected ◽  
Conduction Electrons ◽  
Experimental Values

The Boltzmann equation for scattering by impurities and lattice vibrations is solved numerically for a metal having a multiply-connected Fermi surface. It is found that the relaxation time for scattering by lattice vibrations at high temperatures or by impurities is approximately constant over the Fermi surface. For scattering by lattice vibrations at low temperatures the relaxation time is highly anisotropic. These results are consistent with the experimental values of the electrical conductivity but cannot predict a positive thermo ­ electric power.

The theory of electronic conduction in polar semi-conductors

1953 ◽  
Vol 219 (1136) ◽  
pp. 53-74 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Boltzmann Equation ◽  
Low Temperatures ◽  
Electron Gas ◽  
Electronic Conduction ◽  
Scattering Process ◽  
Thermo Electric ◽  
Conduction Electrons ◽  
The Boltzmann Equation ◽  
Set Up

The Boltzmann equation is set up for the conduction electrons in a crystal in which the scattering is due to the polarization waves of the lattice, and it is pointed out that at low temperatures it is impossible to define a unique time of relaxation for the scattering process. The Boltzmann equation is solved by means of a variational method, and exact expressions for the electrical conductivity and the thermo-electric power are obtained in the form of ratios of infinite determinants. By approximating to the exact solutions, relatively simple expressions are derived which are used to discuss the dependence of the conduction phenomena upon the temperature and upon the degree of degeneracy of the electron gas.

scholarly journals The electrical conductivity of transition metals

1936 ◽  
Vol 153 (880) ◽  
pp. 699-717 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Transition Metals ◽  
Temperature Coefficient ◽  
Noble Metals ◽  
Formal Theory ◽  
Mean Free Path ◽  
Point Of View ◽  
Transition Elements ◽  
Conduction Electrons ◽  
The Mean

1— In a recent paper certain property of the transition metals Ni, Pd, and Pt and of their alloys with Cu, Ag, and Au have been discussed from the point of view of the electron theory of metals based on quantum mechanics. In particular, a qualitative explanation was given of the relatively high electrical resistance of the transition metals. It was shown from an examination of the experimental evidence that the conduction electrons in these metals have wave functions derived mainly from s states just as in Cu, Ag, and Au, and that the effective number of conduction electrons is not much less than in the noble metals. On the other hand, the mean free path is much smaller, because under the influence other the lattice vibrations the conduction electrons may make transitions to the unoccupied d states, and the probability of these transitions is several times greater than the probability of ordinary scattering. Since the unoccupied d states are responsible for the ferromagnetism or high paramagnetism of the transition elements, there is a direct connexion between the magnetic properties and the electrical conductivity. The purpose of this paper is as follows: in 2, 3, and 4 we develop a formal theory of conductivity for metals, such as the tradition metals, where two Brillouin zone are of importance for the conductivity; in 5 we apply the theory to show why, at high temperatures, the temperature coefficient of the paramagnetic metals Pd and Pt falls below the normal value; and in 6 we discuss the resistance of ferromagnetic metals, and show in 7 qualitatively why constantan (Cu-Ni) has zero temperature coefficient at room temperature.

Electron and lattice conduction in metals

1957 ◽  
Vol 239 (1217) ◽  
pp. 247-266 ◽  
Keyword(s):  
Electric Power ◽  
Low Temperatures ◽  
Present Theory ◽  
Distribution Functions ◽  
Lattice Vibrations ◽  
Complex Character ◽  
Lattice Distribution ◽  
Thermo Electric ◽  
Complex Temperature ◽  
Non Equilibrium

The theory of the transport phenomena in metals is re-examined, the departure from equilibrium of both the electron and the lattice distribution functions being simultaneously taken into account in a consistent fashion. Simple expressions are derived for the conduction magnitudes which are exact at sufficiently high and sufficiently low temperatures and which are assumed to be approximately valid for all temperatures. The behaviour of the terms which arise from the non-equilibrium of the lattice depends upon the relative importance of the various causes responsible for scattering the lattice vibrations. In the case of the electrical conductivity these terms are estimated to be small in general, but they may have a bearing on some of the observed resistance anomalies at very low temperatures. Further, while the present theory gives nothing new in the case of the thermal conductivity, which is given by the sum of the usual electronic and lattice conductivities, the behaviour of the thermo-electric power is found to be profoundly modified, the non-equilibrium of the lattice leading in general to a considerably increased value which may show a complex temperature variation. The theory can account for the observed thermo-electric power of sodium at low temperatures and it suggests reasons for the complex character of the thermo-electric behaviour of metals in general, although in the present form the theory is not sufficiently general to account for all the observed anomalies even in the monovalent metals.

TEMPERATURE DEPENDENCE BEHAVIOR OF ELECTRICAL RESISTIVITY IN NOBLE METALS AT LOW TEMPERATURES

2014 ◽  
Vol 5 (3) ◽  
pp. 982-992 ◽  
Author(s):  
M AL-Jalali
Keyword(s):  
Experimental Data ◽  
Electrical Resistivity ◽  
Temperature Dependence ◽  
Concentration Dependence ◽  
Low Temperatures ◽  
Noble Metals ◽  
Phonon Scattering ◽  
Theoretical Models ◽  
Residual Resistivity ◽  
Electron Phonon Scattering

Resistivity temperature – dependence and residual resistivity concentration-dependence in pure noble metals(Cu, Ag, Au) have been studied at low temperatures. Dominations of electron – dislocation and impurity, electron-electron, and electron-phonon scattering were analyzed, contribution of these mechanisms to resistivity were discussed, taking into consideration existing theoretical models and available experimental data, where some new results and ideas were investigated.

scholarly journals Anomalous Temperature and Field Behaviors of Magnetization in Cubic Lattice Frustrated Ferromagnets

2015 ◽  
Vol 233-234 ◽  
pp. 3-7
Author(s):  
A.N. Ignatenko ◽  
Andrey A. Katanin ◽  
Valentin Yu. Irkhin
Keyword(s):  
Experimental Data ◽  
Monte Carlo Simulation ◽  
Low Temperatures ◽  
Strong Field ◽  
Wave Spectrum ◽  
Exchange Interactions ◽  
Thermal Fluctuations ◽  
Anomalous Temperature ◽  
Cubic Lattice ◽  
Spin Wave Spectrum

Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions are considered near the frustration point where the coefficient D in the spin-wave spectrum Ek ~ Dk2vanishes. Within the Dyson-Maleev formalism it is found that at low temperatures thermal fluctuations stabilize ferromagnetism by increasing the value of D. For not too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. Anomalous temperature behavior of magnetization is confirmed by Monte Carlo simulation. Strong field dependence of magnetization (paraprocess) at finite temperature is found near the frustration point.

Can the Number of D Electrons in Transition Metals be Measured from White Lines?

1997 ◽  
Vol 3 (S2) ◽  
pp. 957-958 ◽  
Author(s):  
P. Rez
Keyword(s):  
Transition Metals ◽  
Energy Loss ◽  
Electron Energy ◽  
Transition Elements ◽  
White Line ◽  
Line Intensities ◽  
Continuum Region ◽  
The Matrix ◽  
Image Position ◽  
Electron Energy Loss

Sharp peaks at threshold are a prominent feature of the L23 electron energy loss edges of both first and second row transition elements. Their intensity decreases monotonically as the atomic number increases across the period. It would therefore seem likely that the number of d electrons at a transition metal atom site and any variation with alloying could be measured from the L23 electron energy loss spectrum. Pearson measured the white line intensities for a series of both 3d and 4d transition metals. He normalised the white line intensity to the intensity in a continuum region 50eV wide starting 50eV above threshold. When this normalised intensity was plotted against the number of d electrons assumed for each elements he obtained a monotonie but non linear variation. The energy loss spectrum is given bywhich is a product of p<,the density of d states, and the matrix elements for transitions between 2p and d states.

scholarly journals LAGRANGIAN BREAKER CHARACTERISTICS FOR NONLINEAR WATER WAVES PROPAGATING ON SLOPING BOTTOMS

2011 ◽  
Vol 1 (32) ◽  
pp. 15
Author(s):  
Yang-Yih Chen ◽  
Meng-Syue Li ◽  
Hung-Chu Hsu ◽  
Ying-Pin Lin
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Empirical Formula ◽  
Wave Breaking ◽  
Present Theory ◽  
Empirical Formulas ◽  
Third Order ◽  
Wave Shoaling ◽  
Theoretical Results ◽  
Sloping Bottom

In this paper, a new third-order Lagrangian asymptotic solution describing nonlinear water wave propagation on the surface of a uniform sloping bottom is presented. The model is formulated in the Lagrangian variables and we use a two-parameter perturbation method to develop a new mathematical derivation. The particle trajectories, wave pressure and Lagrangian velocity potential are obtained as a function of the nonlinear wave steepness  and the bottom slope  perturbed to third order. The analytical solution in Lagrangian form satisfies state of the normal pressure at the free surface. The condition of the conservation of mass flux is examined in detail for the first time. The two important properties in Lagrangian coordinates, Lagrangian wave frequency and Lagrangian mean level, are included in the third-order solution. The solution can also be used to estimate the mean return current for waves progressing over the sloping bottom. The Lagrangian solution untangle the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile and water particle trajectories leading to wave breaking. The proposed model has proved to be capable of a better description of non-linear wave effects than the corresponding approximation of the same order derived by using the Eulerian description. The proposed solution has also been used to determine the wave shoaling process, and the comparisons between the experimental and theoretical results are presented in Fig.1a~1b. In addition, the basic wave-breaking criterion, namely the kinematical Stokes stability condition, has been investigated. The comparisons between the present theory, empirical formula of Goda (2004) and the experiments made by Iwagali et al.(1974), Deo et al.(2003) and Tsai et al.(2005) for the breaking index(Hb/L0) versus the relative water depth(d0/L0) under two different bottom slopes are depicted in Figs 2a~2b. It is found that the theoretical breaking index is well agreement with the experimental results for three bottom slopes. However,for steep slope of 1/3 shown in Fig 2b, the result of Goda‘s empirical formula gives a larger value in comparison with the experimental data and the present theory. Some of empirical formulas presented the breaking wave height in terms of deepwater wave condition, such as in Sunamura (1983) and in Rattanapitikon and Shibayama(2000). Base on the results depicted in Fig. 3a~3b, it showed that the theoretical results are in good agreement with the experimental data (Iwagali et al. 1974, Deo et al.2003 and Tsai et al. 2005) than the empirical formulas. The empirical formula of Sunamura (1983) always predicts an overestimation value.

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