scholarly journals The resistance of liquid metals

1934 ◽  
Vol 146 (857) ◽  
pp. 465-472 ◽  
Keyword(s):  
Melting Point ◽  
Liquid Metals ◽  
Mean Free Path ◽  
Quantitative Agreement ◽  
Liquid Lead ◽  
Modern Theory ◽  
Wave Mechanics ◽  
Normal Metals ◽  
Order Of Magnitude ◽  
The Mean

The electrical resistance of most normal metals in the liquid state just above the melting point is about twice as great as that of the solid metal just below the melting point. Certain abnormal metals, however, such as bismuth, gallium and antimony, which are rather poor conductors in the solid state, increase their conductivity on melting. The purpose of this paper is to discuss this change of resistance from the point of view of the modern theory of electronic conduction which is based on the wave mechanics, and to obtain a formula for the change of resistance which is in quantitative agreement with experiment for normal metals. No quantitative theory can as yet be given for the abnormal metals, but we shall show that their behaviour is explicable in a qualitative way. In a solid the atoms vibrate about mean positions which are fixed in the solids in a liquid at temperatures near the melting point, it is now generally recognized that the atoms vibrate about mean positions which, though not fixed, move slowly compared with the velocity, of order of magnitude √( k T/M), with which the atoms vibrate. The most direct evidence for this is afforded by the specific heats of monatomic metals, which have, within the limits of experimental error (~7%), the same values (in the neighbourhood of 3R) for a given metal in the solid and liquid states near the melting point. Further evidence is given by the rates of diffusion of gold in mercury (0·72 sq cm/day) or of thorium B (Pb) in non-radioactive liquid lead (2·2 sq cm/day). If one compares these numbers with the formula for the diffusion coefficient in gases, D = 1/3 lc , where l is the mean free path, and c the mean molecular velocity, one finds, on setting c equal to a quantity of the order of magnitude of √( k T/M), that l must be taken to be about one-hundredth of the interatomic distance.

scholarly journals Thermal Diffusion of Isotopes in Pure Liquids

1966 ◽  
Vol 21 (9) ◽  
pp. 1348-1351
Author(s):  
A. Lodding
Keyword(s):  
Mass Flow ◽  
Liquid Metals ◽  
Density Fluctuations ◽  
Pure Liquid ◽  
Theoretical Treatment ◽  
Liquid Model ◽  
Order Of Magnitude ◽  
Mean Size ◽  
The Mean ◽  
Effective Cluster

A theoretical treatment is given of the recently discovered thermotransport effect in pure liquid metals. The isotope effect is related to the diffusive mass flow by a proportionality factor familiar from electrotransport. The mass flow is given primarily by the temperature dependence of the mean size or amount of density fluctuations in the liquid. Very little activation energy is required for diffusive motion, which takes place by cooperative position adjustments of neighbor atoms. The mean displacement length of the diffusing cluster is by an order of magnitude smaller than the effective cluster diameter. The liquid model suggested is coherent with models based on evidence from other experimental methods.

Transient, Sub-Continuum, Heat Conduction in Irregular Geometries

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Saad Bin Mansoor ◽  
Bekir S. Yilbas
Keyword(s):  
Intensity Distribution ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Geometric Feature ◽  
Shape Effect ◽  
Film Material ◽  
Irregular Shapes ◽  
Frequency Independent ◽  
Order Of Magnitude ◽  
The Mean

Abstract Phonon transfer in irregular shapes is important for assessing the influence of shape effect on thermal transport characteristics of low-scale films. It becomes critical for evaluating the contribution of the scattering phonons to the phonon intensity distribution inside the film. Hence, the sub-continuum ballistic-diffusive model is incorporated to formulate the phonon transport in an irregular geometry of low-size film adopting the transient, frequency-independent, equation of phonon radiative transfer. The discrete ordinate method is used in the numerical discretization of the governing transport equation. It is demonstrated that the geometric feature of the film influences the phonon intensity distribution within the film material. The transport characteristics obtained from the Fourier and the ballistic-diffusive models are markedly different in their spatial and temporal behavior. This is true when the device sizes are of the same order of magnitude as the mean-free path of the heat carriers.

scholarly journals The surface impedance of superconductors and normal metals at high frequencies II. The anomalous skin effect in normal metals

1947 ◽  
Vol 191 (1026) ◽  
pp. 385-399 ◽  
Keyword(s):  
Free Path ◽  
Skin Effect ◽  
Classical Model ◽  
Mean Free Path ◽  
Skin Depth ◽  
Normal Metals ◽  
Anomalous Skin Effect ◽  
Skin Conductivity ◽  
The Mean ◽  
Dimensional Argument

Measurements on the skin conductivity of the normal metals silver, gold, and tin show that at low temperatures the skin conductivity tends to become independent of the d. c. conductivity, which is at variance with the predictions of classical skin effect theory. Following a suggestion of H. London that this anomalous behaviour is due to the mean free path of the electrons becoming much greater than the skin depth, an attempt is made to calculate the effect for a semi-classical model of a metal. Although a rigorous solution has not been found, it is shown that the model predicts constancy of skin conductivity when the mean free path becomes very long. Moreover, there is reason to suppose that under these conditions only a small proportion of the conduction electrons contribute effectively to the high-frequency current, and an exact solution is given for a model based on this concept, which also predicts that the skin conductivity should be independent of the d. c. conductivity. A simple dimensional argument may be applied to enable values of the mean free path in copper, gold, aluminium and tin, relative to the value in silver, to be deduced from the experimental results. These values are not in good agreement with theoretical estimates by Mott and Jones. The behaviour of mercury is different from that of the other metals in­vestigated, in that the skin conductivity does not tend to a constant value. It is suggested that the theory based on a crude classical model is inapplicable to a metal such as mercury, in which the anomalous skin effect appears at such temperatures that the ideal resistance is still many times greater than the residual resistance.

The electronic structure of liquid metals

1962 ◽  
Vol 267 (1331) ◽  
pp. 518-540 ◽  
Keyword(s):  
Electronic Structure ◽  
Electronic Properties ◽  
Free Path ◽  
Free Electron ◽  
Knight Shift ◽  
Liquid Metals ◽  
Mean Free Path ◽  
X Ray ◽  
Structure Of Liquids ◽  
The Mean

An analysis is given of the electronic structure of liquids under conditions for which the almost free-electron approximation is applicable. An enumeration of the various conditions that can exist is given, based on the relative magnitudes of the mean free path and range of order in the liquid. An important case is that in which the electronic properties can be described in terms of the X -ray data and this is discussed in detail, the curves of energy against momentum being given with calculations of the resistance and Knight shift. When considerable order is present the analysis is more complicated and the behaviour of the energy momentum curves is given as the range of order varies from the extreme cases of no order to polycrystalline order.

scholarly journals Observation of a transition to a localized ultrasonic phase in soft matter

2022 ◽  
Vol 5 (1) ◽  
Author(s):  
Bernard R. Matis ◽  
Steven W. Liskey ◽  
Nicholas T. Gangemi ◽  
Aaron D. Edmunds ◽  
William B. Wilson ◽  
...  
Keyword(s):  
Phase Transition ◽  
Free Path ◽  
Soft Matter ◽  
Volume Fraction ◽  
Localization Length ◽  
Mean Free Path ◽  
Sound Waves ◽  
Classical Waves ◽  
Order Of Magnitude ◽  
The Mean

AbstractAnderson localization arises from the interference of multiple scattering paths in a disordered medium, and applies to both quantum and classical waves. Soft matter provides a unique potential platform to observe localization of non-interacting classical waves because of the order of magnitude difference in speed between fast and slow waves in conjunction with the possibility to achieve strong scattering over broad frequency bands while minimizing dissipation. Here, we provide long sought evidence of a localized phase spanning up to 246 kHz for fast (sound) waves in a soft elastic medium doped with resonant encapsulated microbubbles. We find the transition into the localized phase is accompanied by an anomalous decrease of the mean free path, which provides an experimental signature of the phase transition. At the transition, the decrease in the mean free path with changing frequency (i.e., disorder strength) follows a power law with a critical exponent near unity. Within the localized phase the mean free path is in the range 0.4–1.0 times the wavelength, the transmitted intensity at late times is well-described by the self-consistent localization theory, and the localization length decreases with increasing microbubble volume fraction. Our work sets the foundation for broadband control of localization and the associated phase transition in soft matter, and affords a comparison of theory to experiment.

Perpendicular Resistance of Co/Cu Multilayers Prepared by Molecular Beam Epitaxy

1995 ◽  
Vol 384 ◽  
Author(s):  
N.J. List ◽  
W.P. Pratt ◽  
M.A. Howson ◽  
J. Xu ◽  
M.J. Walker ◽  
...  
Keyword(s):  
Free Path ◽  
Spin Diffusion ◽  
Mean Free Path ◽  
Ferromagnetic Structure ◽  
Order Of Magnitude ◽  
The Mean ◽  
Electron Mean Free Path ◽  
Determining Factor ◽  
Second Peak ◽  
Key Parameter

ABSTRACTResults are presented of the magnetoresistance of MBE-grown (111) Co/Cu multilayers measured with the current perpendicular to the plane of the layers (CPP). Although for measurements made with the more common geometry of current in the plane of the layers (CIP) there are large differences between the results on samples made by sputtering and those prepared by MBE, for these new CPP data the results on samples made by the two techniques are very much alike. For copper layers with thicknesses between 0.9nm to 6nm the magnetoresistance shows oscillations with copper thickness that were almost non-existent in the earlier CIP data. At the second peak the magnetoresistance in the CPP geometry is an order of magnitude greater than that in the CIP configuration. Although the interfaces in these samples have been shown to be very sharp, they appear to form a mosaic structure with the antiferromagnetic regions embedded in a ferromagnetic structure. It is argued that for CIP measurements the GMR is greatly reduced by these ferromagnetic correlations over lengthscales long compared to the electron mean free path. For CPP measurements, on the other hand, it is the spin diffusion length that is the determining factor with the mean free path no longer a key parameter and with values of the GMR virtually independent of the growth process.

Non-stationary process characteristics of the gas outflow into a liquid

2019 ◽  
Vol 14 (2) ◽  
pp. 82-88
Author(s):  
M.V. Alekseev ◽  
I.S. Vozhakov ◽  
S.I. Lezhnin
Keyword(s):  
Numerical Simulation ◽  
Liquid Column ◽  
Gas Content ◽  
Liquid Lead ◽  
Gas Flows ◽  
Asymptotic Model ◽  
Process Characteristics ◽  
Significant Difference ◽  
Order Of Magnitude ◽  
Volume Method

A numerical simulation of the process of the outflow of gas under pressure into a closed container partially filled with liquid was carried out. For comparative theoretical analysis, an asymptotic model was used with assumptions about the adiabaticity of the gas outflow process and the ideality of the liquid during the oscillatory one-dimensional motion of the liquid column. In this case, the motion of the liquid column and the evolution of pressure in the gas are determined by the equation of dynamics and the balance of enthalpy. Numerical simulation was performed in the OpenFOAM package using the fluid volume method (VOF method) and the standard k-e turbulence model. The evolution of the fields of volumetric gas content, velocity, and pressure during the flow of gas from the high-pressure chamber into a closed channel filled with liquid in the presence of a ”gas blanket“ at the upper end of the channel is obtained. It was shown that the dynamics of pulsations in the gas cavity that occurs when the gas flows into the closed region substantially depends on the physical properties of the liquid in the volume, especially the density. Numerical modeling showed that the injection of gas into water occurs in the form of a jet outflow of gas, and for the outflow into liquid lead, a gas slug is formed at the bottom of the channel. Satisfactory agreement was obtained between the numerical calculation and the calculation according to the asymptotic model for pressure pulsations in a gas projectile in liquid lead. For water, the results of calculations using the asymptotic model give a significant difference from the results of numerical calculations. In all cases, the velocity of the medium obtained by numerical simulation and when using the asymptotic model differ by an order of magnitude or more.

Simple explicit model of liquid mean flow in region above axial impeller

1985 ◽  
Vol 50 (11) ◽  
pp. 2396-2410
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Vortex Flow ◽  
Flow Model ◽  
Quantitative Agreement ◽  
Mean Flow ◽  
Flat Bottom ◽  
Proposed Model ◽  
Minimum Number ◽  
The Mean ◽  
Model Equations ◽  
Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

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