Showing papers on "Free electron model published in 1973"
TL;DR: In this paper, the possibility of creating a structure of two domains with mutually opposite directions of spontaneous polarization is considered, where the domains are divided by a domain wall of metal conductivity with a concentration of free electrons or holes of about 1021 cm-3.
Abstract: The possibility of creation of a structure of two domains with mutually opposite directions of spontaneous polarization is considered. These domains are divided by a domain wall of metal conductivity with a concentration of free electrons or holes of about 1021 cm-3, the thickness of the conducting layer being about 10-7 cm.
84 citations
67 citations
TL;DR: In this paper, the authors report on energy loss experiments with 50 keV electrons transmitted through thin films of the metals Al, Mg, Li, Na, and K. Since these substances oxidize rapidly they were evaporated and studied in ultra high vacuum.
Abstract: We report on energy loss experiments with 50 keV electrons transmitted through thin films of the metals Al, Mg, Li, Na, and K. The valence electrons of these materials behave like a gas of free electrons to a good approximation and, in particular, give rise to significant collective effects. Since these substances oxidize rapidly they were evaporated and studied in ultra high vacuum. The apparatus and the measurement technique are described.
66 citations
TL;DR: In this paper, the band structure of metallic Be is calculated at various values of the lattice constants with proper emphasis on the deviation from the free electron model, and the calculated value of the coefficient of the electronic specific heat is 0.145 mJ/mole·deg 2.
Abstract: Band structure of metallic Be is calculated at various values of the lattice constants with proper emphasis on the deviation from the free electron model. It is found that Be keeps to be a metal up to the lattice constant by 1.6 times as large as the normal lattice. The density-of-states at the normal lattice has a deep valley at the Fermi energy. The charge distribution of conduction electrons in the real space is more concentrated along a line connecting the atoms in the direction of the c -axis. There seems to be a kind of the energy separation between a bonding and an anti-bonding orbitals due to a strong hybridyzation of s and p wave functions. The calculated value of the coefficient of the electronic specific heat is 0.145 mJ/mole·deg 2 , while the observed value is 0.171 mJ/mole·deg 2 , so that the enhancement factor is determined as 0.18. The calculated dimensions and the shape of the Fermi surfaces agree well with experiment.
44 citations
TL;DR: In this article, a photo-electron injection technique was used to obtain a better understanding of the nature of the negative charge carriers produced in liquid hydrocarbons by ionizing radiation or by electron injection.
38 citations
TL;DR: In this paper, a multiple plane wave pseudopotential calculation for the residual resistivity in alloys is presented, where the electronic wavefunctions, the Fermi surface, and the scattering rates are all determined from a 4-OPW calculation, while the mean free path is determined from an iterative technique developed for solving the Boltzmann equation.
28 citations
TL;DR: In this paper, the authors measured spin wave resonance for a series of fcc Fe-Ni alloys in order to study the exchange stiffness constant D, which is considered to be due to the inhomogeneous demagnetizing field of the sample.
Abstract: Spin wave resonance for a series of fcc Fe-Ni alloys has been measured in order to study the exchange stiffness constant D . In general the resonance field vs the square of the spin wave mode number ( n ) curve is linear for high values of n , whereas some amount of deviation from linearity occurs for low values of n . This is considered to be due to the inhomogeneous demagnetizing field of the sample. We can determine the value of D from the linear part of the curve, provided we have a sufficient number of observed modes. As a supplementary means, we have also made low temperature magnetization measurements from which the value of D was derived. Consistency between these two kinds of measurements is ascertained. The composition dependence of D is not quite coincident with that derived from the neutron small angle scattering experiments by Hatherly et al. The data are discussed both from the standpoint of localized electron model and collective electron model.
24 citations
TL;DR: In this paper, the width of the free electron cyclotron resonance in InSb has been studied as a function of resonant magnetic field, by means of laser spectrometers operating at seven different wavelengths.
22 citations
TL;DR: In this article, the reduction of free electron concentration in pure n -type InSb as a function of a strong magnetic field was calculated based on a model of a single hydrogen-like impurity.
20 citations
TL;DR: In this article, the authors studied the quantum size effect using the Shockley model of a one-dimensional lattice terminated by arbitrary surface potentials, and the way the energy levels change as the surface potential changes from very high (kappa identical to psi '(0)/ psi (0)= infinity ) to very low ( kappa = 0) is discussed.
Abstract: The quantum size effect is studied, using the Shockley model of a one-dimensional lattice terminated by arbitrary surface potentials. The way the energy levels change as the surface potential changes from very high ( kappa identical to psi '(0)/ psi (0)= infinity ) to very low ( kappa =0) is discussed. Surface states are included in the discussion. For states near a band edge, which for many purposes are the most important states, the eigenvalue equation is simplified. Then the general features of the solutions can be understood analytically. Numerical computation of the solutions is simple if the bulk band structure is known. The wavefunctions and energy levels are found; for sufficiently thick layers they are similar to those in a square well with an effective well depth. The widely used effectively free electron model is accurate for sufficiently thick films, apart from the omission of surface states. However, the convergence to the effectively free electron model is slower if the effective mass is small, and a significant correction is necessary in many practical cases.
18 citations
TL;DR: In this article, the magnetic behavior of spinless electrons confined in a cylinder of radiusR by a harmonic oscillator potential is calculated over the entire range of sizesR/rH, whererH is the radius of the classical electron orbit due to a constant magnetic field.
Abstract: The magnetic behavior of spinless electrons confined in a cylinder of radiusR by a harmonic oscillator potential is calculated over the entire range of sizesR/rH, whererH is the radius of the classical electron orbit due to a constant magnetic fieldH. The magnetic moment is shown to be large and positive in the small size limitR/rH≪1 in agreement with recent experimental work, while in the usual large size limitR/rH≫1 the Landau susceptibility is obtained. The model is compared with a similar calculation in which a periodic boundary condition is applied in order to show explicitly how qualitative differences arise in the small size limit, and the relevance of the results to calculations for rectangular and spherical geometries with hard wall boundary conditions is examined.
TL;DR: In this article, the separation energy spectra and the momentum distributions obtained from the (e, e′p) reaction on 6 Li, 7 Li, 9 Be, and 12 C are presented.
TL;DR: In this paper, a simple model based on the nearly free electron approximation was developed in order to calculate the surface state energies in heteropolar compounds using the matching of the Green's function method.
Abstract: A simple model, based on the nearly free electron approximation, is developed in order to calculate the surface state energies in heteropolar compounds using the matching of the Green's function method. The analysis is based on the effect of the crystal ionicity on the surface state energies. The results are compared with experimental data, and general trends are obtained fairly similar to the experimental evidence. Finally, the effect of using a tight-binding model instead of a nearly free electron model to describe the crystal is studied and only minor differences are obtained.
TL;DR: In this paper, a quantum model and a semi-classical model for the bounding probability of excitons in semiconductors are presented. But the quantum model does not predict our recent low temperature measurements.
TL;DR: In this article, the effect of the electronic density of states on the electronic mean free path has been investigated by introducing Mott's density-of-states ratio g for Li and Cs among the liquid alkali metals.
Abstract: Only for Li and Cs among the liquid alkali metals do the density of states and its energy derivatives show significant departures from the free electron model. In addition, the density of states of liquid Hg numerically calculated has a depression near the Fermi energy. The effect of the electronic density of states on the electronic mean free path has been investigated by introducing Mott's density of states ratio g.
TL;DR: The Compton profile of single crystal chromium has been measured for the [100] and [111] directions with AgKα X-rays and found to be narrower than the profile calculated for the free atom as discussed by the authors.
Abstract: The Compton profile of single crystal chromium has been measured for the [100] and [111] directions with AgKα X-rays and found to be narrower than the profile calculated for the free atom. This is consistent with the X-ray scattering factor observations of Diana and Mazzone and suggests that the 3d electrons in the metal are spatially more extended than in the free atom. Approximate metallic wave functions are given for chromium which are consistent with the scattering factor and Compton profile observations including the observed anisotropics in both. The momentum distributions of the 3d metals Ti, V, Cr and Fe all show rapid changes of values of momenta, and hence of kinetic energy, significantly larger than those predicted by free electron theory, as might be expected for 3d valence electrons.
TL;DR: In this paper, an expression for the compressibility of a pure metal is derived and is shown to yield the Bohm-Staver formula in the free electron case, which is relevant to the analysis of scattering data.
Abstract: It is observed that the long wavelength density fluctuations of the conduction electrons are dependent on those of the ions. This implies certain relations between the partial structure factors, which are relevant to the analysis of scattering data. An expression for the compressibility of a pure metal is derived and is shown to yield the Bohm-Staver formula in the free electron case.
TL;DR: In this paper, the surface properties of a network model of electrons in solids are discussed in the model where electrons are restricted to move along lines connecting node points of a periodic network Each node point on the network corresponds to an atom A potential well is introduced for each atom or node point so that as the depth of the potential becomes large, one has the tight binding model and, as the potential vanishes and the number of node points increases, the Sommerfeld free electron model.
TL;DR: The results of a detailed investigation of the de Haas-van Alphen effect in calcium are presented in this article, showing that the Fermi surface consists of a multiconnected monster-like hole sheet in the first band and lens-shaped electron sheets in the second band.
Abstract: The results of a detailed investigation of the de Haas-van Alphen effect in calcium are presented. The data, taken for the two major crystallographic planes in magnetic fields up to 36 kG and temperatures down to 0.1 K, indicate that the Fermi surface consists of a multiconnected monsterlike hole sheet in the first band and lens-shaped electron sheets in the second band. This indicates a Fermi surface geometry much more nearly free electron like than previously believed, and analysis in terms of a multi-OPW local pseudopotential model yields good agreement with the data.
TL;DR: In this paper, a Boltzmann equation is derived for the joint probability distribution of the wave function and its logarithmic derivative, and the Fokker-Planck approximation reduces to that derived by Halperin for a one-dimensional random white-gaussian noise potential.
Abstract: A study is made of the electronic structure of a network by adapting the free-electron model. In this model, a tight-binding structure is represented by free electrons constrained to move upon lines joining the bonded atoms of the network. A Boltzmann equation is then derived for the joint probability distribution of the wavefunction and its logarithmic derivative. In the Fokker-Planck approximation this equation reduces to that derived by Halperin for a one-dimensional random white-gaussian noise potential. This model strongly suggests that localization persists in a network long after percolation is possible.
TL;DR: In this article, the authors re-examined Kuhn's analysis and found that while the Drude model does not have the usual kind of optical activity, it does exhibit rotatory power which is proportional to the intensity of the incident light for low intensities.
Abstract: According to Kuhn, in a classical treatment of Drude's one-particle model, an electron constrained to move along a helix exhibits no optical activity. On the other hand, Condon, Altar, and Eyring showed that a quantum-mechanical one-particle model, an electron confined in a twisted anisotropic harmonic-oscillator well, possesses optical activity even in the classical limit. We therefore re-examined Kuhn's analysis and found that while the Drude model does not have the usual kind of optical activity, it does exhibit rotatory power which is proportional to the intensity of the incident light for low intensities. This effect has a simple physical interpretation.
TL;DR: In this paper, the authors used the single valley model for the calculation of transport parameters corresponding to pure Bi2Se3 crystals, and the Fermi level was calculated to lie 0·14 eV above the bottom of the conduction band.
Abstract: The “single valley” model proposed byKohler andLandwehr is used for the calculation of transport parameters corresponding to “pure” Bi2Se3 crystals. From the measurements of transmission, reflectivity and the Hall constant the effective masses are determined,m
⊥c
=0·13m
0 andm
∥c=0·56m
0; using a simplification described in the paper the Fermi level is calculated to lie 0·14 eV above the bottom of the conduction band. This result allows us to conclude that a mixed mechanism of free carrier scattering exists inn-Bi2Se3 crystals, viz., the scattering by acoustic phonons prevails contributing about 75% and the scattering on ionized impurities contributes the remaining 25%. This result applies to “pure” Bi2Se3 crystals with free electron concentration 2×1019cm−3.
TL;DR: The interstitial-electron model for metals supplements the concepts of band theory to give a detailed interpretation of the properties of metals as discussed by the authors, leading to the expectation of parallel gradations for electronic heat capacity and magnetic susceptibility and an inverse relation of both of these properties with electrical conductivity.
Abstract: The interstitial-electron model for metals supplements the concepts of band theory to give a detailed interpretation of the properties of metals. The instantaneous picture of vacant and electron-occupied interstices given by the model clarifies the complex gradations in electrical conductivity which are not explained by an electron per unit volume term. The consideration of polarization of the itinerant electron cloud by ion cores with high positive fields and of interpenetration of the more deformable ion cores by itinerant electrons is another new feature of the model. The interstitial-electron model leads to the expectation of parallel gradations for electronic heat capacity and magnetic susceptibility and an inverse relation of both of these properties with electrical conductivity. The presence of (\bare2) in the metal structure is associated with a positive Hall Coefficient for a metal, and a new correlation between positive Hall Coefficient and superconductivity for a metal is pointed out.
TL;DR: In this article, the dipole approximation of optical resonance absorption in discontinuous metal films was studied in the free electron regime and in the interband transition region, where free electron effects were further damped and the resonance frequency was shifted.
Abstract: Optical resonance absorption in discontinuous metal films is studied in the dipole approximation. In the free electron regime the phenomenon is closely related to plasma oscillations and can be treated analytically. When damping is present, approximations may be employed and the quantities of interest can still be expressed in closed form. In the interband transition region the free electron effects are further damped and the resonance frequency may be shifted. In this case no analytical treatment is practical. Real situations may be simulated, however, by adding a lightly damped oscillator term to the free electron dielectric function of the metal. A suitable choice of parameters can describe a real metal.
TL;DR: In this paper, a laser excited Fabry-Perot interferometer for measuring electron densities (Nel>5*1015 cm-2) is described; Ne is recorded directly as a function of time.
Abstract: A laser excited Fabry-Perot interferometer for measuring electron densities (Nel>5*1015 cm-2) is described; Ne is recorded directly as a function of time. The plasma is produced in a z-pinch discharge (helium gas) and is located in the space (length l) between two tubes which define the resonator axis. The dependence of Ne on l shows the tubes do not contaminate the plasma, and measurements at two wavelengths confirm that the plasma refractivity is produced by free electrons. The resolving time for the density records is of the order of 50 ns.
TL;DR: In this article, the Gudden-Pohl effect (GPE) was used as a model to demonstrate the influence of surface states on the storage of optical excitation in A 2 B 6 semiconductor compounds.
TL;DR: In this paper, a simple, "nearly free electron" model for the dihydrides of Be, Mg, Ca, Sr and Ba is investigated, and effects of band structure are included in second-order pseudopotential perturbation theory.
Abstract: A simple, “nearly free electron” model for the dihydrides of Be, Mg, Ca, Sr and Ba is investigated. To zeroth order the valence electrons are assumed to form a free gas. Effects of band structure are included in second-order pseudopotential perturbation theory. The stability of three probable crystal structures is investigated, and lattice parameters are calculated for two different choices of the pseudopotential.
TL;DR: In this paper, high and low temperature bremsstrahlung isochromats of Pd and Rh are compared with free electron densities of states derived from γ- and χ-measurements.
Abstract: Measured high and low temperature bremsstrahlung isochromats of Pd and Rh are reported and compared with free electron densities of states derived from γ- and χ-measurements. The Pd- as well as the Rh-isochromats do not show any significant dependence on the target temperature except the temperature dependent smearing out of the Fermi edge at high temperatures. From this result we conclude, that isochromats—in contrast to γ- and χ-measurements—are not influenced by enhancement effects.