It is shown that, if a band gap in one metal overlaps the corresponding gap in another, then no state exists in the region of overlap in any alloy of the two, provided only that the alloy potential is everywhere intermediate between the potentials of the pure metals. This theorem is related to the work of Saxon and Hutner and of Luttinger. A condition for the existence of band gaps is derived for models not satisfying the conditions of the theorem.
The earlier Hartree, Hartree and Swirles calculations for oxygen have been repeated with superposition of configurations included in the determination of the wave functions as well as the energy. Results are reported for the 2s2 2pq, q = 0,...4, configurations of O to O4+. In these cases configuration interaction is shown to improve the total energy by less than 0.1%, but may reduce a term interval by almost 50%.
The longitudinal relaxation model, which explains the relaxation effects observed in ferromagnetic resonance for ferrites doped with anisotropic ions, is adapted to investigate the effect of bottleneck in the energy flow to the lattice. It is deduced that this could occur if the heat capacity of the phonon (or magnon) modes to which the doping ions relax were too limited and these modes did not relax rapidly to the bath. Comparison of the expressions which are developed with experiment indicates that bottleneck effects are mild, if present at all, in ytterbium-doped yttrium iron garnet, and that this unwelcome complication is probably not important in general.
It has recently been predicted that in a suitable semiconductor the electron temperature may be reduced below the lattice temperature by an applied electric field. These calculations have either employed a three-term expansion of the electronic distribution function, or neglected all scattering other than that arising from polar optical modes. In the present paper the electron temperature is calculated as a function of electric field for both polar and non-polar semiconductors, including polar optical, deformation potential optical and acoustic, and intervalley scattering without expansion of the distribution function. Results are presented for n-type GaAs, InSb, Si and GaP. Finally, in discussing the approximations which remain in this theory, particular reference is made to p-type Ge, for which experimental data are available.
As a first stage in the investigation of suitable potentials for the noble metals, the energy bands and Fermi surface of copper have been calculated by the Green function method. The potentials of Herman and Skillman used by many workers are found to be unsuitable; the d bands are too narrow and too low and the Fermi surface does not contact the boundary of the Brillouin zone. Attempts to modify the potential between the muffin-tin spheres failed to improve the results. The amount of exchange energy included in a Gáspár-type potential is found to affect the band structure considerably. Satisfactory agreement with experimental and other theoretical results is nevertheless obtained if the exchange is reduced to about 30-40% of the amount proposed by Gáspár.
A new formula is derived for the dipole-dipole term in the van der Waals interaction between two spherically symmetrical atoms. The approximation consists in taking the distortion of each atom in the instantaneous dipole field of the other atom to be proportional to the corresponding adiabatic distortion, and the co-efficients of proportionality are variationally determined. Good agreement with the results of other calculations is obtained in a number of cases involving atomic hydrogen and the inert gases.
Experiments on an absorber vibrated at ultrasonic frequency are described. The spectrum is used to calibrate the spectrometer for a measurement of the 57Fe hyperfine spectrum, and it is found that the hyperfine fields in the bulk iron and in the domain walls are equal to within 0.1%.
The wave function used by Rudge as a basis for modifying the Ochkur approximation is generalized The results obtained with the new function cast doubt on the validity of the arguments used by Rudge and Crothers in support of Rudge's modification.
The process of one-electron loss during the passage of fast helium atoms through gaseous targets has been investigated. Apparent cross sections σ01 are shown to be dependent on the conditions of formation of the fast helium atoms.
Measurements have been made of the susceptibilities of copper-zinc alloy phases containing small amounts of chromium, manganese, iron and cobalt. A Curie-Weiss analysis is possible for some of the alloys and effective moments derived from it are discussed in terms of current theories of such materials; in other alloys unmagnetized configurations are found. In solution in the copper-zinc phase a moment appears on solute iron atoms as the copper content increases from 15 to 19 at. %.
Both the change in Knight shift with concentration and the quadrupole broadening of the magnetic resonance of the 7L1 nucleus in a series of dilute lithium alloys has been investigated. An attempt is made to correlate both sets of experimental data in the terms of Friedel's model of the scattering of electrons at the Fermi surface. It is shown that a set of phase shifts chosen empirically to give the experimental Knight shift also accounts satisfactorily for the residual resistivity and the quadrupolar broadened line shapes.
The perturbed stationary-state approximation is used to calculate the cross section for electron detachment and charge transfer in H-H- collisions. The problem of the absence of bound states of H2- is overcome by the introduction of resonant states. For incident energies between 50 eV and 10 000 eV the electron-detachment cross section decreases monotonically from 18 × 10-16 cm2 to 6 × 10-16 cm2, and the charge-transfer cross section decreases from 70 × 10-16 cm2 to 0 2 × 10-16 cm2.
Neutron paramagnetic scattering is discussed generally in terms of the relaxation function of the magnetic system. The expansion of the scattering function F(κ, ω) in terms of moments of the energy transfer is evaluated to the fourth moment for the Heisenberg Hamiltonian and for limitingly high temperatures. Consideration of these moments leads to a better approximate form for the cross section at large scattering vector than the usual Gaussian form. The interpretation of experimental data is discussed and it is shown that important inaccuracies may arise from the use of the Gaussian approximation. A procedure for making good use of experimental information is given for data from both single crystals and polycrystals. In the single-crystal case it is possible to determine exchange constants to a large number of different atoms, whilst for the polycrystal it may be difficult experimentally to separate more than two different exchange constants.
A two-neighbour Born-von Kármán model is applied to the diamond crystal. The nearest neighbours are assumed to interact with general forces and central, angular and torsional forces are considered in the second-neighbour interactions. One of the five force constants that occur in this model is taken as a free parameter and is fitted to the experimental frequencies at the zone boundaries in the (100) and (111) directions. A good qualitative fit, substantially better than the corresponding fit in the case of germanium and silicon, is obtained. The phonon spectrum is calculated using the Fourier series expansion method. The specific heat of diamond is evaluated in the temperature range 0-300 °k and is found to agree quite well with the experimental results. Finally, the analysis of the dependence of the frequency and amplitude of the localized mode due to an isotopic impurity on its mass is made.
A Green function method has been devised to treat the effect, in a nucleus, of four nucleons coupling to zero momentum (quadrupling). The method permits the computation of the respective contributions by the quadruples and the pairs to the energy gap in nuclear spectra. A rough numerical estimate shows that the quadrupling gap is considerably larger than the pairing one, and is in good agreement with the experimental values for the energy gaps in light nuclei.
The problem of continuous bands of Bloch states is rewritten as one of discrete roots of Dyson's equation for a given k vector Equivalent potentials which conserve chosen energy levels are shown to obey a general theorem of which the orthogonalized plane wave pseudopotential theorem is a particular case. Another interesting family is obtained by studying the kernel of the energy shift expansion. Combining both families yields equivalent potentials, from which a criterion is suggested for (1) giving a more technical meaning to the arbitrariness of the orthogonalized plane wave pseudopotentials, and (11) making the best choice The criterion is related to the radius of convergence of the perturbation expansion in terms of the strength of the coupling The conclusion favours the Austin pseudopotential
A new test of the superposition approximation for the triplet distribution function in a classical fluid is reported. This test is based on an exact equation between the pair and triplet distribution functions. The results confirm that the superposition approximation is poor at moderate density.
Experimental data on optical absorption, electron scattering and optical refractivity are used to construct a model dipole spectrum of molecular nitrogen which is consistent with the oscillator strength sum rule. The spectrum is used to calculate various dipole properties. The spherically symmetric van der Waals coefficient for a pair of nitrogen molecules is 73.4 A.U., the mean excitation energy describing the slowing down of fast particles is 82.1 eV and the Rayleigh scattering cross section at Lyman α is 5.6 × 10-24 cm2. The vibrational Raman scattering at Lyman α is estimated to lie between 10-27 and 10-26 cm2.
The absorption spectrum of AlO has been observed in the wavelength region 2000-3000 Å using a shock tube. Discrete band absorption and continuous absorption were observed. It is suggested that the continous absorption is a dissociation continuum of AlO and its long-wavelength edge gives a value of 4 54 ± 0.01 eV for the dissociation energy.
The six third-order elastic constants of a pure specimen of indium antimonide have been measured at room temperature These have been obtained from measurements of the change in acoustic velocity with applied stress using an improved version of the ultrasonic `sing-around' system. Possible contributions to the constants other than those arising directly from interatomic forces are considered and are shown to be negligible in our measurements The results are interpreted and discussed in terms of a recent theory in which the third-order constants of covalent materials are dominated by three anharmonic force constants between first- and second-nearest neighbours.
