Table of contents

In sodium chloride crystals doped with both CN^- and Mn²⁺ the CN^- and Mn²⁺ are found to be associated. A Mn²⁺ vacancy dipole associated with CN^- is the centre responsible for Spectrum IV (Watkins) in the esr spectrum of NaCl.Mn²⁺. The 'trimer' lines previously reported are not due to Mn²⁺ vacancy trimers but are found when CN^- is added to the system. The effect of CN^- on the dielectric properties and aggregation of Mn²⁺ in NaCl.Mn²⁺ has been investigated.

On X-irradiation, cobalt-doped NaCl crystals show a new relaxational loss peak, designated as an S peak. The S loss peak occurs on the higher frequency side of the A and B loss peaks observed in unirradiated crystals. The intensity of the S loss peak increases with the dose of X-irradiation and with the concentration of cobalt. The dc conductivity and heights of A and B loss peaks decrease with the creation of S centres. On heating the X-irradiated crystals to about 200 degrees C, the S centres disappear and the conductivity and the heights of the A and B peaks are partially restored to their original value. A possible method for S centres is mentioned.

Brillouin scattering at 90 degrees from thermally excited first sound in superfluid ⁴He has been measured with a Fabry-Perot etalon and digital scanning. The line shifts confirm that there is no dispersion compared with low frequency orthodox measurements over the range of temperature 1.25 K to 2.15 K.

The coefficients of linear expansion alpha for silver, copper and aluminium are determined by a sensitive method and compared with those of other workers. The reduced parameters alpha /( alpha )_m/2 and T/T_m give a common curve for all metals. Here T_m is the melting point and ( alpha )_m/2 is the value of alpha at T=¹/₂T_m. The curve is a straight line within the approximate limits 0.2<T/T_m<0.45 and is found to deviate considerably from linearity at higher temperatures. Assuming that the deviation is due to defects, the energies of monovacancy formation in close-packed cubic metals are estimated and are found to agree excellently with the observed values.

A two-parameter expression for the local mode vibration frequency is useful for predicting the variation of frequency with impurity mass over a wide mass range in GaP and GaAs. The expression is valid for materials with small but non-zero effective charge.

A simple rule is presented which predicts the dispersion of the damping constant of a collective mode in the hydrodynamic regime.

The time dependent wave equation for the macroscopic pair wave function in superconductors is derived in a macroscopic manner from the assumption of off diagonal long range order and the neglect of long range three-particle correlations. It is shown that the equation is satisfied in equilibrium by the conventional microscopic theory.

Photoluminescence excitation and cathodoluminescence on a series of zinc doped alloys in the composition range 56-100 mole % GaP are in agreement with previous absorption measurements which indicate that the cross over composition from direct to indirect band gap is 60(+or-5) mole % GaP.

Neutron scattering techniques have been used to measure the phonon dispersion relations in a single crystal of ³⁶Ar at 4 degrees K. Data have been taken along the (110) and the (111) crystallographic directions. The analysis is expressed in terms of a two-neighbour force-constant model with five disposable parameters; one linear combination of three of these parameters is not determined well by the data. It is shown that the measurements are not inconsistent with a Mie-Lennard-Jones potential where the parameters are determined entirely from other macroscopic measurements on argon. However, there is a discrepancy with recent measurements of the elastic constants.

Analysis is made of the asymptotic form of the coefficients in high temperature series expansions for the Ising model of spin ¹/₂, the classical Heisenberg and planar classical Heisenberg models. For these models, if suitable expansion variables are chosen, only lattice constants of multiply connected graphs need be considered. Numerical investigations indicate that in the initial stages of each expansion the largest contribution is due to one simple basic graph. For the specific heat this graph is a polygon, and for the pair-correlation function and susceptibility it is a chain. If all other contributing graphs are ignored, critical indices are related to the geometrical properties of a self-avoiding walk on the lattice; hence this is termed the 'self- avoiding walk approximation'. Critical indices of higher derivatives with respect to magnetic field are then related to the virial coefficients of chains.

It is pointed out that the spectra of X-ray induced fast photoelectrons from metal should have a characteristic skew line shape resulting from Kondo-like many-electron interactions of the metallic conduction electrons with the accompanying deep hole in the final state. The same line shape should also occur for the discrete line spectra of X-rays emitted from metals. This mechanism could account for the well-known asymmetries observed for K alpha lines.

35 GHz electron spin resonance signals have been obtained at 77 degrees K from CdF₂:V³⁺, CdF₂: Cr³⁺, PbF₂: V²⁺, CdCl₂: V²⁺ and impurity centres in CdF₂ and PbF₂. V³⁺ occupies a cubic site in CdF₂ with g=1.940+or-0.001 and ⁵¹A=91+or-2G. Cr³⁺ in CdF₂ occupies a cubic site with trigonal distortion arising from a Jahn-Teller effect or local interstitial fluoride compensation with g/sub ///=1.94+or-0.01, g_{perpendicular to} =1.97+or-0.01 and b₂⁰=1.67 cm^-1. The impurity centres in CdF₂ and PbF₂ were associated with broad line electron spin resonance signals at g=2. V²⁺ in CdCl₂ occupied a substitutional distorted octahedral site with xy magnetic plane coincident with the cleavage planes and g/sub ///=1.974+or-0.001, ⁵¹A=⁵¹B=80+or-2G and b₂⁰=0.208 cm^-1.

Electron spin resonance spectra for Cr³⁺ in a number of sites were observed in NH₄Cl single crystals. The Cr³⁺ ions were in interstitial sites with magnetic axes close to (110), (110), (001) directions. The symmetry of the sites, thought to arise from two nearby vacancies, was axial with a small rhombic distortion. Parameters obtained for the most intense spectrum at 77 degrees K were D=3.189 GHz, E=0.247 GHz, g_x=1.9795, g_y=1.9798, g_z=1.9859. The various spectra merged at 180 degrees K. This was explained in terms of bound vacancy motion, D and E were obtained between 77 and 330 degrees K, both showing a sharp increase approaching the lambda point.

Spin-wave dispersion in antiferromagnetic FeF₂ has been investigated by inelastic neutron scattering using a chopper time-of-flight spectrometer. The single mode observed has a relatively flat dispersion curve rising from 53 cm^-1 at the zone centre to 79 cm^-1 at the zone boundary. A spin Hamiltonian which includes a single-ion anisotropy constant D (H_sⁱ=-DS_iz²), three exchange parameters J_l(H_ex¹²=J_lS₁.S₂) and dipolar interactions has been fitted to the measured energies. The authors find D=6.46 (+0.29, -0.10) cm^-1, J₁ (coupling neighbouring ions along the c axis)=-0.048 (+or-0.060) cm^-1, j₂ (coupling neighbouring ions at the corner and body centre of the cell)=+3.64(+or-0.10) cm^-1, and J₃ (coupling neighbouring ions along the a axis)=+0.194 (+0.060) cm^-1.

The problem of one and two spin deviations from the fully aligned state is studied for regular solids in two and three dimensions for the Hamiltonian (J(i,j)>0) H=-¹/₂ Sigma _(nn)J(i,j)S_i.S_j-¹/₂ alpha Sigma _(nnn)J(i,j)S_i.S_j where (nn) and (nnn) mean nearest and next nearest neighbour interactions, respectively, using a Green function technique. It is shown that for S=¹/₂ the two spin wave bound states are somewhat sensitive functions of alpha . As alpha increases they tend to go into the continuum. On the boundary of the Brillouin zone K_x=K_y= pi in two dimensions, and K_x=K_y=K_z= pi in three dimensions, the critical values of alpha for merging into the continuum are l/ pi and 0.093 respectively.

Magnetic susceptibility measurements have been made between 4.2 and 1.1 K on single crystals of cerium ethyl sulphate diluted with various amounts of lanthanum ethyl sulphate. It has been observed that the splitting between the ground and first excited levels of the Ce³⁺ ion varies with the degree of dilution, the levels actually inverting. This is attributed to the change in the crystal field, and a group theory argument is given for a simple model to show that such an inversion of the levels is permissible.

The transverse magnetoconductivity of photo-excited electrons in KCl, KBr, KI, NaI and RbCl has been studied at low temperatures as a function of the orientation of the magnetic field with respect to the crystal axes. The minimum of the lowest conduction band in these substances is found to be highly isotropic. The first studies are reported of the dependence on the orientation of the conduction electron spins of electronic transport in alkali halide crystals containing F centres. These measurements can be understood in terms of the interaction of spin polarized conduction electron with spin polarized F centres. It appears that the transport of photoelectrons at 4.2 degrees K in KCl, KBr and KI containing 10¹⁶ to 10¹⁷ F centres per cm³ occurs by a diffusive motion as in conventional transport theory and that a spin-dependent scattering or trapping time may be defined.

A long-range Ising chain, which has ferromagnetic 1/r³ type interactions, has been studied by exact numerical calculation of thermodynamic properties of the sequence of systems of N spins (N<or=30). By expressing the sequence in terms of a series and using extrapolation methods such as the Pade approximant, the authors have found a consistent way to obtain critical temperatures which is accurate to 0.4% for the very long-range equivalent neighbour model. The authors have estimated the high-temperature susceptibility and the low- temperature long-range correlations of the infinite chain and thence have made estimates for the critical exponents gamma and beta . Although the nature of the phase transition appears to be classical for 1<s<or approximately=1.3, it is certainly not classical for 1.6<s<2; in particular, as s approaches 2 from below, gamma increases regularly to about 2 or greater and beta decreases regularly to near 0.

The structure trend that is observed across the transition metal series as the number of valence electrons N increases 3 to 11 is explained quantitatively. The difference in the total one-electron band structure energy between the close-packed structures face-centred cubic and hexagonal close-packed is shown to determine completely which structure is favoured, whereas an additional hard-core repulsive contribution is necessary when comparing the body-centred cubic and close-packed structures at the noble metal end of the series. The calculations were performed assuming a model transition metal characterized by only the two d-resonance parameters epsilon _d and Gamma , from which the densities of states for the three structures were obtained using energy levels calculated by the hybrid nearly- free-electron tight-binding scheme of Pettifor.

For pt. I see abstr. A33227 of 1969. A method for calculating the energy bands of transition metals has been developed for 'complex' crystals (i.e. crystals with more than one atom per unit cell). This is an extension of previous work by Hum and Wong carried out to study the band structure of 'simple' crystals. The results obtained for hexagonal close-packed cobalt are reported.

A simple test of the validity of perturbation theory in the evaluation of energy differences between different crystal structures for sp- bonded metals is provided by a model in which the effect of only one band gap is considered. This model, which was previously discussed semi-quantitatively by Harrison and by Pick and Blandin, is here solved exactly for a local pseudopotential. Former ideas concerning the nature of 'Brillouin zone-Fermi surface interactions' are discussed in the light of perturbation theory and this more exact model.

The steady magnetic susceptibility of dilute substitutional alloys, in the absence of spin-orbit coupling is discussed. Band characteristics of the host are retained. A general expression for the Fourier transformed susceptibility tensor is given which may in principle be expanded in powers of the impurity potential. The zero-order term gives the perfect crystal susceptibility previously derived by Hebborn and Sondheimer. The first-order term is very complicated by a 'rigid band' model allows the impurity shift to be expressed in terms of the known pure crystal result.

Results of calculations of self-consistent potentials without exchange are given for Mg, Al and Zn impurities dissolved in Cu, Al and Mg metals. The contributions of the perturbing potentials around these impurities to changes in lattice parameter and compressibility are evaluated, and the results shown to be in fair agreement with the experiment. Finally, an estimate of the binding energy of beta -brass is obtained from the charge distribution around a Zn impurity in Cu.

The authors have calculated in detail the excitation spectrum and superconducting critical temperature for dilute non-magnetic alloys containing transition-metal impurities, the host metal being an isotropic Bardeen-Cooper-Schrieffer superconductor. The localized d states at the impurity sites are considered to affect the superconductivity due to the resonance scattering interaction as proposed by Zuckermann, and the model of Ratto and Blandin is used to take account of the Coulomb repulsion between d electrons of opposite spin. It is shown that these alloys are essentially Bardeen-Cooper- Schrieffer superconductors, with an effective coupling constant which decreases approximately linearly with impurity concentration until the superconductivity is quenched.

Measurements of the longitudinal and transverse magnetoresistance and Hall coefficient of indium antimonide in the magnetic freeze-out range are described. For magnetic fields greater than 5 kG, the longitudinal magnetoresistance can be readily interpreted, assuming conduction is only due to electrons remaining in the conduction band. This is considered to be more plausible than the interpretation of the Hall coefficient used by previous authors, in which it is assumed that a two-band model can be used up to quite high fields. On the basis of conduction by a single band, values of the donor ionization energy as a function of magnetic field are calculated, with no adjustable parameters, and compared with the theory of Yafet, Keyes, and Adams.

Simple models based on the free-electron approximation are developed to describe linear and non-linear optical absorption and dispersion in cubic semiconductors. The resulting formulae are programmed to enable numerical results to be obtained, and these are shown to be in good agreement with experiment.

The sensitivities of four common methods of analysing ultrasonic data on superconductors to common systematic errors and to deviations of the data from the Bardeen-Cooper-Schrieffer form are examined in this paper. Each method of analysis gives different weights to attenuation data taken at different temperatures. As a result the methods react differently to various forms of bias introduced either in the experiment or in the analysis. Some of the methods have particular advantages in that their graphical presentation of the data shows clearly the presence of systematic error or bias.

Spin diffusion in a degenerate Fermi liquid is studied, taking into account the effects of the 'molecular field' resulting from the interactions between quasiparticles. It is shown that even in the hydrodynamic limit no equation of the conventional form delta M/ delta t=Dgrad²M exists in general; the true equation is nonlinear and depends on the strength of the interactions. Substantial new effects are therefore predicted when lambda Omega ₀ tau _D> approximately 1, where Omega ₀ is the Larmor frequency, tau _D the spin diffusion lifetime and lambda a dimensionless parameter which measures the strength of the molecular field. Specifically, it is predicted that the spin-echo attenuation in a ' phi -180-180' experiment will in general not be exponential and will depend on the external field and the initial pulse angle phi . The new effects should lie in the experimentally accessible region both for pure ³He and for mixtures.

In a study of the mobility of ions in liquid He II in the temperature range 0.89 degrees K to 1.0 degrees K, the existence of the sharp periodic velocity discontinuities, first detected by Careri, was confirmed. The discontinuities were found to occur at integral values of a critical drift velocity v_c⁺=5.21+or-0.08 m s^-1 for positive ions, and v_c^-=2.12+or-0.16 m s^-1 for negative ions. Velocities were measured by a time-of-flight method, and at low values of the grid- source field, the previously undetected first discontinuity of the negative ions was found. Measurements were made of the magnitude Delta mu and shape of the first three discontinuities. The constant Delta mu values found for successive discontinuities and the observed lack of dependence of Delta mu on the grid-collector separation are is disagreement with the predictions of the vortex ring creation theory of Huang and Olinto.

The effect of a turbulent counter flow of liquid He II on the drift velocity of ions has been studied in a triode cell near 1 degree K. It was found that when the ion drift velocity in the applied field and the normal fluid flow were in the same direction then the apparent ion velocity was enhanced with a velocity increase greater than the maximum normal fluid velocity through the holes of the grid, while the critical velocity for a discontinuity was only slightly affected by the normal fluid flow. Negative ions were more strongly affected than positive ions.

The results were consistent with the trapping of ions in superfluid turbulence. The ions were trapped and then released closer to the collector so that their flight distance and hence their measured time of flight was effectively shortened to give an apparent increase in velocity. With trapping present it was not possible to determine whether the critical velocity of a discontinuity was to be considered as a velocity with respect to the superfluid or to the normal fluid. The origin and the spatial distribution of the turbulence are discussed and it is concluded that ion trapping occurred in superfluid vorticity which had been fed back with the normal fluid passing through the grid holes.

A re-interpretation of the Gaeta diode experiment is proposed in terms of the recombination of ions trapped in the vorticity produced by the high-energy particles emitted from the source.