Table of contents

The theory of Brillouin scattering by superfluid helium is discussed, and the predicted scattering for helium under pressure is shown to differ significantly from that quoted by Ganguly (Phys. Rev. Lett., vol. 26, 1623, 1971).

A method is described for calculating the variation of energy bands with composition in mixed zincblende type semiconductor systems using an empirical pseudopotential approach.

GdB₆ and GdB₄ have Neel temperatures (I_N) much lower than those expected from a comparison with the Tb and Dy compounds. Magnetic susceptibility, electrical resistivity and esr measurements reveal anomalies in the vicinity of the expected T_N. It is suggested that a significant amount of short range order sets in between here and the observed T_N.

Using a single crystal of MgO enriched in ¹⁷O transferred hyperfine interactions between isolated Mn²⁺ ions in the MgO lattice and nearest neighbour ¹⁷O nuclei have been measured by the ENDOR technique. The results can be interpreted to give the spin density in the oxygen 2s orbitals as 0.83%, while for the 2p_sigma and 2p_pi orbitals, the difference in spin unpairing f_sigma -f_pi , is approximately 0.7%.

The singlet density profile rho _Lg₍₁₎(z) at the liquid-vapour interface of argon at the triple point is determined by numerical evaluation of a modified Born-Green-Yvon equation. The resulting density transition is not monotonic but exhibits an oscillation. The possibility exists that certain simple liquid systems, particularly the liquid metals, could show pronounced density oscillations in the vicinity of the interface at the triple point. The monotonic profile is regained as the critical point is approached.

A variational determination of the angular form of the pair density rho ₍₂₎(z,r) at the surface of liquid argon at the triple point is given. It is found that a description in terms of the first and second unassociated Legendre harmonic functions allows several of the thermodynamic functions to be expressed directly in terms of the hybridization of the harmonics. The harmonic mode analysis of the pair density may be simply extended to more complex conditions of atomic anisotropy.

The Mossbauer fraction has been calculated for ⁸³Kr in solid krypton over the temperature range 5-100K, taking into account both the quasiharmonic approximation and the explicit temperature dependent anharmonicity. Calculations are reported for g( omega ) derived from the Mie-Lennard-Jones (MLJ, m-6) as well as Buckingham (exp-6) potentials. The results are compared with the experiment and discussed in the light of earlier calculations. The inadequacies of the model used are pointed out.

The following contributions to the potential at an isoelectronic impurity in a semiconductor are considered: (a) the nonrelativistic pseudopotential (b) spin-orbit coupling (c) strain effects. By a comparison of atomic potentials in relation to the periodic table, one finds that bound states are only probable when a first row element is involved or when a large, heavy atom replaces a lighter one.

For pt. I see abstr. a72486 of 1970. Recent evaluations of the frequencies of the dielectric relaxation modes in NaCl doped with Mn²⁺ and of the rates of two of the four types of jump available to a vacancy attached to a divalent ion, together with an experimental assessment of dipole population, are used as the basis of a reappraisal of an earlier experiment on anelastic relaxation by Dreyfus and Laibowitz (1964). It is shown that for the NaCl:Mn²⁺ system a new decomposition of the anelastic loss peaks is required which includes all of the relaxation modes. The kinetics of the vacancy jump rates W_i can be expressed in the Arrhenius form W_i=P_iexp(-h_i/kT).

Dielectric loss measurements show only one loss peak at a frequency f_m at any fixed temperature in the range 80 degrees to 150 degrees C. The values of f₀ and E in the equation f_m=f₀exp(-E/kT) are determined for lead doped KCl, KBr and KI crystals. The electrical conductivity measurements give the values 0.4 eV (KCl), 0.3 eV (KBr) and 0.4 eV (KI) for the energy of association of Pb²⁺ with a cation vacancy. On colouring the crystals, the dielectric loss peak disappears, the electrical conductivity decreases and new optical bands in the range of 240 to 300 nm are obtained. These results are attributed to the conversion of Pb²⁺ ions to Pb⁺ ions on coloration. On heating the KCl:Pb coloured crystals to a temperature in the range 300 degrees -500 degrees C, Pb⁺ changes to Pb⁰. On heating the crystals to higher temperatures, Pb colloidal particles are formed. Pb⁰ centres give rise to an absorption band at 214 nm and Pb colloidal particles, one at 240 nm.

Optical measurements have been made of the concentration of F and other colour centres produced in alkali halides by proton irradiation in the energy range 100-400keV. A treatment is given of a model of interstitial-vacancy recombination at high defect concentration which appears to explain many of the features of the approach to a saturation level of defects. At ambient temperatures F-aggregate centre formation is considered as the process which ultimately produces a real saturation in the F-centre concentration. At low temperatures the limiting process is thought to be the formation of substitutional hydrogen ions (U centres) as protons are captured by F centres. The observation of infrared absorption associated with substitutional hydrogen ions confirm that this combination of protons with F centres does occur, and may also contribute to the fall in F centre concentration which follows saturation.

Infrared absorption from the fundamental local mode vibrations of substitutional H^- ions (U centres) paired with Sr²⁺ and Ba²⁺ impurities in calcium fluoride has been observed. The spectra include absorption peaks near 965 cm^-1 which are shown to be due to two distinct types of centre, depending on whether the hydride ions occupy first or second neighbour fluorine ion sites to the alkaline earth impurity. The results are compared with those obtained previously for hydride ions paired with divalent rare earth ions in the same host lattice and with cation impurities in various mixed alkali halide crystals.

The elastic constants of a single crystal of NiO are determined by an ultrasonic measuring technique. Near the Neel temperature clearly defined anomalies are observed in ¹/₂ (C₁₁-C₁₂) and ¹/₂(C₁₁+C₁₂+2C₄₄) but not in C₄₄. These results are discussed in terms of the thermodynamic theory for second order phase transitions and the necessity for further measurements are emphasized.

The authors give a derivation of the van der Waals free energy of interaction between two semi-infinite media. The treatment, which includes the case of magnetic and conducting media, is valid for all temperatures and includes retardation effects. The method is an extension of one used by van Kampen (1968) and considers the free energy of electromagnetic surface modes in the region between the two media. The result reduces to that derived using Green function techniques by Lifshitz et al. (1961) for nonmagnetic media.

Lattice-dependent scaled temperature and field variables are shown to produce a generalization of the law of corresponding states. This generalization equates the appropriately scaled free energy of a system on different lattices in the critical region. The theory is tested by making use of the results of series analysis-in particular the critical amplitudes-for the Ising, XY and Heisenberg models, as well as the exact results known for the spherical model. The theory is found to be consistent with all the available data. The scaled field variable appears to be model independent, depending only on the underlying lattice, while the scaled temperature variable is found to be model dependent. It is shown that lattice-lattice scaling is a weaker form of scaling than that which includes the homogeneity hypothesis. It is therefore possible for lattice-lattice scaling to hold for those systems for which the homogeneity arguments does not apply.

Dispersion relations of phonons propagating along three symmetry directions in calcium oxide have been measured by the triple axis neutron spectrometer method. The experimental results have been interpreted in terms of a shell model showing that the electronic polarizability of both ions must be taken into consideration. The parameters of the most satisfactory model obtained by least squares fitting to neutron, elastic and dielectric data have been used to calculate the frequency distribution at room temperature. The results of the analysis are compared with those of similar analyses of the related crystal, magnesium oxide.

Tables are given of the isomorphism between real orbital operators and states and fictitious operators and states for all (3d)ⁿ ions in cubic symmetry. From these tables the spin-phonon Hamiltonian can be written down in terms of displacements of neighbouring ions for octahedral or tetrahedral coordination. Further tables of the parameters involved are given.

A canonical transformation of the original Hamiltonian of an interacting exciton-phonon system is used to obtain a new exciton-phonon interaction term. From the partly diagonalized Hamiltonian the mean free path of the renormalized exciton is calculated. Numerical results are obtained for the 40000 cm^-1 line of anthracene. The polarization has only a small effect on the selfenergy in this case but the mean free path, particularly its temperature dependence, is changed significantly by the renormalization.

A numerical method is employed to determine the nature of the eigenstates near the band extremities in two dimensional disordered arrays of potential wells. The states are found to be strongly localized within the band tails for both structurally and cellularly disordered systems. The range of localizing is found to be determined by the average size of a region which, at the current energy, is able to support a Bloch type state independent of its environment. The exponential modification of the wavefunction elsewhere in the lattice simply guarantees the localization. Comparison is made with the analogous behaviour of the wavefunctions near the band edges in disordered chains. The Anderson model for cellular disorder in a tight-bound band is also investigated. The observed localization of computed eigenstates enables a critical appraisal of existing localization criteria derived from a analysis of this model. It is found that the eigenstates are localized far beyond the Anderson and Ziman localization criteria.

A modified 'local density' approximation (LDA) is employed in a derivation of the density of state tails of the Anderson model for two representative disorders. The cumulative density of states N(E) is shown to be given by the number of special regions in the lattice which, at the energy E, are able to support a single localized electron state. A variational treatment relates the size of these regions to their local parameters and enables their average size to be determined. This latter quantity may be identified with the average range of localization of the eigenstates for energies deep in the band tails. Using it as the appropriate sampling size in the LDA results in an unambiguous expression for the density of states. The results obtained are in excellent agreement with numerical values.

The results of a nonspin polarized band calculation of the compound FeGe in its hexagonal phase B-35 are presented. The energy bands were obtained via the APW method and the energies were evaluated at 100 points in the first Brillouin zone. Slater's free-electron approximation for the exchange operator was used. The density of states histogram was constructed for a grid in the energies of 0.03 Ryd.

The possibilities of the Hohenberg-Kohn-Sham local density theory are explored in view of recent advances in the theory of the interacting electron gas. The authors discuss and provide numerical data for the effective exchange-correlation potentials mu _xc for ground state problems and V_xc for excitation spectra. The potential mu _xc(r) is written as a factor beta ( rho (r)), which depends on the local density rho (r), times the Kohn-Sham-Gaspar potential mu _x=-e²k_F/ pi . The factor beta , which is represented by a simple analytical formula, varies between 1 for very high densities and about 1.5 for very low densities, where mu _xc thus approaches the Slater approximation. The potential V_xc is given in the form of a table. The explicit predictions of the approximate theories are mapped in their linearized versions. The theory is also developed for the case when the ion cores are treated separately, and the local density approximation is applied only to the valence electrons.

The transverse components of the conductivity tensor of a number of specimens of n type indium antimonide in a magnetic field large enough to cause appreciable freeze-out are analyzed to give the electron concentration remaining in the conduction band. For magnetic fields greater than 5kG, the two-band model used by Miyazawa and Ikoma (1967) gives the same results as is obtained by assuming the contribution to the component of the conductivity sigma _xy of electrons frozen out is negligible. The donor activation energy E_D deduced from these measurements is compared with the values obtained from the longitudinal component of the conductivity sigma _zz.

The theory is developed of the propagation of high frequency thermal waves in dielectrics under circumstances in which phonons can undergo both normal and resistive interaction processes, each characterized by a frequency independent relaxation time. The first-order deviations from the classical results are examined in detail and it is suggested that measurement of these would allow independent estimates to be made of the normal and resistive process relaxation times. It is shown that present techniques should allow measurement of the effect to be conducted with reasonable accuracy.

The diagrammatic technique of Spencer (1968) is applied to the model of KDP and KDDP in which the long range electrostatic forces between protons and the long range coupling of protons with an optical phonon mode are considered. The results of the calculation are identified with the molecular field approximation and the random phase approximations.

The authors present a new technique for discussing the behaviour of spin waves in a ferromagnetically ordered system where the spins occupy random positions on a lattice. It is shown how a Hamiltonian and Green function appropriate to this random ferromagnet may be set up and used to describe the dynamics of such a system. An approximate evaluation of the averaged Green function gives the renormalization and damping of a spin wave mode due to disorder. An estimate of the critical concentration of the spin system is then given, and the authors conclude with a discussion of the effects of disorder on the spectral density function and density of states.

Dispersion curves for magnons and phonons propagating in KCoF₃ at low temperatures have been determined by means of neutron inelastic scattering techniques. Two branches of magnetic excitations have been observed corresponding to a transition between the two members of the ground state doublet (j=¹/₂) of the Co²⁺ ion and a transition between the ground state and the lowest member of the j=³/₂ spin-orbit level. Neither branch shows evidence for the directional anisotropy which has been suggested for the exchange interactions in KCoF₃; any splitting of the doubly degenerate magnon branch is shown to be less than 8% in frequency. The magnon branch of lowest frequency interacts with a phonon branch in the vicinity of the magnetic zone centre. The strength of the magnon-phonon interaction is found to be 0.35+or-0.10 THz and from the temperature dependence of the modes the magnon-phonon interaction is shown to be appreciable only within a radius 0.2*2 pi /a of the magnetic zone centre. The magnetic modes of higher frequency show a market decrease in intensity with increasing temperature but little change in frequency in accordance with expectations for a transition that depends strongly on the spin-orbit coupling but only weakly on the exchange.

For Pt. I see ibid. vol. 4, 2127. The theory of the low lying magnetic excitations of KCoF₃ is developed and the parameters describing the magnetic interactions are obtained by comparison with the experimental results of the previous paper. The branch of the elementary excitation spectrum of lowest frequency is well described by a phenomenological model with an effective spin s'=¹/₂. The exchange interaction has the Heisenberg form, and the pseudo-dipolar form of anisotropic exchange proposed for KCoF₃ is shown to be less than 8% of the isotropic exchange. A model which takes the orbital angular momentum of the Co²⁺ ion into account is developed by relating the elementary excitations to the quasiboson excitations between the ground state and all eleven excited states of the ⁴T₁ orbital level. This model fits the experimental results for the two branches of lowest frequency extremely well. The interaction between real spins is found to of the Heisenberg form and the spin-orbit coupling constant is found to be 82% of the free ion value. Calculations of the relative intensity of neutron scattering as a function of wavevector transfer for the modes belonging to the two lowest branches of magnetic excitations give good agreement with experiment.

Accurate high temperature neutron diffraction experiments have been carried out between 800 degrees C and 1200 degrees C on polycrystalline Fe_1-xO at compositions between Fe_0.947O and Fe_0.906O. The ratio of octahedral iron vacancies to tetrahedral iron interstitials is close to the value of 3.25 which would be expected if Koch-Cohen clusters persist in the high temperature equilibrium region.

It is shown that metastable states in systems of interacting bosons can be considered formally as corresponding to a broken gauge symmetry for the order parameter, or for the 'unstable mode'. An approach based on this result is used to study the Ising model, spin flop transitions, and the general theory of spin wave interactions. It is found that kinematic effects for the Heisenberg antiferromagnet can be strong, and representation dependent.

A theory of proton spin-lattice relaxation due to the rotation of hindered methyl groups is described. The theory bridges the gap between low temperatures when the motion may be described as a tunnelling rotation, and high temperatures when it is better visualized as a random jumping between three equivalent orientations. In this higher temperature range the theory reduces to that of Bloembergen, Purcell and Pound (1948). Two kinds of thermally activated transitions are identified between eigenstates of the tunnelling methyl group. Together these give rise to a frequency spectrum for the motion which differs very considerably from the Lorentzian spectrum assumed by the BPP theory. As a consequence, the temperature dependence of the spin-lattice relaxation time should be much more complex at low temperatures than has previously been recognized. The theory offers an explanation for some hitherto unexplained published results and indicates that T₁ studies are a sensitive way of studying the details of low temperature rotational motion.

The temperature dependence of the infrared absorption spectrum of NaNO₂ has been studied in the spectral range 700 cm^-1-2000 cm^-1. The absorption bands in this region are due to summation and difference bands of the internal vibrations of the NO₂^- radical with various lattice modes. Due to the high frequencies of the internal modes these combination bands are not swamped by one or two phonon lattice mode absorption. This has made it possible to tentatively assign frequency values for various lattice phonons at points away from q approximately 0 in the Brillouin zone. Combination bands also enable longitudinal optic and transverse and longitudinal acoustic modes to be assigned. An anomalous mode has been observed at temperatures greater than 373 K whose strength is highly temperature dependent but whose frequency is essentially constant at 240 cm^-1. The origin of this mode is discussed in terms of a change in the force constants between the ions due to the onset of the order-disorder ferroelectric transitions.

Expressions for the free carrier Faraday rotation and ellipticity are presented for p type cubic semiconductors with nonquadratic energy surfaces. At microwave frequencies, and in the limit of weak magnetic field strengths and small losses, the expressions are found to be sensitive to the extent to which the valence bands are warped. In addition, it is found that ionized impurity scattering affects the ellipticity more so than the rotation.

Under open circuit conditions a longitudinal emf is generated in a bar of p type germanium exposed to CO₂ laser radiation due to the transfer of photon momentum to mobile holes. At room temperature the polarity corresponds to positive holes being driven down the bar by radiation pressure but in some samples the polarity reverses on cooling. The authors describe this effect and the way in which the reversal temperature varies with doping concentrations greater than about 10¹⁵ cm^-3 the reversal temperature decreases rapidly so that with hole concentrations greater than 2*10¹⁶ cm^-3 no sign reversal occurs. These results are accounted for theoretically in terms of the known band structure of p type germanium and the effects of impurity and phonon scattering of light and heavy holes.

Mossbauer scattering measurements have been carried out on solid cyclohexane between 87 K and the crystal to plastic crystal phase transition at 186 K. Below the transition the mean square vibrational displacement of the carbon atoms has been derived. Limiting values for a relaxation time tau related to the molecular motion have also been derived. Just below the transition tau >7*10^-7s and just above tau <10^-8s.

Measurements are reported of photoluminescence from three defect centres in diamond which have characteristic absorption and emission lines at 1.673 eV, 1.944 eV and 2.498 eV respectively. When excited with plane polarized light the emission from the 1.673 eV centre was found to be unpolarized in agreement with a centre possessing tetrahedral symmetry. Analysis of the polarization of emission of the other centres suggests that the symmetry of the 1.944 eV centre is either monoclinic I or trigonal, and that of the 2.498 eV centre is monoclinic I. A comparison of the absorption and excitation spectra indicates that the lines at 2.887 eV and 2.954 eV and a broad absorption extending from 2.8 eV to higher energies are all associated with the 1.673 eV defect.

Irradiation of hexagonal germanium dioxide by fast electrons has been found to produce two paramagnetic centres. These are the oxygen vacancy, and the other is tentatively assigned to an oxygen vacancy-interstitial pair. The threshold energy for the production of both centres is 120+or- 5 keV, corresponding to a displacement for the oxygen atom of 18.1+or-0.1 eV. Annealing studies yield a unique activation energy of 1.1 eV at temperatures above 450 K for the retrapping of electrons at the oxygen vacancy. Below this temperature no unique activation energy for the annihilation of the vacancy by mobile oxygen atoms was found. For the supposed oxygen vacancy-interstitial pair two activation energies of 0.4 eV and 0.8 eV were found, corresponding to the displacement of oxygen atoms to two different interstitial sites.