Table of contents

The coherent scattering intensity from a binary system in which one component forms a lattice and the other is distributed at random is discussed. The treatment of the Ag-S term by Tsuchiya et al (see ibid., vol.11, p.651 1978) is commented on.

A sum rule is derived for the lattice gas relating the temperature derivative of the frequency dependent conductivity to the specific heat. The sum rule, which is exact to lowest order in the transfer term, shows that the frequency dependent conductivity has a singularity at the critical temperature of the lattice gas order-disorder phase transition. Related singularities have been observed in superionic conductors.

A representation of the free energy for the phi ⁶ theory in the range n limit is given in terms of the non-linear scaling fields. This is particularly useful for the study of the first-order transition in a tricritical system. In agreement with the picture of Nienhuis et al. (1976) the coexistence curve is characterised as a renormalisation group trajectory by the vanishing of a non-linear scaling field.

It is shown that the neutron spectra of superfluid He in the energy range about 2 Delta can be well explained by assuming the roton-roton coupling constant g₄ in the m=O channel to be repulsive. The endpoint of the single photon-roton curve is reconsidered by generalising Pitaevskii's theory to incorporate the finite lifetime of the single roton. The end point Q_c is shown to depend on temperature. Theoretical estimation of Q_c at 1.1K gives very good agreement with the experiment.

A Monte Carlo computer experiment gives the bulk conductivity of a 200*200 site square resistor network consisting of two kinds of unit resistor with difference conductance. An enumeration of clusters of one phase in the networks with 200*200 sites and 500*500 sites provides the percolation probability and an estimate of the critical probability 0.59<P_c<<0.60 for the square site system. The critical conductivity exponent is reported to be t=1.26+or-0.03 for the critical percolation probability p_c=0.591+or-0.001. The critical exponent of the percolation probability is found to be s=0.20+or-0.03 for the square site system.

The incoherent electron-phonon scattering rate determines an energy scale which can be larger than the temperature. This causes the transition temperature to the charge density wave state to occur at a constant value of resistivity. Experiments on 2H-NbSe₂ and 2H-TaSe₂ are in agreement with this result.

The photoluminescence spectrum of GaAs(Cr, Si) is studied over a wide range of Cr and Si doping levels. The 0.84 eV line associated with an internal (⁵E to ⁵T₂) transition of Cr²⁺ disappears in sufficiently n-type (N_e>or approximately=1*10¹⁷ cm^-3) material due to the conversion of all the chromium into the Cr¹⁺ charge state.

The multiple-scattering-X_alpha method is used to calculate the crystal-field parameters for Pr³⁺:LaCl₃. The necessity of using more than one Watson sphere for highly charged clusters is discussed. The calculation shows that this multiple-scattering-X_alpha method can be applied successfully to the description of crystal-field effects in rare-earth ions in solids.

Magneto-impurity resonances have been observed in all components of the magnetoresistance tensor of n-type InP at 20K, and in the warm electron coefficient beta determined by third harmonic measurements. The extrema show central cell structure similar to that found in the electronic transitions between shallow donor states, which can be observed by infrared techniques. This demonstrates that a simple electrical measurement can resolve differences of the order of 1% in the binding energies of impurities. The resonances are found to correspond to electron heating, suggesting that the dominant resonant process is Auger relaxation of the electrons to donor 1 s states.

A stringent test is applied to a set of approximations used, in an earlier work (CCFA) see Frank et al. (ibid., vol.11, p.208 (1978) to calculate T_c for the spin-¹/₂ Ising ferromagnet. In CCFA, all cumulant averages M_2n(2n>or=6) were approximated, for all the cubic lattices, and justified a posteriori. Here, a spin operator reduction relation allows one, for the SC lattice, to approximate only M₆, and moreover, to understand the approximation used. The extreme closeness at every stage (within 0.01%) of the present T_c values to those of CCFA gives one confidence method of approximating the M_2n for the BCC and FCC lattices as well. Here also, as in CCFA, the M₆₀ value of T_c is within 0.5% of the series approximation value of Sykes et al. (1972).

The frequency spectrum of the transverse current correlation function for the dense classical one-component plasma is investigated by means of a memory function which is derived on the basis of the strong coupling between the single particle motion and the density fluctuations around it for large values of the plasma parameter. The agreement with the computer simulation studies of Hanse et al., (1975), is good. In particular, for the largest value of the wavenumber investigated, the memory function displays features which are very close to those of the memory function of the velocity autocorrelation function for the value of plasma parameter Gamma =152.4. It is proposed that this similarity is probably responsible for the satisfactory reproduction of the three peak structure in the frequency spectrum for this value of wavenumber.

By constructing a microscopic form for the velocity field the author's have derived an expression for the velocity autocorrelation function in a simple liquid. It represents an analysis of the correlation function in terms of the longitudinal and transverse momentum current densities and correctly describes both the long and short time behaviour. The authors have applied the result to a model of liquid rubidium in order to see how the collective modes in the system influence the individual particle motion. It is found that the longitudinal current component is responsible for the oscillatory behaviour of the velocity autocorrelation function; the principle peak in the associated frequency spectrum is generated by the coupling of the particle velocity to the transverse current; the coupling to the longitudinal current produces the peak or shoulder at higher frequencies which is observed in computer experiments; and the diffusion coefficient is determined almost entirely by the transverse current component.

The author considers the effects of the presence of other atoms on the bonding between two atoms are studies in detail the changes in binding energy of a Van der Waals diatomic molecule in the presence of a hexagonally packed layer of atoms. For the diatom aligned parallel to the surface it is found that as the diatom is moved out from the surface (for fixed diatomic separation) the bond strength is at first enhanced due to two-atom interactions and then weakened as three-body forces dominate. This result would not be possible from a model treating the surface as a flat continuum and demonstrates the importance of structure in interactions near a surface. For the diatom aligned normal to the surface the bond strength is always enhanced. The importance of treating the many-body problem to all orders is noted. Computer calculations are made for rare gas atoms near a layer of the same type and estimates of the magnitudes of the changes in binding energy for various orientations of the molecule are given.

An estimate is made, using a bond polarisability model, of the long-range Van der Waals correlation energy in silicon. A value of -0.41+or-0.04 eV/bond is found, which compares reasonably well with a semi-empirical estimate of Harrison and Ciraci (1974). A Drude model approximation to the polarisability is discussed which simplifies the calculation considerably but gives good agreement with an estimate based on the experimental dielectric function. The estimated long-range correlation energy indicates that this contribution to total binding energy should not be ignored.

Measurements have been made of the concentration dependence of the size of the frequency crossing signals due to V³⁺ ions in Al₂O₃. These occur in the low-temperature thermal magnetoresistance at 3.1 T for fields along the c axis. The signal height varies approximately as (concentration)^0.7 and the width as (concentration)^0.15 and these variations are shown to be consistent with theoretical analysis when account is taken of the hyperfine splitting of the V³⁺ levels. The data confirm that the Delta M=2 transition is much more strongly coupled to the lattice than the Delta M=1 transition and lead to values of (G₄₄²+G₅₁²)¹2/=15+or-5 cm^-1 and (¹/₂G²+2G₁₅²)¹2/=425+or-210 cm^-1.

The experimental data on the phonon scattering by V³⁺ ions in Al₂O₃, including low-temperature thermal conductivity measurements, are reviewed and re-analysed in some cases. The revised experimental values of the spin-phonon coupling constants are compared with the results obtained from two theoretical models: the multi-mode full-lattice Jahn-Teller model and the 'crystal field' limit with no Jahn-Teller effect. It is shown that it is not possible to explain all the experimental data consistently, in particular the fact the the Delta M_S'=+or-2 transition is much more strongly coupled than the Delta M_S'=+or-1 transition.

The electronic contribution to the Kapitza conductance due to the overlap of metallic electronic wavefunctions and bulk He⁴ is calculated. A transfer Hamiltonian method is used. The magnitude of the interaction is obtained from Tankersley's calculation (1973) of the ground state of an electron in helium. It is found that the magnitude of the calculated conductance is larger than pure acoustic mismatch but typically not as large as experimental results. However, it is sensitively dependent on the nature of any states of adsorbed helium at the interface.

A numerical study of two-dimensional disordered electron systems in strong magnetic fields is performed. An extension to periodic boundary conditions is made, and the results for the ground and higher Landau sub-bands are obtained. The behaviours of the spatial extents of the eigenfunctions are investigated to study the Anderson localisation of the states near the edges of the Landau sub-bands, and the results are analysed in terms of the minimum metallic conductivity in this system. To further explore localisation from transport properties, the matrix elements of the current operator j have been calculated. It is shown that the matrix elements of j between localised states are smaller by one or two orders of magnitude than those between extended states. These results provide further evidence of the occurrence of the Anderson localisation in the present system from both the spatial behaviour of the wavefunctions and the transport properties.

The relaxed exciton trapped by a foreign alkali ion (V_Ke)_A in KBr has been studied through optical absorption and emission measurements by means of pulse radiolysis techniques as well as conventional X-ray excitation. The decay times of the pi -polarised 2.9 eV emission (V_Ke)_Na and 2.75 eV emission of (V_Ke)_Li are found to have a constant value of 2.5*10^-5 and 1.5*10^-5 s, respectively, below 60K. Transient optical absorption bands of (V_Ke)_A are observed at 1.65 and 1.5 eV for (V_Ke)_Na and 1.75 and 1.6 eV for (V_Ke)_Li, features of which are very similar to those of the self-trapped exciton. The initial state of the emission of (V_Ke)_A is thus identified unambiguously as the lowest triplet state. It is also found that the formation of (V_Ke)_Na decreases above 30K. The shifts of transition energies and changes in decay rates of (V_Ke)_A from those of the pure self-trapped exciton are discussed in terms of perturbation of a nearby foreign alkali ion.

For pt.I see ibid., vol.7, p.1595 (1974). Electroabsorption data are presented for anthracene in its crystalline and disordered forms. Particular emphasis is placed on the role of the substrate temperature T_s in determining the structure of vacuum-deposited films. For substrate temperatures below the optimum temperature for surface quality (T₀=-60 degrees C) two electroabsorption peaks are observed; the one at 396 nm is thought to be associated with anthracene molecules in a crystalline arrangement. However, the other at 405 nm is attributed either to a disordered phase or more probably to diffraction effects produced by orientational randomness of the anthracene crystallites. The magnitude of both peaks vary with the square of the electric field (quadratic Stark effect). The magnitude of the higher-wavelength peak reduces rapidly and monotonically as T_s reaches the region of T₀.

The d-dimensional, quantum-mechanical Ising model in a transverse field Gamma displays a critical line, Gamma = Gamma _c(T), which terminates in a multicritical point, ( Gamma ,T)=( Gamma _c(0),0), with the exponents of the (d+1)-dimensional, nonquantal Ising model. Analogous behaviour is found for a nonquantal, (d+1)-dimensional n-component model of finite thickness, L in the last dimension, with the replacement Gamma to T,T to 1/L. A field theoretic method is used to study crossover behaviour in the vicinity of the multicritical point, for 3<d<4, where the multicritical exponents are mean-field-like. Multicritical behaviour is found to be governed by a Gaussian-like fixed point of the renormalisation group, yielding the crossover exponent, phi _T=¹/₂(4-d). Crossover scaling functions are constructed to first order in epsilon =4-d for the longitudinal susceptibility and specific heat.

The EPR and optical absorption spectra of X-ray irradiated single crystal of Na beta -alumina have been examined. The most prominent absorptions are tentatively ascribed to an F⁺ centre at the O(5) oxygen ion site in the conduction plane. To this defect the authors assign an axially symmetric EPR spectrum which shows a resolved hyperfine structure due to interaction of the single unpaired spin with two equivalent ²⁷Al(I=⁵/₂) nuclei. The measured spin-Hamiltonian parameters are g/sub ///=2.0076(2), g_{perpendicular to} =2.0032(2), A/sub ///=1.665(2) mT, A_{perpendicular to} =1.617(2) mT, the defect symmetry axis coinciding with the crystal c axis. From the EPR linewidth it is inferred that the hyperfine interaction with three equivalent ²³Na nuclei is of order 0.2 mT. This defect is also optically active having a strongly polarised s to p_z transition with mean energy E_F=4.15(5) eV. The corresponding s to p_x,y optical transitions are not observed in the range of photon energies from 4.2-6.8 eV.

EPR measurements have been made on Ag²⁺ in sodium beta -alumina single crystals. Silver is introduced into the conduction plane as Ag⁺ by exchange with Na⁺ in amounts varying from 5 to 26%: Ag²⁺ is produced by X-ray irradiation at 300K. EPR results indicate that the Ag²⁺ occupies two sites of orthorhombic symmetry in the conduction plane. The measured g-values are g_x=2.0230(2), g_y=2.0678(15), g_z=2.2730(5) and g_x=2.015(4), g_y=2.0580(15), g_z=2.2335(4) where x, y, z are parallel to a*, c, a axes respectively. The hyperfine interaction with the ¹⁰⁷Ag nuclei is unresolved and estimated to be less than 1 mT. No motional effects are observed. Models are discussed for the two sites which involve an excess of O^2- ions in the conduction plane.

Mossbauer spectra of Rb₂FeF₅ show that it undergoes an ordering to a four sublattice antiferromagnetic state at 9.3+or-0.5K. The saturated value of the hyperfine field is 43.0+or-0.5 T, and is the same for both pairs of sublattices. This value is anomalously low for a high-spin ferric ion and corresponds to a zero-point spin reduction of about 28%. At finite temperatures the hyperfine fields at the iron nuclei are appreciably modified by the application of an external magnetic field. This behaviour is a characteristic of one-dimensional antiferromagnets. Relationships for the spin reduction as a function of the magnitude and direction of the external field are developed on the basis of spin wave theory. The measured values of the hyperfine fields are compared with those calculated from these relationships which leads to the ratio J'/J of the intrachain to interchain exchange constants being less than 10^-3 and the ratio B_A/B_E of anisotropy to exchange fields being around 4*10^-3.

Shake-up satellites in the X-ray photoelectron spectra (XPS) of transition-metal compounds are calculated on the model system of four clusters forming a square. Each cluster has a completely filled bonding orbital and a half-filled antibonding orbital besides a core orbital, and a small electron-transfer between the antibonding orbitals of neighbouring clusters is taken into account. The result of the model calculation shows that spread in the distribution of the shake-up satellites is induced by the transfer when it is comparable to the shake-up matrix element, and that, when the shake-up matrix element is very small as compared with the Coulomb interaction between electrons, the satellite intensities become very small. It is pointed out that the transfer-induced broadening may be operative in the shake-up satellites associated with the 2p-XPS of transition-metal halides, and that a large reduction of the shake-up matrix element may be responsible for the absence of similar shake-up satellites in beta -NiS and beta -CoS.