Table of contents

An idea suggested by Egelstaff, March and McGill (see Can. J. Phys., vol.52, p.1651 (1974)) that electron correlation functions for liquid metals could be extracted by containing X-ray neutron and electron scattering data is extended. Direct evidence is presented for liquid sodium and aluminium, using data already in the literature, showing a 'medium range' ordering of electrons.

Both the dielectric and the dilatometric measurements were made under various pressures up to 2 kbar. With increasing pressure, the transition temperature (T_n) decreases rapidly with the pressure coefficient dT_n/dp=13 degrees C kbar^-1, and this decrease in T_n supports the tunnelling model of the proton as a microscopic model for the phase transition. The large anomaly of the strain along the a(c) and the b axes was found close to T_n.

The formation volume per vacancy in a solid is usually determined from the slope of the isothermal plot ln D versus P where D is the diffusion coefficient and P the pressure. This analysis is based on the theoretical prediction that the local compressibility k^f is equal to the macroscopic one. It is shown that in some cases this theoretical prediction is possibly incorrect by a factor of approximately 2 and hence the analysis of the experimental data must take into account a correction factor of the form exp (- integral ₀^Pk^fdP). This correction factor can be explicitly expressed through anharmonic properties of the bulk material.

The (tracer) diffusion coefficient D has been measured by Mundy (1971) in Na, for various pressures up to 9.46 kbar, at T=288K. The plot ln D versus P showed a strong curvature, which has been previously attributed to the coexistence of various diffusion mechanisms. By following the theory described the authors calculate the local compressibility kappa ^f, of a single vacancy and they find that it exceeds the bulk one by a factor of 2-3. Therefore an important factor of the form exp integral ₀^p kappa ^fdP has possibly been disregarded in the previous analysis of the curve in D versus P. Considering the correction introduced by such a factor, they confirm that the curvature in the isothermal plot ln D versus P is exclusively due to the vacancy high local compressibility, over all the pressure range. The mean kappa ^f-value, calculated only from bulk properties, is in striking agreement with a recent analysis made by Gilder and Lazarus (1975).

The contributions to anion transport in AgBr by vacancies and vacancy pairs have been obtained from analysis of anion diffusivities and the temperature dependence of the Frenkel defect formation energy, as deduced from diffusion of sodium tracer. At high temperature, the two contributions are comparable. For the single-vacancy process, the activation energy and pre-exponential factor are anomalously large.

The author considers the equivalence between a disordered electronic system and the n to 0 limit of a Ginzburg-Landau field theory, with special attention to the convergence of the relevant functional integrals. It is shown that a non-zero density of states and a finite localisation distance are only possible if the loop expansion of the field theory diverges. This divergence is controlled by the existence of non-trivial solutions of the classical field equations which can be interpreted as the envelope of the localised wavefunction, at least at short distances. For the case of Gaussian randomness, a density of states is obtained in the tail of the band proportional to (-E)^d(5-d)/4 exp(-constant(-E)^2-d/2) in d<4 dimensions. For a finite band, the density vanishes near the band edge E₀ like (E-E₀)^-(d+1)/2 exp (-constant/(E-E₀)).

The author notes the possibility of nonlinear, collective transport and response mechanisms in a model superionic conductor, making use of (i) recent advances in the non-equilibrium thermodynamics for a driven system of interacting Brownian particles in a periodic potential, and (ii) evidence from recent molecular dynamics simulations for CaF₂.

By using the replica trick and a duality transformation, the bond-diluted random Ising model is mapped onto a new Hamiltonian. This demonstrates the higher order critical nature of the percolation point and identifies the appropriate crossover scaling variables. Taking the n to 0 limit of the replica method near the percolation point is shown to be equivalent to the q to 1 limit of the Potts model. The critical line near p_c is calculated, yielding for a square lattice exp(-2K_c)=2ln2(p-¹/₂)+0(p-¹/₂)².

An evolution of the activation energy of Debye's dipolar relaxation of NH₄Cl doped ice microcrystals is observed as a function of time. This evolution is characterised by the rotation of the relaxation line (log nu _c, 1/T) around a fixed point R in the direction of a decrease in the energy. The temperature corresponding to R is 273+or-4K for all the specimens, but the corresponding relaxation frequency rises with the salt content up to a limiting value corresponding to the crystal saturation.

The dispersion of the volume plasmon in single-crystal InSb films has been observed, by measurements of the inelastic scattering of 56 keV electrons with momentum transfers up to q=1.0 AA^-1. For momentum transfers q>0.2 AA^-1 parallel to different crystal axes, different dispersion curves have been found. In addition, the dependence Delta E_p(q²) yields a change in the slope in the region 0.15 AA^-2<q<0.25 AA^-2. These results are compared with those of other substances.

It is found that the dependence of angle-resolved photoemission spectra from a Cu(111) surface upon the direction of the polarisation of the electric field can be explained by a model based upon atomic dipole selection rules.

Based on a general theory given in an earlier paper the author presents results of numerical calculations of the dynamical structure factor S(q omega ), for liquid aluminium. Comparisons are made with recent molecular dynamics data.

KCN and NaCN crystals present a structural cubic to orthorhombic phase transition respectively at T₁=168K and 288K with a ferroelastic ordering of the CN^- ions and an antiferroelectric phase transition respectively at T₂=83K and 172K. The optical properties of F centres are studied between 4.2K<T<300K. In absorption the single Gaussian band observed in both crystals in the cubic phase (T>T₁) and attributed to the 1s to 2p transition splits in to three components in the orthorhombic phase (T<T₁). Below T₂ one observes a marked blue shift of the low energy band and, in KCN, the appearance of a small new band at 1.5 eV. These phenomena are explained theoretically by the symmetry change of the crystalline structure at T₁ and by the presence of a local electric field for T<T₂ due to the alignment of the CN^- electric dipoles which produces a internal Stark effect. The small absorption band in the near IR is assigned to the partially allowed (field mixing) 1s to 2s transition.

A consistent set of shell parameters for alkali halide crystals of both rocksalt and CsCl structures is reported. The fitting procedure, values of the parameters and their sensitivity are discussed. Short range interionic potentials are determined and are shown to give a good description of both static and dynamic properties of the crystals.

For pt.I see ibid., vol.11, p.1523 (1978). A set of interionic potentials of the Born-Mayer form is derived for the alkali halides. The specification is completely in terms of parameters of two types, (a) parameters which relate to the constituent ions and (b) parameters which apply to all crystals. Thus the parametrisation scheme contains no crystal dependent terms and is of a form which may readily be applied to systems of mixed alkali halides. Each of the nine ions is described by five parameters, its polarisability, its shell charge and three parameters which relate to the ion size. The van der Waals coefficients are calculated consistently from the ion polarisabilities. The model system, which has 47 free parameters, reproduces the lattice constants, high and low frequency dielectric constants and transverse optic frequencies for the 20 crystals to high accuracy. Of crystal properties which are not included in the fitting procedure, the cohesive energies are given in most cases to better than 1%, the NaCl/CsCl structural relative stability is correctly described in all cases except CsF, and reasonable phonon dispersion relations and elastic constants are obtained.

The phonon dispersion curves or TiC_0.95 at room temperature have been measured by inelastic neutron scattering in the main symmetry directions. Additional measurements have been performed on a sample of lower carbon content, i.e. TiC_0.89. The measured phonons are well reproduced within the framework of a shell model with free electron screening. The authors results confirm the correlation between the lattice dynamics and the formal valence of the metal atom found on other transition metal carbides.

The lattice dynamics of crystalline chlorine and bromine has been studied, using the simple bond charge (SBC) model previously applied to crystalline iodine. The model takes account of intermolecular as well as intramolecular covalent bonds. Good agreement with experimental zone-centre optical mode frequencies has been achieved, and mode instabilities of previous models are absent from the present calculations. The values of the model parameters, compared to those for the free molecules, and their variation from iodine to bromine to chlorine are quite reasonable. The consistency of the model is also supported by calculations of the cohesive energies of these crystals.

Neutron elastic and inelastic scattering studies have been made on single crystal samples of Pb_1-xSn_xTe (x=0.13, 0.20). Soft mode and Bragg peak intensity measurements gave no indication of the occurrence of a displacive phase transition. The energy widths of the soft TO phonons were observed to be strongly temperature dependent, ranging from approximately zero at liquid helium temperature to about 0.5 THz at room temperature.

The behaviour of correlation functions of the one-dimensional Fermi system at large distances has been investigated by reducing it to the Sine-Gordon model. The latter is dual to the low-temperature phase of a plane xy model. In this case the fermion operator is the product of the order and disorder parameters. The transitions to the coupling constants between different states of the Fermi system states of the Fermi system may be considered as phase transitions equivalent to xy models. The elasticity modulus and spin susceptibility serves as superfluid density. The question on the phase transition of the xy model is discussed.

Presents a simple qualitative model for the Stark Ladder spectrum based on the concept of a local band. The predictions of the model are supported by a numerical computation of the energy spectrum and wavefunctions for a finite one-dimensional model crystal potential. The results clearly show how a Stark Ladder develops when the potential difference applied to the crystal exceeds a given threshold value.

The formalism of Matsubara and Toyozawa (1961) is extended to consider the effect of non-orthogonality of the electronic orbitals centred on different impurities. A hard-core is introduced into the overlap matrix elements in order to eliminate possible spurious effects of non-physical superposition of impurity sites in the averaging procedure. The results of the non-physical superposition of impurity sites in the averaging procedure. The results of the density of states are compared to those of a similar work by Yonezawa et al. (1976) on liquid metals, and to Monte-Carlo calculations on a finite cluster made by Weissmann and Cohan (1977). The present results and the Monte-Carlo calculations agree as to the presence of several maxima in the density of states, eventually separated by gaps, when the concentration is within the range of validity of the Matsubara and Toyozawa diagram summation techniques. All calculations with overlap show a behaviour qualitatively different to models excluding its effect, particularly a smaller band-width, and a tail on the high energy side.

Magnetic ordering in the metamagnet ferrous bromide has been investigated by a variety of magneto-optical techniques. The optical spectrum in the region of the spin-forbidden crystal field transitions (12000-20000 cm^-1) closely resembles that of FeCl₂. The principal features have been assigned and a detailed field and temperature-dependent study (0-5 T, 4.2-15K) has been made of the band at 5026 AA, whose assignment as a magnon-exciton combination band is confirmed. Like a similar band in FeCl₂, its intensity varies as T² exp(-A'/k_BT) in the range 5-10K, giving the zone-centre gap in the magnon spectrum A' as 17.0+or-1.8 cm^-1 in agreement with neutron scattering experiments of Yelon and Vettier (1975). The intensity of the 5026 AA band also varies with an applied magnetic field (H//c) and at 10K reaches a maximum at 3.0 T, close to the metamagnetic transition field, reflecting a maximum in the sublattice disorder. The boundaries of this region have been mapped in the (H, T) plane. Using a transmission technique, the Faraday rotation of FeBr₂ has been measured in units of 90 degrees to angles exceeding 3000 degrees .

A general treatment is given of the response of vibrating-sample magnetometer pick-up coils to non-uniformly magnetised specimens. It is shown that the nth term in a multiple expansion of the sample magnetisation gives rise to a component of the induced EMF at the oscillation frequency, proportional to the (n+1)th derivative of the 'pick-up field', h, along the direction of the sample motion (h is the field such that h.m is the flux produced in the coils by a magnetic moment m). The analysis has been tested by observations of the signals produced by systems of small coils carrying a DC current. To illustrate the method, experiments on the remanent states of several ordered magnetic materials are described. Application of the method, using a SQUID magnetometer, to the possible measurement of the sublattice magnetisation of antiferromagnetic materials is described.

g shifts arising from interactions with singlet groundstate host lattice Tm³⁺ ions have been measured by EPR for Yb³⁺ at orthorhombic sites in cubic Tm₃Al₅O₁₂. The g values in absence of any Yb-Tm interactions (g^CF) have been deduced by two methods. The first involves measurement of the Yb hyperfine parameters (both by EPR and by Mossbauer techniques) which are related to the g^CF using the fact that J remains a good quantum number. The second method involves measurement of the g values as a function of host lattice susceptibility chi , the extrapolation to zero chi giving the g^CF. Complete agreement between the two sets of g^CF values was not obtained. The results show that in fact extrapolation of the g values as a function of the bulk isotropic susceptibility can lead to erroneous results when the local symmetry is lower than cubic. Obtaining the g shifts from the hyperfine values could be a generally useful method in low symmetry systems.

The relation between the frequency dependent dielectric constant and the fluctuations in the dielectric polarisation is re-examined from the standpoint of Felderhof's macroscopic theory of electric and magnetic fluctuations. Contributions of the electronic degrees of freedom to the polarisation are included in the formalism; they are treated as an instantaneous and non-fluctuating response to the electric field. The authors results provide a confirmation and extension of results obtained earlier using cavity and reaction fields. As such they should dispel any remaining doubts concerning this subject, which has been controversial for some time.

Room temperature measurements of the phonon dispersion relations in ferroelectric lithium niobate have been carried out by inelastic neutron scattering. Most of the measurements were made along the c* direction with two acoustic branches measured along an a* direction. The q to 0 slopes of the acoustic branches are found to be in good agreement with the ultrasonic sound velocity measurements. Results on the phonon frequencies are compared with the optical data. Measurements carried out at elevated temperatures up to 900K failed to detect any softening of the 'ferroelectric mode' (the lowest-frequency optic Gamma ₁ mode), thereby suggesting that the ferroelectric phase transition in lithium niobate is not associated with a soft phonon-mode instability. The possibility that the phase transition is of the order-disorder type, rather than the displacive type, is discussed, and, in this respect, similarities with the isomorphous lithium tantalate are pointed out.

This work concerns the experimental and theoretical study of Raman scattering in fluorides with the rutile structure. The authors measure the absolute value of the inelastic scattered light by comparison with the 992 cm^-1 band of benzene. They describe the experimental apparatus which has been used and discuss all the corrections that it is necessary to take into account. Some results on the Raman spectra of MgF₂, MnF₂ and FeF₂ crystals are reported.

Tin tetraiodide was chosen for a temperature and pressure dependent lattice dynamical study because of its pronounced anharmonic properties. The variation of the Raman spectrum with temperature from 100K to 298K has been measured using a single-crystal specimen. The temperature dependence of the mode frequencies and linewidths are given together with symmetry assignments. Further measurements were made at room temperature using a powdered sample under pressure, showing considerable variation in internal as well as external modes. Isochoric and isobaric temperature shifts, relative pressure shifts and Gruneisen parameters are obtained from these data. The group theory for this system is presented. The authors' analysis was confirmed by extensive lattice dynamical calculations, first using a model in which the molecules were assumed to be rigid units, and then using a model which gave the internal modes as well as the lattice modes. The pressure variation was also calculated using both models.

Thin films of solid oxygen were grown on smooth, glass substrates at 10K. The thicknesses and indices of refraction of the films were measured using a modified version of the Lummer-Gehrcke interferometer. The orientation of the molecules within the films is deduced from the birefringence by comparing the measured with the calculated indices of refraction for the possible orientations. It is found that these films are negative uniaxial with the optical axis normal to the substrate, and that the molecular axes are preferentially oriented parallel to the plane of the substrate. In addition, the internal reflection spectra of these films were recorded with the same apparatus as a function of light polarisation. It is found that the (0-0) band of the dominant, visible, double-molecule transition derives roughly the same fraction of its intensity from light polarised in the plane containing the molecular axes as it does from light polarised normal to this plane; whereas the (0-1) band of this transition derives the largest fraction of its intensity from light polarised normal to the plane containing the molecular axes.