Table of contents

The screened interaction V(r) between two opposite charges in the classical two-dimensional Coulomb gas is discussed. This interaction appears in certain response functions of the one-dimensional fermion system, when the latter is mapped onto the two-dimensional Coulomb problem. The effect of the power-law behaviour of V(r) on these response functions, when the large momentum transfer coupling constant (g₁) goes to zero from below and above the g₁=0 line, is discussed.

The coupling of lattice vibrations with the rotational motion of hindered methyl groups is considered. It is shown that the apparent activation energy for methyl group rotation is determined at relatively high temperatures by the methyl group torsional energy splittings, but at low temperatures it depends on the frequencies of short-wavelength lattice modes which couple relatively strongly with methyl-group rotation. The temperature dependence of the proton spin lattice relaxation time from 6 to 50K is reported for three samples containing methyl groups whose tunnelling frequencies have previously been measured very precisely. They are 4-methyl-2,6-ditertiarybutylphenol (MDBP) and two deuterated derivatives. The activation energy measured at temperatures between 18 and 50K is in good agreement with the splitting between ground and first-excited methyl group torsional states, as computed from the known tunnelling frequencies assuming a three-fold hindering potential. At temperatures below 15K the observed activation energy is only about half this value.

The authors present results of a theoretical study of the defect properties of Li⁺ doped MgF₂. The basic structure of the defect solution involves the creation of a self-compensated defect population of Li substitutionals and interstitials. These cluster to give a structure in which two Li⁺ ions occupy one cation site-a defect already proposed for these crystals by Kim and Nowick (Bull. Am. Phys. Soc., vol.21, p.265 (1976) and J. Phys. C, vol.10, p.509 (1976)). The authors also consider transport properties of the doped materials, and suggest that interstitial Li⁺ plays a major role.

The central force constants associated with the nearest-neighbour fluorine ions and the next-nearest-neighbour calcium ions have been calculated for trivalent rare-earth impurity ions in CaF₂. The results are consistent with force constants used to fit absorption induced in the far-infrared by rare-earth impurities. It is concluded that there is very little variation in the nearest-neighbour central force constant across the lanthanide series.

A high-resolution investigation has been made of the luminescence associated with the decay of excitons bound to neutral Al acceptors in Si. The principal bound exciton line, associated with the transition A degrees X to A degrees , shows a thermalizing structure due to J-J coupling between the two holes and the electron at the acceptor site. The first satellite line on the low-energy side of the principal bound exciton line shows a doublet structure with a component separation and intensity ratio similar to two of the components of the principal line, identifying it with the transition A degrees XX to A degrees X. The second satellite line is a singlet. These observations support one of the recent models for multiple bound exciton transitions.

The authors extend their theory (ibid., vol.10, p.49 (1977)) of collective modes in layer compounds to explain experimental electron energy loss results for graphite. The theory shows that four separate plasmons are produced, three of which are essentially free electron like but the fourth is a manifestation of 'local field effects' parallel to the C axis. A large peak in the epsilon ₂(q, omega ) spectrum is also found and shown to be a consequence of local field effects. This peak is thought to correspond to the pure anisotron proposed by Tosatti (1970). The authors also discuss the possibility that a low-frequency energy loss peak in recent experiments (performed at finite momentum transfer) may be due to an acoustic plasmon as predicted by their theory.

The author reformulates the proof by Aharony, Imry and Ma (Phys. Rev. Lett., vol.37, p.1364 (1976)) that, to all orders in perturbation theory, the critical exponents of a d-dimensional system with short-range interaction and a quenched random field are the same as those of a (d-2) dimensional pure system. The author thus shows explicitly the equivalence between these systems for terms with several momentum integrations, which involve non trivial combinatorial factors. If the forces are of long range, varying with distance R like R^{-(d+ sigma )}, the proposed equivalence between a d-dimensional random system and the corresponding pure system in (d- sigma ) dimensions is shown not to hold in general and this is demonstrated explicitly by a calculation to second order in in (=3-d).

The exponential absorption edge in amorphous semiconductors is discussed in relation to the Mott-Street model (Phys. Rev. Lett., vol.35, p.1293 (1975)) for chalcogenide glasses. It is shown that the absorption of a photon leads to neutralization of a donor-acceptor pair. The concentration of such pairs is exponentially dependent on the creation energy. The temperature, frequency and pressure dependence of the absorption and electroabsorption in amorphous materials are discussed.

For a phase transition between two phases of symmetries H and L<H, the authors reconsider the problem of finding the irreducible representation T_i of H that (according to Landau's theory) determines the transition. They show how this representation can be found directly (without going into the intricacies of the theory of induced representations and Landau's theory) from the permutation representation of H determined by the pair L<H. In all the examples considered, the group L is maximal with respect to the property that it acts trivially on some non-zero subspace of the representation space M_i of T_i.

The subgroups that arise in phase transitions from a high-symmetry phase are characterized as those subgroups that are maximal with respect to the property of acting trivially on a given non-zero subspace U_i of the representation space M_i of a given irreducible representation T_i of H. In the case of subgroups of finite index the problem is reduced to that of studying faithful irreducible representations of finite groups. The use of permutation representations considerably simplifies the theory. Tables of the equitranslation epikernels of the space groups are given.

A lattice model of crystal growth is defined in terms of conditional probabilities and is shown to be equivalent to an Ising model with multispin interactions subject to constraints. In special cases the crystal growth models and corresponding Ising models are exactly soluble and some of these solutions correspond to Ising models at their disorder points.

Powdered Ni-I-boracite, Ni₃B₇O₁₃I, was studied by X-ray diffraction between 77K and 300K. No deviation from cubic symmetry could be detected. However the cubic lattice constant changes abruptly at 120K, with volume increase of 0.23%, and also the Debye-Waller factor increases below 120K. This crystallographic change is correlated with observed anomalies in the temperature dependence of the magnetic susceptibility and the dielectric constant.

The authors have developed new potentials describing the short-range interactions between ions in the alkali halides. They have used the measured elastic constants to fix the near-neighbour overlap repulsion and study the second-neighbour potentials. The description of the next-neighbour interactions requires the inclusion of large van der Waals attractions, in general accord with latest estimates of these forces. They have used theoretical estimates of the repulsive part of the second-neighbour interaction and added a variable attractive part to fit the crystal data. The authors have first used a conventional Buckingham potential, but a more flexible form is required to provide a completely coherent picture of these interactions in the whole series of alkali halides.

The perturbation to the cubic crystalline field at rare-earth ions substituting the cation in CaF₂ is treated as a point-charge Coulomb field of the compensating ion. The cubic field energy states and the local charge compensation have enabled the author to calculate the wavefunction and g-values of Yb³⁺ and Ce³⁺ with tetragonal symmetry in CaF₂. The results for Yb³⁺ turn out to be in reasonable agreement with experimental g-values, while those for Ce³⁺ seem not unsatisfactory.

Two kinds of F centres, F_I and F_II, having the symmetry C_s may exist in BaCl₂ and BaBr₂ crystals. The calculation of the positions and the intensities of the optical absorption bands is made within the framework of the rigid point ion lattice model. The results obtained show that very likely there is one kind of F centre, these being F_I centres. Moreover this hypothesis enables the author to account for the EPR spectra with a good accuracy and to determine the hyperfine parameters.

The Mott-Littleton method (1938) for the calculation of defects in ionic lattices has been extended to include surfaces. The computational procedures derive from those developed by Norgett and Lidiard (1972). Calculations are reported for intrinsic defects at the (001) and (011) surfaces of NaCl and MgO and for Ca²⁺, Li⁺ and K⁺ substitution effects in NaF.

Landau's theory of fluctuations in second-order phase transitions is generalized for non-equilibrium open systems having one degree of freedom and displaying phase-transition-like phenomena in steady states. Taking diffusion into consideration, the fluctuations induce a spatial correlation function p(r,r') of the form (exp-( mod r-r' mod / xi ))/ mod r-r' mod when the situation is simple enough for a correlation length xi to exist. A general formula for xi is obtained. The stochastic master equation is formulated and solved for such systems in the absence of diffusion. Both thermodynamic and stochastic theories are applied to an intrinsic semiconductor model which shows a recombination-induced non-equilibrium phase transition as the external electric field is increased.

The small-signal transient and sinusoidal steady-state responses of a material with generation and recombination (G/R) of charge are considered. Immobile positive charge and mobile negative charge arise from the dissociation of intrinsic or donor centres and recombine bimolecularly. The mobile charge may react at electrodes. An exact solution for the steady-state admittance of the system is presented, along with exact and approximate equivalent circuits. The simple approximate circuits, made up entirely of frequency-independent elements are found to approximate the exact admittance to better than 1% for all frequencies and for realistic G/R conditions in the completely blocking situation. Similar accuracy is obtained for partly blocking conditions provided G/R and electrode reaction time constants are well separated.

The electron correlation effects in magnetite doped with impurities (Me_xFe_3-xO₄ with Me = Zn, Ni, Co, Ti, Sn, Li, Cr, Mg, Al, B-site vacancy) are studied on the basis of a Hamiltonian which describes the electron-electron and the electron-impurity interactions and is an extension of the Cullen-Callen model of magnetite. Treating this model in the case of low impurity concentrations x by means of a cluster approximation for Green functions the temperature dependence of the charge density oscillations around an isolated impurity and the Verwey transition temperature T_v(x) are calculated. The theoretical results for T_v(x) agree well with experiments except for titanium-substituted magnetite. For this ferrite the theory predicts an increase of T_v(x) with increasing x which represents a combined electron correlation and lattice structure effect.

The renormalization-group method is applied to the analysis of the critical singularities in Gamma _y(q), the correlation function of a non-ordering parameter y. The coupling between y and s, the order parameter with n components, is s²y. When alpha , the specific heat index, is negative, four types of tricritical behaviours are accessible within this Hamiltonian, while the other two may be accessible in other systems in which the non-ordering parameter is a vector. The scaling law gamma _y=(2- eta _y) nu is not only trivially fulfilled (zero identically) between the indices characterizing the leading term of Gamma _y(q), which is a constant, but is also fulfilled between the corrections to scaling, which are the leading singularities when alpha <0, although these are negligible compared with the regular terms.

For previous work by the authors see ibid., vol.10, p.581 (1977). The spin-1 antiferromagnetic system in the presence of biquadratic exchange has been investigated by making use of the angular momentum (spherical tensor) operator Green function in the RPA. Expressions for the sublattice magnetization and Neel temperature are given. The Neel temperature is found to increase with increasing biquadratic exchange parameter. In the limit of zero biquadratic exchange a result consistent with that obtained by Lee and Liu (1967) using Callen's approximation (1967) is obtained.

Formulae are derived for the relaxation and response functions of a paramagnet by generalizing the approach of Blume and Hubbard (1970). By circumventing their decoupling procedure it was possible to express both functions in terms of cumulants of spin operators of all orders. To the lowest order, the relaxation-function formalism gives the conventional mode-mode coupling equations (MMC), while the response-function formalism leads to a generalization of those which allow a consistent fit with the time-independent correlation function C_k=(S_k^zS_-k^z). If C_k is restricted to that from the spherical model the MMC equations are recovered. The relaxation function, considered in the next approximation beyond MMC, also results in no restriction on C_k.

The ²³Na nuclear quadrupole coupling constant is calculated for six compounds of the alpha -NaFeO₂ type, namely NaInO₂, NaCrO₂, NaTiO₂, NaTlO₂, NaScO₂ and NaAlO₂. The authors assume point-charge distribution at the lattice sites and take into account the effect of charges and effective (induced) oxygen dipole moments within a sphere of 50 AA around the site of interest. These calculations emphasize the importance of the dipolar contributions, with resultant polarizabilities in the range 0.2-1.4 AA³, in agreement with the results obtained previously by calculations of the EFG at the Fe site in alpha -NaFeO₂, CuFeO₂ and AgFeO₂.

The nuclear magnetic moment (uncorrected for diamagnetic shielding) and hyperfine structure parameters of ¹⁵⁵Gd³⁺ in ThO₂ have been obtained from ENDOR measurements performed at 35 GHz. The complete angular dependence of the ENDOR spectra can be explained by including a fourth-rank mixed tensor operator of second order in electronic and nuclear spin variables. Tetragonal stress-induced nuclear quadrupolar splittings were also observed and good agreement with estimates based on a point-charge model was obtained.

A comparison of H⁺ and H₂⁺ implantations has been used to change the equilibrium levels of intrinsic defects and thereby test the di-interstitial model of the V₄ centre. The H₂⁺ implants enhanced the aggregate defects, V₄ and M centres, as was expected in the high-flux conditions obtained along the component ion track. This observation is in accord with the di-interstitial model of the V₄ centre. A major change in the F/M ratio was also recorded.

The authors determine the magnitude of phonon-induced transition interference in the ESR and far-infrared spectra of Fe²⁺:MgO. The ion-lattice coupling constants are predicted for Fe²⁺:MgO using the ligand superposition model. An improved formulation of the theory of spectral moments is included. The broadening component associated with phonon-induced transition interference has a sign dependent on the mechanism for the optical coupling (E2 or M1), a temperature dependence identical to that of the conventional contributions, and a magnitude typically of 20% of the corresponding conventional contributions.

The authors describe a numerical technique for analysing thermoluminescence data when the thermoluminescence process involves a quasi-continuous distribution of activation energies, and first-order kinetics. The technique proceeds by synthesis of glow curves, isothermal decay plots and thermal quenching cycles until agreement with the experimental data is obtained. A possible method of documenting the spread of glass-to-rubber transition temperatures in organic polymers by analysis of thermoluminescence data in the appropriate temperature region is discussed.

An experimental investigation of thermoluminescence glow curves, thermal quenching cycles and isothermal decay plots in polystyrene has been carried out. It is concluded that the luminescence emission process follows first-order kinetics with respect to the concentration of trapped electrons, and that a quasi-continuous distribution of electron trap activation energies exists. The distribution of occupied electron traps immediately after irradiation peaks at 0.08 eV and stretches from a maximum lower bound of 0.05 eV to an upper cut-off of 0.45 eV. The effects of addition of various organic dopants, the application of an electric field, and increasing irradiation dose on the thermoluminescence emission have been investigated.