Table of contents

The property of additivity of equations of state, when these are considered in terms of the excess entropy and density as the independent thermodynamic variables, is tested for the two-dimensional Lennard-Jones fluid.

Classical rate equations for the diffusional response of a tracer atom are solved exactly in the limit of small vacancy concentration. Analytical results valid in the small-wavevector, small-frequency limit are obtained which lead to exact results for the vacancy-assisted tracer diffusion coefficient. Numerical results for the dynamical correlation factor, as well as the incoherent response function, are given for cubic lattices over a wide range of frequencies and a variety of wavevectors.

The successive phase transition in (N(CH₃)₄)₂FeCl₄ is investigated by means of X-ray scattering. The incommensurate phase appears at 8.5 degrees C and the phase is characterised by the modulation wavenumber k_z= zeta c* with zeta =0.444 at the temperature. The parameter zeta decreases with decreasing temperature, and below -7 degrees C the monoclinic phase is realised, where zeta takes the commensurate value of ¹/₃. In the temperature range -2.5 to -6.5 degrees C, however, zeta is locked into another commensurate value of ³/₇. At atmospheric pressure, the ferroelectric phase characterised by zeta =²/₅ does not appear.

In a recent paper by G. Gumbs and C. Mavroyannis (see ibid., vol.14, p.2199, 1981), it is claimed that the Coulomb interaction between two electron-hole pairs on the same lattice site never produces excitons. It is shown that this statement is incorrect.

Egri (see ibid., vol.15, p.L461, 1982) has argued that one may ignore an identity when the RPA is applied. This identity ensures that the on-site Coulomb interaction does not contribute to the equation of motion of the Green's function. It is shown that Egri's statement is in disagreement with the Pauli principle. When the spin degeneracy of the system is removed, the derived results are in agreement with those obtained in the authors previous study.

A novel approach is applied to the problem of impurity states in anisotropic crystals. This approach combines the variational method with the perturbation method. It is largely independent of the existence of a naturally appearing perturbation parameter because it creates its own small parameter. Any trial function can be incorporated into the perturbative calculation and its validity can be assessed immediately. Some of the previous variational and perturbative results on the anisotropic impurity states are reviewed in this light. The method is very general and other possible applications are indicated.

It is shown that the valence of Eu in the Chevrel-phase compound EuMo₆S₈ remains divalent under pressures up to 16 kbar. Thus the possibility of a pressure-induced valence change (Eu²⁺ to Eu³⁺) accounting for the observed superconductivity of this compound under pressure must be discounted.

Measurements are presented of the temperature dependence of the elastic properties of two Gd-Y alloys. Both the 68.9 and the 70.3 atomic %Gd alloys exhibit at least two magnetic phase changes. However, temperature hysteresis in the 68.9% sample indicates that the high-temperature ordered phase is a spiral spin antiferromagnet, while for the 70.3% sample there is no hysteresis, indicating a ferromagnetic component even in the high-temperature phase.

Discusses the relative merits of time-resolved optically detected magnetic resonance (TRODMR) for investigating materials such as a-Si:H where there exists a wide range of luminescence lifetimes. The authors introduce the method of TRODMR by frequency response spectroscopy and determine the frequency response of the quenching and enhancing signals in a-Si:H. The technique is clearly applicable to a wide range of crystalline and amorphous semiconductors.

It is suggested that phase transitions induced by a magnetic field H//(111) in certain type I FCC antiferromagnets provide a physical realisation of the q=3- and q=4-state Potts models. The (H, T) phase diagram associated with these antiferromagnets for a field lying in the (110) plane is studied using mean field approximation and renormalisation group calculations in d=- epsilon dimensions. The phase diagram exhibits a critical and two first-order surfaces connected by lines to tricritical and polycritical points.

Several elastic constants of the perovskite-type layer-structure compound (CH₃NH₃)₂FeCl₄ have been measured. The anomaly of the C₆₆ mode and the lambda -type heat capacity near the structural phase transition from the tetragonal high-temperature phase to the orthorhombic room-temperature phase gave the critical exponents for heat capacity alpha = alpha '=0, the amplitude ratio A/A'=1.01 and the crossover exponent phi =1.21. This set of exponents confirms the results of the renormalisation group methods for the three-dimensional XY model (n=2, d=3). The elastic soft mode C₆₆ in the tetragonal low-temperature phase has been observed. The authors surveyed the somewhat questionable orthorhombic low-temperature phase under hydrostatic pressure up to 6 kbar.

Presents specific heat measurements on CsPbCl₃ near the three structural phase transitions, from the cubic (I) to the tetragonal (II) phase at T_c^I.II=319.1K, from the tetragonal to an orthorhombic phase (III) at T_c^II,III=314.3K, and then to a second orthorhombic phase (IV) at T_c^III,IV=310.0K. All phase transitions were found to have a large Landau contribution below T_c. At T_c^I,II and T_c^II,III Landau theory analysis indicates that the phase transitions are close to a tricritical point. At T_c^II,III and T_c^III,IV the specific heat has an additional contribution exceeding the Landau specific heat, with exponents 1.5 and 0.4, respectively. A hysteresis of 0.4K was observed at T_c^I,II.

Kawamura (see Prog. Theor. Phys., vol.61, p.1584, 1979) studied the solid-fluid phase transition of a two-dimensional hard disk system by using the Collins model when he neglected 4 coordination. The authors take account of 4 coordination and the attractive interaction. The thermodynamic functions of the two-dimensional system are calculated. The dependence of the transition point on the quantity of 4-coordination is studied. The equation of state and specific heat are discussed.

Details of the electron band structure have been calculated for NbSe₃ and FeNb₃Se₁₀. The structures of both compounds contain end-sharing trigonal NbSe₆ prisms, linked in chains parallel to the monoclinic axis. Partially occupied d electron bands are associated with these chains, and their quasi-one-dimensional nature is responsible for the characteristic charge-density waves and consequent unusual conductivity behaviour observed in these materials.

Correlation in extended systems can be treated by pairing spin orbitals which are occupied in the restricted Hartree-Fock scheme with virtual ones. The structure of the paired spin orbitals is analysed and specialised for each one of the eight classes in Fukutome's classification of general Hartree-Fock spin orbitals.

The solutions of the general Hartree-Fock equations for the electron gas are discussed with reference to Fukutome's classification. Solutions of different character are constructed by pairing occupied and virtual restricted Hartree-Fock spin orbitals. The results of illustrative calculations for k-independent pairing are described and discussed.

The authors study the effect of attractive Hubbard interaction on a disordered electron system. They map the interacting system back to the non-interacting one and determine self-consistently the disorder change due to interaction in the system.

It is shown that covalency provides a positive contribution to the c_k parameters describing the spin-correlated crystal field (SCCF). Estimates of the magnitude of this contribution are made which are consistent with experiment. A simple method of calculating the matrix elements of the SCCF is described and some examples are given in the hope that the SCCF can be routinely included in crystal field fits in future.

The energy distribution function for hot photoexcited electrons in GaAs is studied by means of numerical calculations. The calculations are appropriate to conditions of continuous monochromatic photoexcitation and lattice temperatures in the liquid helium range. A Boltzmann equation approach is used to take account of the following effects: injection of electrons into the conduction band (at an energy below the threshold for LO phonon emission), collisions between electrons of unlike spin, collisions between electrons of like spin, scattering of electrons by acoustic phonons via the piezoelectric and deformation potential interactions and departure of electrons from the band via recombination. The Boltzmann equation is solved numerically by using an iterative technique. The numerical results are used to show how the distribution functions are characteristic of the scattering events undergone by the photoexcited electrons. The results also lead to quantitative estimates of the range of electron densities in which the electrons have a quasi-equilibrium distribution and the range of electron densities in which the electron distribution does not have a quasi-equilibrium form.

The critical behaviour of the two-dimensional bond-diluted transverse Ising model is investigated by an approximate decimation transformation. The full critical surface is obtained and the behaviour of the correlation length in various scaling regions is also presented.

A scaling transformation is developed for the pure square-lattice-spin-¹/₂ Ising model with different exchange couplings J₁, J₂ in the two lattice directions. The transformation preserves Onsager's exact duality relationship and so can treat cases of strong lattice anisotropy. It is generalised to the dilute case and used to obtain critical exponents and critical curves (transition temperature T_c as a function of concentration p of magnetic bonds for various exchange ratios gamma =J₂/J₁). For gamma small, corresponding to weakly coupled chains, the transition temperature falls rapidly with dilution, then levels off, finally vanishing at the two-dimensional percolation concentration. Extensions are made to three-dimensional dilute magnets, including weakly coupled layer and chain magnets as special cases. Critical curves and exponents are calculated, and a quantitative description is obtained of various crosscovers between low- and high-dimensional behaviour which occur in the quasi-low-dimensional magnets as the transition temperature falls with dilution and the weak exchanges become significant.

Using the cluster Bethe lattice method the author formulates the quasi-spin model for itinerant magnetism in order to investigate the coupling between charge and spin fluctuations. Three ordering parameters are introduced: the concentration of up moments, the short-range and long-range spin correlations. Within this model it is shown that the introduction of short-range order can decrease the Curie temperature. The charge transfer between sites with up and down moments which can be of several tenths of an electron indicates that inter-atomic Coulomb and exchange interactions cannot be neglected in this model.

For pt.I see ibid., vol.11, p.2579 (1978). Reports measurements of the anisotropy of the effective masses of electrons and of holes in the layer-structured material red mercuric iodide, HgI₂. Cyclotron resonances were well resolved at 137 GHz, both with applied magnetic field parallel to and perpendicular to the c axis of the crystal. Assuming ellipsoidal constant-energy surfaces for the polarons masses the authors deduce the following values where subscripts e and h refer to electrons and holes while subscripts // and perpendicular to refer to motion parallel or perpendicular to the c axis: M_e//=(0.39+or-0.02)M₀; M_{e perpendicular to} =(0.36+or-0.02)M₀; M_h//=(1.55+or-0.1)M₀; M_{h perpendicular to} =(1.02+or-0.1)M₀. M₀ is the mass of the free electron. Band masses for the carriers are deduced and the results are compared with recent studies of Raman and of Brillouin scattering.

The orientation of the Fe³⁺ antiferromagnetic axis with respect to the crystal axis in ErFeO₃ has been deduced from Mossbauer measurements. Under various conditions of temperature and magnetic field applied along a specific crystal axis transitions have been observed whereby the Fe³⁺ antiferromagnetic axis rotates from one crystal axis to another. Spin reorientation transitions give information on the magnetic anisotropy energy of the Fe³⁺ system. The parts played by different mechanisms in contributing to this anisotropy energy are discussed.

The structure analysis of GaAs(110) surface is performed at room temperature using Jona's model for the GaAs crystal potential and the direct summation method for LEED intensity calculations. The author finds that for this lowest index non-polar surface of GaAs, the best comparison between theory and experiment is achieved for a rumpled first layer in which the As atoms move outward with respect to the Ga atoms such that the Ga-As bond rotation angle is 27.3 degrees . In addition to bond rotation, the surface layer contracts by 5% of the bulk interlayer spacing.

A very careful LEED analysis of the Ni(110) surface is given with two purposes in mind: (a) firstly, the authors clarify a controversy concerning the actual normal relaxation of the top layer: (b) secondly, they compare the merits and drawbacks of the three procedures used in their analysis (the R-factors of Zanazzi and Jona (1977) and of Pendry (1974) on the one hand, and the I(g) method on the other). In the present paper the authors describe the experimental aspects concerning two large and diversified data bases which they have collected with their home-made LEED goniometer, for the R-factor and the I(g) analysis respectively. The authors also show how qualitative information on the relaxation and/or on the presence of steps can be gained from the isointensity maps recorded for the specular beam.

For pt.I see ibid., vol.15, p.3223 (1982). The authors report on the r-factor analysis of the I(E) experimental part presented in the first paper. A critical discussion of the two more commonly used r-factors (Zanazzi-Jona (1974) and Pendry (1974)) is given, particular attention being paid to the size and to the nature of the data based on the final result. It is shown that small data bases may lead to different structural parameters depending on the choice of the r-factor. In this connection the normal incidence subset is a striking example of disagreement. On the other hand both types of r-factor analysis lead to similar models when the data base is diversified and large enough. Among the results obtained for the best model, the top layer is found contracted by 7%, much more than in all previous studies either by LEED or by medium-energy ion scattering. The energy dependence of the refractive potential is not only confirmed but is really a necessary ingredient for the quality of the final result. In addition, the surface refractive potential is found smaller than the bulk value by 2 eV. No evidence of more than a very few per cent random steps is found on the studied surface.

For pt.II see ibid., vol.15, p.3231 (1982). A LEED analysis of the Ni(110) surface is performed using the I(g) method. This method, which utilises the relative intensities of beams at individual energies, uses much less computer time than I(E) methods. Care must be taken with the normalisation procedure and choice of comparison scheme if it is not to be adversely affected by errors in the weakest or strongest beam intensities. A criterion for comparison is found which appears to give reliable results. The I(g) method yields results similar to those obtained from I(E) methods and is more sensitive to the surface potential barrier or a step distribution and is comparable with the best r-factor for normal relaxation.

The authors have investigated the diffraction of volume EM waves into surface EM waves (or vice versa) by surface acoustic (SA) waves, i.e. the three-wave mixing of volume EM, surface EM and SA waves, using a Kretschmann (prism/Ag film/air) configuration with the SA waves propagating in the Ag film. The diffraction intensity was measured as a function of the angle of incidence in the prism in a forward- and a backward-diffraction configuration. In the forward-diffraction configuration, the intensity shows a peak at angles of incidence corresponding to resonant coupling of volume and surface EM waves by the prism. In the backward configuration, the diffracted intensities show minima when either the input angle, or the output angle, corresponds to the resonant coupling of volume EM and surface EM waves by the prism. The observed maxima and minima in the diffracted intensities arise from the superposition of the volume to volume diffraction and the volume to surface (or surface to volume) diffraction contributions, which are in phase in the forward configuration and are out of phase in the backward configuration.

This paper deals with the theory of light scattering from a thin metallic film where corrugations exists at both surfaces. The scattering cross section for backward and forward diffraction is computed by solving perturbatively the Maxwell equations to first order in the corrugation amplitude. A comparison is made with the experimental results presented in the preceding paper where the corrugations are of dynamic character (surface elastic waves). The different behaviour of the backward and forward cross sections is explained in terms of interference effects.