Table of contents

An analytic formulation is given of the scattering intensity of a random stacking model for tetrahedrally bonded amorphous semiconductors such as amorphous Ge or Si, or amorphous III-V compounds and evaluated for an arbitrary probability of finding stacking faults. The formalism is obtained by modifying earlier work due to Wilson (1942) for the problem of stacking faults. The scattering intensity obtained is expressed as the sum of a discrete part and a continuous part. The discrete part corresponds to the 'invariant vectors' which were found by Betteridge (1973) and studied by Betteridge and Heine (1974). Through a careful analysis of the formalism a detailed explanation is given of the invariant vectors. Some preliminary results of numerical calculations are also presented.

Sound velocity measurements in Co-P are reported. The velocity of longitudinal and transverse waves has been measured around 90 MHz, down to 0.4K. The acoustical properties are similar to those observed in all other amorphous materials but the coupling parameter is very small (5*10⁶ erg cm^-3).

Zone-centre optical phonons in the layer crystal SnS have been studied by Raman scattering. The phonons observed for the given polarization configurations are consistent with the predictions of group theory. It is shown that SnS behaves approximately like a two-dimensional crystal. This work suggests that SnS is less anisotropic than GeS and GeSe, which have been studied previously.

The result of heat capacity measurements of chalcogenide systems Mo₅SnGa_0.5S₆ and Mo₅GaS₆ are presented. Near 20K the similar anomalies in the temperature dependences of C_p were found for both systems. Most probably these anomalies are connected with a magnetic phase transition in the magnetic compound Mo₅GaS₆, which exists as a second phase in the quaternary system Mo₅SnGa_0.5S₆.

It has been commonly observed that the Kapitza resistance between solids and liquid ³He at temperatures of 1 to 10 mK is one or two orders of magnitude lower than that expected theoretically. This has generally been explained by means of magnetic coupling between magnetic spins in the solid and the nuclear spins in the liquid ³He. It is proposed that the results can be explained alternatively by a size effect; when the temperature is sufficiently low for the dominant phonon wavelength to be comparable with the size of the solid, then the acoustic mismatch theory is modified and a lower boundary resistance is predicted. Qualitative, but not quantitative, agreement is found from this preliminary analysis.

LEED intensities, work function changes and fine structure in the Auger electron spectrum are reported for W(100) which show conclusively that the clean surface reconstructs on cooling below 400K to a c(2*2) structure. The work function of the c(2*2) surface is within 15 mV of the (1*1) surface. However, changes in the N₇VV AES transition during the transformation (1*1) to c(2*2) show some attenuation of the surface-sensitive feature which has been attributed to a W(100) surface state.

Single-crystal X-ray investigations reveal V-V pair formation and cation disproportionation in the insulating T phase of V_0.985Al_0.015O₂. At 173K the V(1) chains, which are comprised of V(1)-V(1) bonds of length 2.545 AA, have an effective charge of +3.8 per cation, whereas the V(2) chains containing V(2)-V(2) bonds of length 2.747 AA have an effective charge of +4.2 per cation. This indicates that 20% of the V⁴⁺ have disproportionated into V³⁺ and V⁵⁺. This disproportionation process explains why the lengths of the V(1)-V(1) and V(2)-V(2) bonds do not have roughly the same value. Also, it explains why the T to M₁ transition does not take place at lower temperatures. In the M₁ phase there is only one type of V atom and the V(1)-V(1) distance is equal to that of V(2)-V(2).

A superposition model of the anisotropic g-shifts of S-state ions substituted in crystals is developed. Its relationship to the existing theoretical and experimental situation is explored.

A band Jahn-Teller type mechanism is proposed for the 2*2 superlattice distortion observed in TiSe₂ below approximately 200K.

It is shown that for a class of models having Goldstone modes, any single-site theory must predict unphysical results.

A new effect is reported: weak ferromagnetism induced in a ferroelectric antiferromagnet (BaMnF₄) by means of a linear magnetoelectric interaction. The direction and magnitude of spin canting in BaMnF₄ are calculated and found to be in agreement with experiment.

The mixed phase region of the magnetic phase diagram of Fe_pMg_1-pCl₂ (p=1.00-0.71) has been mapped by a direct optical method. The tricritical temperature falls with increasing dilution by magnesium and is extrapolated to zero at p approximately 0.6, close to the percolation limit for a plane triangular lattice rather than the three-dimensional analogue, despite the essential three-dimensional nature of the metamagnetic transition. In contrast, the tricritical field tends to a finite value as p decreases.

The long-wavelength non-equilibrium properties of an incompressible Navier-Stokes fluid, in which the velocity field satisfies a non-linear Langevin equation with a bilinear streaming velocity, are studied using field-theoretic techniques. The velocity autocorrelation function (VAF) is expressed in terms of a renormalized perturbation theory, in which cut-off Feynman integrals display infrared divergences for dimension d<2. The VAF is studied for epsilon =2-d<O in terms of a self-consistent equation formed with the neglect of vertex corrections.

The nature of ionic hydration for the cations in NiCl₂ solution and the anions in NaCl solution has been investigated by neutron diffraction experiments on samples which have been isotropically enriched. Well defined hydration numbers are found for both the Ni²⁺ ion and Cl^- ion.

The main features of the nickel-nickel partial structure factor derived from neutron scattering data for a solution of NiCl₂ in D₂O are discussed within the framework of a model in which both ions are strongly hydrated and in which the interaction between the hydrated ions is represented by a hard-sphere potential.

For pt.I see ibid., vol.9, p.3911 (1976). The non-configurational entropy change associated with the formation of a Schottky defect in potassium chloride has been calculated by a method formulated by Mahanty and Sachdev (1976). The result of this calculation is compared with other theoretical estimates and with entropies derived from experimental measurements.

The field dependence of the elastic constants c₆₆ and ¹/₂(c₁₁-c₁₂) has been measured at 9 GHz in the cooperative Jahn-Teller system TmVO₄. The experiments have been performed at liquid helium temperatures using an ultrasonic pulse-echo overlap technique with a sensitivity of about 1 part in 10⁴. For the B_2g mode the Jahn-Teller coupling constants were found to be lambda /k_B=-1.0K and mu /k_B=3.2K. The ratio of mu to lambda is in good agreement with the molecular-field value of about -3. For the B_1g mode lambda '/k_B=-0.1K and mu '/k_B=0.35K; mu '/ lambda ' approximately=-3.5. From the critical behaviour of c₆₆, the critical index gamma was found to be 1.00+or-0.02. Measurements were also performed on the mixed crystal Tm_0.82Lu_0.18VO₄, and from the field dependence of the elastic constant ¹/₂(c₁₁-c₁₂), the importance of random strains in this dilute TmVO₄ system has been confirmed.

A strong scattering of phonons at level anticrossings in the low-lying states of Cr²⁺ in MgO has been observed as a function of magnetic fields. The observed spectra was found to be turning points, with respect to strain, of the magnetic fields at which level anti-crossings occurred. The B//(100) data could be accounted for by a computer diagonalization of the lowest fifteen eigenvalues on the basis of the theory of Fletcher and Stevens (1969) the values 3 Lambda =32+or-6 cm^-1 are obtained for the tunnelling splitting and D=2.5+or-0.5 cm^-1 for the reduced spin-orbit coupling, with the sign of the warping parameter, B positive.

The systematic improvement of complementary variational bounds on lattice thermal conductivity by scaling and Ritz procedures are discussed. A calculation is performed to show that a Ritz procedure gives a well converged limit of the improvement of a lower bound on the conductivity. This limit is found to be a far better result than a single scale factor yields. It is suggested that only a very small number of terms in the Ritz procedure are needed to reach the above limit when a much better lower bound is improved. The well converged limit is compared with results of various methods of calculating thermal conductivity using the same physical model.

In order to examine the cause of errors in atomic interaction energy calculation, the algebra for calculating energies by TFD methods has been developed, but using realistic electron densities derived from self-consistent field (SCF) wavefunctions. Electrostatic, kinetic and exchange energy terms are considered. Specific systems treated are: (i) lattice energy, pressure dependence of volume and phase transition pressures of ionic crystals; (ii) energy per atomic cell and lattice parameter of metals with non-overlapping ion cores; and (iii) repulsive energy of overlapping metallic ions. A simple method for the extraction of an experimental Born-Mayer potential from shock-wave data is also given.

For pt.I see ibid., vol.10, p.1855 (1977). In the previous paper, algebra was developed for calculating atomic interaction energies and derived properties by Thomas-Fermi-Dirac (TFD) methods, but using realistic self-consistent field (SCF) electron densities. The results of some calculations and comparison thereof with experimental values are reported in this paper. The main conclusion drawn is that TFD methods of calculating energy are reasonably accurate if realistic SCF electron densities are used. In all cases tested, the use of ²/₃ of the Slater-Dirac exchange energy improves agreement with experiment.

The charge density, momentum density and Compton profile of the electronic ground state of trigonal and polycrystalline selenium have been determined in the local-density formalism using the self-consistent symmetrized OPW method. Crystalline and core-orthogonalization effects are analysed in detail. The results are compared with experimental Compton profiles.

The influence of stacking disorder on Wannier excitons in layered semiconductors is discussed. In particular it is found that in the presence of stacking disorder the excitons are confined to a finite number of layers. The experimental results are discussed for GaSe. In this case the absorption spectra turn out to be strongly sample dependent. In general they show a pronounced fine structure near the exciton groundstate energy, which can be understood as a consequence of the disorder-induced localization of the excitons. The variety of absorption spectra observed in GaSe can be related to the different stacking orders occurring in this material.

The results of model experiments for critical behaviour of conductivity in two-dimensional percolation problems are presented. It is found that for the system consisting of conductive and non-conductive elements conductivity vanishes as sigma (x) infinity (x_c-x)^t; where t is equal to 1.15+or-0.2 for both bond and site percolation problems. For the two-component system consisting of metallic and dielectric elements it is found that if the fraction of the dielectric phase x with the conductivity sigma _D tends to the percolation threshold x_c above, the conductivity of the system increases as sigma (x)= sigma _D(x-x_c)^-q, where q is a new critical index. The value q=t=1.15+or-0.25 is obtained in agreement with the prediction of Efros and Shklovskii (1976).

A renormalization method recently proposed by Stinchcombe and Watson (ibid., vol.9, p.3221 (1976)) for the percolation conduction problem is modified by the introduction of a scheme for construction of the renormalization transformation based on a periodization of the lattice. There results a family of transformations, in which the larger domains give rise to the transformations which are increasingly more accurate (but more difficult to implement). The three exponents s, t and v are estimated for several two-dimensional cases and one three-dimensional case.

The role of self-consistency and of the atomic distortions in determining the electronic structure of the cleavage surfaces of GaAs and ZnSe has been investigated using the layer method and an iterative tight-binding approach, which takes account of the difference between the surface and bulk electronic configurations. Several surface bands and resonances are identified near the gaps and empty lenses of the projected bulk band-structure and their sensitivity to the modifications of the surface potential are discussed. In the case of GaAs the inclusion of the atomic distortions at the surface is essential in order to obtain theoretical results in reasonable agreement with the experimental data. For ZnSe the available experimental information does not permit discrimination between the ideal and distorted configuration of the surface atoms, in spite of the sensitivity of the occupied surface states to the atomic displacements.

A method is presented for calculating the directional photoemission spectra for arbitrary surface structures, including those which possess no translation symmetry parallel to the surface. The method is applied to several surfaces of copper and the results are compared with recent experiments. The determination of electronic structure for adsorbates is discussed, along with comments on the accuracy of current models of clean metal surfaces.

For pt.II see ibid., vol.9, p.2575 (1976). The two-dimensional spin-¹/₂ XY model is investigated for the two cases of quenched-site dilution and annealed-site dilution. On the square and triangular lattices, seven terms have been derived in the low-concentration expansion for the free energy and for the fluctuation in the perpendicular magnetization. Analysis of the fluctuation series provides evidence for a phase transition. High-temperature specific-heat curves are presented for possible comparison with experiment.

An exactly solvable model of a random classical Heisenberg model which shows the spin-glass state, is presented. The phase diagram at zero external field and curves of the susceptibility as a function of the temperature are given. The obtained formulas are compared with those of Edwards and Anderson (1975).

The pressure dependence of the dielectric behaviour of BaTiO₃, around the ferroelectric-paraelectric phase transition, has been investigated at pressures up to 45 kbar using a solid encapsulation technique and a specially designed test cell. It is found that, as the pressure increases, the line of first-order transitions goes over continuously into a line of second-order transitions at 34+or-2 kbar, 18+or-4 degrees C. The physical mechanism of the tricritical point is discussed in terms of the Landau theory and an expression is obtained which accurately describes the variation of transition temperatures in the vicinity of the tricritical point.

Field-induced spin reorientation in single crystals of the canted antiferromagnet GdFeO₃ has been observed using the Mossbauer effect with a magnetic field applied along the antiferromagnetic axis. Spin reorientation occurred continuously with increasing field. At sample temperatures of 4.2K and 2K complete reorientation was observed at critical fields of 1.2 T and 0.7 T respectively. At temperatures of 293K and 77K extrapolation gave complete reorientation at critical fields of 7.6 T and 8.1 T. The temperature dependence of the critical field is explained in terms of the interaction between iron and gadolinium ions.

The absorption spectra of ErCrO₃ due to the transitions from the groundstate ⁴I_15/2 of Er³⁺ to one of its excited multiplets ⁴I_9/2 have been measured, where spin reorientation induced by temperature and by magnetic field has been observed. The Kramers splitting energies and the g-values are obtained for the ground and excited states. The effective fields acting on Er³⁺ are deduced to come from the erbium-chromium exchange interaction.

The higher band, >or approximately=60000 cm^-1, observed by Sabatini, Salwin and McClure (1975) and Chase and McClure (1976) in the vacuum ultraviolet absorption spectra of divalent transition metal ions in fluorides is attributed to the 3d to 4p spin-allowed transitions. The interpretation is based on three characteristics: larger oscillator strength, low-temperature absorption enhancement and good correlation with the corresponding free-ion data.

The magnetically induced circular-polarized emission associated with the vibrational sideband of the ²E_g to ⁴A_2g transition of V²⁺ and Cr³⁺ ions at sites of cubic symmetry in MgO is reported. The Zeeman selection rules are derived and used to obtain a measure of the relative strength of the coupled T_1u and T_2u vibrations. In MgO:V²⁺ the intensity arises predominantly from T_1u rather than T_2u vibrations, whereas in MgO:Cr³⁺ the situation is reversed. The distribution of T_1u and T_2u vibrations coupling to the transition are obtained and it is noted that they compare favourably with published calculated distributions.

New fluorescence line-narrowing experiments carried out on the 6011 AA line of Pr³⁺ in LaCl₃ show evidence of a temperature-dependent process of relaxation between hyperfine states of the excited level ¹D₂A₁. Frequency distribution of the additional lines due to this relaxation leads to a determination of the second-order Zeeman hyperfine interaction. A detailed discussion of the small spectroscopic effects arising ( approximately=10^-3 cm^-1) on the levels under study is also presented.

Electroluminescence has been observed in anthracene doped by acridine (10^-3 mol.%) at 300K. No single relation for the dependence of brightness B on the voltage V_rms or frequency v of the applied electric field could be obtained to fit the entire range of observations. In the frequency range 50 to 500 Hz the brightness/voltage relationship is linear at low exciting voltages, but at higher voltages the relation B=B₀ exp(-C/ square root V) provides a better description.