Table of contents

An atomistic model of a dislocation, in which the scattering properties of each atom were described by a screened pseudopotential, was used to calculate the dislocation resistivity of aluminium. A value of 2.7*10^-25 Omega m³ was obtained, in good agreement with experiment.

Thermal expansion values of NaCl, KCl and CsBr are reported. It is found that the plot of a/a_m/2 versus t/t_m gives a common curve for the halides. Here T_m is the melting point and a_m/2 is the coefficient of linear expansion at T=¹/₂T_m. The plot is a straight line in the limits approximately=0.30<T/T_m< approximately=0.65 but deviates considerably from linearity at higher temperatures. Assuming that the deviations are due to vacancies, a relation between the energy of formation of Schottky defects and melting point is obtained.

Measurements of the temperature dependent quadrupole splitting in potassium ferricyanide are presented to show that there is a change in the local environment of the iron ion. These results correlate with the evidence of other measurements and are interpreted as a change in the crystalline state of the salt.

Mossbauer spectra from a single crystal of hydrated sodium ferrocyanide indicate a shift in line position with crystal orientation which is consistent with a quadrupole splitting of 0.56 gamma _o. Voigt profile analysis of spectra from powders indicates a smaller broadening of the Lorentz component, 0.27 Gamma _o; the inconsistency is explained by preferred orientation in the absorber samples.

Silver thiogallate is a transparent, pale yellow crystal belonging to point group 42m. The electro-optic coefficients of single crystal specimens grown from the melt were found to be r₆₃=3.0+or-0.1 and r₄₁=4.0;+or-0.2 in units of 10^-12mV^-1. The 25 MHz dielectric constants measured along and perpendicular to the optic axis are 14 and about 10, respectively. The results are discussed in terms of Miller's (1964) rule and the properties of comparable II-VI compounds.

It is shown how the methods employed in the second quantization formalism of the quantum many body problem can be adapted to study the statistical thermo-dynamics of an assembly of cross linked polymers. As an example, the distribution of a single multiply linked polymer is solved, assemblies are studied in the subsequent papers.

For pt. I, see ibid., vol. 3, no. 4, (1970) 739. The problem of the equation of state of n polymer chains each of length L, monomer length l, with m cross links between them, is studied. It is shown that this problem depends on two dimensionless coupling constants p=m/n and q=V/(n(Ll)³2/), i.e. the number of cross links per polymer, and the ratio of the specific volume per polymer to its 'natural' volume i.e. the cube of its mean square radius. The equation of state is derived. Polymer- polymer correlation functions which are of interest in light scattering experiments are discussed in the appendix.

For pt. II, see ibid., vol. 3, no. 4(1970) 750. A further application of the second quantization formalism is given in a study of syneresis of polymer solutions on cross linking. It is assumed that chains are long enough to neglect end effects, but that the chain segments are still able to move freely and that the only effect of molecular forces is to make them noninterpenetrable. Under these circumstances, the polymers will contract upon cross linking until the pressure, caused by the restriction of a chain by entanglement with its neighbours, balances the negative pressure due to the cross links. Formulae are given for large syneresis, but they simplify for that degree of cross linking at which the contraction begins.

The continuity equation has been used to determine the diffusion coefficient of colour centres in potassium chloride crystals by observing the radial variation of absorption coefficient in an electrolytically coloured semicircular disk. It is deduced that the diffusion of F centres is governed by the self diffusion of K⁺ ions.

The high-temperature value of the vibrational self-entropy of a point defect in a crystal is shown to be expressible rigorously in terms of the frequencies of pseudo-molecules built out of the point defect. The method is illustrated by taking as examples a few lattice models.

The vibrational absorption of a charged impurity in valency crystals has recently been discussed by the authors. It was concluded that the absorption by the impurity is determined mainly by non- electrostatic short-range effects, while the actual charge on the impurity is only of secondary importance. A part of this argument was based on a relation which contained the photoelastic constants of the pure valency crystals; in that relation the fact was neglected that in a diamond lattice an xy shear induces an 'optical' displacement in the z direction and that the measured photoelastic constant p₄₄ includes the effect of this optical displacement. In the present paper the effect of the optical displacement is investigated and it is shown that it does not affect the previous conclusions.

With specific application to diamond it is argued that inclusion of a large electron-lattice coupling can lead to a significant reduction in the value of certain integrals. In turn this can result in the violation of Hund's rule and give rise to mixed trigonal and tetragonal distortion. These effects are exactly those assumed to occur in the application of Hartree models by Watkins (1964) to predict the ground states and site symmetry of vacancy centres in silicon. The results indicate the conditions under which such models are likely to give valid conclusions. Extension of the ideas developed to excited states provides an independent check on their validity.

The integral equation for the Gruneisen parameter that governs the volume dependence of self consistent phonon energies is solved numerically for a model approximating to solid Ar at 0 and 80K and Ne at 0 and 23K. The equation is solved for several wave vectors that lie in the irreducible portion of the face centred cubic lattice's Brillouin zone. Exact solutions are compared with an approximation suggested by Horner (1967) and by Gotze and Michel (1968). For Ar at 0 and 80K respectively the true solution is found to be about 91 and 64% of the approximate one. For Ne at 0 and 23K respectively the corresponding numbers are 76 and 63%. The implication of this result for the calculation of self consistent elastic constants is discussed briefly.

The parameters for a representative two-body Morse potential are determined for the solidified inert gases by fitting to 0 degrees K solid data. This is done using first the harmonic approximation and subsequently the first-order self-consistent harmonic approximation, to describe the solid at 0 degrees K. On comparing the two cases, the effect on the potential of neglecting anharmonicity is found to be insignificant for xenon and krypton, small for argon but most important for neon. For neon, dispersion curves are calculated using the potentials found in the two cases and other Lennard-Jones potentials determined using various solid models to fit the 0 degrees K properties. The effect of the potential changes on the dispersion curve is marked.

The reliability of different forms for the bare electron-ion model pseudo-potential and for the dielectric screening function has been studied by calculating, at variable volume, phonon dispersion curves in the simple metals sodium, aluminium and lead. It is found that inclusion of exchange and correlation effects in the dielectric function is essential for agreement with experiment. Pressure derivatives of the elastic constants for these metals, as predicted from the Heine-Abarenkov potential, are reasonably accurate, while the pressure derivatives of the maximum phonon frequencies yield good qualitative agreement with the experimental pressure derivative of the superconducting transition temperature in aluminium.

Using the isotope ⁵⁷Fe, a Mossbauer study of the three Laves phase compounds PuFe₂, NpFe₂, UFe₂ has been made at helium (4K), nitrogen (77K) and room temperatures. Both PuFe₂ and NpFe₂ exhibit magnetic splitting at room temperature, but UFe₂ displays only a quadrupole pair. This material has a Curie temperature of 195K, and magnetic splitting is seen in the nitrogen and helium spectra. It is deduced that for these three materials in the spin-ordered state the hyperfine magnetic field points in a (111) direction, and that the magnetic spectra consist of two eight-line contributions, though the less intense lines are not resolved.

The difference in line position for two absorbers, one of ⁵⁷Fe in ⁵⁴Fe and the other of ⁵⁷Fe in ⁵⁶Fe, has been measured at room temperature and again at liquid nitrogen temperature. In terms of line energy E(=14.4keV) and displacements Delta E from this energy. ( Delta E₅₄- Delta E₅₆)_77K-( Delta E₅₄- Delta E₅₆)_290K=(0.9+or-0.6)*10^-15E. If the actual Debye temperature of the host were the determining factor, a result of 4.2*10^-15 E would be predicted, but a null result is predicted by the concept of an effective Debye temperature theta _eff= theta _host(M_host/M_impurity)^1/2 for an impurity in a lattice isotope with it.

For pt. I. see ibid., vol. 3, no. 4 (1970) 846. The magnetic hyperfine fields at the ⁵⁷Fe nuclei in host lattices of ⁵⁴Fe. ⁵⁶Fe and ⁵⁷Fe have been compared at 295 degrees K by a sensitive differential scanning technique. They were found to be the same within the experimental error of three parts in 10⁴.

Satellite lines in the emission spectra of compounds are explained by assuming cross transitions; that is, an electron vacancy in the energy level of one of the constituent atoms is filled by an electron from an energy level of another atom. The energy levels of the constituent atoms is filled by an electron from an energy level of another atom. The energy levels of the constituent atoms can be scaled relatively to each other by means of these cross transitions. Energy levels and the electron transitions between them are illustrated in a composite diagram. The energy levels in the composite diagram can be scaled relatively to the Fermi level once one level has been determined. The scaled composite diagram accounts for the X-ray absorption lines and for the systematic shift of the K_beta , emission line observed for elements and their compounds of the third row of the Periodic Table.

Eight polycrystalline samples of the spinel series Mg(Cr_xAl_2-x) O₄ with 0<or=x<or=2 have been prepared. The lattice parameters have been determined by the centroid method, and the variation with chromium concentration shows a positive deviation from Vegard's law, in agreement with recent measurements on single crystal material. An analysis of the integrated intensities from each sample shows that the normal spinel structure is maintained throughout the series investigated and that the temperature factor B increases from 0.4 to 1.1AA² as x ranges from 0 to 2. This effect and other similarities to certain manganese ferrites are interpreted as evidence that the Cr³⁺ ions are behaving as Jahn-Teller ions.

Previous theories of light scattering at low temperatures by magnons in a ferromagnet and in a simple two-sublattice antiferromagnet are extended to apply the entire temperature range. The Green function method is used to calculate the temperature dependence of the intensity and frequency shift of the light scattered in first-order by the spin systems. Numerical results are presented for MnF₂ and FeF₂. Theoretical expressions are also obtained for the temperature dependence of the strength of the antiferromagnetic resonance absorption.

For pt. I. see abstr. a4893 of 1970. A qualitative investigation of magnon interactions in alpha -Fe₂O₃ is given, and it is shown that the optic magnon modes may play an important part in the mechanism of the Morin phase transition.

The staggered susceptibility of a randomly dilute Heisenberg antiferromagnet is calculated and the critical temperatures estimated for various values of spin and dilution. For the first mode of ordering of the body-centred cubic lattice it is found that theta ₃/X=5.0p+e where e=1.37, -1.10. -0.88 for S=¹/₂. 1 and infinity respectively. theta _c is the antiferromagnetic ordering temperature, X=S(S+1) and p is the concentration of magnetic sites in the crystals.

The ground state of the one-dimensional antiferromagnetic model, with the Hamiltonian H=¹/₂ j Sigma _i=1ⁿ sigma _i. sigma _i+1+¹/₄j Sigma _i=1ⁿ sigma _i. sigma ₁₊₂ⁿ sigma _i. sigma ₁₊₂ (j>O, N even, N+1 identical to 1, N+2 identical to 2) can be given explicitly in terms of spin eigen-functions. Various properties of the ground state are studied. An approximate determination of the low-lying excited states shows the usual linear frequency-wave-vector relationship.

The properties of helicon waves propagating through polycrystalline metallic sodium have been studied. The 10 cm long cylindrical sample was about 8mm in diameter, and the experiments were performed inside a superconducting magnet at liquid helium temperature. The influence of the fields outside the sample was observed for the three modes investigated: the axisymmetric (m=0) and the dipole (m=+or-1) modes. Their dispersion relations and attenuations are compared with theory. The azimuthal phase variation (exp(+or-im theta )) was measured for the dipole modes and enabled them to be identified.

The mossbauer spectra of 1 at.%⁵⁷Fe in copper manganese alloys containing up to 90 at.% manganese have been obtained at 300K and 4.2K, and the ordering temperatures of the hosts found by observing the onset of magnetic splittings in the spectra. The 300K results show a double structure and have been analysed on the basis of a point charge model. However the alloys were, in general, not completely random and clustering of iron and manganese atoms around the iron impurities has been observed. The 4.2K data show that the broad spectra reported previously for copper-iron alloys are due in part to this clustering, and that the magnetic state of the iron atom changes according to the types of nearest neighbour atoms.

The results of the nonlinear analysis of acoustoelectric effects previously derived in connection with the acoustoelectric domain are applied here to the time independent amplification of ultrasonic waves of finite amplitude, and the correction to the linear theory which arises out of the acoustoelectric current is derived. The coupled space charge mode plays a critical part in maintaining electrical neutrality and in determining the correction to the growth constant is enhanced for omega > omega _om, unaffected for omega = omega _om and decreased for omega < omega _om, and a downward frequency shift occurs for all frequencies ( omega _om=frequency for maximum gain). The frequency shift is an order of magnitude weaker than change in growth constant.