Table of contents

Thin films of indium and tin have been deposited on to substrates maintained at liquid helium temperature. The films are annealed in steps of approximately 15 degK towards room temperature. After each annealing the normal resistivity and enhanced superconducting transition temperature are measured. The resistivity is related to the mean grain size in the films. The analysis of the results shows that the variation of enhanced transition temperature with grain size can be explained by a model based upon the influence of `soft' phonons in the surfaces of the grains.

At energies above the lattice minimum electrons can only be localized by coherent wave-mechanical diffraction from the assembly of atoms. In crystalline semiconductors, for example, this gives rise to band gaps containing impurity levels. What features of the arrangement of atoms are necessary to produce such effects? Can band gaps be produced by diffraction from a structure without long-range order?

The linear chain model is useless, because it cannot be topologically disordered. We suppose only that we know the successive probability distributions for configurations of 2, 3, 4, etc., atoms. As shown by Edwards, these give rise to successive terms, Σ₂, Σ₃, Σ₄, etc., in the perturbation series for the self-energy correction Σ(, k) in the average Green function. These terms are rederived and expressed rather compactly by the method of cumulants.

Assuming directional averaging over many crystallites, we find that we must go to Σ₄ to produce the known band gaps even in a coarsely polycrystalline specimen. In any system without long-range order, the four-body distribution must have short-range orientational order - a tendency for the atoms to lie in chains, squares, tetrahedra, etc. - to make similar contributions to Σ. The Bernal liquid does not have this property; in other close-packed structures, local orientational correlations merely imply polycrystalline order. But the `tetrahedral glass' model of amorphous germanium, which is topologically disordered, nearly preserves relative bond angles, and hence may still give rise to gaps in the electron spectrum.

An exactly solvable model of a disordered Hamiltonian, valid in three dimensions, is presented. The ensemble-averaged Green function, and hence the density of eigenstates, for the model are found exactly. It is shown that the states in the tail of the distribution are not localized as has been suggested by several authors.

Electron-irradiated, additively coloured, halogenated and as-grown KBr crystals have been plastically deformed at 80 °K. Thermoluminescence and thermally stimulated current peaks have been observed during warming to 290 °K. These peaks are attributed to the release of electrons from traps produced by dislocation motion. The visible luminescence with a maximum at about 4500 Å is observed from electron-irradiated and halogenated KBr during warming to 290 °K after deformation at 80 °K, and is also observed during and after plastic deformation at 290 °K. It is suggested that the luminescence is due to electron-hole recombination at a trapped-hole centre which may be of interstitial halogen type.

Studies of the x-ray diffraction pattern from different potassium graphites have shown that intercalation of graphite by potassium is accompanied by an expansion of the carbon layers. This expansion is uniform within a single layer and is constant for all n carbon layers separating successive intercalate layers in the stagen compound of composition C_12nK (n > 1). Preferred values of the C-C bond length for stages 1 to 6, derived from the value of the a-axis parameter extrapolated to θ = 90° are:

Stage 1	1·43204 (3) Å
2	1·42592 (3)
3	1·4240 (1)
Stage 4	1·42305 (7) Å
5	1·42267 (6)
6	1·4221 (1).

Lower accuracy in stages 3 and 6 is due to slight variation between samples, attributed to deviations from the ideal stoichiometry. Before intercalation, the C-C bond length of the pyrolytic graphite was 1·42114 (3) Å.

The bond-length expansion is consistent with electron transfer from potassium to the antibonding orbitals in the upper π band of the graphitic region between successive intercalate layers. The discontinuous change of bond length with stage can be approximately represented by the relation: C-C (stagen) = (1·4203+0·0113/n)Å.

Application of hydrostatic pressure preferentially increases those overlap integrals which depend solely on the interplanar spacing of graphite, resulting in an increase of carrier density n, whereby d ln n/dP = 37·5 × 10⁻⁶ bar⁻¹. At absolute zero, the associated conductivity dependence d ln σ/dP = 28 × 10⁻⁶ bar⁻¹ is independent of crystal direction, but as the temperature is raised towards 295 °K the c axis coefficient falls to 25·5 × 10⁻⁶ bar⁻¹ whereas the basal plane coefficient falls to near zero. Pre-irradiation with fast neutrons (10¹⁶ to 10¹⁸nvt) restores all pressure coefficients measured on pristine material towards d ln n/dP. A qualitative explanation of these phenomena is obtained by the introduction of carrier-carrier scattering terms.

Vanadium-doped silver chloride is prepared by dipping vanadium metal into molten silver chloride. The vanadium enters the lattice substitutionally in the doubly ionized state. Silver-ion vacancies are associated with the vanadium ions in next-nearest cation positions at 93 °K. The symmetry of the crystal field at the vanadium ions is tetragonal and the values of the constants in the spin Hamiltonian are D = (557·2 ± 0·9) × 10^-4 cm^-1, A = (77·7 ± 0·5) × 10^-4 cm^-1, B = (76·3 ± 0·5) × 10^-4 cm^-1, g_parallel = 1·9657 ± 0·0007 and g_{perpendicular} = 1·9666 ± 0·0007. At 415 °K the vacancies are no longer associated. The field symmetry is octahedral and the values of the constants in the spin Hamiltonian are A = (77·7 ± 0·5) × 10^-4 cm^-1 and g = 1·9657 ± 0·0007. The situation is similar to that reported by Grossberg and by Daehler for manganese in silver chloride. The temperature variation in the width of lines which constitute the outer fine-structure components of the spectrum gives an activation energy of 0·30 ± 0·05 ev for vacancy motion. Vanadium-doped silver chloride is not found to be noticeably photo-active.

The acoustic paramagnetic resonance spectrum of V³⁺ in MgO has been found to have axial symmetry about a <100> axis of the MgO and can be described by an effective spin of one with g_parallel = 0·69, D = 10·2 cm^-1 and the hyperfine structure constant|A| = 0·0042 cm^-1. The ion is strongly coupled to the lattice with|G₁₁-G₁₂| >or= 1000 cm^-1 but|G₆₆| <or= 30 cm^-1.

The symmetries of paramagnons can be determined by considering the transformation properties of the appropriate wave-like magnetic-excitation creation operators. With the known symmetries of the magnons below the Néel temperature of an antiferromagnet it is possible to determine, in many cases unambiguously, the symmetries of the paramagnons above the Néel temperature. The method is illustrated by determining the symmetries of paramagnons in MnF₂ and NiF₂.

The dispersion curves for the coupled spin-phonon single-particle excitations in a linear chain are studied. Eigenfunction and eigenvalues of the collective modes are found using a particular version of perturbation theory for a part of the interaction, and treating the rest exactly. The results are compared with those obtained by other authors, and the relations among the various methods are investigated.

We consider for the conduction in ferromagnetic metals a model with two currents in parallel for supward arrow and sdownward arrow electrons and introduce the effect of spin-flip collisions. We calculate the contribution of spin wave-electron collisions to the mixing of the two currents and compare with the experimental results.

The theory of states at surfaces and interfaces is formulated applying the equivalent potential method previously used in the analysis of pseudopotentials. The surface boundary conditions are replaced by an equivalent `perturbation' localized at the surface, which exactly conserves scattering amplitudes and energy eigenvalues. For an abrupt discontinuity at an interface between two media, A and B, a central formula is obtained which factorizes the surface Green function. The factors involved depend only on the surface values of G_A and G_B, these being the Green functions of the corresponding medium continued into the entire space. This yields a completely new secular equation for the energies of the surface states, which avoids the need to do a complex band structure calculation. The method can also be used to study surface scattering (e.g. LEED theory) as well as surface impurities.

The formalism of the previous paper is applied to calculate surface states on two very simple models of a solid, in order to show the type of Green functions needed in practical applications of the theory. The first model is that of Shockley states in the gap of a nearly-free-electron band structure in one dimension. In the second model a band of surface states is split off from a single band in three dimensions.

A relativistic study is made of the surface states of one-dimensional heavy atomic crystals. Adopting Tamm's procedure, the Dirac equation is solved for a perturbed Kronig-Penney potential. Depending on certain existence conditions, the surface states can be classified into two categories, called relativistic Tamm and Dirac surfaces states. In the non-relativistic limit, the Dirac states disappear and the relativistic Tamm states become the well-known Tamm surface states. A detailed discussion is given of the surface energy spectrum.

The L and M X-ray emission bands of metallic copper are calculated in the one-electron approximation using augmented plane wave Bloch functions analysed into s, p and d symmetry components. The effect on the calculated intensity distributions of lifetime broadening due to Auger processes is estimated in a simple manner, and appropriately broadened curves are compared with the available experimental data.

A comparison is made between the temperature dependence predicted by short-range order and long-range order theories for the amplitude of the extended x-ray absorption fine structures of metals. It is shown that the difference between these predictions should be sufficient to permit a meaningful experimental comparison.

The energy bands and Fermi surfaces of silver and gold have been calculated by the Green function method. The exchange energy coefficient in a Gáspár-type potential was regarded as a variable parameter in order to provide optimum agreement with experimental values for Fermi surface dimensions. The original Gáspár potential provides excellent agreement with experimental results for both the Fermi surface and band gaps of silver. The optimization procedure is not as successful for gold, but agreement is nevertheless quite satisfactory when the exchange is reduced to 60% of the amount proposed by Gáspár. An attempt to correlate Krolikowski's optical desity of states peaks with our band structures for all the noble metals is not without success and comparison with other theoretical investigations indicates our band structures for silver and gold to be the most reliable ones produced so far.

The optical absorption spectra of copper and of gold have been measured polarimetrically as a function of temperature, while in ultra-high vacuum. The copper spectrum was obtained from 1·7-5·9 eV over the temperature range 77-920 °K and that of gold from 0·5-5·9 eV over the temperature range 295-770 °K. The main absorption peaks of both metals were found to vary with temperature and by comparison with calculations for the band structure of copper for various lattice parameters it was possible to identify peak positions with the following transitions: for copper, X₅ -> X₄prime at 3·97 eV, L₂prime -> L₁^u at 4·78 eV and L₁¹ -> E_F(L₂prime) at 5·32 eV, for gold L₂prime -> L₁^u at 4·08 eV and X₅ -> X₄prime at 4·55 eV.

The temperature dependence of the optical absorption spectrum of nickel has been measured over the wavelength range of 0·21-2·7 μm by means of Drude's method up to 500 °K in ultra-high vacuum. The following characteristics were found: (i) a small bump near 1·4 ev which nearly disappears above the Curie temperature, whose energy is unchanged with temperature; (ii) a large absorption peak centred at about 5 ev. The peak position decreases linearly with temperature at a rate of 4·4 × 10^-4 ev °K^-1. The width of this peak decreases with increasing temperature up to the Curie temperature. The change in width is interpreted in terms of exchange splitting of the bands. We assign the low energy (1·4 ev) bump to the transition between the bands near the W and K symmetry points and the main peak (similar 5 ev) to the transition from L_2prime to L₁ upper.

Using a triple-axis neutron spectrometer all branches of the phonon dispersion curves along the three major axes of zinc have been measured. The results for the Δ and Σ axes are in fair agreement with those of previous workers. Results for the T, Tprime axes have not previously been reported. All results have been fitted by a model with seventeen independent interatomic force constants. Though the fit to the measured phonons is adequate, the agreement with elastic constants is quite unsatisfactory. The more basic pseudopotential models cannot fit the data.

The surface resistance of single crystal terbium, dysprosium and holmium has been measured at microwave frequencies and at low temperatures. The results are combined with electrical resistivity measurements to yield an effective microwave permeability μ_R as a function of temperature. It is found that μ_R remains close to unity except for pronounced peaks in the neighbourhood of the Curie and Néel temperatures. The data on μ_R are used to obtain estimates of enhancement factors for nuclear magnetic resonance in the three metals. An anomalous absorption effect in powdered terbium is briefly discussed.

The phonon dispersion curves of β-brass have previously been measured by Gilat and Dolling and a fit was obtained to a Born-von Kármán model with forces extending to the fourth nearest neighbours. Although a factor of 10 was found between the second-nearest-neighbour Cu-Cu and Zn-Zn force constants, the data did not allow an identification of these constants. By comparisons of neutron group intensities from two β-brass crystals, one with normal Cu and the other isotopically enriched with ⁶⁵Cu, we are able to identify conclusively these force constants: α_Zn-Zn^2nd similar, equals 10α_Cu-Cu^2nd.

A vast number of experimental results is available for the cavitation pressures of many liquids but it is only in the past decade or so that such measurements have been carried out in the case of helium II. In this paper an attempt is made to estimate, theoretically, the cavitation pressure of helium II from a knowledge of the pair potential energy function and the radial distribution function. Finally there is a discussion of the limitations of the theory.

A hypothesis about ferromagnets near their critical points is used to deduce that certain combinations of critical amplitudes should have the same values for all lattices of the same model and dimensionality. This is confirmed rigorously for the spherical model and, to reasonable accuracy, for the Ising model.

A non-relativistic augmented plane wave calculation of the 5d-6s bands in gold has been carried out. A neck radius of 0·18 k_s for the Fermi surface agrees well with experiment but the TX belly radius of 1·036 k_s is too small and the TK one of 0·959k_s too large. Optical data indicate that the calculated s-d band overlap is too small.