Table of contents

Neutron inelastic scattering experiments have been performed to measure the scattering function S(Q, nu ) for liquid lead at 623K in the range of wavevectors Q from 0.4 to 1.6 AA^-1. For Q<or approximately=1.2 AA^-1 peaks in S(Q, nu ) are observed for non-zero frequencies nu , and their positions are found to lie on a fairly well defined 'dispersion curve'. The maximum frequency ( approximately 1.8 THz) occurs at Q_O/2, where Q_O(=2.2 AA^-1) is the value of Q at the first peak in the static structure factor S(Q). At small Q the 'dispersion curve' appears to have a slope consistent with the velocity of sound in liquid lead. No experimental evidence for transverse excitations in the liquid is found.

Measurements of magnetic excitations are reported for a wide range of temperature of Cr-Re alloy in the incommensurate spin density wave region. It is shown that the rapid decrease of the excitation intensity with falling temperature below the Neel temperature arises mainly not from the spin waves but from other types of scattering smeared out around the (100) point.

Using magnetoresistance measurements, it is shown that in PdCo and PtFe dilute alloys strict ferromagnetic order is broken down by weak random crystal fields. The disorder can be suppressed by applying moderate magnetic fields.

Results of the measurements of the residual conduction electron spin resonance linewidth in copper foils and silver foils and films are presented. From these results the probabilities of spin disorientation, epsilon , at the sample surface of both copper and silver are determined. For copper foils the value obtained is epsilon =(3.4+or-0.2)*10^-4 whilst for silver foils and films it is found that epsilon =(4.6+or-0.2)*10^-4 and epsilon =(5.9+or-0.6)*10^-4 respectively. All these values fall substantially below those predicted from simple theory based on spin-orbit coupling. It is indicated that a reconsideration of previous epsilon interpretations is necessary.

Nuclear acoustic resonance on ¹¹⁹Sn was observed in a single crystal of white tin with natural isotopical composition. At a temperature of 4.2K the following values of the Knight shift were determined: K_iso=0.717%, K_ax=0.0288%.

Equilibrium grain boundary segregation is assessed in terms of its measurement, theory and industrial significance. Aspects of the phenomenon of this segregation, namely the localisation, chemical system dependence, response to environmental parameters, etc., are discussed in relation to the measurement techniques for grain boundary segregation. These techniques-the interfacial energy approach, AES, XPS, STEM with X-ray analysis and the atom-probe FIM-are analysed in terms of their unique contributions. The theories of segregation are presented in a unified framework which uses analogues of the theories for gas adsorption on free surfaces. The cases of limited and unlimited numbers of sites are treated. Thus, McLean's segregation theory is seen to be the counterpart of Langmuir adsorption and a self-interacting segregant is seen to follow the analogue of the Fowler theory. The Fowler theory is extended to ternary systems and accurate methods of estimating the value of the relevant fixed parameters are presented. The kinetics of segregation and desegregation are then outlined. A range of material aspects affected by grain boundary segregation are described.

For pt.III see ibid., vol.9, p.2307 (1979). In part III theoretical images of small edge and non-edge dislocation loops in an isotropic BCC crystal were presented. The results demonstrated that the images from edge loops are indeed modified on going to the non-edge configuration, but that with certain exceptions the simple classification proposed for edge loops (in parts I and II) still provides a means of describing non-edge images. It was further established that several features of the images provide a powerful method of analysing the geometry of non-edge loops. Their practical application in analysing a mixed population of ¹/₂a(111) and a (100) vacancy loops in ion-irradiated molybdenum is explored. The results show that close agreement can be achieved between theory and experiment when the loop geometries and conditions under which the two images are obtained correspond. Further, this approach of comparing two-dimensional computer simulated images and experimental images in several diffraction vectors allows a thorough analysis of small non-edge dislocation loops.

Using the local Heine-Abarenkov model potential, the effective ion-ion potential and interatomic force constants of alkali metals are calculated, and are compared with the results obtained using other models. The interatomic force constants so obtained are in good agreement with those derived from fitting the experimental phonon spectra and give a set of important data for the binding forces of crystals with various lattice defects. Dynamical elastic constants are also calculated using the long-wave phonon method and are also compared with results obtained using other models. The compressibility problem, proposed by Brovman and Kagan (1970), is that the two (static and dynamical) methods for calculation of the elastic constants in terms of second-order perturbation based on the same pseudopotential do not give identical results. This problem is investigated quantitatively and is shown to be important for alkali metals.

The low-temperature specific heats of an initially amorphous Pd-Si alloy subjected to various heat treatments are measured in the temperature range 1.5-4.2K. All the results fit well to the usual equation C= gamma T+ alpha T³+ delta T⁵. As recovery, or crystallisation, proceeds with heat treatment, the Debye temperature theta _D is found to increase, while the delta coefficient decreases. It is found that the lattice specific heat behaviour can be interpreted on the basis of a comparison to the observed relationship between theta _D and delta in a number of crystalline metals and alloys. This comparison suggests that the lattice vibrational modes of an amorphous and of a crystalline Pd-Si alloy at low temperatures are rather similar to those of many crystalline metals and alloys, and that the observed change in the theta _D and delta coefficients due to the heat treatment merely results from an increase in the packing fraction of the constituent atoms.

The correct qualitative features of the excess volume and excess entropy curves for liquid Al_cMg_1-c alloys are obtained by ab initio calculation. The main feature in each curve is pronounced minimum on the Mg-rich side and this is unequivocally given by the theory (albeit in exaggerated form). A further feature in the observed excess entropy is a slightly positive region for Mg concentrations of less than about 10%. This can also be explained provided we use the calculated excess volumes in this region, these being about half the observed ones. The pseudopotentials used describe well the pure liquid components near the melting temperatures.

The structure of the Sigma =5 tilt grain boundary in aluminium was simulated by molecular dynamics using the Morse potential. Two types of structure were obtained. The local density of states (LDS) of phonons was calculated by the recursion method developed by Haydock and colleagues. The Debye parameters ( theta _D(n)) were found to be very small near the boundary plane and there were large mean atomic displacements in the direction perpendicular to the boundary plane.

The Lloyd formula (1967) for the density of states (DOS) of a finite cluster on nonoverlapping potentials in free space is derived in a direct way by local integration of the Green function of the system in the r representation. Similarly a new expression is derived from the DOS per atom in a disordered binary substitutional alloy, which is valid within the muffin-tin single-site coherent potential approximation. It is shown that this expression is equivalent to the one that is usually derived from the Lloyd formula, but that its numerical evaluation is simpler. Alternative expressions for the component DOS are also discussed.

The electronic density of states in a long-period superlattice is investigated. Using the transfer matrix formalism, exact solutions are obtained for a one-dimensional model consisting of two square well potentials of finite depth and width. New energy bands and minigaps are found to develop not only in the bound state region but also in the ionisation region.

The relativistic augmented spherical wave (RASW) method of Takeda (1979) is applied to energy band calculations for gold. Based on the atomic sphere approximation, calculations are performed for different potentials; the X alpha potential with various values of alpha (2/3, 0.8, 0.9 and 1.0) and the potential proposed by Hedin and Lundqvist (1971) (HL potential). It is shown that the bandstructure for gold is very sensitive to the choice of potentials. By comparing the numerical results with experimental values, the following conclusions are reached. The HL or the X alpha ( alpha =2/3) potentials give the most reasonable values for the Sommerfeld coefficient of specific heat. The X alpha ( alpha =2/3) potential is the best for the cohesive energy. The X alpha ( alpha =0.8) potential gives a very good reproduction of both the optical transition energies and the Fermi surface parameters. The last value of alpha , alpha =0.8, is in good agreement with alpha =19/24 approximately 0.79 reported by Kupratakuln (1970).

The self-consistent semi-relativistic APW method has been employed to calculate the bandstructure of lead and its electronic density of states from first principles. The results of the calculation agree with optical and specific heat data to within 30 and 1% respectively. Calculated frequencies for the second band hole surface agree with experimental Fermi surface results to within 4%. An application of the bandstructure results to the study of the electron-phonon interaction and superconductivity is made including the variation of these properties upon alloying lead with bismuth. These results are also in good agreement with experiment and demonstrate the increase of the superconducting transition temperature for the Pb-Bi alloys.

Results of bandstructure calculations of Tc, which has a HCP lattice structure, are used to calculate the superconducting transition temperature T_c and the Fermi surface of the metal. The strong-scattering theory of Gaspari and Gyorffy (1972) is used in conjunction with McMillan's formula (1968) to calculate T_c in the spherical band approximation. As the bandstructure calculations were made for potentials constructed with and without correlation, the superconducting transition temperature is calculated for all potentials. The theoretical values of T_c are found to be very sensitive to changes in the electron-phonon enhancement factor lambda and the Coulomb pseudopotential mu *. However the theoretical value of T_c calculated for a potential which includes correlation agrees well with the experimental value for a particular choice of mu *. The Fermi surface cross sections are obtained for all the potentials and a qualitative comparison is made with the available preliminary experimental results.

A general procedure for constructing doubly occupied Wannier functions for metals is described. It is based on the direct minimisation of the total crystal energy. The result is a non-iterative scheme that gives a self-consistent description of the electronic properties of metals. An application to BCC Na shows good results in the lower approximation for integrated properties.

The liquid alloys of Li and Cd, the electrical resistivity and the Knight shift have been measured over the entire concentration range. The resistivities can be explained fairly well within the Ziman diffraction model. The Knight shift versus concentration exhibits a sudden change of slope at the composition Li_0.5Cd_0.5. NMR linewidth measurements on the solid compound LiCd provided evidence for an appreciable mobility of the Li atoms through the lattice; the corresponding activation energy for diffusion is found to be 0.49+or-0.03 eV.

Resistivity measurements made on beta -Co_52.0Ga_48.0 from 22 to 750 degrees C reveal a negative temperature coefficient of resistivity up to approximately 625 degrees C. Based upon ageing experiments, a division of the resistivity behaviour into a dynamic and a kinetic process is performed. The dynamic process is associated with the spin cluster model, while the kinetic process is associated with the growth or shrinkage of the cluster. The activation energy for the kinetic process is evaluated from coarsening theory.

Using functional derivative techniques, the authors develop a systematic theory of the effect of substrate spin fluctuations on the electronic spectral density of hydrogen chemisorbed on a transition metal. The authors augment the standard Newns-Anderson model Hamiltonian to include exchange interactions (I) between the substrate d electrons as well as an exchange interaction (J) between substrate and adatom electrons. To second order in J, the adatom self energy involves the dynamic spin susceptibility of the substrate d-band. As the Stoner ferromagnetic instability is approached, the adatom energy levels are increasingly broadened due to excitation of substrate paramagnons. In a very small region above T_c, it is found that a magnetic moment ((n_spinup) not=(n_spindown)) may be induced on the adatom due to the large static substrate spin susceptibility. The exchange interaction (U) between electrons on the adatom is treated in the Hartree-Fock approximation. The authors show that, by itself, the energy level broadening near T_c has no effect on the net chemisorption energy. The metal spin fluctuations only contribute if there is an induced magnetic moment on the adatom.

The magnetic-field-dependent change in the sound velocity was measured in the mixed state of V-42 at.% Ti at T=4.14K, using shear and longitudinal waves with frequencies 10-30 MHz, in magnetic fields of up to 90 kG. For H<H_c2, the results are compared with phenomenological models in which the flux-flow resistivity is used as an effective resistivity in the Alpher-Rubin theory. Good agreement between theory and experiment is observed for longitudinal waves. However, for shear waves, these models overestimate the observed mixed state velocity changes.

Measurements of the temperature dependence of the resistivity and the magnetoresistance of PdMn alloys are reported for the concentration range 1%-10% Mn. These alloys order quasiferromagnetically for concentrations below 4% Mn and as spin glasses for concentrations above 4% Mn. Strong negative magnetoresistance associated with changing spin disorder scattering is observed in both regimes. The zero-field temperature dependence of the spin glass alloy resistivities is essentially due to changes in the inelastic scattering rate only. No evidence is found for a spin glass state in a Pd-5% Mn-0.35% Fe alloy.

Expressions for both the orbital and spin contributions to the dynamic susceptibility are derived using the Shaw-Harrison model wavefunction transformation. For the Heine-Abarenkov-type transition-metal model potential, they are separated into two parts; one caused by the non-nodal character of the model wavefunction and other by the depletion hole around the ion core. The formalism is applicable to d and non-d band metals depending upon the choice of the model potential. Numerical results are presented for simple, noble and transition metals at various values of momentum and energy transfer. Al, Cu and V are chosen to be the metals used in the present investigations. The depletion-hole contribution is found to be of the same order of magnitude as the contribution of the smooth part. It is noticed that the structural features of the magnetic susceptibility are dominated by the spin response rather than by the orbital response. The orbital susceptibility as a whole is found to be about 10-80% that of the spin susceptibility except at very small momentum transfer where it dominates over the spin susceptibility. Therefore it is emphasised that the orbital contribution cannot justifiably be neglected when comparing the results with experimental measurements. The diamagnetic behaviour dominates in Cu and Al while the paramagnetic behaviour dominates in V.

The magnetic susceptibility of noble metals is investigated using the Animalu transition metal model potential. The d band effects are included through the resonance term and the anisotropy of the Fermi surface is included through the Ziman eight-cone model. The exchange and correlation corrections are also taken into account. The calculated results are found to be in good agreement with the experimental data.

The even magneto-optical modulation of the transmitted light by Ni epitaxial films has been measured for the first time, and the detected light modulation is strongly dependent on the crystal orientation. A comparative study of even magneto-optical effects in polycrystalline Ni at Voigt configuration in the reflected and transmitted light is also reported. The experimental results are discussed in terms of recent electron energy band calculations. The even magneto-optical spectra previously reported for Fe and Co are also discussed.

A phenomenological model has been proposed in which it is emphasised that the dilute alloy problem should really be seen as that of the stabilisation of already existing local moments. It is then argued that the onset of ferromagnetism as a function of concentration, in atomically disordered (i.e. metallurgically homogeneous) transition metal alloys is a cooperative magnetic phase transition which is always magnetically inhomogeneous.

The contributions to the ultrasonic sound velocities or the elastic constants and the high-field susceptibility due to the magnetoelastic coupling and their anisotropies in cubic itinerant electron ferromagnets are calculated. The anisotropic spontaneous and forced magnetostrictions and the magnetoelastic contributions to the compressibility are also calculated. From the thermodynamic relations among these quantities which are tensors the enhancement due to the magnetoelastic coupling in the compressibility, high-field susceptibility and forced magnetostriction is obtained. It is shown that the experimental results on the magnetoelastic contributions to the ultrasonic sound velocities or the elastic constants and on the magnetostrictions are consistent with each other in Ni and the values of the magnetoelastic coupling constants are estimated. The present theory is also applied to Fe-Ni and Fe-Pt Invar alloys.

The ESR of Gd in single crystals of PrNi₅ is observed to exhibit significant angular dependence of the resonance position and linewidth at low temperatures. This is interpreted in terms of the axial spin Hamiltonian which takes the anisotropic susceptibility and the Gd-Pr exchange into consideration. A lineshape analysis enables the authors to derive the axial crystal field parameter D=165+or-30 G and an isotropic Gd-Pr exchange of 1.0+or-0.2 meV. The Gd ESR linewidth exhibits a dramatic increase with increasing temperature; the thermal broadening is angularly dependent. This dramatic increase of the linewidth versus temperature is similar to that observed by others for the Pr NMR in PrNi₅ single crystals. Both the NMR and the ESR thermal broadenings are attributed to low-frequency fluctuations of the Pr ions induced by the Pr-Pr exchange coupling. A model, originally developed to explain the ionic relaxation rate in cubic Van-Vleck compounds, is adapted to the present case of hexagonal Van-Vleck compounds.

A theoretical treatment of the conduction-electron scattering with spin reversal due to dislocations in metals is given. A general expression for the spin-relaxation time (SRT) of conduction electrons is obtained in terms of the structure factor variation caused by dislocations and the parameters of model pseudopotential of Animalu for the spin-orbit interaction. A detailed calculation of SRT is given taking account of the scattering by both the straight dislocations and the circular dislocation loops. The spin scattering caused by the cores of the dislocations is considered. A comparison is made between calculated and measured spin-relaxation rates for Cu, Ag and Al.

The series of pseudobinary intermetallic compounds Gd(Al_xFe_1-x)₂ has been studied by Mossbauer spectroscopy in the concentration region where the compounds crystallise in the cubic system. The experimental spectra are complex and have been analysed in terms of seven configurations corresponding to 0, 1, 2...6 Fe neighbours. In the region rich in Fe (0.25>or=x>or=0.05) the spectrum associated to six Fe neighbours shows a constant magnetic hyperfine (HF) field, and a decreasing electric quadrupole interaction. In the region rich in Al(0.75<or=x<or=0.90) the computer analysis is more difficult; in this range the ⁵⁷Fe HF field that corresponds to the most probable configuration (zero Fe neighbours) shows a change in sign. Estimates of the s and d contributions to the HF field are made at the various concentrations.

A study of the solution of ¹¹⁹Sn in nickel-iron and palladium-iron alloys by Mossbauer spectroscopy is presented. An attractive interaction is found between Sn atoms and nickel or palladium atoms in their first-neighbour shells of 0.1 and 0.28 eV respectively. The values of the solubility of tin in 6% and 8% Ni alloys, and 1% and 2% Pd alloys are measured as a function of temperature in the ranges 520-650 degrees C and 950-1150 degrees C respectively. From the slope of the log solubility curve, a heat of formation of the precipitate Ni₃Sn₂ of 12 kcal per gram atom and of an unidentified PdSn compound of 33 kcal per gram atom is obtained. The presence of a Ni or Pd atom in the first-neighbour shell of a Sn atom makes the hyperfine field at ¹¹⁹sn about 21 kOe more positive; a Ni atom in the second-neighbour shell makes it 23 kOe more negative. Pd atoms in the second-neighbour shell were not observed.

An analytic model for the dielectric matrix in a non-simple metal is presented using parabolic bands to approximate the known bandstructure. General results are obtained and applied to the case of the transition metal nickel by using the resulting matrix to calculate the electron energy loss spectrum. Agreement between the predicted and observed spectra is found to be reasonable in view of the simplicity of the model. By using a generalisation of the Thomas-Reich-Kuhn sum rule the authors find that the valence predicted by the model is 10.9+or-0.4 electrons, in good agreement with the required ten electrons.