Table of contents

A method of deriving the thermodynamic properties of mixing in liquid alloys Delta G, Delta S and Delta H, from low-Q scattering data has been presented. As an example, the method has been demonstrated with liquid Na-Ga alloys for which both thermodynamic and diffraction data have recently been obtained by the authors.

Recent experimental observation by Titcomb et al. (1972) has shown that ferromagnetism of PrCo₂ disappears when dissolved hydrogen is degassed. It is proposed that degassed PrCo₂ behaves as a strongly exchange-enhanced paramagnet with a susceptibility which follows the logarithmic temperature dependence predicted by the Fermi liquid model of magnetism.

The results of measurements of the electronic specific-heat coefficients of ordered Pt₃Mn_xCr_1-x (0<x<1) alloys are compared with the values calculated from a band model for x>0.5. The two sets of values show some agreement.

Small-angle X-ray scattering results are presented for a number of liquid alloys of the Na-K system. The analysis in terms of the concentration-fluctuation structure factor S_CC(0) proves to be rather cumbersome and is considered in some detail. There are distinct indications that concentration fluctuations occur in the liquid. Comparisons with the related Na-Cs system are made throughout. Some simple theoretical models are considered and comparison with thermodynamic data has been made.

In irradiated dilute Al(Cr) alloys, the trapping of aluminium self-interstitials by chromium atoms exhibits unusual features above 58K. One of the proposed interpretations implies a mobility of the resulting impurity-interstitial complex, which should result in the formation of chromium pairs. The NMR study of an Al (150 PPM Cr) alloy before and after neutron irradiation showed no detectable change in the chromium distribution. This makes the above-mentioned hypothesis unlikely.

High-precision measurements of the temperature dependence of positron annihilation in Al, over the range 290-930K, have been made via the Doppler-broadening technique and using an internal ⁶⁸Ge positron source. The results are considered mainly in terms of two lineshape parameters. These are denoted L and W and describe, respectively, the intensities of well defined central and wing portions of a normalised annihilation photopeak area. Both L and W exhibit the characteristic, overall S-shaped temperature-dependence profile associated with the change from free to vacancy-trapped annihilation modes. In detail, however, the temperature dependences of L and W are quite distinct.

The temperature dependence of the Doppler-broadening lineshape parameter has been studied for Cu in the temperature range 30-1040 degrees C, with special attention given to the prevacancy region (T<500 degrees C). Effects attributable to positron trapping were observed in the prevacancy region for samples annealed at temperatures T<or=950 degrees C. Measurements at T>500 degrees C allowed a quantitative comparison to be made between the prevacancy traps and thermally generated vacancies. This comparison permitted a determination of both the fraction of positrons trapped in the prevacancy region and the lineshape parameter characteristic of annihilation in the prevacancy traps. It was found that the fraction of positrons trapped in the prevacancy temperature region depends upon the thermal and mechanical history of the sample, and possibly also on its impurity content. In addition, two possible explanations of the prevacancy trapping are discussed.

Recent measurements by the positron-annihilation technique showed that the vacancy-formation volume v^f in metallic indium is 6.1+or-0.2 cm³ mol^-1. Self-diffusion under pressure showed that its vacancy activation volume v^act is 8.1+or-0.4 cm³ mol^-1. The application of a recent macroscopic model shows that v^f lies between 5.5 and 7 cm³ mol^-1 whereas v^act is calculated to be between 9.9 and 8.3 cm³ mol^-1. For tin the calculated value for the activation volume is 4.73 cm³ mol^-1 whereas the experimental value is 5.3+or-0.5 cm³ mol^-1.

The relaxation volumes and dipole tensors associated with point defects in metals are commonly deduced from the results of lattice statistics and computer simulation calculations. Often an approximation introduced by Hardy for weakly disturbing defects is applied in such deductions. However, for strongly disturbing defects such as interstitials, and even in some models vacancies, this approximation breaks down. A more rigorous treatment of the problem which avoids these difficulties is presented.

The rare-earth metals Y, Sm and Yb have been irradiated with electrons over the energy range 0.4 to 1.7 MeV at a temperature of T_irr<or approximately=12K, and the damage production as well as the annealing spectra were determined. By fitting the electrical resistivity change rates to theoretical displacement cross sections, the authors have determined the minimum threshold energies for atomic displacement: T_d^Y=(14.6+or-1) eV, T_d1^Sm=(9.5+or-1.5) eV, T_d1^Yb=(8.7+or-0.7) eV. Tentative values for the Frenkel pair (FP) resistivities have been proposed taking into account the magnetic order of Sm: rho _F^Y=(50+or-20)*10^-4 Omega cm (FP)^-1, rho _F^Sm=(140+or-30)*10^-4 Omega cm (FP)^-1, rho _F^Yb=(75+or-25)*10^-4 Omega cm (FP)^-1. The threshold energies and the temperatures for interstitial long-range migration for the three metals have been compared with empirical expressions deduced from earlier work and their dependence on the corresponding crystallographic structure and on the ionic configuration has been emphasised.

It was shown by channelling-backscattering measurements that Ge atoms were displaced from lattice sites during 70-90K He⁺ irradiation of Al-0.1 at.%Ge crystals. This displacement was about 1.1 AA in (100) directions, and was due to the trapping of self-interstitial Al atoms by Ge atoms, predominantly in the mixed dumbbell configuration. The displaced Ge atoms returned to normal lattice sites during isochronal annealing from 180-300K. The recovery behaviour in this temperature range was somewhat more complex than that observed for other binary Al alloys, indicating that either clustering of Ge atoms or strong binding between vacancies and Ge atoms impeded the annihilation of mixed dumbbells with vacancies.

Pulse-echo overlap measurements of the shear modulus, G, and the bulk modulus, B, have been carried out on polycrystalline samples of two Ti-V alloys and two Cr-Fe alloys of the body-centred cubic (BCC) structure to supplement earlier measurements on four BCC alloys of the V-Cr system. The Ti-V samples contained 57.8 and 80.2 at.%V, and the Cr-Fe samples 10.8 and 22.2 at.%Fe. Between the electron concentrations X=4.6 and X=6.5, both G and B increase with increasing X from X=4.6 to X=5.8 and decrease from X=6.2 to X=6.5. At X=4.6, G=0.34 and B=1.29*10¹¹ N m^-2 while at X=6.5, G=1.00 and B=1.87*10¹¹ N m^-2. For all the alloys G is lower than the value of G=1.16*10¹¹ N m^-2 for chromium, corresponding to X=6.0. In B there is at X=6.0 the characteristic drop arising from the antiferromagnetism. The extrapolated values for the bulk modulus of chromium obtained from the alloys with X<6 and X>6 are about 2.04*10¹¹ N m^-2, in agreement with results of high-temperature measurements on Cr. The contributions to G and B from the decrease in atomic volume, V, increase in the alloy series from Ti to Fe. The decrease in B with X in the range X>6 seems to be related to the change in the slope of the V against X curve at X=6.

A microscopic theory is presented to explain how the melting point in metallic small particles is dependent on size. The systems are described by an effective pair interaction of the Gaussian type, constructed to give the basic thermodynamic properties in the bulk metal at low temperatures. The thermodynamic melting temperature, at which the difference between the total Helmholtz free energy of a solid particle and that of a liquid particle of the same mass vanishes, is used as a criterion of the actual melting point in small particles. The variational principle based on the Gibbs-Bogoliubov inequality is used to calculate the Helmholtz free energies of both phases. Applications to the FCC metals Al, Pb and Ag are made and the calculated size dependences of the melting points are similar for all these metals. The result for Pb is in reasonable agreement with experimental data.

In the s-f two-band Hubbard model, the magnetic part of the free energy is investigated by means of the functional-integral technique in a self-consistent mean-field approximation. It has been shown previously that the magnetic ordering in this system is determined by the direct f-f coupling as well as by the indirect coupling of f moments through the conduction electrons. For this system it is reasonable to use a quarter-filled s band and a half-filled f band. Here it is shown that, for a suitable choice of parameters, a temperature-induced antiferromagnetic-ferromagnetic phase transition (on lowering the temperature) can be described within the model framework. On including, phenomenologically, the lattice part of the free energy and the dependence of the magnetic part on the lattice parameter, this phase transition becomes a first-order transition with a volume instability at the transition temperature; this qualitatively simulates the magnetic behaviour in the heavy rare-earth metals.

A simple theoretical analysis of the properties of plasmon modes at a bimetallic interface reveals that the observed excitation known as an 'interface plasmon' is not a pure mode but arises from excitations of plasmons in a narrow band of states. The interface is responsible for the presence of this band but the states within the band are not spatially localised in the interface region.

The first sixteen moments of the density of states of the d electrons in CuNi alloys have been calculated in the tight-binding approximation and analysed using continued fractions. No s-d hybridisation has been taken into account and the disorder has been assumed to complete and diagonal. The densities of states are given for atomic Cu concentrations equal to 0.1, 0.5 and 0.9 and are compared with the CPA computations.

It is shown that the fundamental equation normally solved in a KKR-CPA calculation leads to an effective lattice which satisfies the CPA condition more generally than has been noted before. This fact allows the authors to study the partially averaged charge density beyond the unit cell surrounding the selected site and fluctuations about the CPA.

Measurements of electrical resistivity, rho , and thermopower, S, of solid (above room temperature) and liquid high-purity Eu and Yb are reported. No evidence for the suggested 'transition' in solid Yb at about 300 degrees C is seen in either rho (T) or S(T). Measured values for rho , d rho /dT, and S for these liquid metals at their melting temperatures are, respectively, 241, -0.066, and 6.6 (for EU), and 113.8, -0.023, and -12.2 (for Yb), where the units are mu Omega cm, mu Omega cm degrees C^-1, and mu V degrees C^-1, respectively. These liquid values are compared with recent calculations based on the t matrix.

A simple approximation for the scattering rate is shown to yield values for the electron-electron contribution to the thermal resistivity that are in good agreement with experiment in simple metals. These metals have been modelled by a uniform electron gas with a modified mass and electron-electron interaction to account approximately for crystalline effects. The scattering function was approximated by using an exact expression for the forward-scattering limit in terms of the model-system Landau parameters with scattering events of finite momentum transfer accounted for by the s-p approximation given by Dy and Pethick. Estimates of the contribution from electron-electron scattering to the electrical resistivity based on the same scattering function have also been calculated for the alkali metals.

The neutron polarisation analysis technique has been used to measure the atomic disorder and magnetic defect scattering from an antiferromagnetically commensurate Cr-6.5at%Fe alloy. The atomic disorder scattering is consistent with a model in which iron atoms cluster, each impurity iron atom having on average 1.6 further iron atoms in its first-near-neighbour shell. The magnetic defect scattering suggests that the presence of an iron impurity atom reduces the magnetic moment on chromium sites in the first- and second-neighbour shells to almost zero. Although no static moment has been observed on the iron site it is inferred from the results, in conjunction with previously reported magnetic measurements of CrFe, that the iron atoms are coupled together magnetically to form superparamagnetic assemblies which remain uncorrelated with the antiferromagnetically ordered chromium matrix.

The magnetic properties of Laves phase compound PrFe₂, synthesised at high pressure, were studied by Mossbauer spectroscopy and saturation magnetisation. The ferromagnetism in PrFe₂ has been confirmed. The rotation of the easy axis of magnetisation on the (110) plane to (111) with respect to (001) was observed as temperature increased. The authors have calculated the single-ion crystalline field magnetic anisotropy and have found this model to account for the experimental results in principle.

Young's modulus and the Delta E effect of Fe-Pd Invar alloys have been investigated. The Delta E effect at room temperature exhibited a similar concentration dependence of the longitudinal linear magnetostriction. The temperature dependence of Young's modulus was analogous to that of Fe-Ni and Fe-Pt Invar alloys, namely Young's modulus increased below the Curie temperature with increasing temperature. The variation of Young's modulus at room temperature with Pd content showed a minimum around 30% Pd.

The pressure dependence of the Curie temperature dT_C/dP in dilute transition metal alloys and rare earth Co₂ compounds is calculated in the combined model of localised spins and itinerant d electrons. It is found that dT_C/dP varies as -T_C at low T_C and this result agrees qualitatively with many experimental results in dilute transition metal alloys. The calculated values of d ln T_C/d ln V for Pd-Fe, Pd-Co, Pd-Ni, Pt-Fe and Pt-Co alloys and for the GdCo₂ compound are compared with the experimental results. The calculated values of d ln T_C/d ln V for Pd-Fe alloys agree well with the experimental values, which show a maximum at about 60K. The calculated results predict that there also exists a maximum in the experimental values of d ln T_C/d ln V for (Gd-Y)Co₂ compounds and Pd-Co alloys.

The nuclear spin relaxation rate R has been studied in liquid alloys Pb_1-CX_C with X=Li, As, Ag, In, Sn, Sb, Te, Au, Tl and Bi at various concentrations C, and for X=In, Sb, Bi as a function of temperature T at C=0.5. The 47 mu s isomer ^207mPo, for which the quadrupolar contribution to R, R_Q, is dominant, was used as the probe nucleus; it was produced and aligned by the nuclear reaction ²⁰⁶Pb ( alpha , 3n) and the relaxation rate was measured by the perturbed angular distribution technique. For most of the alloys studied here the contribution to R_Q due to density fluctuations, R_QNN, dominates. Thus these data complement the earlier measurements by the authors of alloys where the concentration fluctuation contribution, R_QCC, dominated. They confirm the earlier findings that the magnitude of R_Q in alloys is essentially determined by the valence difference between the partner elements and that the long-range components of the interaction are decisive for quadrupolar relaxation (i.e. distances larger than the nearest-neighbour distance).

The effect of absorbed hydrogen on the magnetic structure of FCC iron-nickel base Invar alloys was studied by means of the ⁵⁷Fe Mossbauer effect. As the electrolytic hydrogenation proceeded, hydride phases of the same FCC type as the matrix were formed and the characteristic absorption of the Mossbauer spectrum with low field components, which is believed to be an origin of the Invar effect of these alloys, was drastically changed to a simple strong ferromagnetic one. By further hydrogenation, however, the internal field of the hydride phase became smaller. This effect of hydrogen on the magnetic structure of Invar alloys was interpreted in terms of Stoner's band model or more rigorously, a flexible band model with the local bonding state induced by hydrogen. The observed increase of the thermal expansion coefficient of Invar alloys by hydrogen was accounted for in the same way.