Toshinosuke Muto

The Theory of Order-Disorder Transitions in Alloys

Publisher Summary There are two main classes of alloys: homogeneous (one phase) alloys and eutectics (two phase systems). In the former, the concentration of each component is constant throughout the alloy, whereas, in the latter, there are small crystals. Some of these contain more of one component while others contain more of the other. Such eutectics are formed when the mutual solubility of the components of the alloy is limited and the concentration in the given alloy is beyond the solubility limit. This chapter is primarily concerned with the homogeneous alloys. The qualitative characteristics of the order-disorder transition in alloys appear to be well clarified, for some examples, by the statistical treatments of a rather simplified model with appropriate assumptions. However, from the standpoint of quantitative comparisons with the experiments, the present theory is still far from satisfactory and there remains much to be done in making more accurate computation of the partition function and in improving the model by careful consideration of the actual situations in alloys. Individual factors ignored in the customary theoretical treatments of the order-disorder transition have been investigated separately; it is shown that the neglect of these factors appears not to be justifiable, particularly if quantitative comparisons with experiments are to be made.

Electronic Structure of the Exciton I. Localized Exciton in KCl

The present situation of the exciton problem is discussed briefly. The localized excitons of KCl in both optical and X-ray absorption have been worked by using Wannier-Slaters equation for the perturbed lattice, which may be considered to essentially correspond to the quantum-analogue of von Hippels semi-classical model of the exciton. The perturbing potential fields in Wannier-Slaters equation are evaluated numerically by the use of Hartrees data and then the best-fit analytical functions are constructed with fair accuracy. The solutions of the equation are worked by the variational method. The result for the optical exciton is observed to be in fair agreement with the experiment. As for the X-ray exciton, the quantitative comparison with our results can hardly be carried out at present, since the position of the bottom of conduction band can not be measured accurately on the X-ray absorption spectra. On the basis of our results for X-ray exciton, however, some discussions on the characteristic struc...

TEMPERATURE-EFFECT OF KNIGHT SHIFTS IN ALKALI METALS

Abstract The effect of lattice vibrations upon Knight shift has been worked out theoretically, which is caused by two kinds of mechanisms ; the effect of lattice vibrations upon hyperfine interaction and the influence of lattice vibrations upon charge distribution of conduction electrons. A correction term to the usual expression of Knight shift has been obtained successfully, which depends explicitly upon not only temperature but also ion mass. It, therefore, is expected for both temperature-effect and isotope-effect of Knight shift to be observed experimentally The observed changes with temperature of Knight shift of alkali metals at constant volume are found to get fair agreement with our numerical calculations.

On Indirect Knight Shift and NMR in Ferromagnetic Metals Part I. General Formulation and Qualitative Discussions

It is well-known that the exchange-polarized core s -electrons by partially filled magnetic d -band electrons are able to make characteristic contributions to effective magnetic field felt by nucleus within crystal, which leads to temperature-dependent and negative Knight shift (indirect Knight shift) and nuclear magnetic resonance absorption in ferromagnetic metals. The mentioned exchange-polarization of core s -electrons has been worked out quantitatively only for the case of isolated atom and ion, and the extension to the crystal electrons in energy band has not been worked as yet mainly for the formidable labour of numerical computations. In view of the above situation we have adopted the perturbation-theoretic approach for working the mentioned problem. The empirical formula of indirect Knight shift by Clogston et al. and of NMR in ferromagnetic metals by Portis et al. have been derived successfully and the extension of our formalism to dilute ferromagnetic alloys has been worked.

Electrodisintegration of He 4 Nucleus

The inelastic continuum of scattered electrons by He 4 nuclei, observed experimentally by the Stanford group, is worked theoretically by using the conventional forms of wave functions for He 4, He 3, and the triton. It is pointed out that two kinds of scattering are involved in the cross section; one is connected with the direct process in which a nucleon can be ejected through the direct interaction with the electromagnetic field induced by the ess in which a nucleon is capable of being ejected through the intermediary of nuclear interaction with another nucleon which does interact with the electromagnetic field. Comparison with experiments appears to be rather good, though qualitatively, allowing far the approximate nature of the method of computation. The main nuclear reaction connected with the observed inelastic continuum is shown to be the ejection of nucleon from He 4 except for the low-energy tail where the pion production is observed to take place according to the Stanford group. (auth)

Electrodisintegration of He4 Nucleus

The inelastic continuum of scattered electrons by He 4 nuclei, observed experimentally by the Stanford group, is worked theoretically by using the conventional forms of wave functions for He 4, He 3, and the triton. It is pointed out that two kinds of scattering are involved in the cross section; one is connected with the direct process in which a nucleon can be ejected through the direct interaction with the electromagnetic field induced by the ess in which a nucleon is capable of being ejected through the intermediary of nuclear interaction with another nucleon which does interact with the electromagnetic field. Comparison with experiments appears to be rather good, though qualitatively, allowing far the approximate nature of the method of computation. The main nuclear reaction connected with the observed inelastic continuum is shown to be the ejection of nucleon from He 4 except for the low-energy tail where the pion production is observed to take place according to the Stanford group. (auth)

On Indirect Knight Shift and NMR in Ferromagnetic Metals Part III. Numerical Calculation of NMR Frequency and Hyperfine Field in Ni, Co and Fe

By using our theoretical formula derived in part I, the numerical computation of the hyperfine fields in ferromagnetic nickel and cobalt has been performed in addition to a revised calculation of that in ferromagnetic iron. By taking appropriate values of the effective nuclear charge involved in 3 d -atomic orbital ( Z ) and of the mixing amount of 4 s wave function into the 3 d band (η·10 -2 ) the obtained results are found to show remarkably good agreements with the experiments, allowing for the various approximations involved in deriving our theoretical formula. In conclusion a simple band theory of ferromagnetic metals together with the perturbation-theoretic approach to exchange-polarization of crystal electrons seems to be quite useful for explaining the currently available observed results of NMR and the corresponding hyperfine field of ferromagnetic metals.

On Inequality of Knight Shifts for Li6 and Li7

The isotope effect of Knight shift is discussed using both K/sub o/ and K/sub i/, the Knight shift for rigid lattice and the effect of lattice vibrations, respectively. (R.E.U.)

Note on Electrodisintegration of He4

Cross sections of He/sup 4/ electrodisintegration were calculated for the range 45 to 105 deg at 400 Mev and fitted to experiment data on scattered electron energies in the same range. The agreement between calculated and experimental data was good. (C.J.G.)