## Vol. 21, No. 10 (1965)

##### 1965-05-20

###### CONTENT

1965, 115 (10): 1711-1724.
doi: 10.7498/aps.21.1711

Abstract +

The experimental procedure for observing the low frequency anomalous internal friction peaks in Al-0.5% Cu alloy was systematically investigated in order to be able to obtain reproducible results. It is shown that, when the specimen is plastically deformed on a tensile testing machine to a suitable extent and then the internal friction measured in the course of aging at a suitable temperature, an aging internal friction peak exhibiting an anomalous amplitude effect may be observed. After the specimen has been "sufficiently" aged and its internal friction has reached a steady value, an amplitude internal friction peak at a given temperature can be observed when the strain amplitude for measuring internal friction is successively increased. Furthermore, when the internal friction of the "sufficiently" aged specimen is measured at higher temperatures with a given strain amplitude, a temperature internal friction peak exhibiting an anomalous amplitude effect may be observed. These experimental results demonstrated conclusively the existence of the previously observed amplitude internal friction peak at a given temperature and of the temperature internal friction peak exhibiting an anomalous amplitude effect.In order to find out why the anomalous internal friction peaks previously observed in Al-0.5% Cu alloy have a poor reproducibility, the effect of strain amplitude upon the appearance of the amplitude internal friction peak, as well as the effect of the amount of the previous plastic deformation upon the appearance of the aging internal friction peak and the temperature internal friction peak was systematically studied. An analysis was made on the experimental conditions for the appearance of these anamolous internal friction peaks.The observed experimental results concerning the anomalous internal friction peaks can be explained in a qualitative manner with a model in which the solute atom "atmosphere" was assumed to be dragged along with the dislocation. The concrete model and its theoretical analysis will be reported in a later paper.

1965, 115 (10): 1725-1743.
doi: 10.7498/aps.21.1725

Abstract +

By means of the BCS wave functions and projected wave functions the absolute values of a reduced width of even-even isotopes of 84Po and odd-even isotopes of 85At are calculated. The change of absolute values and the behaviour of the relative values due to the change of the parameters b, R0, and G have been investigated, where b is the parameter of harmonic oscillator well, R0 the channel radius, and G the parameter of pair correlation. The analysis of the results of calculation shows that:(1) Pair correlation favours the formation of a particle; it may increase the reduced width by an order of magnitude, and it may induce the relative behaviour to be more compatible with experiment.(2) The nonconservation of particle number of BCS wave function is a serious defect for those nuclei for which the number of particles outside the closed shell is few. The projected wave function, for which the number of particles is conserved, may increase the absolute values by 1-2 times, and may improve the relative behaviour.(3) On taking account of the blocking effect, the reduced width may decrease by 10%, this has the result that the hindered factors of odd A nuclei may agree with the experimental values.(4) The absolute values are very sensitive to the selection of parameters, but the relative behaviour is not very sensitive. In order that the absolute values may approach the experimental values, R0 should be within 8f.

1965, 115 (10): 1744-1751.
doi: 10.7498/aps.21.1744

Abstract +

The classical problem of diffraction of radio waves around a spherical earth is briefly reviewed, with the purpose of pointing out a mistake in the mathematical derivation of the theory which has been generally accepted. The correct way of analysis is indicated.

1965, 115 (10): 1752-1766.
doi: 10.7498/aps.21.1752

Abstract +

In this paper the effective mass wave function of the bound shallow donor electron in Ge was used to obtain the spin-Hamiltonian. It was shown that the resonance frequency is anisotropic only if the minima of the conduction band deviate from the symmetry points (2π)/α[111], provided there is no stress. This makes it possible to determine whether the minima of the conduction band slightly deviate from the (2π)/α[111] points ornot by means of experiments of double resonance.The general expressions of the resonance frequency and anisotropic line width were obtained by taking the smoothly varying nonhomogeneous stress as perturbation. Furthermore, we calculated in detail the nonhomogeneous broadening of the resonance line under the action of the stress of dislocations in Ge generated during the growth of single crystals by the pulling method or by means of plastic deformation (edge dislocation of the [211] direction and screw dislocation of [110]). It was pointed out that the anisotropy of line width is essentially different for different types of dislocations, and also for different equivalent directions. In comparison with the experimental results of Wilson, we concluded that, as the density of dislocation is smaller than 104εcm-2, the dislocation stress is not the main cause of broadening, so that the line width should have similar anisotropy as the magnetic field is oriented in different (110) planes. When the density is larger than 105εcm-2, dislocation stress gives the main contribution to broadening. This effect can be easily examined experimentally.

1965, 115 (10): 1767-1775.
doi: 10.7498/aps.21.1767

Abstract +

In the present paper, the energies of vacancy relaxation and vacancy formation of the face-centred cubic metals (lead, silver, nikel, copper, and aluminium) are calculated by using the idea of metallic bond and the Morse potential of pure metals.In the calculation of relaxation energy, both the atomic and the electronic redistribution are considered. The energies of vacancy relaxation calculated by using the present method are 1.27-1.36,>1.73, 1.93-2.29, 1.52-1.84, and >1.09 eV respectively. These results are more reasonable than those obtained without taking into account the electronic redistribution. These results indicate that the contribution of electronic redistribution to the effect of relaxation is very important.The formation energies of vacancy calculated by using the present method for the five metals mentioned above are 0.64-0.74, <1.22, 1.78-2.15, 1.52-1.85, and <1.67 eV respectively. They are larger than the experimental values by a fraction of one electron volt. This result gives a reasonable theoretical upper limit to the formation energy of vacancy.

1965, 115 (10): 1776-1784.
doi: 10.7498/aps.21.1776

Abstract +

The magnetization and the resonant frequency of the anisotropic ferromagnet are calculated by means of rotation of the coordinate system. On the basis of the relations between the resonant frequency and the tensor of the exchange interaction, which have been obtained in this paper, the principal values of the exchange interaction and the directions of the principal axes of the exchange interaction may be determined by using the experimental data of resonance.

1965, 115 (10): 1785-1797.
doi: 10.7498/aps.21.1785

Abstract +

The method of binary collision expansion has been employed to obtain series developments in powers of the scattering length between two particles for double-time-temperature-dependent Green's functions of statistical mechanics. We have studied the cases of Bose and Fermi statistics as well as the case of a Bose system in the presence of a condensed phase, and have established rules for computation of the successive terms of expansion with the aid of diagrams. The present method is applicable to many particle systems with strong and short-ranged mainly repulsive two-body interactions.

1965, 115 (10): 1798-1809.
doi: 10.7498/aps.21.1798

Abstract +

This paper suggests an approximation method for solving the problems of diffraction due to perfectly conducting cylinder, the section of which is a smooth curve C of arbitrary form. The principle of the method is similar to that of H. Bremmer: The field of diffraction due to a cylinder with a polygonal section (which is an inscribed polygon of the curve C) is expanded into a series. The first term of the series is the geometrical field. The second term of the series is the sum of the elementary diffraction fields due to the wedges of the polygonal cylinder. These fields are taken as those of Sommerfeld's problem, i.e., both sides of each wedge are infinitely extended. Each of these elementary fields falls on the neighbour wedge and is diffracted by the latter, and this diffracted field in turn falls on the next neighbour wedge and is again diffracted by the latter, etc. The field diffracted by the wedges one after another in such a way is called the main tangential elementary field. The third term of the series is the sum of these main tangential elementary fields. The field diffracted by wedge A, being diffracted again by the neighbour wedge B, reflects back on wedge A again, and then propagates in this direction progressively in a manner mentioned above. Such a field is called once-reflected elementary field. The fourth term of the series is the sum of these once-reflected elementary fields, etc. In general, the m-th term of the series is the sum of the (m-3) times-reflected elementary fields. Every elementary diffracted field due to any wedge is taken as the solution of Sommerfeld's problem for this wedge in the manner mentioned above. As the sides of the inscribed polygon approach to zero, the inscribed polygon approaches to the curve C, and each term of the series becomes an integral, the limit of the summation of the series approaching to the rigorous solution of the initial problem.The first three terms of the series are deduced individually. For the general m-th term a recurrent formula is given. Finally the condition of convergence of the series is discussed.