## Vol. 13, No. 4 (1957)

##### 1957-02-20

###### CONTENT

1957, 37 (4): 245-251.
doi: 10.7498/aps.13.245

Abstract +

It is shown that the probability of an disordered atom to be ordered in unit time can be correlated to the coefficient of diffusion by the relation a=9/4 d/a2 (m2/m1)1/2 (△S2-△S1)/k(Tc/T-1) where a=the probability of ordering, D=the coefficient of diffusion, a =the lattice constant of AuCu3,m1 and m2 the mass of an atom of gold and copper respectively,△S1, △S2 being respectively the entropy change when a gold and a copper atom jumps to a neighboring vacancy, k, the Boltzmann constant, Tc, T, the critical temperature and the absolute temperature under consideration.This relation has been verified with experimental data. With experimental value of a and D0, it gives an activation energy of 2.10 eV which is equal to the activation energy of self-diffusion of copper within the limits of experimental accuracy. This expression explains the existance of a temperature at which the rate of ordering is maximum both qualitatively and quantitatively.

1957, 37 (4): 252-256.
doi: 10.7498/aps.13.252

Abstract +

The paper discusses radiation directivity patterns of noise generating stacks of various simple shapes (rectangular, square, circular). Earlier computation of Wells, R. and Crocker, B. E. is improved with regard to the assumption of baffles. The new formulae predict patterns for a wider region than the half space covered by the earlier computation and agree favorably with published experimental data.

1957, 37 (4): 257-270.
doi: 10.7498/aps.13.257

Abstract +

The neutron distribution in an infinite medium around an infinitely long black cylinder is investigated. The medium satisfies the conditions typical for Milne's problems. By the method of expanding the distribution function in terms of the spherical harmonics, we transform the Boltzmann transport equation for our case [eq. (1)] into an infinite set of ordinary differential equations for the infinite number of coefficients of expansion feq. (10)]. We obtain approximate solutions-P1, P3, and P5 approximations [expressions (21), (25)and (26)] by retaining only the first two, six and twelve terms of the expansion.Numerical results of the calculation of the extrapolated length λ for various values of aare shown in Table 2 and plotted in the figure. Both λ and a are expressed in units of l-themean free path of neutrons in the medium.For comparison, we plotted also the curve given by Davison (curve D in our figure). His curve is based on his approximate solutions of the Peierls integral equation for the two limit cases a?1 and a?1 and an interpolation for intermediate values of a according to the result of P3 approximation. It appears from the figure that for large a the result of P5 approximation is already very near to the curve D and that it seems more reasonable to lower a little the part of the curve D near a=1 in order to conform better with the tendency of the curve P5 (as, e.g., shown by the dotted line).In the Appendix, some relations concerning spherical harmonics needed in the text are obtained.

1957, 37 (4): 271-293.
doi: 10.7498/aps.13.271

Abstract +

The only previous work known to us on the polaron problem in atomic lattices gives a result which would mean that polarons of the adiabatic type (in the first approximation, a self-trapping state with static deformation) should exist in crystals such as Ge and Si. (The method used in dealing with the elastic energy is shown to be in error.) We have reconsidered the problem and found that most probably the reverse is the case. The problem is then investigated on the basis of the perturbation theory. It is shown that the volume change, strongest at the electron, extends essentially as far as one de Broglie wave length of an electron moving with the speed of sound; beyond this distance, the elastic displacement is of the 1/r2 type. The volume changearound the electron totals E/(a+4/3μ)(E being the deformation potential constant, a and μ beingrespectively the bulk and shear molulus). This local volume change induces a uniform strain in the specimen, the two effects together gives a total volume change E/a. The elastic deformation caused by an electron in a hydrogen-like impurity state is also considered. The total volume effect turns out to be identical with the above. The effect is quite considerable; for instance, it can be comparable with the observed volume change caused by a Ⅲ,Ⅴ type of impurity atom in a Ge or Si lattice. Energy change of a low speed electron in a conduction band is roughly ((electron mass)/(mass of lattice cell))(E/(kΘD))E which amounts to 0.001-0.1 eV for E=1-10 eV in Ge. The corresponding change in effective mass is 1/1000-1/10 electron mass. The energy change for an electron in a hydrogen-like impurity state is much smaller, it thus appears theoretically possible that the electron-lattice interaction may render an impurity state unstable against ionization!

1957, 37 (4): 294-312.
doi: 10.7498/aps.13.294

Abstract +

We consider a circular ring plate with inner edge fixed and outer edge fixed and supported under the action of uniformly distributed load over entire actual surface. We write down the boundary conditions and the von Karman equations for the large deflection of such a plate in a dimensionless form and then solve them by the perturbation method based upon the smallness of the maximum deflection at the inner edge. Design formulae for stress and maximum deflection, which are of practical importance, are given at the end of the paper.

1957, 37 (4): 313-338.
doi: 10.7498/aps.13.313

Abstract +

In a previous paper, it has been shown that the perturbation method is much, superior to the method of numerical integration in treating the problem of the bending with large deflection of a circular plate by uniform edge moment. Now, we extend the perturbation method successfully to the case of a circular ring plate with one edge clamped and uniform moment along another edge. As in the previous paper, all our results are presented in such a form that the direct application to design problem is possible.