The stability of a f.c.c. phase and two f.c.t. phases, one has the axial ratio more than unity and the other less than unity, of In–Cd, In–Sn, In–Hg and In–Pb are discussed. On the basis of the nearly free electron model, the internal energies for these phases are calculated. The phase which has the least internal energy in any electron/atom region can actually exist. The calculated regions of these phases agree comparatively well with the actual phase diagram.
A reasonable explanation on the change in the transport properties at the phase boundaries is also given by the model.

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For a crystal which is of displacement type in its ferroelectric phase, the concept of “ferroelectric modes” of lattice vibration is introduced which is different from and more basic than that introduced by Cochran and called in the same name by Landauer and Thomas. On the basis of this concept, a statistical theory of ferroelectricity is developed. Two cases are distinguished according to whether the crystal has only one or more ferroelectric modes of lattice vibration. The bulk of the present paper deals with the former case. An examination is made not only of ferroelectric phase transitions and the susceptibility to a static electric field but also of the susceptibility to electric fields alternating in high frequencies. Incidentally, a deduction is made of the complete expression for the temperature dependence of the frequency of the Cochran and others’ ferroelectric mode of lattice vibration in the vicinity of the Curie temperature.

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Cyclotron resonance study of thermally quenched germanium has been made. Various cyclotron resonance characteristics indicate that the introduced thermal acceptors are not due to the diffused-in copper which is likely to enter during the high temperature treatment. On the implicit as-sumption that the acceptor is an isolated vacancy, its electron scattering mechanism is discussed. Simple treatments of the scattering by an elastic strain or a three-dimensional square well potential around a vacancy do not explain the resonance behavior well, while the observed magnitude of the scattering cross section and its temperature dependence have a strong resemblance to those for other acceptor impurities such as indium, gallium or zinc. Especially the similarity to zinc is indeed surprising. Such resemblance might suggest a picture that electrons trapped in a certain way at the dangling bonds around a vacancy corresponds to the core of an impurity acceptor.

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Single crystal films of γ-Fe₂O₃ were epitaxially grown on a (100) surface of MgO by the halide-decomposition method. Chemical analysis, electrical conductivity and, optical absorption measurements showed that the crystals contain no ferrous ions. X-ray diffraction assigned a cubic spinel structure and ruled out the presence of ordering of cation vacancies. Magnetization measurement and ferromagnetic resonance experiments were performed on these films which revealed the value of saturation magnetization and the anisotropy constants. The effective Bohr magneton number per iron atom was determined to be 1.45 at 0°K, which is considerably larger than that expected from Néel’s theory. The Curie temperature is 743°K, which is lower than that found in ordinary γ-Fe₂O₃ powder. These results conclude that the vacancies at 16d sites are randomly distributed and nearly twenty percent of the total vacancies occupy 8a sites.

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The effect of thermal vibration on the transmission or reflection of neutrons in a single crystal was investigated theoretically.
The formula of imaginary potential which is used to get the absorption coefficient was given as a result of thermal inelastic scattering of neutrons. It was made clear that the surface integral taken over the scattering surface is necessary to obtain the imaginary potential of a single crystal for one-phonon inelastic scattering of slow neutrons.

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A relativistic generalization of the Green’s function method for the energy-band calculation is presented. The wave function within the atomic spheres is expanded in terms of four-component spherical waves. The resulting expression which gives the relationship between E and k is very similar to the nonrelativistic one. Matrix elements between the spherical waves can be easily computed provided structure constants used in the nonrelativistic calculations are available.

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The antiferromagnetism of polycrystalline and single crystal samples of disordered γ Fe-Mn alloys containing between 20 to 50 at% Mn was investigated by means of a magnetic balance, a sensitive torque magnetometer and neutron diffraction. The alloys with 20 to 27 at% Mn exhibited ε↔γ trans-formation in the same temperature range as the magnetic transformation. The relation between the magnetic and the crystallographic transformations was investigated and a phase diagram of Fe-Mn alloys in this composition region was obtained. A neutron diffraction study of single crystal samples confirmed the generalized antiferromagnetic spin structure proposed by the powder neutron diffraction study of Kouvel and Kasper. The torque measurements, made on single crystals which had been cooled through the Néel point in a strong magnetic field, indicated that the spin structure is intrinsically cubic, the spins on the four sublattices being directed toward the different cube diagonals. The results are discussed from the viewpoint of a molecular field theory based on the localized electron model. However, the temperature dependence of the susceptibility below and above the Néel point cannot be interpreted on the basis of a localized electron model, although the latter can account for the proposed spin structure.

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Transport properties and the magnetoresistance of single crystal InSb at 77°K have been studied for high applied electric (E_α) and magnetic (B) fields as functions of the two field intensities and the angle between them. Unusual oscillatory behavior was observed in the angular dependence of the magnetoresistance at high magnetic field (ω_cτ<1) and high average current densities. A current-controlled negative resistance and a negative magnetoresistance were observed at angles between E and B of less than 30°. These observations can be understood qualitatively as the result of impact ionization due to the presence of a transverse component of the applied magnetic field.

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New features were observed in synthetic CaF₂ crystals which were colloidally colored by intense proton bombardmemt. There are (1) a surface of discontinuity at the end of the proton range, (2) a colloidally colored thin layer between the bombarded plane and the range end, and (3) the presence of plane where the dislocations were most decorated. These phenomena were explained to result from the inhomogeneous ionization and heat release during the proton penetration, and the atomic displacements and hydrogen introduction upon stopping of the protons in the crystal.

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The growth of F centers and the change of d. c. conductivity by X-irradiation were measured around room temperature in NaCl grown in chlorine atmosphere both pure and doped with Ca⁺⁺, Cd⁺⁺, Sr⁺⁺, and Mn⁺⁺. The enhancement of coloration by divalent impurities at room temperature was found to be proportional to the square root of the concentration of each impurity. It was also found that the ionic conductivity in doped NaCl was decreased by X-irradiation in such a way that the decrease in the concentration of the positive ion vacancies was nearly equal to the increase in the F center concentration. From these results it was concluded that the isolated positive ion vacancies are the source of the F centers at the early stage of coloration. The temperature dependence of the formation rate of F centers in doped NaCl was measured and the activation energy 0.08±0.01 ev was obtained.

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The nuclear magnetic relaxation times in Fe₃O₄ have been measured. The experimental values of T₁ and T₂ range from 1.4 sec to 0.4 ms between 4.2° and 300°K. For the A ion, T₁ and T₂ are roughly equal, increasing with a magnetic field, above 120°K and show the minima at about 80° and 40°K, respectively, independent of the field. For the B ion, T₁ and T₂ are independent of the field with T₁⁄T₂≈2 from 130°K to 300°K. The results are explained semi-quantitatively by the effect of the electron migration in the B sites. Detailed calculations show: (1) T₁ and T₂ for the A ion are governed by the coupling of the nucleus with the migrating electrons through the dipolar interaction below 120°K and through the hyperfine and the A-B exchange interactions above 120°K; (2) the anisotropic and the isotropic hyperfine interactions give the essential contributions to T₁ and T₂ for the B ion, respectively.

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The electronic structure of the super-lattice Ni₃Fe is evaluated by the tightbinding approximation. The energy bands are approximately, though not completely, divided into two groups by the widely extended energy gap, and, roughly speaking, five bands are above the gap and other fifteen bands are below the gap. This band structure seems to be quite favorable to produce the ferromagnetic state in Ni₃Fe and Ni₃Mn.

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Absorption transitions between two excited optical states in ruby have been studied by comparing the absorption coefficients measured under optically pumped and unpumped conditions. The spectrum has been determined in the π-and σ-polarizations in the photon energy range from 5,500 to 45,000 cm⁻¹. Several absorption bands have been found which arise from the transitions from the excited states t_2g^{3 2}E_g and t_2g^{3 2}T_1g of the Cr³⁺ ion. From the locations and intensities of these bands, the terminal states of the observed transitions are assigned to the charge transfer state, the t_2g^{3 2}T_2g state, and the doublet states belonging to the electron configuration t_2g³e_g. Calculated energies between these states and the metastable states, t_2g^{3 2}E_g and t_2g^{3 2}T_1g, are in good agreement with the peak energies of the observed absorption bands. The present experiment gives new information inaccessible by the ordinary ground state absorption measurement, such as the locations of several doublet states with the configuration t_2g²e_g and the intensities of doublet-doublet transitions in ruby.

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The absorption spectrum in the excited states of ruby reported by Kushida is analyzed on the basis of the crystalline field or ligand field theory. Remarkably sharp absorption peaks observed in the infrared region are identified to the t_2g^{3 2}E_g→t_2g^{3 2}T_2g transitions, and a temperature-sensitive broad band also in this region is identified to the t_2g^{3 2}T_1g→t_2g^{3 2}T_2g transitions. Several broad peaks observed in the visible region are assigned to the t_2g^{3 2}E_g→t_2g²(³T_1g)e_g ²T_2g, t_2g²(¹T_2g)e_g ²T_1g, t_2g²(³T_1g)e_g ²T_1g, t_2g²(¹T_2g)e_g ²T_2g transition. Unidentified broad peaks in the infrared region are discussed in some detail with the assumption that they are due to the phonon-induced electric dipole transitions.

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Damping of strong electron waves due to the excitation of many weak waves by elastic scattering in a parallel-plate crystal is discussed on the basis of many-beam theory of electron diffraction. The effect of the weak waves is expressed by using the correction term to Fourier coefficients of potential. Simple expressions for the real and imaginary parts of the correction term are obtained. The result of the present theory is compared with pseudo-kinematical theory in the case of the thinnest crystals. The damping of electron waves due to the thermal diffuse scattering is dealt with as an application of the result of the theory.

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An expression for the electrical potential difference observed when a uniform membrane with fixed charges separates electrolyte solutions containing permeable ions at different concentrations is obtained from molecular theory. The membrane is considered as a multi-component system of ions and neutral molecules with the restriction that a subset of these species have zero mobility. The electric potential is equated to the isothermal steady state electrical contribution to the stress tensor. The expression for the membrane potential thus derived is shown to be in agreement with the experimental results. A brief analysis of assumptions involved is included.

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The theory of hypochromicity in the ordered polymer is revised by taking into account the effect of nonvanishing permanent dipole moment of each component monomer. It is found by numerical calculations on the single stranded helical poly-C and the α-helical polypeptide that the effect contributes a considerable amount to hypochromicity. The ratios of the helix absorption to base absorption are 0.75 and 0.70 respectively in the former and the latter cases, compared to those ratios 0.54 and 0.82 obtained by neglecting the present effect.

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The dispersion relations for the waves propagating in a magnetoactive plasma are obtained from the Boltzmann equation with a collision term of the electrons. Two cases in which the wave vector parallel and perpendicular to the uniform magnetic field are studied. Under the assumption that the unperturbed distribution is a spherical shell in velocity space in each case, and two dispersion relations to the zeroth approximation in k are obtained as follows:
(Remark: Graphics omitted.)
where ω_c and ω_p are the cyclotron and the plasma frequencies respectively, and ν is the collision frequency with the neutral particles. After some calculations under an assumption ν(v)=const×v^h it is found that initial perturbations grow exponentially for h>3 in (B) and the growth rate is the largest in the magnetic field-free case.

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From Midzuno’s scattering theory in the Born approximation, formulas are derived for the phase shift of coherent microwaves caused by cylindrical plasmas. Experiments are made on helium plasmas of 17 to 96 mm diameter at 34GC and on a 45 mm diameter plasma at 9GC with standard type micro-wave interferometers to examine the applicability of the formulas. Agreement between the values of phase shift predicted by theory and those obtained by experiment is remarkably good when judged from the calibration by Langmuir probe. By the use of the derived formulas, a new method of analysis is proposed for measuring the electron density of underdense cylindrical plasmas for which the phase shift analysis based on the plane slab approximation may not simply be applied. It is found by experiment that the effect of glass wall of the discharge tube on the phase shift is only to shift the point of balance of the interferometer bridge.

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The moments of the velocity change, ⟨Δv⟩⁄Δt, ⟨ΔvΔv⟩⁄Δt, ···, of a particle in a magnetoplasma are calculated in the wave theory, Here Δv is the change in velocity of the particle during a small time interval Δt and ⟨ ⟩ means an average over all the interactions between the particle and the other plasma particles. With use of these moments a kinetic equation for a magnetoplasma is derived.

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This paper describes the principle, simulated experiment, reflection and refraction of waves, and physical significance of the Doppler-effect-like phenomena which occur whenever a wave or pulse go through a moving boundary between two media. The significant properties of this phenomenon are the time length change and energy amplification, as shown in the two-dimensional time-space case analyzed. The qualitative experimental results were in accordance with the theory.

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Flow of a visco-elastic fluid near an oscillating plate and between two plates oscillating with a phase difference, with the same frequency and different amplitudes, under a transverse magnetic field fixed relative to the fluid and fixed relative to one of the plates has been considered employing a well known simple complex variable technique. Expressions for velocity profile, the induced magnetic field and the shear stresses on the plates in all the situations have been calculated exactly as well as approximately in the two limiting cases of small and large values of the Reynolds number.
In the case of two oscillating plates, the skin friction on the two plates tend to the same value in the limiting case when the Reynolds number tends to zero. The shearing stress on the lower plate, in the limiting case when the Reynolds number tends to infinity, behaves as if the other plate were absent. These results hold whether the magnetic lines of force are fixed relative to the fluid or to one of the plates.

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This study presents the hydromagnetic and cross-viscous effects on the forced flow of a non-Newtonian liquid against a rotating disk. The problem has been solved by using Kármán-Pohlhausen method. It is found that the cross-viscous and magnetic effects depend on two non-dimensional numbers R_c and m respectively. Numerical solutions have been obtained. for the radial shear stress, torque acting on the disk, boundary layer thickness and the dimensionless moment coefficient for various values of R_c and m. The effect of cross-viscosity is to decrease the magnitudes of the radial and tangential components of the velocity. The radial velocity component of the fluid increases while the tangential component decreases as the strength of the magnetic field increases.

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The steady shock discontinuity in the flow of a perfectly conducting gas with aligned magnetic field is considered by taking, as the parameters, the Mach number and the Alfvén number ahead of the shock and the shock angle. The jumps across the shock, which satisfy the various conservation laws as well as the entropy and evolutionary conditions, are calculated by making use of an electronic computer. The possible types of MHD shock polar are shown in the speed-deflection plane for various combination of parameters.

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This paper deals with the Knudsen layers in Rayleigh shear flow and other related flows of rarefied gas. A matching procedure is presented by which the outer solution for continuum regime and the solution for the Knudsen layer are determined simultaneously. Numerical discussions are made of the flow velocity and shear stress. A brief discussion as for the coefficients of slip and temperature-jump is also given.

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