Vol. 22, No. 4 (1966)
1966-02-20
CONTENT
1966, 22 (4): 385-403.
doi: 10.7498/aps.22.385
Abstract +
A new method of measuring excess carriers lifetime in semiconductors is described. This method is for measuring photoconductive phaseshift of spreading resistance under a point contact. The expressions of various results are derived at various spectral components of exciting light and under various surface conditions. The calculated results for numerical values are given for commonly used conditions of measurement i.e. ground surface and exciting light of long wavelength. At the same time, a more detailed analysis and discussion are presented for these results. This method possesses many advantages, for example, (l) it can be used for measurement on ingot crystal; (2) the surface treatment is very simple; (3) no fixed electrode has to be made on the specimen; (4) measuring apparatus used is simple and easy to operate; (5) enough accuracy is obtainable.This method can be applied to test inhomogeneous specimen. It is used for study in scientific research institutions and it is more suitable for examining single crystal materials in the works. The measurements are made by this method on Ge and Si specimens. Results are in agreement with those obtained by other methods.
1966, 22 (4): 404-411.
doi: 10.7498/aps.22.404
Abstract +
In this paper electrical properties of silicon containing Boron and phosphor (or arsenic) have been measured from 20° to 300°K in the range of carrier concentration 2×1012 to 1×1020 cm-3 at room-temperature. The weak-field transverse magneto-resistance and impurity activation energy methods were used to determine the degree of impurity compensation for some p-type silicon samples and these methods have been compared. Analyses of Hall coefficient and electrical conductivity vs temperature curves indicate the ionization energy of Boron (phosphor) acceptor (donor) levels to be 0.045 eV for low impurity concentration; Fermi degeneracy is found to occur in the range of 1018 to 1019cm-3. Impurity conduction has been observed for carrier concentration 2×1017 to 1×1018 cm-3 for p-type silicon and 5×1017 to 4×1018 cm-3 for n-type silicon respectively. Extrinsic Hall mobility is computed from Hall coefficient and conductivity. The temperature dependence of lattice-scattering mobility is found: μL=2.1×109T-2.7 for holes; μL=1.2×108T-2.0 for electrons.Carrier concentration vs. resistivity and Hall mobility vs. resistivity curves had been plotted for our silicon material in the range of carrier concentration 5×1011 to 1×1020 cm-3. It is aimed to give as reference for preparing silicon material.
1966, 22 (4): 423-428.
doi: 10.7498/aps.22.423
Abstract +
A phase diagram of the alloys of the ternary system of copper-germanium-tin was constructed on the basis of the data obtained by x-ray analysis. The isothermal section at room temperature was found to consist of eight single-phase regions (i.e. α,ζ,δ,ε1,ε,η′,Ge, and Sn), thirteen two-phase regions (i.e. α+ζ,α+δ,ζ+δ,ζ+ε1,ε1+δ,ε1+ε,δ+ε,ε1+Ge,ε1+η′,ε+η′,η′+Ge,η′+Sn,Ge + Sn), and six three-phase regions(i.e. α+ζ+δ,ζ+ε1+δ,ε1+δ+ε,ε1+ε+η′,ε1+η′+Ge,η′+Ge+Sn). No new phase was observed in these alloys of the ternary system.
1966, 22 (4): 429-439.
doi: 10.7498/aps.22.429
Abstract +
The equilibrium diagram of the Fe-Ga system below 1000℃ has been determined mainly by X-ray investigation incorporated with differential thermal analysis. The system consists at room temperature of three intermediate phases ε, χ, and ψ. The ε phase with a very narrow homogeneous range has an ordered face-centred structure corresponding to the ideal formula Fe3Ga. At about 550℃, it transforms into another phase ζ which separates at higher temperature directly from the solid solution of Ga in Fe. The structure of the high temperature phase ζ has not been determined. The homogeneous range of the χ phase extends at room temperature from 55 at. % Ga to 60 at. % Ga. The structure of this phase appears to be very complicated, presumably corresponding to the structural formula Fe4Ga5, Fe3Ga4 or Fe2Ga3. It is formed at about 960℃ by a peritectic reaction. The ψ phase is formed by another peritectic reaction at 820℃. The structure is tetragonal, with a=6.2628? and c=6.5559? at 20℃. The space group is D4h14-P42/mnm, and each unit cell contains four formula units corresponding to FeGa3. No noticeable solubility of Fe in Ga has been observed. There exists an eutectic isothermal ranging from FeGa3 to Ga, the eutectic point being very near to the pure component. There exists also an eutectoid isothermal at about 590℃, the eutectoid point being approximately at 50 at. % Ga, at which the solid solution of Ga in Fe decomposes simultaneously into ζ and χ. The most remarkable feature of this system is the primary solid solution region of Ga in Fe. The solubility at room temperature is 15.2 at. %. It gradually increases with temperature, and above 700℃, it increases suddenly up even to 50 at. %. The structure below 625℃ is body-centred cubic, designated as a in the phase diagram. But above 625℃, it changes into two other structures with their respective phase regions, designated as α1 and α2. The structures of α1 and α2 have not been elucidated yet, but most probably they are derived from a by stacking together the fundamental unit cells with atomic rearrangement or vacancy defect.
1966, 22 (4): 440-448.
doi: 10.7498/aps.22.440
Abstract +
The angular distribution and differential cross-section of the proton groups from the C12(d,p)C13 and Ca40(d,p)Ca41 ground state reactions have been measured at the deu-teron energy of 13.3 MeV. Measurements were made at 2.5° or 5° intervals and covered the angular range from 3° to 167° and from 10° to 164° for the C12 and Ca40 reactions respectively. It is found that: (1) The experimental points near the main stripping peak agree fairly well with the theoretical angular distribution curve calculated by using the simple Butler theory and normalized at the stripping peak, for both proton groups. The parameters of the nuclear levels thus determined are in good accord with the results previously obtained. (2) For large angles, the experimental cross-sections do not decrease to such small values as required by the Butler theory. They also show very prominent subsidiary maxima at the positions not in accord with the prediction of the Butler theory. These features can be interpreted by the distorted wave theory, but may also be partly due to contributions of reaction mechanisms other than the deuteron stripping. (3) In the C12(d, p)C13 reaction, the cross-section decreases strongly at the forward angle and shows an uprising at the backward angle. Neither of these features is in accord with the Butler theory, but they can also be explained by the distorted wave theory. The uprising at the backward angle may also be due to contributions of other reaction mechanisms. (4) The reduced widths of the ground levels for the C12(d, p)C13 and Ca40(d, p)Ca41 reactions, obtained from the peak cross-sections by using the Butler theory are γ2 = 0-17 and 0.041 respectively. The distorted wave theory gives larger values which will be closer to the values expected from the single particle model. Owing to these facts, it seems worthwhile to analyze the data of the present experiment with the detailed distorted wave theory.
1966, 22 (4): 449-459.
doi: 10.7498/aps.22.449
Abstract +
A new method is developed to treat the ferromagnetic and the antiferromagnetic kinematic interactions. All the kinematic interactions can be represented by means of every order correlation functions. It is shown that the ferromagnetic system (s=1/2) does not involve the T3-term at low temperature. For the antiferromagnetic system, we find that the kinematic interaction is large than the dynamic interaction even at low temperature. Our theory is good for all spin values s as well.
1966, 22 (4): 460-470.
doi: 10.7498/aps.22.460
Abstract +
Using the properties of the Young diagrams, we have constructed a complete set of polynomial bases for representing the SUn group. The basis of irreducible representations in the product space of two irreducible representations is then discussed. Finally by methods of construction of an invariant, an explicit expression for the Clebsch-Gordan coefficients of group SU3 is obtained.
1966, 22 (4): 471-486.
doi: 10.7498/aps.22.471
Abstract +
The dynamical Jahn-Teller effect has been treated in the case of strong coupling for which the static distortional energy of electrons is larger than the energy of a typical vibrational quantum. A perturbation method which applies to strong coupling is developed. The eigenfunction and eigenvalue are expanded as power series of the ratio of the vibrational quantum to the static distortional energy. We have dealt explicitly with the Jahn-Teller effect of the Г8 state of an Oh point group; the energy levels of electronic-vibration system are obtained. The characteristics of strong coupling as compared with weak coupling are: 1) although no static distortion actually appears, the degeneracy and frequency spectra of vibrational modes are changed; 2) the collective modes of electronic-vibration system will appear, if the vibrational modes coupled to the electrons are "tuned". The theory is employed to interpret the experimental results obtained by Weinstock et al. on TcF6 and ReF6 from the infra-red and Raman spectra.
1966, 22 (4): 487-497.
doi: 10.7498/aps.22.487
Abstract +
A statistical dislocation theory of brittle fracture of crystals is suggested. The process of brittle fracture is described as a stochastic process by which microcracks form, grow and propagate under very small plastic deformation. A differential equation describing this stochastic process is derived, and a statistical distribution function of microcrack size is obtained.A quantitative description of the important part played by the plastic deformation and work hardening and the number of active slip sources in the process of brittle fracture is given. In the past, the effect of plastic deformation was only ambiguously included in the conception of effective surface energy, and the effect of work hardening and the number of active slip sources had been neglected.The statistical distribution function of fracture strength is derived from statistical distribution function of microcrack size and the condition of microcrack propagation, and from which the criteria of brittle fracture, brittle strength and brittle-ductile transition temperature have been deduced.
