Vol. 21, No. 6 (1965)
By using the method of point relation for identification of SiC polytype, more than 1100 Laue patterns of SiC single crystals were analysed and 61 kinds of new modifications of α-SiC were found, in which the largest lattice parameter of c-axis in the hexagonal unit cell is 2622.8?. So far the number of SiC polytypes reaches 110 kinds, in which the hexagonal polytypes are of 30 kinds and the rhombohedral polytypes are of 80 kinds.According to the experimental data, the three different mechanisms of forming the SiC polytypes at the present time were discussed:1) the screw dislocation theory,2) the growth condition theory,3) the thermodynamic theory.
THE USE OF SIGN RELATIONSHIP IN THE DETERMINATION OF HEAVY ATOM CONTAINING CRYSTAL STRUCTURES——I. A SIGN-REFINEMENT PROCEDURE
1965, 122 (6): 1105-1113. doi: 10.7498/aps.21.1105
For crystals composed entirely of light atoms with atomic numbers close to each other, the Sayre equation gives the sign relation of the structure amplitudes. It has been successfully applied to the determination of crystal structures of organic compounds. Nevertheless, for crystals containing "heavy atoms", the Sayre equation is no longer valid; instead, the so-called "heavy atom method" is generally used. In the present work the interrelation between the respective signs of structure amplitudes, the Sayre equations, and heavy atoms has been considered, and the possibility of combining the heavy atom method and that of Sayre is pointed out. This leads to the suggestion of a sign-refinement procedure, with which the initial signs of heavy atoms can be refined to the correct signs of the structure amplitudes. This procedure has been verified with a hypothetical one-dimensional structure and proved to be efficient. Some problems concerning its application to the actual crystal-structure analysis are also discussed.
THE USE OF SIGN RELATIONSHIP IN THE DETERMINATION OF HEAVY ATOM CONTAINING CRYSTAL STRUCTURES——II. "COMPONENT RELATIONSHIP" AND ITS APPLICATION
1965, 122 (6): 1114-1118. doi: 10.7498/aps.21.1114
In Part I of this article, the possibility of combining the "heavy atom method" and the "sign relation method" has been pointed out, and a sign-refinement procedure has been suggested to replace the ordinary successive electron density syntheses. The present part deals with the problems concerning the combination of the procedure previously suggested with the isomorphous replacement method or anomalous scattering method in the case of noncentrosymmetric crystals.
1965, 122 (6): 1119-1122. doi: 10.7498/aps.21.1119
The possibility of applying the Treiman-Yang criterion to the study of such reactions as n+p→p+p+π- is discussed. For this, the contributions, from all possible one-pion exchange Feynman graphs, to the definite final state are considered. This allows one to single out from experimental data events corresponsing to some Feynman graph. Such an approach makes it possible to apply the Treiman-Yang criterion also to processes in which there are identical particles in the final state.
Sawyer's method of "summation of most singular terms" is applied to the case of π-N scattering. It is found that the leading singularity in the complex angular momentum is a fixed cut of the square root type. The high energy behaviour in the crossed channel is obtained.
1965, 122 (6): 1132-1138. doi: 10.7498/aps.21.1132
In this paper we have discussed the SU3 and G2 transformation properties of the weak interactions. By assuming selection rules for certain operators in SU3 different from isospin, a series of relations between the amplitudes of the nonleptonic decays of the strange particles are obtained, which include some results obtained in previous works. Assuming the G2 symmetry of the strong interactions, we discuss the selection rules in these processes in a similar manner and show that the weak interactions cannot transform according the representations 7 or 14 of G2.
1965, 122 (6): 1139-1161. doi: 10.7498/aps.21.1139
The spin Hamiltonian of the hyperfine interaction between a shallow donor and the Si29 nuclei has been derived on the basis of the effective mass wave function. The interference effect between the Bloch functions of different valleys is shown to be largely responsible for the anisotropy of the electron-nuclear hyperfine interaction. An expression for the resonance frequency was derived in the high field approximation. The theory is shown to account for the experimental observations of Feher on the anisotropic hyperfine interaction quantitatively. The coefficient of the 2p core function in the OPW conduction band edge Bloch functions has been determined by comparison with Feher's results to be 0.20 approximately. It is pointed out that on the basis of the theory given, the positions of the conduction band minima and the anisotropy of the donor effective mass wave function can be precisely determined by the method of ENDOR and its pressure effects.
THE CALCULATION OF THE ENERGY-BAND STRUCTURE OF SOME SEMICONDUCTORS WITH THE PSEUDOPOTENTIAL PERTURBATION METHOD (APPLICATION TO GaAs, GaP AND Ga[As1-xPx]ALLOY)
1965, 122 (6): 1162-1169. doi: 10.7498/aps.21.1162
The energy-band structures of the GaAs, GaP, and Ga [As1-xPx] alloys have been calculated on the "empty lattice" assumption by taking the pseudopotential as perturbations.The pseudopotential parameters are chosen so as to make the calculated direct and indirect energy gap agree with that given by the experiments. The results thus obtained are in good agreement with experimental data at room temperature. Assuming that the lattice constant and pseudopotential parameters vary linearly from GaAs to GaP, we have calculated the energy band of the Ga[As1-xPx] alloys for x=0.2, 0.5, and 0.8. The direct and indirect energy gap is equal at x=0.41 which is in reasonable agreement with the results of Spitzer and Fenner.
1965, 122 (6): 1170-1174. doi: 10.7498/aps.21.1170
We have used a nonrefrigerated cadmium trap in a 2-stage glass mercury diffusion pump vacuum system. Experiments show that the cadmium trap is capable of isolating mercury vapour effectively, as high vacua of 10-5-10-7 mmHg is attainable in an evacuated container. Systematic investigations of the effect of the cadmium film under various conditions on the ultimate pressure were carried out. It is found that newly evaporated cadmium films are most effective for that purpose, while after exposure in air of 10-2 mm Hg, the ultimate pressure does not change appreciably, and that had the cadmium film been exposed to the atmosphere, it would be one order higher than before. Improvement on the ultimate vacuum can be effected by decreasing the cadmium trap temperature and utilizing two or more cadmium traps in series as well as through bake-out of the evacuated container. When such measures are put in force, an ultra-high vacuum of 10-9 mm Hg is obtained in our test.
AN EXPERIMENTAL STUDY OF PROTON FREE PRECESSION IN A WEAK MAGNETIC FIELD AND ITS APPLICATION TO FIELD WORK
1965, 122 (6): 1175-1187. doi: 10.7498/aps.21.1175
A Packard-Varian type experiment was done, in which the free precession of proton magnetic moment about a very weak magnetic field was observed, by first lining up the protons in an aqueous sample with a separate magnetic field and then allowing them to execute the free precession. In out experiment the studies on the non-adiabatic process of withdrawing the polarizing field, the absolute value of the signal strength and the reduction of sample size to minimize the effect of inhomogeneity of the magnetic field were emphasized. The effect of rotating the sample coil upon the measured signal frequency was also noted, and it is pointed out that this is the most direct way to determine the sign of the nuclear magnetic moment.The phenomenon of proton free precession in weak magnetic field has important practical applications in earth's magnetic field measurement at high altitudes, in geological prospecting, and in petroleum recovery from oilfield rocks. The present studies may be helpful in solving the problems likely to occur in these applications.In order to check the performance of the entire experimental set-up for field works, and especially to investigate the influence of magnetic substances in surroundings on the signal frequency, a series of experiments was carried out on a lake. Affirmative results were obtained. The relative accuracy of the measurement of the precessional signal frequency, which in turn determines the magnetic field strength, is 1×10-5.
1965, 122 (6): 1188-1212. doi: 10.7498/aps.21.1188
The method of correlation function has been utilized to discuss the nonlinear effects in the ferromagnetic resonance at high power levels. For ordinary ferromagnetic crystals, the present theory includes the results of the semiclassical theory developed by H. Suhl as a classical limit. In the case of YIG doped with rare-earth ions, the frequency shift and the additional losses due to the rare-earth ions have been discussed. Besides, the threshold field of the so-called first order process with parallel pumping and the first and second order processes with perpendicular pumping have also been derived. The results obtained show that the rf critical magnetic field increases with the addition of rare-earth ions. In samples with small concentration of rare-earth ions, the influence on the threshold is attributed to the increase of the losses of spin waves. The temperature dependence and the anisotropy of the threshold field are entirely similar to those of the ferromagnetic resonance linewidth at low power level. The experimental results may be satisfactorily explained by the present theory.
1965, 122 (6): 1213-1227. doi: 10.7498/aps.21.1213
In this article, the highly compressed matter has been considered as a model for simple anisotropic metals. A perturbation method was set up to determine the energy spectrum of a Fermi system in a periodic field. By taking account of the static potential of ion lattice, the Coulomb interaction and interaction via phonon fields, the spectrum of single particle excitations was studied. Detailed calculations of the Fermi surfaces and the density of states have been carried out for f.c.c. and b.c.c. lattices, with the numerical results presented in Fig.8-Fig.10.
A theory is given for the effect of the second order electric moment of crystal on dispersion by means of the Green's function method, in which account is taken of the an-harmonic potential. When we ignore the effect of the anharmonic potential, the result obtained is reduced to that of M. Born and Huang Kun; the effect of the unharmonic potential is to modify the distribution of the strength of absorption.
INTERACTION OF SOLUTE ATOMS WITH DISLOCATIONS IN Al-4% Cu ALLOY AT VARIOUS AGING STAGES UNDER FATIGUE LOADING
1965, 122 (6): 1242-1252. doi: 10.7498/aps.21.1242
Torsional fatigue experiments were carried out with Al-4% Cu specimens at various aging stages in order to study further the dislocation pinning process occurring under fatigue loading. The area and the shape of the hysteresis loop after various stress cycles N were determined, from which the energy loss AE in each cycle and the maximum forque Tm of the specimen were calculated.The temperature and the time of aging were so chosen that G. P.  zone, G. P.  zone, θ′ phase or the stable θ phase appeared respectively in one of the specimens. On the basis of comparing the mode of changes of the experimental curves of △E-N and Tm-N, it is concluded that the dislocation pinning occurring in the initial stage of fatigue loading is not concerned with the transformation products such as the G. P.  zone and G. P.  zone.The changes of the energy loss in the first cycle of fatigue loading, (△E)1, of specimens at various aging stages were compared and analysed, and it is shown that, in the case of the Al-Cu alloy studied, the energy loss △E is produced because of the occurrence of a fluctuating internal stress field in the lattice near a dislocation, since work has to be done when the dislocation moves to and fro in such a stress field. This fluctuating internal stress field may appear because of the occurrence of point defects (vacancies and solute atoms), atom clusters, G. P.  zone, G. P.  zone, or other defects when they do not segregate or nucleate on the dislocation line.On the basis of the above analysis, it may be considered that the dislocation pinning process occurring under fatigue loading is associated with the formation of atmospheres of solute atoms. The solute atoms migrate to dislocations in the process of fatigue loading with the help of the vacancies produced in fatigue loading, so that atmospheres are formed around dislocations. The mobility of these pinned dislocations is reduced, and consequently △E is lowered. The θ′ and θ phases that nucleate on dislocation lines during the process of aging can also pin the dislocations to a certain extent.It can also be contemplated from the above picture that the G. P.  and G. P.  zones do not nucleate on a dislocation line, while the θ′ and θ phases do.
1965, 122 (6): 1253-1263. doi: 10.7498/aps.21.1253
Torsional fatigue experiments were carried out with aluminium-magnesium alloys containing 0.52, 0.91, 3.46 and 5.15% magnesium at the quenched state, and △E-N and Tm-N curves were determined. Experimental results showed that, in the cases of the specimens containing 0.52% and 0.91% magnesium, △E drops with an increase of the stress cycle N when the torsion strain is small. However, when the torsion strain is higher, the △E-N curve keeps flat at the beginning, but △E increases subsequently and becomes stable after a fairly high value is reached. As the magnesium content in the specimen is 3.46%, the change of the △E-N curve is similiar to that of the Al-4% Cu alloy when the torsion strain is not too high. When the torsion strain is sufficiently large, △E increases at the beginning and decreases after it passed through a maximum value. The change of the △E-N curve of the specimen containing 5.15% magnesium is entirely similar to that of the Al-4% Cu alloy and no peak value was observed on the curve with the highest torsion strain used in the experiment. The Tm value shows an initial increase for specimens with all the magnesium contents studied.The results described above can all be explained with the assumption that "atmospheres" of solute atoms are formed because of the gradual migration of magnesium atoms to dislocations during fatigue loading. It is considered that, in the case of aluminium-magnesium alloys, the origin of the energy loss, △E, and the factor that controls the magnitude of △E in the initial stage of fatigue loading are all primarily due to the formation of atmospheres of solute atoms. When the magnesium content is relatively small, the atmospheres formed may be considered as "loose" for a sufficiently high torsion strain, so that a dislocation can drag its atmosphere along and work is done under fatigue loading. This leads to an increase of both △E and Tm. However, when the magnesium content is relatively high or the torsion strain is not sufficiently large, the atmospheres formed at the beginning of fatigue loading become already "dense" enough to pin the dislocations. With the continuation of faligue loading, the mobility of dislocations is further lowered by the migration of solute atoms to these dislocations. This leads to an initial decrease of △E and an initial increase of Tm. Fatigue experiments were also carried out on Al-0.52% Mg and Al-3.46% Mg alloys at various aging stages, and the phenomena of strain aging were observed. Such phenomena are in accord with the assumption of atmospheres of solute atoms described above.
1965, 122 (6): 1264-1275. doi: 10.7498/aps.21.1264
The temperature dependence of the critical resolved shear stress (CRSS) of molybdenum single crystal has been investigated. It was found that the logarithm value of CRSS varies linearly with the absolute temperature which is not in agreement with Cottrell-Bilby's relationship based on atmosphere locking. Assuming that a chemical exchange bond between the impurity and dangling atoms would be weakened with rise in temperature and using the Morse function, the experimental linear Inσ-T relationship could then be accounted for and a slope of the right order of magnitude established.
In this article, the simultaneous set of nonlinear equations for photon transport and inverted population in active medium is solved by taking the pumping effect into account. The analytic expressions of the space-time distribution function of inverted population and photon density are then obtained for an arbitrary initial distribution of inverted population. The cases of a single or a series of square pulse input are discussed in detail. In addition, the effects of incidence of very intense beam on steady-state operation of the laser are also studied. Under certain conditions, the perturbation method may be used to derive the formulas for photon density and inverted population density in laser. Calculations are made, with ruby laser as an example, and it is shown that the incidence of very intense beam may possibly be used for strengthening giant pulses.
THE ANALYTIC WAVE FUNCTIONS FOR ATOMS——II. THE ANALYTIC WAVE FUNCTIONS AND ENERGIES FOR THE ATOMS AND IONS OF ELEMENTS OF THE SECOND PERIOD
1965, 122 (6): 1293-1303. doi: 10.7498/aps.21.1293
The energies of the atoms and ions of the elements of the second period in the periodic table are calculated with a set of simple variational wave functions. The form of the wave functions used is as follows: 1s:ψ1(r)=N1e-μar, 2s:ψ2(r)=N2[(μr)e-μr-Ne-μar], 2p:ψ3(r)=N3(μr)cosθe-μr,ψ4(r)=N4(μr)sinθeiφ-μr,ψ5(r)=N5(μr)sinθe-iφ-μr.There are only two parameters in all. The parameter ft is a scale factor, the best value of which can be determined analytically, leaving but only one parameter a to be determined numerically. N1, N2, N3, N4, and N5 are normalization factors. The constant N is fixed so that ψ2 is orthogonal to ψ1. The results of this calculation are better than those calculated by Кириллова, Веселов и Братцев with their wave functions containing three parameters and are very close to those calculated in a previous paper by us with wave functions containing five parameters.