Vol. 30, No. 4 (1981)
In this paper, we considered the scattering of a plane sound wave in a medium which contains many spherical particles, for example, a concentrated suspension in a liquid. The sound interaction field and the equivalent scattering cross section of a partical have been calculated. When dimensions of the particles are much less than the sound wave-length, the following conclusions can be drawn, a) On account of the interaction, the scattering cross section must have a multiplying factor Q. Geometrically, it is due to the masking effect on each other, and Q= |1-(γ0A0(1)+γ＇1A1(1)|2 is called masking factor, b) The dependence of scattering coefficient on partical concentration is no longer a linear one. c) When the dimensions of them are much less than the sound wavelength but larger than viscous wavelength, the scattering coefficient of them will obey Rayleigh's law. But when their radii are near or less than viscous wavelength, the scattering co-efficients will show a dependence on frequency that is higher than the fourth power.
As well known, the measurements of the sound attenuation on a single bubble can be explained by thermal conductivity, viscousity and radiation losses. But when the measurements were made in a bubble screen, it will not be so simple. Since the theoretical loss is much less than the measured one, this problem is open until now.In this paper, taking the sound interaction among bubbles in water into account, a 90 phasor between the primary incident sound and the multi-scattering sound has been ob-tained. The latter is equivalent to a retard force acting on every bubble, and they suffer an additional damping.Comparing our theory with Carstensen and Foldy's experiments, a satisfactory agreement has been, found. In addition, we point out that the resonant frequencies of bubbles do not vary with the interaction among them, but the resonant curves will be widened. When the sound frequency is lower than the resonant frequency of a bubble, the mass which accompanies it will get an increase and the stiffness get a decrease. When the sound frequency is higher than its resonant frequency, the situation will be converse.
1981, 30 (4): 448-458. doi: 10.7498/aps.30.448
In this paper, by using the concepts " entropy production" and "excess entropy production", the Lyaponov stability of the master equation in linear and nonlinear range has been discussed. The results obtained are consistent with the stability theory of the time evolution equation of macroscopic non-equilibrium systems discussed by I. Prigo-gine. In addition, the concept of "probability flow" is proposed for the multivariable master equation of the stochastic model of non-equilibrium systems, and the method of decomposition of "probability flow" is given.
1981, 30 (4): 459-471. doi: 10.7498/aps.30.459
The electron optical properties of magnetic deflection systems are generally described in terms of the parameters H0, H2 and H4. In this paper, basing on the Biot-Savart's law, we derive the analytical formulas for the flaring saddle coil with a single turn. And then using the method of Fourier harmonic anlysis we obtain the field-para-meters experssions for the different winding distributions. So the relations between the field-parameters and the harmonics and some useful results are obtained. These formulae are useful for designers of deflection systems in television tubes, kinescopes, radars, scanning electron microscopes and electron beam exposure equipments.
ON THE LINEAR TRANSFORMATIONS OF GAUSSIAN TRAJEC-TORY PARAMETERS AND THEIR INFLUENCE UPON ELECTRON OPTICAL ABERRATIONS
1981, 30 (4): 472-477. doi: 10.7498/aps.30.472
In this paper, we describe electron trajectory by vector form and express aberra-tions in matrix form. According to the more general viewpoint, we discuss some general linear transformations of gaussian trajectory parameters. The third order aberrations, aberration coefficients and their partial differentials in an electron optical system undergone these transformations are derived. Therefore the general electron optical Fraunhofer conditions for correcting isotropic and anisotropic coma are obtained. It is shown that under this condition, astigmatism and field curvature have extreme or stationary values. According to these results, some concrete problems are discussed; for example, the effect of aperture position on aberrations in the fixed or scanned electron beam systems, and the effect of magnetic immersion on aberrations in the emission electron system (cathode lens).
1981, 30 (4): 478-486. doi: 10.7498/aps.30.478
In this paper, a representation theory in 6-dimensional phase space for Klimonto-vich-Vlasov system is introduced. By using this theory, the relation between the Mis-guich-Balescu's one-particle asymptotic propagator and the Dupree's average Green function is analyzed. It is found that they coincide in the stationary Markovian process, by using them the divergence difficulty of resonance function in the MB's non-linear dispersion relation is resolved. It is pointed out that the divergence difficulty arises from the failure of the concept of fluctuation production operator introduced by MB in their sub-dynamics for the multiple-time-scale perturbation theory.
EQUILIBRIUM THEORY AND ADIABATIC COMPRESSION THEORY OF TOKAMAKS WITH AN ELLIPTIC CROSS SECTION WITH SOME TRIANGULAR DEFORMATION
1981, 30 (4): 487-496. doi: 10.7498/aps.30.487
MHD equilibria of tokamaks with a droplet-shaped cross section (an elliptic cross section with some triangular deformation) have been dealt with in this paper, all equilibrium solution and the current distribution in external coils required by producing the appropriate configuration are presented. The problem of heating the plasma with such configuration by adiabatic compression is discussed, the variation of all the equilibrium configuration with time during the compression is given. Calculations of the equilibrium configurations and the variations in configuration and in pressure during the adiabatic compression have been carried out for several giving current density profiles, some numerical computations are shown in figures.
1981, 30 (4): 497-502. doi: 10.7498/aps.30.497
Using a narrow line output of tunable pulsed dye laser, the inhomogeneously broadened absorption band of 4I9/2→4G5/2 in Nd3+ doped germate, silicate, phosphate, fluo-rophosphate and fluoroberyllate glasses were selectively excited at low and room temperatures. Wavelength dependence of fluorescence decay were observed to investigate the decay nature and interaction of Nd3+ ions at different site in different glass hosts.
A new representation of the light field is proposed in this paper. It is shown that the wave theory of the light propagation can all be putted into a more convenient and more complete scheme of a matrix theory when the new representation is adopted. Some general fundamentals of this matrix theory are given, and the convergence of the action matrix is also proved in the general case.The expression of the light field proposed here involves the general characteristics of the monochromatic scalar wave field with only one propagation axis. It can also demonstrate explicitly the axial symmetry and the radial distribution features of this field on the plane which is perpendicular to the propagation axis. By virtue of this expression, some general laws of the distribution of the field on the plane, including the qualitative law of the distribution of the symmetries of the field along the radial direction, are obtained for the first time.
1981, 30 (4): 514-519. doi: 10.7498/aps.30.514
Using a diagrammatic computation method of the Wigner distribution function for geometric-optical systems, a 2-dimensional coordinate transform system is designed theoretically. The precision of this system may be better than that of the Bryngdahl co-ordnate transformer.
1981, 30 (4): 520-525. doi: 10.7498/aps.30.520
The algorism of indexing hexagoanal and tetragonal Debye-Scherrer photographs has been thoroughly discussed. It is pointed out that the procedure of finding a common solution for a series of Diophantine linear simultaneous equations, even for the low angle diffraction lines, seems to be untenable, because the solution is not unique.It is proposed that by adopting the same principle used in the new graphic method suggested by one of the authors, one may utilize three independent low angle sin2θ's and the density of the crystal, and form a series of conditional linear equations together with a series of equations representing equiatomic curves, a unique solution may be obtained which is the intersection of three conditional lines arising from different sin2θ's and one equiatomic curve. This gives the primary translations of the unit cell, and simultaneously the number of formula weight units contained therein.A computer program in FORTRAN has been written, the identification of which is POWDBX-HT. The time required to index one photograph is less than one minute.
A STUDY ON THE ELECTRON STIMULATED INTERACTIONS OF RESIDUAL OXYGEN CONTAINING GASES WITH Ni (001) SURFACE
1981, 30 (4): 526-537. doi: 10.7498/aps.30.526
When an electron beam bombards the residual oxygen-containing gases, such as H2O, CO2 and CO, these gaseous molecules will be dissociated as follows: H2O→Oad+H2,CO2→Oad+CO,CO→Oad+Cad, and the oxygen, and carbon atoms will coad-sorb on Ni(001) surface forming respectively many independent adsorption domains. The structure of them is either p(2×2) or c(2×2),depending upon the oxygen and carbon concentrations on the surface. The electron beam bombardment assists the nuclea-tion, growth, coalescence and ordering of these domains. When the oxygen and carbon atoms have occupied about one half of four-fold adsorption sites of the Ni(001) surface, the above- mentioned reactions will be in a state of equilibrium with following desorp-tion reactions: C*+Oad→CO,O*+Cad→CO, where * denotes the electron excited atoms, and the nickel oxide or carbide begins to nucleate. As the content of oxygen in the residual gases surpasses that of carbon, the nucleation of nickel oxide will be predominant. Once nickel oxide is growing, the desorp-tion reaction of carbon becomes effective and the already adsorbed carbon atoms will desorb or diffuse away and the oxygen concentration will increase quickly. As a consequence, the oxygen concentration inside the electron beam spots becomes much higher than that outside and the reverse is true for the carbon concentration. During the electron beam bombardment a change of carbon Auger peak shape, indicating diffrent bonding states between the carbon and substrate atoms, takes place. In the initial stage of adsorption the dissociative effect of an electron beam plays an important role, but during the growth of nickel oxide its thermal effect in enhancing diffusion becomes predominant.
1981, 30 (4): 538-541. doi: 10.7498/aps.30.538
Inelastic scattering spectra of Aluminium hydride (AlH3)n have been measured before and after the application of a hydrostatic pressure up to 50 kbar. Some fine structure peaks were observed. The results is compared with Roszinski's infrared spectrum, in the range from 600 to 1700 cm-1. They are in general agreement. Besides, three other peaks were observed, which are difficult to measure with infrared in lower frequeacy range. It seems that this material does not change in its thermodynamic character and microstructure after hydrostatic pressure treatment.
1981, 30 (4): 542-544. doi: 10.7498/aps.30.542
The change of reflectivity of P-implanted Si with time under high power CW CO2 laser irradiation has been measured by infrared detector. We discover that the reflectivity increases irreversibly in both the laser heating and cooling processes. This means that the surface carrier concentration of ion-implanted Si would change similarly.
1981, 30 (4): 545-548. doi: 10.7498/aps.30.545
By analysing the dielectric function of an interacting Bloch electron gas, the condition for the formation of acoustic plasmons (AP) as well-defined quasiparticles in metals has been derived. Discussions are given on whether this condition is satisfied for A-15 compounds, with the conclusion that the evidence for the existence of AP as a kind of quasiparticle in these compounds is insufficient until now.
1981, 30 (4): 549-554. doi: 10.7498/aps.30.549
The electron irradiation effects on the crystal structure of α-lithium iodate (α-LiIO3) have been observed by TEM. Under the irradiation of medium-intense electron beam with energy 100 KeV, α-LiIO3 transforms into γ-LiIO3 at first and then into Li2O and an other new type of Li-O compound which is probably a nonstoichiometric one and re-fered to as X compound. If the irradiation is carried out with more intense electron beam, α-LiIO3 crystal melts quickly. In that case, either a decrease in intensity of electron beam or a break in irradiation leads to recrystallization of the melted substance in the form of X compound which gradually transforms into Li2O and metal Li under subsequent electron irradiation. The phase tansformation form X compound into Li2O is reversible to certain extent. Besides, it is found that the electron irradiation effects on the structure of α-lithium iodate monocrystal is clearly anisotropic.
1981, 30 (4): 555-558. doi: 10.7498/aps.30.555
The room temperature section of the phase equilibrium diagram of the Al-Cr-Cu ternary system has been investigated by means of X-ray powder diffraction method. Beside the single phases of the three binary systems, there exist five new phases in the diagram, which we call ω1, ω2,εf, εx, and γx phase, so that the diagram of the system is divided into 19 single-phase regions, 41 two-phase regions, and 22 three-phase regions.The new phase γx has an orthorhombic cell, its diffraction pattern is similar to that of γ2. By comparing with that of γ2, we find that some strong diffraction lines are absent in γx, and some other strong diffraction lines exist, therefore the crystal structure of γx differs from cubic, and has an orthorhombic cell. It exists in such a narrow region, that it may probably be a compound.The other new phases ω1 and ω2 are very similar to each other in their feature. The new phase εf has a comparatively wide range in composition, and it seems to change rather continuously in its diffraction pattern as the composition is changed. On the other hand, the new phase εx has only a small region, and the diffraction pattern is completely diffrent from that of the other new phases.
THE CRYSTAL GROWTH OF BaB2O4 LOW TEMPERATURE PHASE AND THE STUDY OF PHASE DIAGRAMS OF RELATED SYSTEMS
1981, 30 (4): 559-564. doi: 10.7498/aps.30.559
The pseudo-binary systems BaB2O4-Na2O and BaB2O4-Na2B2O4 in the ternary system BaO-Na2O-B2O3 have been studied by means of thermal analysis and X-ray diffraction. The system BaB2O4-Na2B2O4 is a eutectic one and it's eutectic reaction occurs at 826 ±3℃. A new compound BaB2O4·Na2O which melts congruently at 846 ± 3℃ has been discovered in the BaB2O4-Na2O system. There exist eutectie horizontals from BaB2O4 to BaB2O4·Na2 at 755 ±3℃ and from BaB2O4·Na2O to Na2O at 573 ± 3℃. According to the obtained phase diagrams of the mentioned binary systems, the single crystals of BaB2O4 low temperature phase with dimensions of 2×4×6 mm3 and 2×4×8 mm3 have been grown by the Czochralski method from the melt containing 15 mol% Na2O or 13 mol% Na2B2O4 as flux.
1981, 30 (4): 565-572. doi: 10.7498/aps.30.565
The crystal structure and the atomic parameters of Li2K(IO3)3 and Li2NH4(IO3)3 have been determined by means of the X-ray powder diffraction method. The Li2K(IO3)3 and Li2NH4(IO3)3 are isomorphic with Li2Rb(IO3)3. The unit cell is monoclinic. The space group is P21/α. There are four formula units per unit cell. Lattice parameters are α= 11.198?, b = 11.046?, c = 8.254?, β= 111.53° and α =11.327?, b = 11.078?, c = 8.341?,β = 111.87° respectively. The relation between formation of Li2M(IO3)3 compounds and Mionic radius has been discussed.