## Vol. 30, No. 10 (1981)

##### 1981-05-20

###### CONTENT

1981, 30 (10): 1287-1294.
doi: 10.7498/aps.30.1287

Abstract +

In order to develop the ellipsometry used for determination of ion implanted damage layer, we have measured the ellipsometric spectrum of ion implanted silicon in a wavelength range of 4000-7000?. The samples were implanted by 150 keV, l015/cm2 or 1016/cm2 As ions. In this case the amorphous layers were formed at the surface of Si samples, so that a monolayer model could be used to calculate the relations of (n, k)-λ from the data of (ψ, Δ)-λ. The peak of n-λ curve of As ion implanted silicon is situated at ～4800?, and the peak value is about 4.9. The experimental results of ion implanted silicon have been compared with those of sputtering amorphous silicon, evaporated amorphous silicon and single crystalline silicon.

1981, 30 (10): 1295-1306.
doi: 10.7498/aps.30.1295

Abstract +

The study of the transition region at the interface of Si-SiO2 by changing the angle of emission in XPS is reported in this paper. The sample are ultra-thin oxide film on the silicon(111) surface formed at low temperature (700 ℃), the thickness of which was less than 50?. The variation of the chemical displacement (δ) and the intensity ratio (I0x/Isi) of the silicon 2p photoelectron peaks come from the oxide film and the single-crystal substrate with the angle of emission is contradictory with the prediction for an ideal interface model. The comparison of the experiment results with the prediction of the random-bonding model shows that there exists a transition region at the interface of Si-SiO2 and the width of which is about 20?, less than the mean escape length of the Si2p photoelectron in SiO2. The same results are given by the experiment of Ar+ ion sputtering profiles.

1981, 30 (10): 1307-1317.
doi: 10.7498/aps.30.1307

Abstract +

The characteristics of r.f. driven current are discussed. The results show thatonly for u=ω/(kxve)≤2-2.5 the current is carried by the resonant electrons and thedissipative mechanism is the resonant damping. When u≥3 the current will be carried by the non-resonant electrons and the dissipative mechanism will be collision damping. The dissipative power is usually much higher than the Ohmic power and the Lawson condition can be satisfied only for the case of u≤2-2.5. It is also shown that in a r.f. driven tokamak the poloidal rotation of plasma and the correspondent radial electric field are important.

1981, 30 (10): 1318-1324.
doi: 10.7498/aps.30.1318

Abstract +

The method of matrix calculations is widely applied in the theory of electron- and ion-optics, especially in the aberration theory. In the present paper, a rotationally symmetrical electron-optical system and an ion-optical system with crossed toroidal electric and inhomogeneous magnetic fields are treated respestively. The general transfer matrices for the above mentioned electron- and ion-optical systems possessing the primary aberrations are derived. As a direct consequence of Liouville's theorem, we prove that the determinant of the transfer matrix has the value 1 in the approximation up to the primary aberrations. This general conclusion is useful for the electron-and ion-optical a berration theory and the computer-aided design.

1981, 30 (10): 1325-1339.
doi: 10.7498/aps.30.1325

Abstract +

In this paper, a matrix theory for the propagation of a scalar wave in a system consisting of plane screens (in cylindrical coordinates) is proposed on the basis of [8]. The action matrices characterizing the diffraction by a plane filter close to a thin lens, the phase transform action of a lens, and the effect of a piece of free space are given. The diffraction by a common aperture in an opaque screen, the action of a reflection plane screen, the interference produced by a plane screen and so on, are naturally taken into account. The transform matrix describing the effect of changing the reference light field on the field distribution vector, and the method to write the light propagation matrices of various systems consisting of these plane screens are also given. But the action of a scattering screen has not been considered. The method to solve for the super limit of the error which results from truncatingthe action matrix to finite order is contained in the appendix of this paper.On account of the coordinates used, the matrix theory is mainly suited forsystems with ideally axial symmetry. The main significance of this matrix theoryis that some problems of light propagation in the system above mentioned, which israther difficult to treat in practice by means of the previous theory, can be treatedrather conveniently by virtue of the present theory.The theory is only valid for systems in which each plane screen is perpendicularto the propagation axis, and the diffraction formula and the approximate conditionspresented in section (2) of this paper are suited for the diffraction by each planescreen.As an example of application of this theory, the matrix equation of the mode inoptical resonator (passive) is obtained and discussed in the section (5) of this paper.It is compared with the well known integral equations obtained previously by Foxand Li. It is shown that the matrix equation has some important advantages ofpractical value.

1981, 30 (10): 1340-1350.
doi: 10.7498/aps.30.1340

Abstract +

It is shown for the case of a discrete sample that an arbitrary transformation can be realized by an optical system composed of a single holographic lens. The design of the amplitude and phase distribution of the single holographic lens for the purpose of realizing a given transformation is given. The amplitude and phase distribution of the holographic lens for realizing the 8-sequence Walsh transformation of three different orderings are obtained.

1981, 30 (10): 1351-1360.
doi: 10.7498/aps.30.1351

Abstract +

In this paper, a method for quantitative determination of spectral distributions of primary radiation from X-ray tubes for diffraction and X-ray fluorescent spectral analysis is presented. The instrument used for this purpose is a diffractometer with a proportional-scintillation counter and a LiF analyzing crystal. The intensity distributions of primary X-ray spectrum obtained using a LiF analyzer are determined. The experimental values of the X-ray intensities of various wavelengths must be expressed in terms of intensities just emitted from the X-ray tube window. For the fluorescent X-ray tubes, several spectral distributions of different directions of primary X-ray beam must be determined and then the mean values of these data are calculated in order to obtain the effective spectral distributions. The errors of the spectral distribution data and its influence on the practical applications such as the fundamental parameter method are discussed.

1981, 30 (10): 1361-1368.
doi: 10.7498/aps.30.1361

Abstract +

The methods of determining Debye characteristic temperatures from X-ray diffraction intensities for the case of homogeneous and isotropic crystals have been fully discussed.It is proposed that if the common logarithms of the ration of the calculated intensities to observed intensities log (Icalc/Iobs) of all diffraction lines are plotted against sin2θ, a straight line should be obtained, the slope of which gives 2Bloge/λ2, where B is a physical quantity to be determined contained in the Debye factor e(-2Bsin2θ/λ2) in the intensity expression, λ being the wave length of the radiation used. In the Debye theory of specific heats, B may be expressed as (6h2T/MkΘD2){Φ(x) + x/4}, where h and k represent Planck constant and Boltzmann constant respectively, M is the mass of the atom or of the group of atoms situated at the lattice points, T is the absolute temperature at the time of taking Debye-Scherrer photographs, and ΘD is the Debye characteristic temperature. X = ΘD/T, and φ(x) is a function of x, given in the original Debye theory. It is seen that if we let G=BMkT/6h2, then φ(x)+x/4=Gx2 Having obtained B, G in this equation is a measurable number, and solution of the equation may be performed graphically. By making Y1=Gx2 and Y2=φ(x)+x/4, the plotting of these two equations should give two curves, the intersection of which should give x which determines the characteristic temperature at that temperature.It is pointed out that owing to the fact that ΘD itself is a function of temperature, the method proposed affords a possibility of determining Debye temperatures at required temperatures.

1981, 30 (10): 1369-1375.
doi: 10.7498/aps.30.1369

Abstract +

Uridine 3′, 5′-cyclic phosphate (c-UMP) crystal is colourless and transparent. The molecular formula is C9,H11O8N2P. The crystal belongs to monoclinic system and its space group is C21-P2. The parameters of unit cell are as follows: a = 10.767(6)?, b = 7.152 (4)?, c = 10.414 (5)? and β = 112.77(31)°. There are two molecules in an unit cell (Z = 2). The diffraction data were collected using PW-1100 four circle dif-fractometer. The number of independent diffraction data amounts to 1658. The structure was determined by applying Patterson analysis, direct method and Fourier synthesis. There are some solvate molecules whose distribution exhibit partial disorder in an unit cell. The structure parameters have been refined by means of block-matrix least-square method, R - 0.084.

1981, 30 (10): 1376-1382.
doi: 10.7498/aps.30.1376

Abstract +

Based on a discussion on the analytical properties of the complex function Fα(y)=∫0(ωph-α)(ω2y)/(ω2y+1)g(ω)dω, we suggest that the partial sum of the Tc series solution proposed by Wu Hang-sheng et al., as an approximate expression for superconducting critical temperature, may still work fairly well within certain range of 1/λ greater thanthe radius of convergence which is limited by the singular point zph. However, the error of the expression that depends upon the highfrequency behavior of the effective phonon spectral g(ω), can not be made infinitely small.

###### BRIEF REPORT

1981, 30 (10): 1383-1387.
doi: 10.7498/aps.30.1383

Abstract +

The Phase equilibria in the systems EbIO3-HIO3 and CsIO3-HIO3 have been investigated by means of X-ray diffraction and DTA and TGA methods.The compound RbH2(IO3)3 belongs to triclinic system. Its lattice parameters are a = 8.338?, b = 8.244?, c= 8.254?, a = 60.66°, β = 85.58° and γ = 66.01°. The measured density Dm= 4.61 g/cm3. Z = 2. The CsIO3-HIO3 system has two compounds, φ-phase and ψ-phase. The components of the φ-phase and ψ-phase are CsIO3: HIO3 = 1:1 (mol) and CsIO3:HIO3 =3:17 (mol) respectively. The φ-phase is a proton conductor.

1981, 30 (10): 1388-1392.
doi: 10.7498/aps.30.1388

Abstract +

The temperature dependence of the linewidth of the 7Li NMR spectrum line of LISICON crystals with different compositions and orientations has been investigated from 124 to 480k. It was found that there are three transition points of Li+ ion motion at ～273 K, ～350 K (for polycrystal ～320 K) and ～400 K respectively. The special behaviour of the electric quadrupole effects has been observed and discussed.

1981, 30 (10): 1393-1399.
doi: 10.7498/aps.30.1393

Abstract +

The molecular formula of chloro-tenaciss igenin is C23H33O5Cl. The crystal belongs to monoclinic system. The space group is C22P21. The parameters of unit cell are a=15.782(7)?, 6 = 8.454(4)?, c = 8.074(4)? and β= 101.08(21)°. There are two molecules in an unit cell (Z = 2). Intensity data were collected on a PW-1100 four-circle diffractometer. The total number of independent diffractions amounts to 2097.The structure was solved by direct method (MULTAN 78). The refinement of the structure parameters was acheived by block-matrix least-square method, R=0.075. All the positions of hydrogen atoms were located by the difference Fourier syntheses and two of them, which are in the methyls, present disorder property.The chloro-tenaciss igenin molecule contained the conformation characteristic of tenaciss igenin. B-ring and C-ring, and C-ring and D-ring all exhibit cisforms obviously.

1981, 30 (10): 1400-1405.
doi: 10.7498/aps.30.1400

Abstract +

In the present work, the tight-binding calculation for the rotational relaxed GaAs (110) surface is studied. In order to simulate the semi-infinite crystal, a saturating slab model is adopted with the last layer of which being saturated by some quasi As and Ga atoms, so that the slab model can be considered as having one surface only. The LDOS thus obtained agrees well with that given by the conventional slab model.

1981, 30 (10): 1406-1409.
doi: 10.7498/aps.30.1406

Abstract +

In this paper, all synchrono spherosymmetrical statical self-dual solutions of Yang-Mills guage field have been obtained. From these solutions, a result on the continuous surface distribution of the magnetic charge is derived.

1981, 30 (10): 1410-1414.
doi: 10.7498/aps.30.1410

Abstract +

We analyse the method of direct quantization suggested in reference [1] for adamped harmonic osillator, in which the quantum condition xp-px=ihe(-(C/M)t) is introduced. It is pointed out that this method can not be generalized to treat the case in which C is a function of time. In order to treat this case in a general approach, Heiaenberg relation xp-px=in must be kept and the force acting upon the osillatormust be supposed to contain a component fR that does not commute with x and satisfies xfR-fRx=ih(C/M).An electronic osillator is analysed as an example to show that ourapproach is consistent with quantum mechanical Langevin theory.