De atoomvormfactor van kwik voor snelle electronen

Abstract

Summary In the present investigation the atomic formfactor for electron scattering has been determined experimentally by measuring the scattering of 20, 30 and 40 kV-electrons through small angles by isolated atoms, in our case a mercury-vapour beam. Fig. 1 shows the diffraction apparatus used and fig. 2 gives a detailed design of the mercury-vapour generator. The electrons emerging from the hot filament kathode A are diffracted by a mercury-vapour beam, which emerges from a small aperture P (fig. 2). They are recorded on a photographic plate I. The number of diffracting centres per cm 3 in the vapour beam could be varied from 2 × 10 16 to 5 × 10 17 (i.e. 0.7 to 20 mm Hg pressure), the diameter of the beam being 0.4 mm. These vapour pressures must be used in order to obtain sufficient scattering intensity in comparison with the scattering appearing without mercury: the ,“blanco” effect. Fig. 3 shows the photometer curves of 4 exposures of different intensity ( B, C, D and E ) and of the “blanco” effect ( A ), the latter at a much greater intensity of the incident electron beam. At the vapour-pressures mentioned the influence of multiple scattering must be taken into account, as Wentzel's criterium 14 ) for single scattering and the conditions given by Kruppke 15 ) and Chase and Cox 16 ) are not fulfilled. By taking exposures at different pressures of the Hg-vapour, the curve for single scattering could be extrapolated from the experimental results. In fig. 4 the Briggian logarithm of the ratio of experimental to theoretical scattering is plotted as a function of sin ½ϑ/λ (ϑ is the scattering angle and λ the De Broglie-wavelength of the electrons). The values for curve A (39,7 kV) have been taken from table I, column VIII. Table I gives the logarithms of the scattered intensities + an adaptation constant for 7 exposures of different intensity (column I–VII). Here the influence of multiple scattering is only small and may be neglected. The values for curves B and C (29.8 kV) result from table II column III and IV respectively. Curve B gives the result, when the correction for multiple scattering has been applied ; curve C shows the result without correction. The theoretical scattering has been determined by adding the values for elastic scattering (calculated from (1) using the data of James and Brindley 1 ) for F R (ϑ), the atomic formfactor for X-rays) to those for inelastic scattering (calculated from Morse's theory 22 )). The decrease of the curves of fig. 4 for sin ½ϑ/λ 8 is presumably due to a failure of the theory of inelastic scattering at small angles. For larger values of sin½ϑ/λ the contribution of this inelastic part is only small, so that here the difference between experimental and theoretical formfactor must be attributed to the inexactitude of the theory of elastic diffraction. This deviation, however, is much smaller ( 8 to 0.40 × 10 8 ) than that found between the theory and the experimental results, when the atomic formfactor for electron scattering is determined by measuring the intensities of the diffraction rings of a microcrystalline foil of a heavy element. Here the deviation for Au is larger than 30 percent for the (2, 0, 0)-ring: sin ½ϑ/λ = 0.238 × 10 8 (30–40 kV). Therefore we may assume, that the latter difference must be ascribed to the theory 11 ) of the scattering of electrons in crystals of intermediate size.