^6 



M. E. MAINE AND A. W. AGAR 



^1* 



xlO 



300 



1' 2 SO 



o 



200 



ISO 



-lOO 



so 



a 



o 



Id 2 



ANGLE e 



2x10 



3xlO 



Fig. 1. Differential scattering cross section for carbon tilms 

 of differing thickness. 



[5] and amounted to about 3 A min. Thus, except 

 for the thinnest films, the scatter pattern could be 

 recorded before the film thickness had changed 

 appreciably. 



The angular distribution of scattered intensity as 

 obtained from the blackening of the photographic 

 plates was converted into the differential scattering 

 cross section by dividing by the number of atoms 

 per sq. cm of the scattering film, i.e. assuming single 

 scattering conditions, which are the basis of the 

 scattering theory. 



The additional scatter due to a thicker film should 

 be exactly balanced by the dividing factor which 

 includes the film thickness provided that the scat- 

 tering mechanism remains unchanged. 



A series of carbon films of different thickness were 

 analysed in this way, and the calculated differential 

 scattering cross-section plotted in figure I . The dotted 

 curve shows the theoretical curve, based on Lenz's 

 expressions for elastic and inelastic scatter, the 

 approximate expression (I) being used for calcula- 

 tion of the inelastic cross section. It will be seen that, 

 while the results agree within a factor of 2 with the 

 theoretically predicted ones, the curves do not lie 

 on top of one another, but show a definite gradation 

 with the film thickness employed. The difference 

 between the curves is too great to be ascribed to 

 faulty measurement of film thickness or incorrect 

 contamination rate (the results for the thinner films 

 have been corrected for the measured contamina- 

 tion rate). 



The "reference thickness'" or "transparency thick- 

 ness" defined by von Borries as the thickness of 

 film in which every incident electron is, on the 

 average, scattered once elastically, is about 450 A 

 for carbon, it might be expected that carbon films 

 thinner than this would give similar results for 

 scattering cross section. Since they do not, it suggests 

 that, at each thickness, there is a rather higher pro- 

 portion of electrons scattered outside the effective 

 aperture than is allowed for in the theory. 



Since the inelastic cross section was expected to be 



10 



ANGLE e 2xlO 



-2 

 3xlO 



Fig. 2. Differential scattering cross sections for different 

 materials. 



independent of atomic number, the experiment was 

 repeated with films of aluminium, copper, silver and 

 gold. The results are shown in Figure 2. The theore- 

 tical curve is shown dotted — it is calculated with 

 the addition of the elastic scattering cross section 

 due to silver; this only affects the curve significantly 

 at angles greater than 10 -. 



In the region of the curve where the inelastic 

 scatter is predominant, it will be noted that similar 

 values of scattering cross section are obtained for 

 carbon, aluminium, silver and gold films. Thick, 

 unsupported films of copper and silver gave much 

 lower results, but, in each case, the film thickness 

 considerably exceeded the transparency thickness. 

 The very thin films of silver and gold had to be 

 supported on thin carbon films, and the curves shown 

 have been corrected to allow for the extra scattering 

 due to the carbon films. 



The results obtained by Biberman et ciL [2] and 

 by Leonhard [8] are shown by a number of points. 

 It will be seen that the present results are in good 

 agreement with them. 



The measurements support the theory of Lenz 

 giving good agreement in magnitude and distribu- 

 tion and showing the scattering to be largely inde- 

 pendent of atomic number in the angular range 

 10-^-10"-. The marked dependence of cross section 

 on film thickness in the case of carbon is not ex- 

 plained. The results suggest that the single atom scat- 

 tering theory and results can be applied to lattices 

 of atoms. 



References 



1. Agar, A. W., (in press). 



2. BiBtRMAN, L. M. et a/., Dokl. Akad. Naiik 69 (4), 519 



(1949). 



3. VON Borries, B.,Z. Naitirforsch. 4d, 51 (1949). 



4. DiGBY, N., Firth, K., and Hercock, R., J. Phot. Sci. 1, 



194 (1953). 



5. Ennos, a. E., Brit. J. Appl. Phys. 4, 101 (1953). 



6. Haine, M. E., (in press). 



7. Lenz, F.,Z. Naturforscli. 9a (2), 185 (1954). 



8. Leonhard, F.,Z. Naturforsch. 9a (12), 1019 (1954). 



