Differential Scatteiini; Cross Section of Atoms at Small A nicies 



65 



Table 1 . Contrast due to various scattering 

 phenomena. 



<^o= 100 kV 



Based on Lenz's scattering formulae 



Lenz's theoretical results. After applying one or two 

 fully justifiable approximations, this expression is: — 



Ca 



% 



Cph 



/o 



Cin 

 % 



Cii 



Microscope resolution 10 A 



4 0.005 0.3 



16 0.02 0.3 



64 0.09 0.3 



Microscope resolution 3 A 



4 0.038 3 



16 0.22 3 



64 0.94 3 



The contrast labelled Cjn is that arising from the 

 coherent wave produced as a result of the loss of the 

 inelastically scattered electrons from the coherent 

 illuminating wavefront. It will be seen that this is 

 comparable with the phase contrast, and therefore 

 contributes to a very important extent to the micro- 

 scope contrast. The last figure Qn represents the 

 annulling effect of the electrons which have suffered 

 energy loss. Even with a mean energy loss of 10 kV, 

 as assumed by Haine, these are spread by the 

 chromatic aberration over so large an area as to 

 make their effect negligible. 



These calculations are based on wave-optical 

 calculations which require for their solution knowl- 

 edge of the scattering cross sections of the atoms. 

 Haine has used for this the data of Massey and 

 Bullard, and also the more recent modifications in- 

 troduced by Lenz [7]. The contrast figures here given 

 are based on Lenz's data. It appears desirable to 

 consolidate the situation by some more extensive 

 experimental data on scattering, particularly at small 

 angles. We should like to have more explicit experi- 

 mental checks on the elastic and inelastic differential 

 cross sections, as well as the velocity loss distribu- 

 tion. It is also desirable to check just how close the 

 differential cross sections, as deduced from experi- 

 ments on thin films, agree with the single atom cal- 

 culations, as this would indicate the extent to which 

 coupling between atomic fields in a lattice affect the 

 scattering. 



Elastic cross sections at small angles are not at all 

 easy to measure because the inelastic scattering is so 

 predominant. There have been no reliable theoretical 

 predictions on energy loss, so that only experimental 

 data can here be used. 



The present experiments are restricted to measure- 

 ments on the total scattering cross section, which, 

 for small angles, differs little from the inelastic 

 differential cross section. For angles relevant to the 

 electron microscope, a simple analytic expression 

 can be derived for the inelastic cross section from 



lo - 8.8 lo-'^ 9^„0^ 



(1) 



where e'l ,> is the electron energy in electron volts, 

 and the scatter angle. It will he noted that the cross 

 section is independent of atomic number. 



in the present experiments, the angular scatter 

 measurements were made directly in the electron 

 microscope. The arrangement was even simpler 

 than that of Biberman et al. [2], who had to remove 

 the projector polepieces and certain screens. The 

 microscope was unmodified, except that the objec- 

 tive was worked at long focal length (1 cm), and a 

 small screening aperture immediately above the 

 object was employed. The condenser lenses were 

 switched off. so that a relatively low beam intensity 

 was employed. This reduced the contamination rate 

 of the specimen, and facilitated the timing of the 

 exposures. The angular scattering distribution of 

 the electrons after passing through the film under 

 test was reproduced in the back focal plane of the 

 objective lens. The projector lenses were used to 

 project an enlarged image of this distribution onto 

 the photographic plate. 



The photographic plates used (ilford Thin Film 

 Half Tone) were known to have a linear density cur- 

 rent density response over the range 0.2 to 1.0 

 blackening density, from the work of Digby, Firth 

 and Hercock [4]. A series of exposures (covering 

 the range 1-60 sec) enabled the whole scatter pattern 

 to be recorded at densities falling between these 

 limits. The incident electron intensity was found by 

 allowing the beam to pass through a hole in the 

 specimen, and by photographing the patch of illu- 

 mination at a known instrumental magnification, it 

 was then unnecessary to know the characteristics 

 of the photographic material, as the scattered inten- 

 sity could be related directly to the incident intensity 

 in terms of the blackening density on the photo- 

 graphic plate. The scatter patterns were analysed w ith 

 a microphotometcr. 



In order to minimise the effect of contamination, 

 a small screening aperture was placed immediately 

 above the object, thus restricting the illumination to 

 the area under observation. It was thus possible to 

 search for a clean and undamaged portion of film 

 without building up a layer of contamination on the 

 specimen. The area of film from which the scatter 

 was recorded was defined by an intermediate aper- 

 ture of known size corresponding to an area of 

 5 sq. micron at the object. 



The first experiments were carried out with thin 

 carbon films of known thickness [1]. By measuring 

 the scatter intensity before and after a timed expo- 

 sure to the electron beam, it was possible to calibrate 

 the contamination rale under the conditions under 

 which the film was being examined. This was found 

 to agree very well with the figures given by Ennos 



a — .568204 Electron Mirroscopi/ 



