ELECTRON MICROSCOPY 





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Fig. 1. (top) Diagram illustrating resolution of 

 the shape of a colloidal particle. The shape of the 

 particle can only be recognized if 6 > 5. (bottom) 

 Comparison of the size of particles of different 

 shape required for resolution of that shape. (After 

 Borries and Kausche). 



defined shapes in microscopes of infinite re- 

 solving power. Such a condition cannot be 

 reahzed in practice, however, and the efi^ect 

 of finite resolving power has to be considered, 

 von Borries and Kausche (4) supposed that 

 the geometrical boinidaries of the object 

 appeared in the image as boimdaries of finite 

 width, within which the intensity fell con- 

 tinuously from that of the particle to that of 

 the background. The effective width of the 

 boundary was considered to be twice the 

 resolving power, 5, of the microscope and the 

 physical boundary of the particle at a point 

 midway between the particle and back- 

 ground intensities. As a consequence of the 

 finite resolving power the image boundary 

 at the intersection of two straight lines is 

 rounded, and it was assumed that the curva- 

 ture was such that the arc of a circle was 

 tangential to the intersecting edges at a dis- 

 tance 5 from the point of intersection ob- 

 tained by geometrical construction (see Fig. 



1). 



Thus recognition of shape is only possible 

 if the length of the straight portions of the 

 edges, b, is greater or equal to 8. li h < 8 

 the particle would appear circular and in 

 fact many early workers found that small 



colloidal particles appeared circular, an effect 

 often due to lack of resolving power. ( )n this 

 basis it is clear that the exact shape of a 

 particle having less than six corners should 

 be easier to recognize and therefore ti'iangu- 

 lar particles should be recognizable as such 

 at much smaller dimensions than the hex- 

 agonal type. Conversely, octagonal plates 

 must be seven to ten times larger than the 

 triangular particles in order not to appear 

 circular. The sizes of particles, relative to a 

 triangle, required for the resolution of a defi- 

 nite shape are illustrated schematically in 

 Fig. 1. 



In order to test the resolution of an elec- 

 tron microscope it is useful to have a suitable 

 test object, and it has been found (5) that 

 silver and silver iodide sols can be prepared 

 which contain particles having sizes ap- 

 proaching the limits of present-day micro- 

 scopes. Particles having dimensions of the 

 order of 5 A can be clearly resolved from the 

 background (Fig. 2) ; the fact that these par- 

 ticles could be reproduced on separate photo- 

 graphic plates clearly established their 

 identity as colloidal particles. The limita- 

 tions in resolving power appear to be mainly 

 governed by chromatic errors (i.e., stabiliza- 

 tion of high tension) and lens aberrations. 

 The precise measurement of particle sizes be- 

 low 10 A becomes difficult due to phase con- 

 trast effects at this level of resolution. A 

 suitable test object for high resolution work 

 is also found in the case of metal phthalo- 

 cyanines; for example, the metal-bearing 



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Fig. 2. Electron micrograph of silver iodide 

 sol of small particle size. 



126 



