The Resolution of Crystal Lattices 



91 



Fig. 9. Sodium faujasite crystal showing (111) planes. 



lattice rows in the direction of the beam is highly 

 relaxed. With a 50 /< objective aperture, the spectra 

 contributing to the image from the phthalocyanine 

 crystals are the (20T), (402), 201) and (402). These 

 spectra are assumed to recombine with the zero 

 order beam in the image plane and form an image 

 of the crystal grating in accordance with the simple 

 Abbe theory of image formation by a lens. This has 

 been confirmed by excluding all spectra except the 

 zero order from the image by using a 10 // objective 

 aperture when it is found that the image of the planes 

 disappears. Further confirmation of this mechanism 

 is obtained from the fact that an array of parallel 

 lines rather than a cross grating of dots is seen in the 

 image. The projection of the lattice in the direction 

 of observation should show a series of planes (010) 

 perpendicular to the (20T) planes. The spacing of 



^^^l^r- 



iHM 



m 



these planes however is 3.81 A and the first permis- 

 sible spectrum from them, (020), corresponds to a 

 Bragg spacing of 1.905 A. This is excluded from the 

 image by a 50 // aperture so that the image of these 

 planes is not seen. 



It is doubtful on other grounds whether such a 

 small spacing could be resolved. Firstly, the permis- 

 sible misorientation of the crystal with respect to the 

 electron beam, arising from the relaxation of the 

 third Laue condition becomes smaller as the spacing 

 to be resolved is reduced. Secondly the effect of 

 spherical aberration in distorting the wavefront of a 

 beam diffracted at a wide angle through the lens 

 becomes so severe as to cause the diffracted beam to 

 be no longer able to interfere coherently vsith the 

 zero order beam and form the image. The effect of 

 spherical aberration may already be severe even 



