ELECTRON MICROSCOPY 



tutod for the Rayloish criterion in the defini- makes an angle (satisfied by equation (S)) 

 tion of the least resolved distance. Equation with a lattice plane of the crystal, essentially 

 (1) can be derived either from the theory of specular reflection may occur from this lat- 

 Fraunhofer diffraction or from the quantum tice plane. If the optical system of the elec- 

 mechanical uncertainty relation. Both rela- tron microscope has a wide enough aperture 

 tions give qualitatively the same results to collect both the primary beam and the 

 within a small numerical factor. reflected (diffracted) beam, and the objective 

 Contrast is also governed to some extent is properly focused so that the two beams 

 by the diffraction phenomena at the edge of are brought to the same focus, the intensity 

 an object. Using the theory of diffraction, distribution in the image of the crystal will 

 the fringe distribution at the edges of an appear to be w^hat may be called "normal." 

 opaque or semi-opaque object can be calcu- If the objective aperture, however, is small 

 lated ; and such calculations have been found with respect to the Bragg angle, such that 

 to be in reasonably close agreement with the reflected beam will be intercepted (most 

 experiment, provided that in the case of of the intensity being in the reflected beam), 

 semi-opaque objects a refractive index of the the directly transmitted part of the image 

 material, corresponding to an internal po- will appear unusually dark. A further mani- 

 tential of 10-15 ev, is assumed. The experi- festation for this phenomenon is when a wide 

 ments show that fringes appear in out-of- aperture system is slightly defocused and 

 focus images and that the fringe spacing both the dark and bright images appear side 

 depends upon the degree of defocusing of the by side. This variation in intensity, due to 

 image. The apparent contrast at the edge of Bragg reflection, contributes also to appear- 

 an image is optimum in the slightly defocused ances of the so-called extinction contours, 

 image. For perfect focusing, the contrast is These extinction contours appear in slightly 

 found to be lower than for the out-of-focus bent crystals where, accidentally, part of the 

 condition. crystal happens to be at the proper angle to 

 The intensity distribution in Fresnel dif- show Bragg reflection. Under action of the 

 fraction fringes can be interpreted as inter- electron beam, thin crystals may warp, show- 

 ference phenomena. Accidentally occurring ing a displacement of the extinction contours 

 interference fringes can be observed also in while under observation, 

 selected specimen areas illustrating again the Related also to Bragg reflection is the ob- 

 role played by interference phenomena in the servation of crystal defects, such as disloca- 

 contrast in the image plane. tions, stacking faults, etc. Due to the exist- 

 In the case of crystalline specimens, dif- ence of these crystal defects, certain lattice 

 fraction from the lattice planes can produce planes show different orientations from the 

 an important modification of the intensity surrounding lattice planes and produce in 

 distribution in the image plane. Electrons this manner a marked contrast in the final 

 which are scattered from a crystal lattice image. 



will show diffraction maxima according to While the above considerations are re- 



Bragg's equation stricted to Fresnel diffraction and to crystal- 



„ , . line diffraction, Gabor has demonstrated 



that dmraction phenomena may be impor- 

 where d is the distance between the lattice tant in noncrystalline specimens too. He pro- 

 planes, is the angle between the direction posed the use of a coherent electron beam for 

 of the incident beam and the diffracting forming a diffraction image, called hologram, 

 planes, and n is an integer. of the specimen. In principle, such a diffrac- 

 If an electron beam is directed so that it tion image should contain all information 



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