18 The Electron Microscope 



The de Broglie wavelength of electrons, however, accelerated 

 by V volts is, if equation (12) is expressed numerically, 



A=^A (13) 



For electrons of 60,000 electron-volts (ev) velocity this is about 

 0.05A, which is about the same as the shortest wavelength of 

 250,000 ev X-rays. Therefore, we should expect diffraction pat- 

 terns of much the same general character. This was indeed 

 found by the experimenters mentioned, who verified also the 

 value of the de Broglie wavelength given by equation (13). 

 Since that time, electron diffraction has become a close rival of 

 X-ray diffraction in the exploration of the structure of materials. 



In electron optics, we work in general with apertures which, 

 though very small as compared with those used in light optics, 

 are enormously greater than A. The smallest apertures used in 

 electron microscopes have a diameter of about 0.001 in. = 

 0.0025 cm = 2.5 X lO^"* A, which is five million times larger 

 than the wavelength of 60,000 ev electrons. Neverthless, the 

 diffraction effect is not only noticeable, but constitutes the effec- 

 tive limitation of the performance of electron microscopes. 



If a wave starting from a point, a homocentric or stigmatic 

 wave, passes through a lens, however perfect in the sense of 

 geometrical optics, it can never again be brought together in a 

 point. The reason is that the unavoidable aperture has cut out 

 a part of the spherical wave front, and, to use Schrodinger's 

 expressive words, **. . . the wound torn by the aperture will not 

 heal." Instead of in a point, the source will be imaged in a dif- 

 fraction figure, calculated, in 1834, by Sir George Airy. This 

 consists of a central disk, Airy disk, surrounded by a succession 

 of dark and bright interference fringes of rapidly decreasing 

 luminosity (c/. appendix). It is convenient to describe this 

 figure instead of in terms of its actual dimensions by the dimen- 

 sions of the object which it appears to represent. The radius of 

 the Airy disk, which extends to the first dark fringe, corresponds 

 to an object of a radius 



