872 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



= 2E^e sin IBq 

 E = total energy of incident electrons in volts 

 ^0 = Bragg angle 



A^ = angular deviation from Bragg condition , 

 AK = beat wave vector 



= r.(<f>' +!•'''■)' 



z = penetration measured normal to surface of crystal 

 D = thickness of crystal 



It is evident from equation (1) that the intensity of the diffracted beam is 

 periodic with penetration in the crystal and with the deviation, Ag. This 

 dependence of intensity upon thickness and deviation accounts for most of 

 the image detail seen in electron micrographs of thin crystalline sections. 

 Inelastic scattering and crystal imperfections are neglected in the deriva- 

 tion of equation (1). 



Experience with thin sections of pure aluminum has indicated that it is 

 nearly impossible to prepare and handle them without introducing some 

 bending or rumpling of the thin area. This bending in conjunction with 

 thickness variations gives rise to the major features of the electron images 

 in the form of intensity maxima and minima called "extinction contours." 

 Those arising through bending of the section are of chief interest in the uni- 

 form area where thickness changes are very gradual. The extinction con- 

 tours are determined by the maxima of equation (1) or where AKD = mr 

 to give 



As=±((^'-4|Fsry »= 1,3,5,... (2) 



Equation (2) predicts that for a bent crystal offering a continuous range of 

 Ag a series of intensity maxima or fringes will be observed. In an electron 

 image of a bent crystal the spacing of the fringes is the only quantity which 

 can be measured other than relative intensity. The central fringe corre- 

 sponds to Ag = with subsidiary maxima occurring at a distance s from the 

 central fringe given by^ 



where R is the radius of curvature of the bending. 



If two crystallites in a thin section differ only slightly in orientation 

 and the bending is favorable, then a series of fringes will occur in the two 

 crystals with a displacement at the boundary as sketched in Fig. 4. 



The displacement / is related to the orientation difference Aa and the 



