ELECTRON MU H< )SCOPY 



a g;rainof salt. In addition, tlie reader should 

 be warned that experimental data on this 

 subject are equally unreliable at present. In 

 fact, some papers on scattering cross section 

 of atoms to electrons do not rei)ort cross 

 sections at all, but relative numbers of elec- 

 trons scattered into small angles. 



Indications of how to enhance the con- 

 trasts may be obtained by studying the 

 above equations. The simplest way is by 

 increasing the atomic number of selected 

 areas of the object. In a specimen of homoge- 

 neous constitution, where the object has 

 only variations in thickness, this may not 

 be always easy to do and shadowing tech- 

 niques can be of great help, preferably if 

 shadowing is done with material of high 

 atomic number. An alternate method is stain- 

 ing. Staining in the electron optical sense is 

 the introduction of higher atomic number 

 elements in the material of the specimen. 

 Reduction of the primary energy of the elec- 

 tron also enhances contrast in special cases, 

 because the scattering cross section increases 

 with decreasing energy. In similar cases the 

 reduction of the objective aperture enhances 

 contrast because of the higher proportion of 

 large-angle scattered electrons from the elec- 

 tron optically denser portions of the speci- 

 men. 



Another mechanism for producing in- 

 tensity modulation in the image is called 

 phase contrast. A variation of the refractive 

 index within the specimen will produce 

 phase changes. By causing various parts of 

 the beam to interfere, one can introduce in- 

 tensity changes caused by the phase changes. 

 The intensity at any point of the image plane 

 is related to a phase change in a correspond- 

 ing element of the object. These phase shifts 

 have been calculated, and they are given 

 by 



Here C\ is the spherical aberration constant 

 of the lens. 



The last mechanism affecting the intensity 

 distribution in the image plane is absorption; 

 both true absorption and what may be called 

 "partial" absorption will be discussed. True 

 absorption refers to an electron which is 

 stuck in the substance of a specimen and 

 cannot get out. Scattering considerations 

 alone show that this is a highly unlikely 

 event. At the conventional energies, at which 

 electron microscopes operate, and the usual 

 specimen thicknesses, the mean free path of 

 an electron exceeds the specimen thickness 

 by a very large amount. The probability of 

 direct absorption is therefore practically nil. 

 We may consider very briefly the number of 

 electrons which may be deflected at 90° angle 

 so that they take off within the specimen 

 plane. Again the above expressions for the 

 distribution of both elastically and inelas- 

 tically scattered electrons as a function of 

 angle show that this is a very unlikely event , 

 and will not contribute substantially to the 

 contrast in the image. 



However, so-called "partial" absorption 

 must be considered. This may be a misnomer 

 because we are considering here the energy 

 losses suffered by electrons passing through 

 a specimen and interacting in an inelastic 

 manner. Any electron W'hich leaves the speci- 

 men with an energy different from the pri- 

 mary energy will contribute to an enlarge- 

 ment of the radius of the circle of least 

 confusion. This radius is usually defined by 



AE 



r = aC. - 



(8) 



where 



7 = /3< - Tlff^ 



-^fi 



(7) 



(r) 



where Cc is the chromatic aberration con- 

 stant of the lens, and the other quantities 

 are as defined above. Assuming that the 

 primary beam has an energy distribution 

 with a certain half width, an additional in- 

 tensity distribution due to energy losses can 

 be linearly superimposed. 



For contrast considerations, w^e have to 

 distinguish between two special cases. One is 



162 



