INORGANIC REPLICATION IN ELECTRON MICROSCOPY 821 



curve (1) shows that two adjacent planes differing in colatitude angle by 

 not less than 7° in the azimuth of incidence are detectable. For pure diffu- 

 sion shading,* curve (4) shows that considerably larger differences in angle 

 are required near 6 = 0; moreover, planes differing by large angles but 

 symmetrical with respect to the electron beam yield the same /, and hence, 

 if adjacent, cannot be detected. This difference between diffusion and inci- 

 dence shading is even more pronounced, because curve (4) is independent 

 of azimuth, whereas for curve (1), (1 — te/te,e=o) is proportional to 

 cos <p. Although this introduces very low contrast in azimuths near <p = 90°, 

 and also the possibihty that two adjacent planes differing considerably in 

 azimuth may yield the same density, incidence shading remains in general 

 more favorable for portrayal of surface topography. 



The intermediate curves (2) and (3) for a = J correspond to the case of 

 condensation of silica at da = 0° and 30° respectively. It is evident that, at 

 normal incidence, appreciable contrast occurs only on the steeper slopes 

 {0 > 45°), and that incidence at an angle is much to be preferred for general 

 surface portrayal. 



APPENDIX II 

 RESOLUTION OF REPLICA FILMS 



a) Incidence Shading 



Figure 2 (a) shows, for the case of pure incidence shading, the repUca 

 film formed at the intersection of two surfacial planes with normals wi and 

 W2. The distance d over which the thickness changes from te\ to te2 is 



d = ta sin da. (5) 



The figure is drawn for the case (p2 = 0, <pi = t. More generally, if jS is the 

 azimuth of the line of intersection of the planes, it may be shown that 



d = ta sin da I sin /? I (6) 



The angle /3 is easily measured on a micrograph. 

 In vector notation, 



J , I (wi X W2) X i 



a = ta \ T-r^ =^-;^ —X ' a 



I I («i X W2) X M " 



Or, in polar coordinates, 



I tan Ox cos <pi — tan 62 cos ^ I 



d = ta sin do 



(tan^^i + tan2 d2 — 2 tan di tan ^2 cos (<^2 - «Pi))* 



* Aluminum or other oxide replica films formed by surface oxidation presumably 

 correspond closely to the case a = 0, which does not occur in evaporated fihns. 



