INORGANIC REPLICATION IN ELECTRON MICROSCOPY 819 



When the principal azimuth is defined by the plane containing a and t, 

 cos ^o = ±1, and, as illustrated, cos^a = —1. With more than one source, 

 in directions ai, 02 • • • Om : 



. _ Ooifll + ^02^2 + • • • tarn am)"}!: (2) 



i-n 

 and the mass thickness is given by 



pj^ = (±ejJ4^ (3) 



where pj is the density of the material deposited by the source /«, ^y, and 



pa is determined by the equation pJaa = 2 pj taj aj, which defines the 



equivalent single source. The distribution of mass thickness of any evapo- 

 rated film, when atoms stick where they strike, is therefore given by eq. 1, 

 with values 6a, <Pa determined by the distribution of sources. The repHca 

 may be called an incidence-shaded replica. 



(b) Calculated Thickness When a Fraction of the Incident Atoms Diffuses 

 Over the Surface 



Figure 3 has shown that, in the case of silica, a fraction a of the impinging 

 molecules stick where they first strike, the remainder diffusing. If the latter 

 condense into a film of uniform thickness normal to the local surface, the 

 shading equation becomes 



da\ Qj(l + tan da cos <pa tan 6 cos <p) + {1 — a) -^ 



[_ A cos Oj 



where A is the total surface area and Aq its projection on the jk plane (Fig. 

 1). Many other materials, and in particular siUcon monoxide and ger- 

 manium, condense Hkewise with values of a less than unity. 



The assumption of uniform local thickness for the diffusing component 

 is not quite correct. More strictly, Aq/A in eq. 4 should be evaluated over 

 areas of the order of the square of the range (i/x). Since the range is large 

 compared to the resolution, and since Aq/A can only be estimated in any 

 event, this refinement is of Httle value. It has been suggested^ that diffusing 

 siHca has a higher probabiHty of condensing in regions of change of gradient. 

 This suggestion is difficult to sustain theoretically; further, observations 

 upon thin shell repHcas such as those of Fig. 3 have tended to indicate ahnost- 

 uniform condensation. 



(c) Replica Contrast as Determined by Relative Thickness vs. Colatitude 

 Angle Curves 



In any photographic presentation, two densities are detectably different 



