I. FANKUGHEN AND H. MARK 



sized that chains with regularly distributed centers of attraction arc 

 unlikely to curl up in a completely random way but will lead to struc- 

 tures of an intermediate degree of order. 



With these limitations and restrictions in mind, we shall now 

 proceed to a more quantitative discussion and interpretation of fiber 

 diagrams. 



Small- and Large-Angle Diagrams 



Inspection of Figure 1 has already shown that there are two dis- 

 tinct areas in which scattered intensity can be observed: 



(a) In the immediate neighborhood of the incident beam, i. e., 

 within very small angles of scattering. 



(b) All over the photographic film, i. e., at comparatively 

 large angles of scattering. 



Because of the reciprocal nature of all diffraction phenomena, * 

 small-angle scattering permits the study of large distances inside the sample, 

 while large-angle scattering permits the investigation of short-range order. 

 It has, therefore, become conventional to divide the quantitative study 

 of a fiber diagram into the evaluation of the "large-angle" and of the 

 "small-angle" pattern. 



If one measures the position and intensity of all observable 

 points in the large-angle region, one can, first of all, compute from the 

 position of each spot the diffraction angle and, with the aid of Bragg's 

 law, the characteristic spacing which is responsible for each individual 

 spot. In this way one ends up with a table of spacings and relative 

 intensities of all observed diffraction points. In Table II, such a list is 

 given for the diagram of silk protein (Fig. 1, page 441). The "evalua- 

 tion" of the diagram is now based on the assumption that the spacings 

 of the lattice planes as they appear in Table II are the consequence of 

 the arrangements of all individual atoms in a three-dimensional lattice; 

 and the first goal is to find the fundamental distances and angles of this 

 lattice. Generally, this can be accomplished from x-ray data alone 



* The famous Bragg diffraction law demands that the product of the scatter- 

 ing spacing, d, and the sine of the glancing angle, 6, must equal half the wave length 

 of the scattered radiation in order that an intensive diffracted beam be produced. 

 Small spacings produce, therefore, large diffraction angles, and large spacings, 

 small angles. 



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