12 C. L. SADRON 



zigzag chain (large values of b) 



c 

 K 



2L\ 2 -l-l^S\ + h™ (27) 



ttwL 2 N I + ttM U7) 



where Nb = L 



It follows from these equations that if the experimental values of c/K 

 for very large values of hL tend to be proportional to sin G/2, the particle 

 is a rod or a zigzag chain with large elements, and if they are proportional 

 to sin 9/2, the particle is a disc or a Gaussian chain or a zigzag chain with 

 small elements. At the same time the value of the proportionality factor 

 gives the weight per unit length for a rod or for a large zigzag or per unit 

 surface for a disc. 



However an important feature is to be noted. From Eq. (24) we see 

 that for a rod the intercept of the linear asymptote with the ordinate is 

 2/ (Mir ), a positive value. On the contrary, for a large zigzag chain the 

 value of N/(*M){2 - (tt 2 /2)[(N - l)/N]} is always negative for all 

 values of N but unity. 



Unfortunately, the observation of a negative ordinate is not unambigu- 

 ously connected to the existence of a large zigzag chain. Benoit and Luz- 

 zati have shown that the same effect can be produced by rod-shaped par- 

 ticles crossing each other, or with branching. For instance, the asymptote 

 for a particle consisting of two long rods of length b crosssing each other in 

 their midst with relative orientations distributed at random is given by 



KkJ^oo m |_tt 



to 4 - 2tt 2 ' 

 M + fl- 



it is then highly probable that the asymptote to the c/K function still has 

 an expression such as 



c . ,hNb 

 K~ A + ;M 



where A has a negative value. 



We can sum up this discussion by giving in Fig. 4 the three different 

 elementary configurations leading to an asymptote with negative value of 

 the ordinate. 



Finally, let us remark that — since the smaller the X, the larger the h — 

 it will be of interest, in order to obtain the asymptotic limit of c/K, to use 

 an incident beam of X-rays, for which the wavelength is about four thou- 

 sand times less than for visible light. 



Conversely, K will be very small, except for very small values of 0, and 

 the intensity of the scattered light will be measurable only at the vicinity 

 of the direction of the incident beam. Hence, the name of "central diffu- 

 sion" for this type of X-ray scattering. 



