92 METHODS FOR DETERMINING MOLECULAR SIZE AND SHAPE 



Thus the sedimentation coefficient containing the product MD is propor- 

 tional to the two-thirds power of the molecular weight. Accordingly, the 

 sedimentation velocity method is much more sensitive to changes in 

 molecular weight than is the diffusion method. Some typical sedimenta- 

 tion coefficients are given in the table below. 



, , , , . , , Sedimentation 



Molecular weight — . 



coefficient 



The unit in which the sedimentation coefficients is given is the svedberg, 

 which is 10~ 13 /sec. This is the standard unit found in the literature. 



4. X-ray diffraction 



When x-rays impinge upon matter, most of the rays pass through 

 unaltered and undeflected, if the matter is not very thick. Some of the 

 rays, however, are scattered, and the pattern of scattering depends on 

 the pattern of the atoms and molecules making up the piece of matter. 

 Given the structure of the piece of matter, the scattering of the radiation 

 can be computed, but given the pattern of the scattered radiation, it is 

 much more difficult, and in some cases impossible, to deduce the structure 

 of the scattering material. We shall first discuss the use of x-ray dif- 

 fraction methods for determining the structures of crystalline materials. 

 The usual experimental procedure yields a photograph of a pattern of 

 lines or spots of varying spacing and intensity. The spacings will be 

 shown to be related to the distances between the molecules (or atoms) 

 in the crystal. Analysis of the intensities of the lines or spots can be 

 made to yield the detailed structure of the (polyatomic) molecules them- 

 selves. The mathematical techniques needed to achieve these results are 

 far beyond the scope of these writings, but an attempt will be made to 

 suggest the essential factors involved in the methods. 



We start with a standard diagram (Fig. 44) showing a beam of mono- 

 chromatic x-rays hitting and bouncing off a crystal which is represented 

 as an array of atoms, indicated by circles. The wavy lines are the paths 

 of two of the rays making up the x-ray beam. The parallel lines are to 

 be thought of as planes perpendicular to the paper and passing through 

 the atoms as shown. Thus we are really talking about a three-dimen- 

 sional crystal of which we see a plane section. The angle is that be- 

 tween the direction of the incident beam and the plane of the atoms. 



The two rays are shown bouncing off atoms in such a way that the 

 path of wave II becomes the same as that of I. This second ray travels 



