40 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



be regarded as a first order of planes indexed 633. This leads to a third 

 meaning of the indices of planes defined in this way, a meaning which 

 will be needed later on. All "reflections" are first order reflections from 

 planes defined in the above way, and there is a path difference of one 

 wavelength between successive planes. Counting the number of planes 

 crossed between one lattice point and the next, therefore, is the same 

 thing as counting the number of wavelengths path difference between 

 waves scattered by neighbouring lattice points. The indices thus repre- 

 sent the phase difference between waves diffracted by neighbouring 

 lattice points along each of the three axial directions. 



The rotation diagram 



Turning now to the special features associated with the study of plant 

 material, it will be seen later that the biophysicist has to deal with 

 photographs closely resembling those given by a single crystal con- 

 tinuously rotated about an axis perpendicular to the X-ray beam, the 

 so-called rotation photograph. A few moments' consideration may, there- 

 fore, be given to the particular features involved. Suppose a crystal 

 is set up in an X-ray spectrometer in such a way that a parallel beam of 

 X-rays falls on the crystal at right angles to one of the crystallographic 

 axes {i.e. one edge, say the b edge, of the unit cell), and let A and B 

 (Fig. 17) be two neighbouring identical points of the lattice, i.e. two of 

 the points shown in the previous figures. Then, considering these two 

 points only, and not any particular planes passing through them, reflection 

 is possible only when the path differences between the beams from A and 

 from B differ by a whole number of wavelengths. For the first order 

 reflection, AP, the geometrical relation required to fulfil this condition is 



A— ^ sin Oi, ..(3) 



and for the second and third orders, AQ and AR, the corresponding 

 relations are 



2X=b sin a^, 3?.=b sin 03. 



All first order reflections from planes passing through A and B must 

 therefore lie along the cone APP', all second orders along AQQ' and 

 so on. If the crystal is continually rotated around the fine AB then these 

 reflections will appear. It is to be noted, however, that since any 

 particular plane will only reflect at its own glancing angle, d, determined 

 by the interplanar spacing, then each plane will reflect only four times 

 per revolution, once upwards to the right, once upwards to the left, 

 once downwards to the left, and once downwards to the right. This will 

 be demonstrated again later. All four beams from each set of planes lie 



