By A. Kitaigorodskii

Structure research relies at the phenomena of the diffraction of radia tion by means of fabrics. within the first ten to 20 years after Laue's discovery, a truly entire thought was once constructed for the diffraction of x-rays and, later, of electrons. This thought resulted in equations via which it used to be attainable to compute the depth trend for a given constitution. the speculation of constitution research got here to intend that of the diffraction of radiation. In 1935, Patterson mentioned a manner resulting in the answer of the inverse challenge: the discovering of the constitution from a given depth distribution development. in the beginning the conservatism of researchers, after which the struggle, hampered the de velopment and large program of the tips set forth during this paintings. It was once in basic terms over the last ten years that every one the wealthy chances of the Patterson strategy - the strategy of the research of the convolution of the electron density - have been delivered to mild and utilized in practice.

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6 Thus +00 L(H)=Z 2 02(;) ~ o(C-Ce). 6'-+00 -OJ J e21ti<~ dx is the classical example of the -00 0 function. Chapter II 44 We see that the image of a series of parallel lines lying in the xz plane and parallel to the ~ axis is a series of lines lying in the 11 (; plane and parallel to the 1) axis. Finally, the last example - a series of planes- gives J ~ (H) = Z ei2~(~"'+'ltl+cZ) ~o (z - Zk) dx dy dz = = Zo (~) 0 (7J) ~e2~jCzk. , the image is a series of points arranged along (;. In all the three cases of one-dimensional periodicity with a period of unity, there is a corresponding one-dimensional periodicity with a period of unity in reciprocal space.

If there were a possibility of evaluating the atomic factor fj(H). This computation is impossible. since the form of fj(H) is affected not only by the kind of atom, but also by the structure of the object. The influence of the structure of the object is manifested first by the interatomic binding. and second, by the presence of thermal vibrations. Thus, in principle fj(H) can be determined only after an experiment on the form of the electron density has been carried out. This is of no interest, since the goal of structure analysis is precisely the study of this electron denSity.

P). But the Fourier transform of the product is the convolution of the corresponding transforms. Introducing, in the same way as on page 36, the form factor of the region occupied by the lattice s = 4? l. ~ ~"" ~w"