Determination of atom positions

When determined in this way, the number of atoms per cell is always an integer, within experimental error, except for a very few substances which have defect structures. In these substances, atoms are simply missing from a certain fraction of those lattice sites which they would be expected to occupy, and the result is a nonintegral number of atoms per cell. FeO and the P phase in the Ni-Al system are examples. 

We now have to find the positions of a known number of atoms in a unit cell of known shape and size. To solve this problem, we must make use of the observed relative intensities of the diffracted beams, since these intensities are determined by atom positions. In finding the atom positions, however, we must again proceed by trial and error, because there is no known general method of directly calculating atom positions from observed intensities. 

To see why this is so, we must consider the two basic equations involved, namely, 

A Fourier series is a type of infinite trigonometric series by which any kind of periodic function may be expressed. Now the one essential property of a crystal is that its atoms are arranged in space in a periodic fashion. But this means that the density of electrons is also a periodic function of position in the crystal, rising 

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DeWit A G J, Bronckers R P N and Fluit J M 1979 Oxygen adsorption on Ou(110) determination of atom positions with low energy ion scattering Surf. Sc/. 82 177-94... 

In Table 2 there are given data pertinent to the lattice-parameter determination, as well as intensity data used in the determination of atomic positional parameters. 

Electron crystallography provides two major advantages over X-ray crystallography for determination of atomic positions in crystal structures extremely small samples can be analysed and the crystallographic structure factor phases can be determined from images. The crystallographic structure factor phases must be known in order to arrive at a structure model,... 

W611, Ch., Chiang, S., Wilson, R. J., and Lippel, P. H. (1989). Determination of atom positions at stacking-fault dislocations on Au(lll) by scanning tunneling microscopy. Phys. Rev. B 39, 7988-7991. 

As important as the diifraction angles are to the exact lattice parameters, the intensities are crucial for the precise determination of atomic position. 

The first X-ray photographs of a protein crystal were described 50 years ago by Bernal and Crowfoot [1], These remarkable photographs indicated that a wealth of structural information was available for protein molecules once methods for the solution of the patterns had been developed. At that time the determination of atomic positions even in the crystals of small molecules was a difficult task. In 1954, Perutz and his colleagues [2] showed that the technique of heavy atom isomorphous replacement could be used to solve the phase problem. The method was put on a sound systematic basis by Blow and Crick [3] and extended to include the use of anomalous scattering [4,5]. Until recently, these methods provided the basis for all protein structure determinations. They have been remarkably effective (as illustrated below) and new developments have both increased the size of the problem solvable and provided greater insights. 

Single crystal X-ray diffraction enables the determination of atomic positions in the unit cell, allowing a three-dimensional visualization of the structure. Because... 

The major uses of XRD are identification of crystalline phases, determination of strain, crystalline orientation and size, epitaxial relationship, and the accurate determination of atomic positions (better then in electron diffraction). Because of the strong Z dependence of X-ray scattering, light elements are difficult to deal with, particularly in the presence of heavy elements. 

X-ray diffraction studies of the molecular structure of solid proteins may be divided conveniently into two categories (1) investigations made directly on protein material, both fibrous and crystalline, and (2) determinations of atomic positions in crystals of amino acids and other compounds related to proteins. The former have been reported and discussed in some detail in a recent volume of this series (12), and will be but briefly mentioned here the latter constitute the subject matter of the present paper. The attack on the constitution and configuration of protein molecules and on the forces which hold them together in natural proteins is thus being carried out both from the top and from the bottom. Eecent advances in experimental techniques and in theoretical interpretations encourage the hope that the time is not far distant when these two complementary programs will meet and the detailed structure of many protein molecules will be known and understood. 

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