Interatomic distances in crystals

Patterson A L 1934 A Fourier series method for for the determination of the components of interatomic distances in crystals Phys. Rev. 46 372-6... 

Covalent Radii of Atoms and Interatomic Distances in Crystals containing Electron-Pair Bonds. 

The Fluorite Structure.—In Table XI are given the observed interatomic distances in crystals with the fluorite structure. There is good... 

The van der Waals radius is defined as a nonbonded distance of closest approach, and these are calculated from the smallest interatomic distances in crystal structures that are considered to be not bonded to one another. Again, these are average values compiled from many crystal structures. If the sum of the van der Waals radii of two adjacent atoms in a structure is greater than the measured distance between them,... 

A set of values of tetrahedral covalent radii 7 for use in crystals of these types is given in Table 7-13 and represented graphically in Figure 7-7. These values were obtained from the observed interatomic distances in crystals of these tetrahedral types and of other types in which the atom of interest forms four covalent bonds with neighboring atoms which surround it tetrahedraliy. For example, in pyrite, FeS. each sulfur atom is surrounded tetrahedraliy by three iron atoms and one sulfur atom, with all of which it forms essentially covalent bonds (Fig. 7-8) the substance is a derivative of hydrogen disulfide, H2S2. That the Fe—S bonds are essentially covalent is shown by the magnetic eri-... 

In Chapter 11 there will be given a discussion of the observed interatomic distances in crystals of the metallic elements and an account of the derivation from them of a set of values of single-bond metallic radii. These values are shown in Table 7-18. They refer to single covalent bonds for which the bond orbitals have the same hybrid character as in the metals themselves, as discussed in Chapter 11. The relation bc-... 

Pauling, L. and M. L. Huggins Covalent Radii of Atoms and Interatomic Distances in Crystals Containing Electron-Pair Bonds. Z. Krist. 87. 205 (1934). 

The variation of the interatomic distance in crystals of the elements is shown in Figure 55. A marked periodicity is observed, the values being greatest in the case of the alkali metals and least with the middle members... 

White, P. S., and Woolfson, M. M. The application of phase relationships to complex structures. VII. Magic integers. Acta Cryst. A31, 367-372 (1975). Hauptman, H. On the identity and estimation of those cosine invariants, cos(V>i + 2 + V a -I- which are probably negative. Acta Cryst. A30, 472-476 (1974). Patterson, A. L. A direct method for the determination of the components of interatomic distances in crystals. Z. Krist. A90, 517-542 (1935). 

Pauling, L., and Huggins, M. L. Covalent radii of atoms and interatomic distances in crystals containing electron-pair bonds. Z. Krist. 87, 205-238 (1934). Pauling, L. The Nature of the Chemical Bond. Cornell University Press Ithaca, New York. 1st edn., 1939 2nd edn., 1940 3rd edn., 1960. 

A.L. Patterson, A Fourier series representation of the average distribution of the scattering power in crystals, Phys. Rev. 45, 763 (1934), A.L. Patterson, A Fourier series method for the determination of the components of the interatomic distances in crystals, Phys. Rev. 46, 372(1934). 

FIG. 7.2. Calculation of ionic radii from interatomic distances in crystals with the sodium chloride structure. 

We shall not be greatly concerned with differences between the various sets of radii since they do not have a precise physical meaning and moreover are of interest chiefly in detailed discussions of interatomic distances in crystals the remarks on Slater s radii (p. 237) are relevant in this connection. However, and in spite of the various complications mentioned above, it is important to have some idea of the approximate relative sizes of ions if only as an aid to visualizing structures and understanding why, for example, pairs of ions such as and F , Cs" and Cl , or Ba and 0 form c.p. arrays in so many complex halides or oxides. As aids to structure determination or in discussing many features of ionic crystals sets of M—F or M-0 distances would obviously serve the same purpose as sets of ionic radii. Thus, any one of the standard sets of radii serves to illustrate the following general points ... 

Patterson, A. L. 1935. A direct method for the determination of components of interatomic distances in crystals. Z. Krist. 90 517. 

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