Radii in Crystals

Solid solutions will only form between ions with similar radii ( 15 %). Table 3.15 shows the radii in crystal lattices of divalent cations that might form solid solutions in soils. Hence, for example Mn +,Fe + and Cd + might be expected to form solid solutions in CaCOs, but Cu + and Zn + would not. However, soils do not necessarily behave the same as pure systems. Thus there is little evidence for strong association of Cd + or Pb + with calcite (CaCOs) in soil systems, despite having similar radii to Ca + (McBride, 1994). However Cd + and Pb + are both commonly associated with hydroxyapatite (Caio(P04)6(OH)2),... 

Tetrahedral Radii.—In crystals with the diamond, sphalerite, and wurtzite arrangements (Figs. 7-4, 7-5, and 7-6) each atom is surrounded tetrahedrally by four other atoms. If the atoms are those of fourth-... 

Since an a priori definition of the effective region is hardly possible, each atomic region is usually approximated by a spherical region around the atom, where the radius is taken as its ionic, atomic, or covalent bond radius. The radial distribution of electron density around an atom is also useful to estimate the effective radius of an atom, particularly in ionic crystals. In an ionic crystal, the distance from the metal nucleus to the minimum in the radial distribution curve generally corresponds to the ionic radius. As an example, the radial distribution curves around K in o-KvCrO., (85) are shown in Fig. 19a. The radial distributions of valence electrons (2p electrons) exhibit a minimum at 1.60 A for K(l) and 1.52 A for K(2), respectively. These distances correspond to the ionic radii in crystals (1.52-1.65 A)... 

Cook (1961). Radii in crystal are calculated from lattice parameters of low-temperature noble gas crystals (FCC). b Pyykko (1997). Also see Zhang Xu (1995) for the discussion of noble gas atomic radius. 

Slater 1C (1964) Atomic radii in crystals. 1 Chem Phys 41 3199... 

The connection between molecular mechanics and crystal structures came about in the attempt to quantify the non-bonded interactions. These were first taken oyer from intermolecular interaction potentials of rare-gas-type molecules. They start from the premise, contained in the van der Waals equation of state for real gases, that atoms are not localized at points, i.e. not at their respective nuclei. They occupy a volume of space and can be assigned, at least as a first step, more or less definite radii, by custom called van der Waals radii, which were initially estimated for many types of atom mainly from packing radii in crystals. Mutual approach of non-bonded atoms to distances less than the sum of these radii leads to strong repulsive forces. The empirical atom-atom potentials that were introduced to describe the balance between atom-atom attractions and repulsions were assumed to be characteristic of the atom types and independent of the molecules they are embedded in. They were assumed to hold equally for interactions between non-bonded atoms in... 

Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371 683-683 Slater JC (1939) Introduction to chemical physics. McGraw-Hill, New York, NY Slater JC (1964) Atomic radii in crystals. J Chem Phys 41 3199-3204 Smith JV (1953) Re-examination of the crystal stractrrre of melihte. Amer Mineral 38 643-661 Smith JV (1977) Enumeration of 4-cormected 3-dimertsional nets and classification of framework silicates. 

Lide, D.R. (2012) Ionic radii in crystals, in CRC Handbook of Chemistry and Physics (eds W.M. Haynes and D.R. Lide), CRC Press/Taylor and Francis, Boca Raton, FL. 

This new Internet edition has added 13 new subsections that can be accessed as interactive tables. These include tables on atomic and molecular polarizabilities, diffusion in gases and liquids, vapor pressure and density of mercury, ionic radii in crystals, surface tension, and other topics. All material in the printed Handbook is accessible in the Internet version as interactive tables and/or pdf displays. 

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