Sodium ionic crystal radius

In deriving theoretical values for inter-ionic distances in ionic crystals the sum of the univalent crystal radii for the two ions should be taken, and corrected by means of Equation 13, with z given a value dependent on the ratio of the Coulomb energy of the crystal to that of a univalent sodium chloride type crystal. Thus, for fluorite the sum of the univalent crystal radii of calcium ion and fluoride ion would be used, corrected by Equation 13 with z placed equal to y/2, for the Coulomb energy of the fluorite crystal (per ion) is just twice that of the univalent sodium chloride structure. This procedure leads to the result 1.34 A. (the experimental distance is 1.36 A.). However, usually it is permissible to use the sodium chloride crystal radius for each ion, that is, to put z = 2 for the calcium... 

It is also shown that theoretically a binary compound should have the sphalerite or wurzite structure instead of the sodium chloride structure if the radius ratio is less than 0.33. The oxide, sulfide, selenide and telluride of beryllium conform to this requirement, and are to be considered as ionic crystals. It is found, however, that such tetrahedral crystals are particularly apt to show deformation, and it is suggested that this is a tendency of the anion to share an electron pair with each cation. 

The different hydration numbers can have important effects on the solution behaviour of ions. For example, the sodium ion in ionic crystals has a mean radius of 0 095 nm, whereas the potassium ion has a mean radius of 0133 nm. In aqueous solution, these relative sizes are reversed, since the three water molecules clustered around the Na ion give it a radius of 0-24 nm, while the two water molecules around give it a radius of only 017 nm (Moore, 1972). The presence of ions dissolved in water alters the translational freedom of certain molecules and has the effect of considerably modifying both the properties and structure of water in these solutions (Robinson Stokes, 1955). 

Ionic crystals can also be described in terms of the interstices, or holes, in the structures. Figure 7-5 shows the location of tetrahedral and octahedral holes in close-packed structures. Whenever an atom is placed in a new layer over a close-packed layer, it creates a tetrahedral hole surrounded by three atoms in the first layer and one in the second (CN = 4). When additional atoms are added to the second layer, they create tetrahedral holes surrounded by one atom in the one layer and three in the other. In addition, there are octahedral holes (CN = 6) surrounded by three atoms in each layer. Overall, close-packed structures have two tetrahedral holes and one octahedral hole per atom. These holes can be filled by smaller ions, the tetrahedral holes by ions with radius 0.225r, where r is the radius of the larger ions, and the octahedral holes by ions with radius 0.414r. In more complex crystals, even if the ions are not in contact with each other, the geometry is described in the same terminology. For example, NaCl has chloride ions in a cubic close-packed array, with sodium ions (also in a ccp array) in the... 

It is clear that from the observed interionic distances we can deduce only the sum of two ionic radii, but that if any one radius is known then other radii may be found. Various independent methods are available for estimating the radii of certain ions, and the values so determined, taken in conjunction with data from the crystal structures not only of the alkali halides but also of many other compounds, lead to the semi-empirical ionic crystal radii shown in table 3.02 and in fig. 3.05. The interpretation of the radii given in this table is subject to a number of qualifications which will be discussed below. For the present, however, it is sufficient to treat the radii as constant and characteristic of the ions concerned. For the alkali halides with the sodium chloride structure it will be seen that the interatomic distances quoted in table 3.01 are given with fair accuracy as the sum of the corresponding radii from table 3.02. 

In essentially ionic crystals it is normally the co-ordinating polyhedra of anions about cations with which we are concerned since the anions are almost always the largest ions present and it is the co-ordination of them about the cations, rather than that of the cations about the anions, which is determined by the radius ratio the co-ordination about the anions is governed by the number of cations available. In the structure of sodium chloride, for example, both Na+ and Cl- ions are admittedly octahedrally co-ordinated by ions of the other kind but it is... 

Only body-centered cubic crystals, lattice constant 428.2 pm at 20°C, are reported for sodium (4). The atomic radius is 185 pm, the ionic radius 97 pm, and electronic configuration is lE2E2 3T (5). Physical properties of sodium are given ia Table 2. Greater detail and other properties are also available... 

As a result of these effects, anions in general are larger than cations. Compare, for example, the Cl- ion (radius = 0.181 nm) with the Na+ ion (radius = 0.095 nm). This means that in sodium chloride, and indeed in the vast majority of all ionic compounds, most of the space in the crystal lattice is taken up by anions. 

Since the electron distribution function for an ion extends indefi-finitely, it is evident that no single characteristic size can be assigned to it. Instead, the apparent ionic radius will depend upon the physical property under discussion and will differ for different properties. We are interested in ionic radii such that the sum of two radii (with certain corrections when necessary) is equal to the equilibrium distance between the corresponding ions in contact in a crystal. It will be shown later that the equilibrium interionic distance for two ions is determined not only by the nature of the electron distributions for the ions, as shown in Figure 13-1, but also by the structure of the crystal and the ratio of radii of cation and anion. We take as our standard crystals those with the sodium chloride arrangement, with the ratio of radii of cation and anion about 0.75 and with the amount of ionic character of the bonds about the same as in the alkali halogenides, and calculate crystal radii of ions such that the sum of two radii gives the equilibrium interionic distance in a standard crystal. 

The definition of crystal radii from the location of the minimum of the experimental electron density between neighbouring ions appears to be physically satisfactory when the individual ions approximate to spherical shape and show little overlap, as is the case in sodium chloride. Where deviations from spherical symmetry become more significant and the zone of electron cloud overlap is appreciable, the concept of ionic radius becomes dubious. 

The type of lattice is not always determined by the radius ratio. For example, the ratio of the ionic radii in GaS and GdS is identical (0 53) but nevertheless GaS crystallizes in a sodium chloride lattice and GdS in a zinc sulphide type. Similar behaviour is observed with the corresponding tellurides. For sulphur, nitrogen and their analogues where the valency state of nitrogen is... 

The alkali metal sodium, having a larger ionic radius than lithium, prefers a pentacoordinated state. This can be accomplished by using the tridentate ligand PMDTA instead of TMEDA in the crystallization experiments. Thus, the adduct [PMDTA Na]2Mg(/z-Ph)4 (69) was isolated (36),... 

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