The Sizes of Ions in Condensed Phases

10 nm particle. The temperature coefficient of / d is rather small, approximately +0.01 cm mol TK Values of and a are shown in Table 2.3 for many ions. Negative values of a and for very small ions (H , Mg , and Al ) should be understood only in connection with their effects on the overall polarizability of compounds containing them. 

A property of softness or hardness can be ascribed to an ion and is loosely related to its polarizability. The originally [16] softness parameters were based on the arbitrary assignment of zero to the hydrogen ion for cations and to the hydroxide ion for anions. A common scale for ions of both charge signs is produced when 0.3zi units are subtracted/added from/to the original cation/ anion values. Positive values of the softness parameter denote soft ions and negative values denote hard ions. The gi values of many ions are recorded in Table 2.3. 

In molten salts (typically, alkali metal halides) the cation-anion distances are 5 % shorter and the anion-anion distances are 5 % longer than in salt crystals at the melting point, but are very near the distances in the crystals at room temperature, the coordination numbers being 10 % lower in the molten salts than in the 

The ionic radius has a much more vague meaning for non-spherical ions. An approximate value of r is the cube root of (3/4it) times the volumes of their ellipsoids of rotation with axes a and b. For elongated rod-like ions, a b and their radii are ri examples being SCN and 13. For planar ions, a  

The relationship between the ionic radii and the ionic volumes vi leads directly to Vi = (4 r/3)(ri) and a set of such volumes, denoted as vm is reported in [17]. The ionic volumes obtained from the formula unit volumes in crystals [28], denoted as vj, is also shown in [ 17], with vj = (1.258 0.01 6)vm having been established with a correlation coefficient of 0.995 for 55 cations. The larger size of vj takes into account the void spaces between the (more or less spherical) ions. Another way to express this, based on the suggestion of Mukerjee [29] regarding such ions in solution, is to use the factor =1.213 multiplying the radius of univalent monatomic ions vi = (4jr/3)( ri). This factor is near the value, 1.159, that is geometrically required for close-packed spheres of arbitrary but comparable sizes. 

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