Earth Materials. John O'Brien
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Название: Earth Materials

Автор: John O'Brien

Издательство: John Wiley & Sons Limited

Жанр: География

Серия:

isbn: 9781119512219

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СКАЧАТЬ Cubic Cube >1.00 12 Cubic or hexagonal closest packed Cubeoctahedron complex

      When predicting coordination number using radius ratios, several caveats must be kept in mind.

      1 The ionic radius and coordination number are not independent. As illustrated by Table 2.6, effective ionic radius increases as coordination number increases.

      2 Since bonds are never truly ionic, models based on spheres in contact are only approximations. As bonds become more covalent and more highly polarized, radius ratios become increasing less effective in predicting coordination numbers.

      3 Radius ratios do not successfully predict coordination numbers for metallically bonded substances.

      The great value of the concept of coordination polyhedra is that it yields insights into the fundamental patterns in which atoms bond during the formation of crystalline materials. These patterns most commonly involve threefold (triangular), fourfold (tetrahedral), sixfold (octahedral), eightfold (cubic) and, to a lesser extent, 12‐fold coordination polyhedra or small variations of such basic patterns. Other coordination numbers and polyhedron types exist, but are rare in inorganic Earth materials.

      Another advantage of using spherical ions to model coordination polyhedra is that it allows one to calculate the size or volume of the resulting polyhedron. In a coordination polyhedron of anions, the cation–anion distance is determined by the radius sum (R). The radius sum is simply the sum of the radii of the two ions (Rc + Ra); that is, the distance between their respective centers. Once this is known, the size of any polyhedron can be calculated using the principles of geometry. Such calculations are beyond the scope of this book but are discussed in Wenk and Bulakh (2016) and Klein and Dutrow (2007).

      2.4.2 Electrostatic valency

      An important concept related to the formation of coordination polyhedra is electrostatic valency (EV). In a stable coordination structure, the total strength of all the bonds that reach a cation from all neighboring anions is equal to the charge on the cation. This is another way of saying that the positive charge on the cation is neutralized by the electrostatic component of the bonds between it and its nearest neighbor anions. Similarly, every anion in the structure is surrounded by some number of nearest neighbor cations to which it is bonded, and the negative charges on each anion are neutralized by the electrostatic component of the bonds between it and its nearest neighbor cations. For a cation of charge Z bonded to a number of nearest neighbor anions (CN), the electrostatic valency of each bond is given by the charge of the cation divided by the number of nearest neighbors to which it is coordinated:

equation Schematic illustration of common coordination polyhedra: (a) cubic closest packing, (b) cubic, (c) octahedral, (d) tetrahedral, (e) triangular, (f) linear.

      Source: Wenk and Bulakh (2004). © Cambridge University Press.

Ion CN = 4 CN = 6 CN = 8
Na+1 0.99 1.02 1.18
K+1 1.38 1.51
Rb+1 1.52 1.61
Cs+1 1.67 1.74
Mg+2 0.57 0.72
Al+3 0.39 0.48
Si+4 0.26 0.40
P+5 0.17 0.38
S+6 0.12 0.29