C in the compound k2 o the radius of the anion is

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Unformatted text preview: .................................... EXAMPLE 2.6–2 Calculate the CNs, assuming ionic bonding, for each of the elements in each of the following compounds: a MgO, b Cr2 O3, c K2 O. Solution 0.078 nm, r Cr3 From Appendix C we find that the relevant ionic radii are r Mg2 2 0.064 nm, r K 0.133 nm, and r O 0.132 nm. The stable ranges of r R for each CN are given in Table 2.6–1. 0.078 0.132 0.59, which corresponds to a. For MgO we find r Mg2 R O2 CN Mg2 6. Since the anion : cation ratio is 1 : 1, each anion will have the same number of nearest neighbors as each cation so that CN O2 6. b. For Cr2 O3 we have r Cr3 R O2 0.064 0.132 0.485, which corresponds to CN Cr3 6. Since there are more anions than cations in the structure, CN O2 must be less than CN Cr3 . We use the anion : cation ratio of 3 : 2 to find that CN O2 2 3 CN Cr 3 4. c. In the compound K2 O the radius of the anion is less than the radius of the cation. Therefore, r R is used to predict the CN of the anion as follows: r O2 R K 0.132 0.133 0.992, which corresponds to CN O2 8. Since there are more cations than anions in the structure, CN K must be less than CN O2 . We use the anion : cation ratio of 1 : 2 to find that CN K 1 2 C N O2 4. ....................................................................................................................................... In contrast to ionic materials, for which CN is determined by geometry, the number of nearest neighbors in a covalently bonded material is determined by the number of electrons in the valence shell of each atom. The governing equation for the electronegative elements in Groups IV through VII is NB 8 Nv (2.6–2) where NB is the number of covalent bonds formed and Nv is the number of valence electrons in the neutral atom. In most covalent solids CN is equal to NB . The exceptions to this rule are the covalent compounds containing double or triple bonds. It should also be recognized that the monovalent electronegative element hydrogen often forms a single covalent bond. Let us consider as examples se...
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This note was uploaded on 02/25/2013 for the course PHYS 2202 taught by Professor Sowell during the Spring '10 term at Georgia Tech.

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