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Coordination

Coordination. And Pauling’s Rules. Coordination Number C.N. # of anions that can fit around a cation For example NaCl 6 CaF 2 8. Radius Ratio. This is the ratio of the radius of the cation to that of the anion This ratio usually determines the CN of the cation.

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Coordination

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  1. Coordination • And Pauling’s Rules

  2. Coordination Number C.N. • # of anions that can fit around a cation • For example • NaCl 6 • CaF2 8

  3. Radius Ratio • This is the ratio of the radius of the cation to that of the anion • This ratio usually determines the CN of the cation

  4. Coordination Number vs Radius Ratio Make sure you remember to give examples on the board

  5. Let’s calculate one of the radius ratios • Use triangular coordination • Handout or on board!

  6. An Example • The ionic radius of Cs+ is 1.67 Å • Of Cl- is 1.81 Å • What would be the predicted CN? • 1.67 divided by 1.81 is 0.92 • This predicts 8-fold coordination

  7. Some words you need to know • CN=4 tetrahedral • CN=6 octahedral • CN=8 cubic

  8. Tetrahedral, 4 Cubic 8 Octahedral, 6 Linear 2 Triangular,3 http://www.tulane.edu/~sanelson/eens211/paulingsrules.htm

  9. Coordination of Common elements in Silicates http://abulafia.mt.ic.ac.uk/shannon/ptable.php

  10. Rule 1 • Around every cation, a coordination polyhedron of anions forms, in which the cation-anion distance is determined by the sum of the radii and the coordination number is determined by the radius ratio. • Different types of coordination polyhedra are determined by the radius ratio, Rx/Rz, of the cation to the anion.

  11. Rule 2. The Electrostatic Valency Principle • An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds that reach an ion equal the charge on that ion. • What does this mean????

  12. Electrostatic valency also known as e.v. • e.v = Charge on the ion/C.N • For example, in NaCl each Na+ is surrounded by 6 Cl- ions.  The Na is thus in 6 fold coordination and C.N. = 6.  Thus e.v. = 1/6.  So 1/6 of a negative charge reaches the Na ion from each Cl.  So the +1 charge on the Na ion is balanced by 6*1/6 =1 negative charge from the 6 Cl ions. • Let’s do other examples on the board!

  13. Rule 2 cont’d: Isodesmic In the case of NaCl the charge is exactly balanced on both the cations and anions.  In such a case, we say that the bonds are of equal strength from all directions.  When this occurs the bonds are said to be isodesmic. Diagram from: http://www.tulane.edu/~sanelson/eens211/paulingsrules.htm

  14. Rule 2 cont’d: Anisodesmic This is not the case for C+4 ion in triangular coordination with O-2.  Here,  e.v. = 4/3. The 3 Oxygens each contribute 4/3 charge to the Carbon ion, and the charge on the carbon is balanced.  But, each Oxygen  still has 2/3 of a charge that it has not used.  Thus, a carbonate structural group is formed known as carbonate CO3-2. In cases like this, where the electrostatic valency is greater than 1/2 the charge on the anion (4/3 > 1/2*2), the anion will be more strongly bound to the central coordinating cation than it can be bonded to other structural groups.  When this occurs the bonding is said to be anisodesmic.  Diagram from: http://www.tulane.edu/~sanelson/eens211/paulingsrules.htm

  15. Rule 2 cont’d: Mesodesmic For Si+4 in tetrahedral coordination with O-2, the e.v. reaching the Si is 4/4 =1.  This leaves each Oxygen with a -1 charge that it has not shared.  Since this -1 is exactly 1/2 the original charge on O-2, the Oxygens in the SiO4-4 group can be just as tightly bound to ions outside the group as to the centrally coordinated Si.  In this case the bonding is said to be mesodesmic.   This property is extremely important when we look at silicate structures!!! Diagram from: http://www.tulane.edu/~sanelson/eens211/paulingsrules.htm

  16. Rule 3. • Shared edges, and particularly faces of two anion polyhedra in a crystal structure decreases its stability. Diagram from: http://www.tulane.edu/~sanelson/eens211/paulingsrules.htm

  17. Rule 4 • In a crystal structure containing several cations, those of high valency and small coordination number tend not  to share polyhedral elements.

  18. Rule 5. The Principle of Parsimony • The number of different kinds of constituents in a crystal tends to be small. 

  19. Structure Type • Crystals in which the centers of the constituent atoms occupy geometrically similar positions, regardless of size of the atoms are said to belong to the same structure type. • Examples on the board!!!

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