CoordinationCoordination Number C.N.Radius RatioCoordination Number vs Radius RatioLet’s calculate one of the radius ratiosAn ExampleSome words you need to knowSlide 8Coordination of Common elements in SilicatesRule 1Rule 2. The Electrostatic Valency PrincipleElectrostatic valency also known as e.v.Rule 2 cont’d: IsodesmicRule 2 cont’d: AnisodesmicRule 2 cont’d: MesodesmicRule 3.Rule 4Rule 5. The Principle of ParsimonyStructure TypeCoordinationAnd Pauling’s RulesCoordination Number C.N.# of anions that can fit around a cationFor example NaCl 6CaF28Radius RatioThis is the ratio of the radius of the cation to that of the anionThis ratio usually determines the CN of the cationCoordination Number vs Radius RatioCN RR CN RR CN RR CN RR CN RR CN2 3 4 6 8 12.155 .225 .414 .732 1Make sure you remember to give examples on the boardLet’s calculate one of the radius ratiosUse triangular coordinationHandout or on board!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 coordinationSome words you need to knowCN=4 tetrahedralCN=6 octahedralCN=8 cubicCubic 8Linear 2Octahedral, 6Tetrahedral, 4Triangular,3http://www.tulane.edu/~sanelson/eens211/paulingsrules.htmCoordination of Common elements in SilicatesCN Ion Shannon Ion Radius (Å) Rx:RO4 Si+40.26 0.1884 Al+30.39 0.2836 Al+30.54 0.3866 Fe+30.65 0.4646 Mg+20.72 0.5146 Ti+40.61 0.4366 Fe+20.78 0.5576 Mn+20.83 0.5938 Na+1.18 0.8318 Ca+21.12 0.7898-12 K +1.55-1.64 1.09-1.1558-12 Ba+21.42-1.61 1.00-1.138-12 Rb +1.51-1.72 1.063-1.211http://abulafia.mt.ic.ac.uk/shannon/ptable.phpRule 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.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????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!Rule 2 cont’d: IsodesmicIn 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.htmRule 2 cont’d: AnisodesmicThis 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.htmRule 2 cont’d: MesodesmicFor 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.htmRule 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.htmRule 4In a crystal structure containing several cations, those of high valency and small coordination number tend not to share polyhedral elements.Rule 5. The Principle of Parsimony The number of different kinds of constituents in a crystal tends to be small.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