Lab 1 Pauling’s rules

Pauling’s Rules for Ionic Crystals Deal with the energy state of the crystal structure 1st Rule: The cation-anion distance =  radii Can use RC/RA to determine the coordination number of the cation

Pauling’s Rules for Ionic Crystals 2nd Rule: The electrostatic valency principle First note that the strength of an electrostatic bond = valence / CN Na+ in NaCl is in [6] coordination For Na+ the strength = +1 divided by 6 = + 1/6 Cl Cl Cl Cl Na

Pauling’s Rules for Ionic Crystals 2nd Rule: the electrostatic valency principle An ionic structure will be stable to the extent that the sum of the strengths of electrostatic bonds that reach an anion from adjacent cations = the charge of that anion 6 ( + 1/6 ) = +1 (sum from Na’s) charge of Cl = -1 These charges are equal in magnitude so the structure is stable + 1/6 Na + 1/6 Na Na Cl- + 1/6 + 1/6 Na

Pauling’s Rules 3rd Rule: The sharing of edges, and particularly of faces, of adjacent polyhedra tend to decrease the stability of an ionic structure

If the edge of the edge of the tetrahedron = 1, B = 0.71 C = 0.58 D = base of tetrahedral poyhedron at maximum separation of the central ion

Pauling’s Rules 4th Rule: In a crystal with different cations, those of high valence and small CN tend not to share polyhedral elements An extension of Rule 3 Si4+ in [4] coordination is very unlikely to share edges or faces

5th Rule: The Principle of Parsimony Pauling’s Rules 5th Rule: The Principle of Parsimony The number of different kinds of constituents in a crystal tends to be small

The limiting radius ratios occur when neighbouring anions are in contact with each other and the central cation. Since the ions are considered to be rigid spheres, this condition is the limiting radius ratio. The limiting radius ratio is then purely a function of the geometry of coordination polyhedron. In each case the limiting radius ratio can be determined from geometric relationships, using, e.g. the Pythagorean theorem and the 30-60º triangle relaltionship. Trigonometry may also be used. Triangular (three-fold) coordination and octahedral (six-fold) coordination and their limiting radius ratios are shown in the following examples.

As RC/RA continues to decrease below the 0 As RC/RA continues to decrease below the 0.225 the cation will move to the next lower coordination: [3]. The cation moves from the center of the tetrahedron to the center of an coplanar tetrahedral face of 3 oxygen atoms What is the RC/RA of the limiting condition?? sin 60 = 0.5/y y = 0.577 RC = 0.577 - 0.5 = 0.077 RC/RA = 0.077/0.5 = 0.155

As RC/RA continues to decrease below the 0 As RC/RA continues to decrease below the 0.732 the cation will move to the next lower coordination: [6], or octahedral. The cation is in the center of an octahedron of closest-packed oxygen atoms

Note that in 6-fold (octahedral coordination, it is only necessary to consider a square plane containing four anions.

As RC/RA continues to decrease below the 0 As RC/RA continues to decrease below the 0.732 the cation will move to the next lower coordination: [6], or octahedral. The cation is in the center of an octahedron of closest-packed oxygen atoms What is the RC/RA of that limiting condition?? 1.414 = 2(RC + RA) If RA = ½ then RC = 0.207 RC/RA = 0.207/0.5 = 0.414 [6]-CN = 0.732>RC/RA<0.414