Structure Maps Plots of r versus Structure Maps-Plots of r, versu rn with structure type indicated with structure type indicated Separation of sEparation of structure types Is structure types is A, BO achieved on structure achieved on structure diagrams-but, the diagrams -but, the bo col Conclusion-Size i Conclusion-Size does matter but not does matter. but not necessarily in any AB necessarily in any 200pa 0如0174op Pauling s rules Pauling s rules for lonic Crystals a Cation environment in a polyhedron(cation anion distance and Coordination Number) Deal with the energy state of the crystal structure a Relationship between bond valence and oxidation number a Corner, edge and face sharing polyhedra .The cation anion distance =2 a Large valence and small Coordination Number cations tend not to share poly hedra elements a Rule of parsimony coordination number of the ca Paulings rules Paulings Rules for lonic Crystals for lonic Crystals 2nd Rule 2nd Rule- the electrostatic valence principle aFirst note that the strength of an electrostatic a An ionic structure will be stable to bond valence/CN strengths of electrostatic bonds that reach an anion from adjacent cations Nat in NaCl is in VI 60+1/6)=+1(sum from Na's) divided by 6 These charges are equal in magnitude so the structure is stable =+1/67 Structure Maps ¾¾ Plots of rA versus rB with structure-type indicated Separation of structure types is achieved on structure diagrams ¾ but, the boundaries are complex Conclusion ¾ Size does matter, but not necessarily in any simple way! Structure Maps ¾¾ Plots of rA versus rB with structure-type indicated Separation of structure types is achieved on structure diagrams ¾ but, the boundaries are complex Conclusion ¾ Size does matter, but not necessarily in any simple way! Pauling’s Rules Cation environment in a polyhedron (cation￾anion distance and Coordination Number) Relationship between bond valence and oxidation number Corner, edge and face sharing polyhedra Large valence and small Coordination Number cations tend not to share polyhedra elements Rule of parsimony Pauling’s Rules for Ionic Crystals Deal with the energy state of the crystal structure 1st Rule The cation-anion distance = S radii Can use r+ /r￾to determine the coordination number of the cation Pauling’s Rules for Ionic Crystals 2nd Rule First note that the strength of an electrostatic bond = valence / CN Cl Cl Cl Cl Na Na+ in NaCl is in VI coordination For Na+ the strength = +1 divided by 6 = + 1/6 Pauling’s Rules for Ionic Crystals 2nd Rule ¾ the electrostatic valence principle + 1 /6 + 1 /6 + 1 /6 + 1 /6 Na Na Na Na Cl￾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