C.N. rra Geometry Coordination Number The critical ratio 2 Geometrical Shapes determined by geometrical 0.155-0225 Cubie hole C.N.=3 0.225-0.414 60.414-0.732 C.N.=4 80.732-1.0 ①O Cuboctahedral and Anti-cuboctahedral Common Coordination Polyhedra Structure 份 Cuboctahedron Cubic close packing Hexagonal close packing CN aB CNaB Ceramic Crystal Structures of ionic radii Greation/ranion )dictates the coordination number of anions around each cation Crystal Structure of AB I As the ratio gets larger ( i.e. as rcation/ranion 1, the coordination number gets larger and on Ratio (r+/r)
6 The critical ratio determined by geometrical analysis 2 <0.155 3 0.155-0225 4 0.225 - 0.414 6 0.414 - 0.732 8 0.732 - 1.0 C.N. rC/rA Geometry Coordination Number vs Geometrical Shapes C.N. = 3 C.N. = 4 C.N. = 6 Cubic hole Cuboctahedral hole Cuboctahedral and Anti-cuboctahedral Structure Cuboctahedron ¾¾ Cubic close packing Anti-cuboctahedron ¾¾ Hexagonal close packing Common Coordination Polyhedra Ceramic Crystal Structures The ratio of ionic radii (rcation/ranion ) dictates the coordination number of anions around each cation. As the ratio gets larger (i.e. as rcation/ranion®1), the coordination number gets larger and larger. Crystal Structure of AB vs Ion Ratio (r+/r-)
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 =+1/6
7 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 (cationanion 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+ /rto 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 ClAn 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
awnings Rules Pauling s Rules for lonic Crystals for lonic Crystals 2nd Rule- the electrostatic valence principle 3rd rule The sharing of edges, and particularly of faces, of adjacent poly hedra tend to decrease the stability of an ionic structure dn ISio l, strengths of Si-O=1, Strength=2, stable df l Al replace 1 Si, sTrength= 1+3/4=1.75, unstable af2 Al replace 2 Si, sTrength =3/4+3/4=1.5 very unstable 争争 Polyhedral Linking Paulings Rules 4th Rule: 器樂郎 An a crystal with different cations, those of high valence and small CN tend not to share polyhedral elements 是 n extension of rule3 The stability of structures with different types of lyhedral linking is vertex sharing edgesharing> ice.sharin Eeffect is largest for cations with high charge and low coordination number Especially large when r, /r approaches the lower Sit in Iv coordination is very unlikely to share limit of the polyhedral stabilit edges or faces Paulings rules Polarization of lon for lonic crystals Polarization of an ion is the distortion of the ctron cloud of the anion due to the influence of 5th Rule- Rule of Parsimony the nearby cation. .The number of different kinds of constituents in Perfect model of ionic compound a crystal tends to be small Not a purely ionic compound wards the cation and result in higher stronger bond is resulted
8 In [SiO4 ], strengths of Si-O=1, åStrength=2,stable If 1 Al replace 1 Si, åStrength = 1+3/4=1.75, unstable If 2 Al replace 2 Si, åStrength =3/4+3/4=1.5 very unstable Pauling’s Rules for Ionic Crystals •2nd Rule ¾ the electrostatic valence principle 3rd Rule: The sharing of edges, and particularly of faces, of adjacent polyhedra tend to decrease the stability of an ionic structure Pauling’s Rules for Ionic Crystals Polyhedral Linking The stability of structures with different types of polyhedral linking is vertex-sharing > edge-sharing > face-sharing effect is largest for cations with high charge and low coordination number especially large when r+ /r- approaches the lower limit of the polyhedral stability 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 IV coordination is very unlikely to share edges or faces Pauling’s Rules for Ionic Crystals 5th Rule ¾ Rule of Parsimony The number of different kinds of constituents in a crystal tends to be small Pauling’s Rules for Ionic Crystals Polarization of Ion Polarization of an ion is the distortion of the electron cloud of the anion due to the influence of the nearby cation. + – + – Perfect model of ionic compound Electron cloud of anion is attracted towards the cation and result in higher electron density between the ion, stronger bond is resulted. Ionic compound with polarization of ion ¾¾ Not a purely ionic compound