4 - EMA 4144 Physical Ceramics Background, Bonds, Energy...

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EMA 4144 Physical Ceramics Background, Bonds, Energy Bands, Models, Crystals and Chemistry
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Objectives for S5 • Present and Apply Pauling’s rules. escribe common ceramic crystal Describe common ceramic crystal structures. 2
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Crystal Chemistry of Ceramics Crystal Structure determined by: – Relative sizes of atoms – Balance of charge of various combinations of atoms – Directionality of the bonds
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Important Crystal Structure Considerations: Ionic Radius Ionic radius = ½ bond length between a pair of ions in a specific structure Ionic radius is affected by • The ion itself (e.g., F - versus Na + ) • Surrounding ions (e.g., Ca surrounded by F is not the same as Ca surrounded by Br, Br>F) Relative amount of covalent and ionic bonding • Charge and Spin state = electrons paired in spin (low spin state) or unpaired (high spin state) + e.g., Co 2+ low spin state, CN = 6, r = 0.790 Co 3+ low spin state, CN = 6, r = 0.665 Co 2+ high spin state, CN = 6, r = 0.885 + Co 3+ high spin state, CN = 4, r = 0.710
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Important Crystal Structure Considerations: Ionic Packing Anions generally larger than cations. Therefore most ionic ceramic crystal structures = 3D stacking of anions with cations fitting to the interstitial positions into the interstitial positions.
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Important Crystal Structure Considerations: Ionic Packing nly cations of Only cations of appropriate size range are stable in r C /r A > 0.225 each interstitial position: too small = unstable just right or a little o big = stable r C /r A > 0.414 too big stable too big = unstable r C /r A > 0.732
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Important Crystal Structure Considerations: Charge Ions are not really hard spheres Bonding is not usually purely ionic ig anions are easily deformed by high charge Big anions are easily deformed by high charge cations osition of ions is limited by their need for charge Position of ions is limited by their need for charge neutrality in the unit cell and throughout the structure. ond strength= V/CN Bond strength V/CN V=valence Bond Strength (cation) = Bond strength (anion)
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Pauling’s Rules Cation Coordination Rule 1: each cation will be coordinated by a polyhedron of anions. The number of ions can be determined by the cation/anion radius ratio 8 *from Schakelford
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What was Pauling thinking? Show that the r/R lower limit for CN8 is 0.732 9
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Example 5.2: What is the crystal structure of NaCl? r C /r A > 0.225 r(Na + ) = 1.16 Å (Cl - = 1 67Å R(Cl ) = 1.67Å r(Na + )/r(Cl - ) = 0.69 r C /r A > 0.414 6 Cl - surround each Na+ r C /r A > 0.732 V A /CN A = V C /CN C CN = V /V CN C C A A = 1 /1 6 =6
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Example 5.2: What is the crystal structure of CsCl? r C /r A > 0.225 r(Cs + ) = 1.88 Å (Cl - = 1 67Å R(Cl ) = 1.67Å r(Cs + )/r(Cl - ) ~1.2 r C /r A > 0.414 8 Cl - surround each Cs+ r C /r A > 0.732 V A /CN A = V C /CN C CN = V /V CN C C A A = (1 /1)* 8 = 8
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Pauling’s Rules Bond Strength The cation-anion “bond-strength” is efined as the valence of the ion divided defined as the valence of the ion divided by its coordination number 12
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Pauling’s Rules Rule 2: the coordination polyhedra are arranged in three dimensions in a Anion Coordination way that preserves charge neutrality. The cation-anion “bond-strength” is
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4 - EMA 4144 Physical Ceramics Background, Bonds, Energy...

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