CERAMIC ENGINEERING 103. HOMEWORK SET #5 Structural and Bonding Theories of Glass Formation

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1 WS00 HW5_bonding -1-2/13/00 CERAMIC ENGINEERING 103 HOMEWORK SET #5 Structural and Bonding Theories of Glass Formation 1. From Pauling's Rules, determine the preferred cation and anion coordination numbers for the following compounds. Use the ionic radii from the 'Shannon and Prewitt" table distributed in class. (Hint: Use the 'octahedral radii' in your initial calculation). SiO 2 : Al 2 : r(si 4+ )/r(o 2- ) = 0.40/1.21 = 0.33 r(al 3+ )/r(o 2- ) = 0.67/1.24 = 0.54 Si CN = 4 preferred Al CN = 6 preferred From z c /z a = CN c /CN a : 4/2 = 4/CN a, CN(O)=2 3/2 = 6/CN a, CN(O)=4 4:2 Structure 6:3 Structure TiO 2 : B 2 : r(ti 4+ )/r(o 2- ) = 0.745/1.26 = 0.59 r(b 3+ )/r(o 2- ) = 0.26/1.21 = 0.21 Ti CN = 6 preferred B CN = 3 preferred From z c /z a = CN c /CN a : 4/2 = 6/CN a, CN(O)=3 3/2 = 3/CN a, CN(O)=2 6:3 Structure 3:2 Structure GeO 2 : La 2 : r(ge 4+ )/r(o 2- ) = 0.54/1.21 = 0.45 r(la 3+ )/r(o 2- ) = 0.94/1.26 = 0.94 on the border between CN=4 or 6 Ge CN = 4 preferred La CN = 6-8 preferred From z c /z a = CN c /CN a : 4/2 = 4/CN a, CN(O)=2 3/2 = 6/CN a, CN(O)=4 4:2 Structure 6:4 Structure r(be 2+ )/r(f - ) = 0.41/1.145 = 0.36 r(ca 2+ )/r(o 2- ) = 1.14/1.26 = 0.90 Be CN = 4 preferred Ca CN = 6-8 preferred From z c /z a = CN c /CN a : 2/1 = 4/CN a, CN(F)=2 2/2 = 8/CN a, CN(O)=8 4:2 Structure 8:8 Structure (or 6:6) r(li + )/r(o 2- ) = 0.73/1.26 = 0.58 r(zn 2+ )/r(o 2- ) = 0.89/1.26 = 0.71 Li CN = 4 preferred Zn CN = 6 preferred From z c /z a = CN c /CN a : 1/2 = 4/CN a, CN(Li)=8 2/2 = 6/CN a, CN(O)=6 4:8 Structure 6:6 Structure

2 WS00 HW5_bonding -2-2/13/00 Use Zachariasen's Rules to predict the glass-forming tendency of the compounds in question 1. SiO 2 : Al 2 : Predict 4:2 structure Predict 6:4 structure Fulfills Zachariasen Rules 1 and 2 Cation, anion CN's too high TiO 2 : B 2 : Predict 6:3 structure Predict 3:2 structure Cation, anion CN's too high Fulfills Zachariasen Rules 1 and 2 GeO 2 : La 2 : Predict 4:2 structure Predict 6:4 structure Fulfills Zachariasen Rules 1 and 2 Cation, anion CN's too high Predict 4:2 structure Fulfills Zachariasen Rules 1 and 2 Predict 8:8 structure Cation, anion CN's too high Predict 4:8 structure Fulfills Zachariasen Rule2, O CN high Predict 6:6 structure Cation, anion CN's too high

3 WS00 HW5_bonding -3-2/13/00 2. Use the ionic radii from the 'Shannon and Prewitt" table distributed in class to calculate the cation-anion field strength for each compound, then use Dietzel s criteria to identify the glass formers, modifiers and intermediates. Note Izumatani Table (Handout): 2 FS>2.5: Glass Former 2 FS<1.0: Glass Modifier 2.5>(2 FS)>1.0: Glass Intermediate SiO 2 : Al 2 : FS = 4/( ) 2 = 1.54 FS = 3/( ) 2 = FS>2.5: Predict Glass Former 2.5>(2 FS)>1.0: Glass Intermediate TiO 2 : B 2 : FS = 4/( ) 2 = 1.00 FS = 3/( ) 2 = >(2 FS)>1.0: Glass Intermediate 2 FS>2.5: Predict Glass Former GeO 2 : La 2 : FS = 4/( ) 2 = 1.31 FS = 3/( ) 2 = FS>2.5: Predict Glass Former 2.5>(2 FS)>1.0: Glass Intermediate FS = 2/( ) 2 = 0.82 FS = 2/( ) 2 = 0.38 Note: using same FS criteria and accounting 2 FS<1.0: Glass Modifier for lower z F, predict modifier. BeF 2, however, is a good glass former FS = 1/( ) 2 = 0.25 FS = 2/( ) 2 = FS<1.0: Glass Modifier 2 FS<1.0: Glass Modifier

4 WS00 HW5_bonding -4-2/13/00 3. Use the dissociation energies listed below to rank the compounds in order of decreasing glassforming tendency using Sun's Bond Strength criteria. Divide the compounds into glass-formers, intermediates, and modifiers using these criteria. (Hint: calculate dissociation energy per metal-oxygen bond using CN's from problem 1). Note Izumatani Table (Handout): S.B.S>100 kcal: Glass Former S.B.S<40 kcal: Glass Modifier 100 kcal>s.b.s.>40 kcal: Glass Intermed. SiO 2 = 424 mole Al 2 = 402 mole Si CN = 4 Al CN = 6 Single bond strength = 106 kcal S.B.S = 67 kcal Predict Glass Former Predict Intermediate TiO 2 = 435 kcal/mole B 2 = 356 kcal/mole Ti CN = 6 B CN = 3 Single bond strength = 73 kcal S.B.S = 119 kcal Predict Intermediate Predict Glass Former GeO 2 = 431 kcal/mole La 2 = 406 kcal/mole Ge CN = 4 La CN = 6 Single bond strength = 108 kcal S.B.S = 68 kcal Predict Glass Former Predict Intermediate CaO = 257 kcal/mole Ca CN = 6-8 S.B.S = kcal Predict Modifier Li 2 O = 144 kcal/mole ZnO = 144 kcal/mole Li CN = 4 Zn CN = 6 Single bond strength = 36 kcal S.B.S = 24 kcal Predict Modifier Predict Modifier

5 WS00 HW5_bonding -5-2/13/00 4. Determine the % ionic character for the following compounds, using the electronegativity and % ionic character values given below. Predict which compounds will form glasses using the Stanworth criteria. Divide the compounds into glass formers, intermediates, and modifiers. Note Izumatani Table (Handout): EN<60%: Glass Former EN>70%:: Glass Modifier 60%>= EN >70%: Glass Intermed. SiO 2 : Al 2 : EN=( ) = 1.7 EN=( ) = 1.7 % ionic charac. = 51%; Former % ionic charac.=63%; Intermed. TiO 2 : B 2 : EN=( ) = 2.0 EN=( ) = 1.5 % ionic charac. = 63%; Intermediate % ionic charac.=43%; Former GeO 2 : La 2 : EN=( ) = 1.6 EN=( ) = 2.4 % ionic charac. = 47%; Former % ionic charac.=76%; Modifier EN=( ) = 2.5 EN=( ) = 2.5 % ionic charac. = 79%; Modifier % ionic charac.=79%; Modifier EN=( ) = 2.7 EN=( ) = 1.9 % ionic charac. = 84%; Modifier % ionic charac.=59%; Intermed. Electronegativities of Ions EN % Ionic Character Si = 1.8 Li = Be = 1.5 Na = Ca = 1.0 Ti = Ge = 1.9 O = Zn = 1.6 F = Al = 1.5 B = La =

6 WS00 HW5_bonding -6-2/13/00 Summary: These empirical rules provide some insight for the effects of the properties of a cation and its oxide bond on glass forming tendency. In general, glass forming tendency is enhanced for oxides with small, highly charged cations. These cations prefer low coordination structures (for both the cations and oxygens), have relative high field strengths and high single bond strengths, and low degrees of bond ionicity. There are exceptions to the rules. BeF 2 is a good glass former despite a low Be-F F.S. and high bond ionicity.