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This article discusses the thermodynamic prediction of glass properties, with a specific focus on glasses containing lead. Topics covered include energy of glass formation, heat demand of melting, batch melting, evaporation, and hydrolytic stability. Various thermodynamic models and their application to glass prediction are also discussed.
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ICF 2005 Thermodynamic Prediction for Glass Properties (with a special focus on Pb-containing glasses) Reinhard Conradt XVII ICF Technical Exchange Conference Telfs-Buchen, October 8th-11th, 2005 conradt@ghi.rwth-aachen.de
CONTENTS • energy of glass formation • heat demand of melting • batch melting • evaporation • hydrolytic stability
GA GB GC G A + B C GLASS Ox|in glass + B C (ox) = G°(ox) + RT ln c(ox)· ƒ(ox)
glasses, melts, and the crystalline reference system „c.r.s.“
thermochemical models: 1. the cell model (Gaye 1984) 2. the quasi-chemical model (Pelton & Blander 1986) F*A*C*TSage 3. the model of ideal mixing of complex components (Bonnel & Hastie 1990) statistical mixing of oxide components on the g-atom level = „ideal“; deviations decribed by adjustable interaction parameters 4.the associated liquid model(Shakhmatkin & Vedishcheva 1994) statistical mixing of oxide components on the g-atom level = „ideal“; deviations described by the evaluation of formation equilibria of all known compounds in a given system 5.the constitutional model(own work 1996) no statistical mixing of oxide components on the g-atom level; deviations described by the evaluation of known constitutional relations in a given system
data set for a one-component system: crystal - melt - glass: solid melt glass Today, such data are available!
Exploite the principles of majority partition, parsimony, HMIX, and SMIX minimization
prediction of Gibbs energies of formation of 4 mineral fibre compositions: experiments by Richet et al. 2003
Conventional industrial melts We need to analyse phase diagrams!
K2O-PbO-SiO2 liquidus temperatures
liquidus temperatures
K2O-PbO-SiO2 phase relations acidic glasses; stable against crystallization extremely PbO-rich glasses; less stable against crystallization poor chemical durability phase separation below this line no glass formation 30 % PbO
Lead Crystal Let us keep it simple!
simplified phase relation: SiO2-PbO·SiO2-K2O·2SiO2 K2O-PbO-SiO2 acidic glasses; stable against crystallization extremely PbO-rich glasses; less stable against crystallization poor chemical durability phase separation below this line no glass formation 30 % PbO
CONTENTS • energy of glass formation • heat demand of melting • batch melting • evaporation • hydrolytic stability
heat input (in) offgas (off) q = H · r [kW/m²] = [kWh/t]·[t/(m²·h)] recovered (re) set free (sf) exchanged (fire) transferred (ht) wall losses, heat exchanger (wx) exploited heat (ex) exchanged in the heat exchanger (exch) wall losses, basin (wu) stack losses (stack) wall losses, upper structure (wo)
H°chem= - 2893.6 kWh - 202.4 kWh + 3172.5 kWh ___________________ + 76.5 kWh HT,melt = + 322.7 kWh ,, Hex = (1 - yC) · H°chem +HT,melt
CONTENTS • energy of glass formation • heat demand of melting • batch melting • evaporation • hydrolytic stability
= max; but long process time very fast process; 0 finite time heat transfer: chemical efficiency: Hin = Hex + (qloss / r) · Kquality Nemec et al. 2005 thermal efficiency: Curzon & Ahlborn, 1963 optimum efficiency ex
4 3 2 1 sensors batch heap (4 kg) 5 cm glass melt (7 kg)
primary melt formation (779 °C) granular bulk solid
1 batch 1 primary melt formation 0 -1 water release -2 log , in -1·cm-1 W = 1150 s reaction foam -3 -4 foam = 2330 -2700 s -5 -6 1 batch 2 Zeit in s primary melt formation 0 -1 water release -2 W = 1880 s log , in -1·cm-1 reaction foam -3 -4 foam = 1420 s -5 -6 0 2000 4000 6000 8000 time in s
conventional batch fast conversion batch
CONTENTS • energy of glass formation • heat demand of melting • transport properties • evaporation • hydrolytic stability
(T) Avramov Adam-Gibbs, for specific SC the structure parameter describes the dependence of (T) on chemical composition
exp: Seward & Vascott, 2005; PTB 1974; Lakatos et al.1976; Richet et al. 1995
exp. data by Seward & Vascott, 2005 low E fibre TV panel log log log log , in dPa·s; - log , in ohm-1·cm-1 - log - log - log Tg / (T·SC) in (g·K) / J
CONTENTS • energy of glass formation • heat demand of melting • batch melting • evaporation • hydrolytic stability
16 K2O + 20 PbO + 64 SiO2 Pb + PbnOn + Pb(OH)2 K + KOH
CONTENTS • energy of glass formation • heat demand of melting • batch melting • evaporation • hydrolytic stability
old paradigm: network modifiers are depleted, network formers are enriched new paradigm: incongruent dissolution according to the solubility of individual oxides
solution altered zone (gel layer) bulk glass intrinsic Na+ mobilization surface equilibrium fast exchange of H+, Na+, H2O condensation of OH groups (gel formation) breaking of HOSi bonds (dissolution) low density, high connectivity, H2O percolation
Use formn. properties, i.e., Ggl= Gƒ(glass), Gaq = Gƒ(soln.)
the dissolution rate is a combined effect of • hydrolytic stability, • surface charging
the dissolution rate is a combined effect of • hydrolytic stability, • surface charging • (as varified for many different glasses)
Pb(OH)2 Pb(OH)3- PbOOH- HPbO2- Pb++
Mg++ Ca++ Zn++ Fe++
the presence of organic species has a high impact on hydrolytic stability
the presence of organic species has a high impact on hydrolytic stability