Montecarlo calculations of ionic structure in silicate and alumino-silicate melts

Borgianni, Carlo; Granati, P.

doi:10.1007/bf02653967

Cited by 13 publications

(6 citation statements)

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“…FeO-Si0 2 melts given by Masson [2,14], Whiteway, Smith and Masson [4,5], Lin and Pelton [15] and by Borgianni and Granati [12,13]. Borgianni and Granati observed only 6-and 8-membered ring ions and these ions always contained a "tail" of at least 6 mer units.…”

Section: Whiteway Smith and Masson (1970)mentioning

confidence: 94%

“…20( a). The variations of X 02 -, the fraction of total oxygen occurring as 0 2 -ions, with composition in hypothetical FeO-Si0 2 melts given by Masson [2,14], Whiteway, Smith and Masson [4,5], Lin and Pelton [15], Yokokawa and Niwa [11] and by Borgianni and Granati [12,13]. (b) The variations of XSiOj-' the fraction of total oxygen occurring on Si01-monomers, with composition in hypothetical…”

Section: Whiteway Smith and Masson (1970)mentioning

confidence: 99%

“…The variations of X 0 2 -, the fraction of total oxygen occurring as 0 2 -ions, with composition in hypothetical MnO-Si0 2 melts given by Masson [2,14], Whiteway, Smith and Masson [4,5], Y okokawa and Niwa [11] and by Borgianni and Granati [12,13]. (b) The variations of X Si04 -, the fraction oftotal oxygen occurring on Si01-monomers, with composition in hypothetical MnO-Si0 2 melts given by Masson [2,14], Whiteway, Smith and Masson [4,5] and by Borgianni and Granati [12,13]. From the mass and charge balances, given by equation (7) and (8), L1S M can be written as a function of N and n o -' The enthalpy of mixing, L1H M , is calculated as where~e is the molar enthalpy change for the reaction given in equation (2).…”

Section: Lin and Pelton (1979)mentioning

confidence: 99%

“…Addition of equations (11) and (13) and substitution for k TS from equation (6) gives and Nn~D a Si02 = (1 + N)2 Figure 1 shows the variations of~GM / R T given by equation (15) with composition for theoretical melts with~G?lRT= 0, aSiO, = (1~oN r- (16) In view of the assumption of random mixing of 0°, 0 -and 0 2 -on (1 + N) equivalent oxygen sites, it might not be unreasonable to also assume random mixing of the N silicons and (1 -N) metal cations, in which case the activities would be given, by the Temkin equation, as [3]. As is seen the free energies of mixing in theoretical melts of~G?/RT = -1.88 are considerably more negative than the measured free energies of formation of PbO-Si0 2 melts, which suggests that the actual entropy of mixing is significantly less than that calculated assuming random mixing of the three forms of oxygen.…”

Section: L+n I+nmentioning

confidence: 99%

“…Curve-fitting of Yokokawa and Niwa's model [11] with the free energies of mixing in PbO-Si02 melts at 1100°C. Borgianni and Granati have used the lattice model of Yokokawa and Niwa as the basis for Monte Carlo calculation of the free energies [12] and ionic structures [13] in silicate melts.…”

Section: Whiteway Smith and Masson (1970)mentioning

confidence: 99%

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Thermodynamic Models of Liquid Silicates

Gaskell¹

1981

Canadian Metallurgical Quarterly

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The development of structure-based thermodynamic models of binary silicates, which has occurred since the publications of Toop and Samis (1962) and Masson (1965), is reviewed. The various approaches used in the construction of these models include consideration of generalized polymerization-depolymerization equilibria involving the three forms of oxygen occurring in silicate melts and involving specificequilibria among discrete chain silicate ions and free oxygen ions, the application of the principles of polymer theory to calculation of the most probable distribution of branching chain silicate ions, calculation of the mixing properties by statistical mechanics. Monte Carlo minimization of free energy, and statistical approaches which consider the distribution of silicon and oxygen in quasi-lattices.The various models are examined and compared. Direct comparison is facilitated by the fact that, in the construction of each of the models, the free energy change for the depolymerization reaction 0°+ 0 2 -= 20 -is considered.Resume-Le present article passe en revue Ie developpement des modeles thermodynamiques de systemes binaires de silicates, fondes sur les structures, qui est apparu depuis les publications de Toop et Samis (1962) et de Masson (1965). Les differentes approches a la construction de ces modeles comprennent entre aut res : la consideration d'equilibres generaux de polymerisation-depolymerisation, impliquant les trois formes d'oxygene apparaissant dans les silicates fondus ainsi que les equilibres specifiques entre chainons d'ions silicates et d'ions libres d'oxygene, l'application des principes de la theorie des polymeres au calcuI de la distribution la plus probable de chainons branches d'ions silicate, ce calcul des proprietes de melange a l'aide de la mecanique statistique, la minimisation de la fonction d'enthalpie libre, la distribution des ions silicium et oxygene sur des quasi-reseaux, a partir de modeles statistiques.Les differents modeles sont etudies et compares. La comparison directe est facilitee du fait que, dans chacun des modeles, Ie changement d'enthalpie libre pour la reaction de depolymerisation 0°+ 0 2 = 20 -a ete considere. Gconf NOMENCLATURE k1•1 Q MO number of moles of free oxygen ions per mole of (XII MO-Si0 2 ; number of moles of singly-bonded oxygens per mole of MO-Si0 2 ; number of moles of doubly-bonded oxygens per mole of MO-Si0 2 ; the mole fraction of SiO2 in the system MO-SiO 2; (XIV the anion fraction of free oxygen; the anion fraction of SiO: -; the anion fraction of SixO~~\\l) -; the standard free energy change for the reaction MOO) + tSi0 2 (1) = tM 2 Si04 (1, completely de-Six polymerized); n the molar free energy of mixing MO and Si02; p the chemical contribution to~GM due to the breaking of oxygen double-bonds; OJn the configurational contribution to~GM due to mixing of the anions; P n the free energy change for the reaction SiO:-+ SixO~~,,+Tl) = Si x +lo~~,,++l) + 0 2 -; the equilibrium constant for the above reaction; the free energy change for the reaction 2Si...

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