Thermodynamic exploitation of the liquidus curves in the M^IPO₃–Pb(PO₃)₂, M^IPO₃–Cu(PO₃)₂ and M^IPO₃–Ce(PO₃)₃ systems (M ^I=Li, Na, K, Rb, Cs, Ag, Tl)

Abstract

The thermodynamic exploitation of the solid–liquid equilibria in the M^IPO₃–Pb(PO₃)₂, M^IPO₃–Cu(PO₃)₂ and M^IPO₃–Ce(PO₃)₃ systems (with M ^I=Li, Na, K, Rb, Cs, Ag, Tl) is carried out using a semi-empirical equation of the liquidus curves already used with success for similar binary systems.

The enthalpy of fusion is calculated for each pure polyphosphate on the assumption that the liquid solution is ideal and only formed by M^IPO₃ and M(PO₃)_q entities (q=2 for Pb and Cu, q=3 for M=Ce). In the most binary systems, a wide difference between the calculated values of the melting enthalpies of these polyphosphates and the measured ones determined from the DTA curves, was observed. This difference is probably due to the existence of some molecular associations in the liquid phase.

The enthalpy of fusion of each terminal phase was then recalculated on the assumption that the liquid contains a molecular association of the type of M^I _pnMn(PO₃)_n(q+p) in the region of the diagram rich in M^IPO₃ or a molecular association of the type of M^I _nM_np(PO₃)_n(qp+1) in the region rich in M(PO₃)_q (q=2 for Pb and Cu, q=3 for M=Ce). In this case, the obtained values are in good agreement with experimental determinations.