Computing Lippmann Diagrams from Direct Calculation of Mixing Properties of Solid Solutions: Application to the Barite-Celestite System

The Lippmann diagram for the system(Ba, Sr)SO₄-H₂O was computed at 25 °Cby determining the solid-phase activity coefficientsfrom first principles calculations. Directcalculations of the mixing properties of thebarite-celestite series indicate this solid solutionbehaves as non-ideal and non-regular. At 25 °C,the enthalpy of mixing shows a minimum around 50 mole% SrSO₄ due to an ordering tendency. Thefree energy of mixing shows two minima that delimit awide and symmetric miscibility gap (from 2.1 to 97.9 mole% SrSO₄) at this temperature. The excessfree energy of mixing requires a Guggenheim expansionseries of 5 terms to be described, where the termswith odd exponents are null as a consequence of thesymmetric distribution of the mixing properties withcomposition. The Lippmann diagram shows a peritecticpoint that corresponds to the composition of an aqueoussolution which is simultaneously at equilibrium withthe two extremes of the miscibility gap. The largedifference between the solubility products of theendmembers involves a strong preferential partitioningof the less soluble endmember towards the solid phase,which explains the extremely Ba-poor composition ofthe aqueous solution (aqueous activity fraction forBa²⁺ = 0.000446 ) at the peritectic point.