Non-equilibrium BaxSr1-xSO4 solid solution compositions at elevated Sr2+ concentration, ionic strength, and temperature

Abstract

The BaxSr1-xSO4 solid solution is ubiquitously present in both geological and industrial processes, where they mostly form under non-equilibrium conditions. Compared with those formed under equilibrium conditions, the BaxSr1-xSO4 solid solution formed at non-equilibrium condition has significantly higher Sr incorporation at the same aqueous phase compositions. The solid composition of BaxSr1-xSO4 formed at non-equilibrium condition is critical for the study of chemical palaeoceanography as well as the solid solution nucleation and growth kinetics. However, few studies have been conducted to investigate the composition of the BaxSr1-xSO4 solid solution when it precipitates at non-equilibrium conditions. In this study, the distribution coefficient of Ba2+ and Sr2+ between the BaxSr1-xSO4 solid solution and the aqueous phases (KD,Sr-Barite) at non-equilibrium conditions was studied with barite saturation index (SIbarite) from 0.9 to 1.5, [Sr2+]/[Ba2+] molality ratio from 0.33 to 30, temperature (T) from 50 to 90 °C and ionic strength (IS) from 0.01 M to 3 M as NaCl, with celestite being undersaturated. The composition of the BaxSr1-xSO4 solid solution formed at non-equilibrium conditions can then be calculated from the KD,Sr-Barite values. The results show that the KD,Sr-Barite value decreases with the increase of aqueous Sr2+ concentration at fixed SIbarite and T conditions. The IS effect on the KD,Sr-Barite value is small. Based on the experimental results, a new empirical model is developed to accurately predict the measured compositions of BaxSr1-xSO4 solid solution at non-equilibrium conditions under a wide T and IS conditions as follows (the plot of the predicted log10KD,Sr-Barite versus the measured log10KD,Sr-Barite with R2=0.9995):KD,Sr-Barite=-1.21-1.84SIbarite+1928.1SIbarite×T+aSr2+,aqaBa2+,aq-1Several theoretical models have also been compared against the experimental data. The birth and spread crystal growth model (B + S model) could accurately predict the solid composition of BaxSr1-xSO4 at higher barite SI and/or higher T conditions (barite SI = 1.5 at 70 °C and barite SI = 1.2–1.5 at 90 °C with [Sr2+]/[Ba2+] = 0.33–10). However, the B + S model predictions show larger deviations at lower SI and/or lower T conditions (barite SI = 0.9 and 1.2 at 50 °C and barite SI = 0.9 at 70 °C with [Sr2+]/[Ba2+] = 0.33–10 in this study). For other theoretical models, such as the CNT model and the BCF model, the predicted solid compositions of BaxSr1-xSO4 are significantly higher than the measured results. This quantitative study of the BaxSr1-xSO4 solid solution compositions could help reconstruct oceanic physical conditions and chemistry. It also establishes a solid foundation to further investigate the kinetics of the BaxSr1-xSO4 solid solution formation during non-equilibrium geological and industrial processes.