Local structural heterogeneity and mixing energetics in the pyromorphite–mimetite–vanadinite system

The ternary Pb₅(XO₄)₃Cl system (X = P, As, V) comprises a key group of lead apatite minerals controlling the environmental behavior of toxic elements such as Pb, As, and V. Despite their closely related crystal structures, the three binary joins within this system exhibit contrasting miscibility patterns in nature, ranging from continuous solid solutions to compositionally restricted series depending on T.

Here, we investigate the thermodynamic origin of these differences by quantifying mixing behavior along the three binary joins: Pb₅(PO₄)₃Cl pyromorphite – Pb₅(AsO₄)₃Cl mimetite, pyromorphite – Pb₅(VO₄)₃Cl vanadinite, and mimetite–vanadinite. Synthetic samples spanning the full compositional range (X_x = 0–1, Δx = 0.1) were analyzed using transmission infrared spectroscopy combined with autocorrelation analysis [1]. The δΔcorr parameter [1] was calculated independently for each binary join and used as a proxy for local structural heterogeneity related to strain induced by PO₄–AsO₄–VO₄ substitution. The analysis focused on the high-frequency vibrational modes of tetrahedral groups in the ranges 600–1200 cm^-1 (pyromorphite–mimetite), 640–1220 cm^-1 (pyromorphite–vanadinite), and 500–1000 cm^-1 (mimetite–vanadinite).

For the pyromorphite–mimetite series, excess enthalpies of mixing derived from δΔcorr (scaled to ΔH_mix [2]) vary between −0.7 and +0.6 kJ/mol whereas density-functional theory (DFT) calculations using the single-defect approach [3] yield a symmetric distribution of ΔH_mix function with a maximum of 3.8 kJ/mol at intermediate compositions X_P=0.5. This discrepancy between spectroscopically and DFT-derived mixing enthalpies remains unresolved. However, the calculated vibrational entropy of mixing [4] stabilizes the solid solution, resulting in negative Gibbs free energies of mixing with a minimum of approximately -2 kJ/mol at X_P=0.5. This thermodynamic behavior explains the absence of a miscibility gap at 300 K and the continuous nature of the pyromorphite–mimetite solid solution observed in nature [5].

In contrast, the pyromorphite–vanadinite join exhibits very small excess enthalpies of mixing derived from autocorrelation analysis, ranging from −0.23 to +0.18 kJ/mol (near 0), suggesting nearly ideal mixing and random substitution of PO₄ and VO₄ tetrahedra. Contrary, the mimetite–vanadinite series shows a slightly positive and asymmetric distribution of ΔH_mix function with a maximum of ~0.9 kJ/mol at X_As≈0.35. This agrees with DFT-derived ΔH_mix = 1 kJ/mol. Like the pyromorphite–mimetite, mimetite–vanadinite series is stabilized by the negative excess vibrational entropy term. This gives a negative Gibbs free energy of mixing oscillating about -3.5 kJ/mol at 300K.

These results demonstrate that subtle differences in local structural heterogeneity and the balance between enthalpic and entropic contributions govern miscibility in Pb-apatite solid solutions. Future work will extend this approach to the full ternary Pb₅(PO₄)₃Cl–Pb₅(AsO₄)₃Cl–Pb₅(VO₄)₃Cl system to quantify mixing energetics and local structural heterogeneity arising from coupled P–As–V substitution. Financial support for BP was provided by the National Science Center, Poland [Grant No. 2025/57/B/ST10/02894].

References

[1] Salje, E. K. et al. (2000). Eur. J. Mineral., 12, 503–519. [2] Majzlan, J. et al. (2023). Eur. J. Mineral., 35, 157–169. [3] Benisek, A. & Dachs, E. (2020). Phys. Chem. Miner., 47, 15. [4] Benisek, A. & Dachs, E. (2012). J. Alloys Compd., 527, 127–131. [5] Markl, G. et al. (2014). Am. Mineral., 99, 1133–1146.