Thermodynamic and structural variations along the olivenite–libethenite solid solution

Many natural secondary arsenates contain a small fraction of phosphate. In this work, we investigated the olivenite–libethenite (Cuinline-formula₂(AsOinline-formula₄)(OH)–Cuinline-formula₂(POinline-formula₄)(OH)) solid solution as a model system for the P–As substitution in secondary minerals. The synthetic samples spanned the entire range from pure olivenite (inline-formulaX_lib=0) to libethenite (inline-formulaX_lib=1). Acid-solution calorimetry determined that the excess enthalpies are non-ideal, with a maximum at inline-formulaX_lib=0.6 of inline-formula+1.6 kJ molinline-formula⁻¹. This asymmetry can be described by the Redlich–Kister equation of Hinline-formula^ex= inline-formulaX_oli⋅X_lib [inline-formulaA+B(inline-formulaX_oli−X_lib)], with inline-formulaA=6.27 inline-formula± 0.16 and inline-formulaB=2.9 inline-formula± 0.5 kJ molinline-formula⁻¹. Three-dimensional electron diffraction analysis on the intermediate member with inline-formulaX_lib=0.5 showed that there is no P–As ordering, meaning that the configurational entropy (inline-formulaS_conf) can be calculated as inline-formula $M21inlinescrollmathml-R(X_{\mathrm{normal\; oli}}\ln X_{\mathrm{normal\; oli}}+X_{\mathrm{normal\; lib}}\ln X_{\mathrm{normal\; lib}}$ 117pt13ptsvg-formulamathimg52aa0657e629b45c533e40c23cb7d950 ejm-35-157-2023-ie00001.svg117pt13ptejm-35-157-2023-ie00001.png ). The excess vibrational entropies (inline-formula $M22inlinescrollmathml{S}_{\mathrm{normal\; vib}}^{\mathrm{normal\; ex}}$ 19pt15ptsvg-formulamathimg4f3877a6f78dba53722e4db12cf389ef ejm-35-157-2023-ie00002.svg19pt15ptejm-35-157-2023-ie00002.png ), determined by relaxation calorimetry, are small and negative. The entropies of mixing (inline-formula $M23inlinescrollmathml{S}_{\mathrm{normal\; conf}}+S_{\mathrm{normal\; vib}}^{\mathrm{normal\; ex}}$ 53pt15ptsvg-formulamathimg81532243ab3fb035e24c018f95ce5a01 ejm-35-157-2023-ie00003.svg53pt15ptejm-35-157-2023-ie00003.png ) also show asymmetry, with a maximum near inline-formulaX_lib=0.6. Autocorrelation analysis of infrared spectra suggests local heterogeneity that arises from strain relaxation around cations with different sizes (Asinline-formula⁵⁺ inline-formula $M26inlinescrollmathml/$ 8pt14ptsvg-formulamathimg6ab83fe49e60fc98c8f39a665eb0d5b9 ejm-35-157-2023-ie00004.svg8pt14ptejm-35-157-2023-ie00004.png  Pinline-formula⁵⁺) in the intermediate members and explains the positive enthalpies of mixing. The length scale of this strain is around 5 Å, limited to the vicinity of the tetrahedra in the structure. At longer length scales (inline-formula≈15 Å), the strain is partially compensated by the monoclinic–orthorhombic transformation. The volume of mixing shows complex behavior, determined by P–As substitution and symmetry change. A small (0.9 kJ molinline-formula⁻¹) drop in enthalpies of mixing in the region of inline-formulaX_lib=0.7–0.8 confirms the change from monoclinic to orthorhombic symmetry.