geosciences Article Gibbs Free Energy of Formation for Selected Platinum Group Minerals (PGM) Spiros Olivotos and Maria Economou-Eliopoulos * Received: 6 October 2015; Accepted: 14 December 2015; Published: 6 January 2016 Department of Geology and Geoenvironment, National University of Athens, Panepistimiopolis, Athens 15784, Greece; [email protected] * Correspondence: [email protected]; Tel./Fax: +30-210-727-4214 Abstract: Thermodynamic data for platinum group (Os, Ir, Ru, Rh, Pd and Pt) minerals are very limited. ˝ The present study is focused on the calculation of the Gibbs free energy of formation (DfG ) for selected PGM occurring in layered intrusions and ophiolite complexes worldwide, applying available experimental data on their constituent elements at their standard state (DG = G(species) ´ DG(elements)), using the computer program HSC Chemistry software 6.0. The evaluation of the accuracy of the calculation method was made by the calculation of (DGf) of rhodium sulfide phases. The calculated values were found to be ingood agreement with those measured in the binary system (Rh + S) as a function of temperature by previous authors (Jacob and Gupta (2014). The calculated Gibbs ˝ free energy (DfG ) followed the order RuS2 < (Ir,Os)S2 < (Pt, Pd)S < (Pd, Pt)Te2, increasing from compatible to incompatible noble metals and from sulfides to tellurides. Keywords: platinumgroup minerals; standard Gibbs free energy; thermodynamics 1. Introduction The platinumgroup elements Os, Ir, Ru, Rh, Pd and Pt (PGE) are among the most valuable elements in nature with strategic importance, due to their growing use in advanced technologies and automobile catalyst converters. Platinum groupelements (PGE) can be classified into two subgroups: the Os-, Ir-, Ru-rich or IPGE (more refractory) and PPGE (low-melting and more soluble) (Irgroup), interpreted to reflect compatible behavior (partition or distribution coefficient between solid and magma, D ¥ 1) during large-degree mantle melting and (Pt, Pd)-rich or PPGE assemblages, reflecting the incompatible behavior (D ¤ 1) of the PPGE, showing enrichment as a function of the differentiation degree [1]. The behavior of PGE during partial melting and crystal fractionation and which minerals are collectors of PGEs have been investigated and reviewed extensively [2–20]. Despite the great interest in the PGE, the thermo-chemical basis of their geochemical properties remains unclear. Thermodynamic data for PGE-minerals (PGM) are very limited, due probably to experimental difficulties and very limited data on the activity-composition models and relevant phase diagrams [21–28]. Assuming that the required thermodynamic data (enthalpy, entropy, Gibbs free energy) of the reactants and physical/chemical conditions (P, T) are available, then the mineral Gibbs free energy can be calculated [26–28]. This paper focuses on: (1) the calculation of the Gibbs free energy of formation for the selected PGM in PGE-bearing complexes worldwide, at standard state ˝ conditions (DfG ), using the current state of knowledge from experimental data on the PGE; and (2) the application of the calculated Gibbs free energy (DG) values to predict the stability of PGM. 2. Methodology ˝ Minerals have a Gibbs free energy of formation (DfG ) value, which describes the amount of energy that is released or consumed when a phase is created from its constituent elements in their Geosciences 2016, 6, 2; doi:10.3390/geosciences6010002 www.mdpi.com/journal/geosciences Geosciences 2016, 6, 2 2 of 13 ˝ standard state. It is well known that the DfG of a mineral varies with changes in pressure (P), temperature (T) and mineral composition (X) and that the more stable position is one of lower energy. The HSC Chemistry software 6.0, includes databases and various modules providing different types of chemical/thermodynamic calculation. The Gibbs free energy is defined [26] by the following equation: G = H ´ T ˆ S (1) The enthalpy and entropy values are available in different databases (HSC 6.0 Thermo-chemical Data Source on PGE [29–37]). The standard Gibbs free energy (DG˝) values of PGM were calculated (Table1,[ 21–24,35]) as the difference between free energy (G) of the products and reactants (Equation (2) using data from the NBS tables of chemical thermodynamic properties [37]). DG = Gpspeciesq ´ SGpelementsq (2) ˝ Table 1. The calculated standard Gibbs free energy (DfG ) values of formation for platinumgroup minerals are compared to available literature data. Mineral Literature Data ˝ ˝ ˝ ˝ Ref. D G D G D H S Cp Formula Name f f f kJ/mol kJ/mol kJ/mol J/mol¨ K J/mol¨ K RuS2 Laurite ´204.1 ´188.1 ´199.2 55.2 66.46 [22,23] OsS2 Erlichmanite ´135.1 ´134.1 ´146.9 54.8 – [21] IrS2 Unnamed iridium disulfide ´123.9 ´131.8 ´143.1 72.8 – [21] IrTe2 Shuangfengite ´68.0 – ´71.13 123.43 – [35] PtTe2 Moncheite ´52.9 ´52.33 ´58.19 120.95 75.09 [24,35] PdTe2 Merenskyite ´60.6 ´47.36 ´50.40 126.67 76.30 [24,35] Ir2S3 Kashinite ´196.4 ´220.5 ´241.4 97.1 – [21] PtS Cooperite ´76.1 ´76.22 ´81.79 54.87 48.17 [24] PdS Vysotskite ´66.7 ´72.25 ´70.87 57.63 48.66 [24] OsAs2 Omeiite ´75.8 – ´76.57 101.32 – [35] PtAs2 Sperrylite ´193.4 – ´217.57 31.928 – [35] Rh2S3 Bowieite ´252.4 – ´262.47 125.52 – [35] RuO2 Ru-oxide ´252.7 – ´305.01 58.158 – [35] ˝ ˝ It is notable that the (“not”) on DfG indicates that the DG value is based on the reaction at standard conditions (1 M solution concentration, 1 atm gas pressure). Temperature is not part of the standard conditions, but commonly, a temperature of 298 K is used. If the concentration is different from 1 M or 1 atm gas pressure, the change of the Gibbs free energy is written as DG. Using the Reaction Equations mode, chemical compounds and reactions were analyzed, in order to ˝ calculate the change of the Gibbs free energy (DfG ) at standard conditions. Calibrating a chemical ˝ reaction, DrG is calculated by Equation (3), when the chemical reaction follows Equation (5): DG = GpProductsq ´ GpReactantsq (3) SGpProductsq ´ SGpReactantsq = pc ˆ GC + d ˆ GD + ... q ´ pa ˆ GA + b ˆ GB + ... q (4) aA + bB + ... = cC + dD + . (5) Although the question of the original existence of bonds between metallic PGEs and sulfur, oxygen or other ligands remains unclear, the calculated Gibbs free energy values were calculated assuming the existence of metallic PGEs and sulfur [21,22,38] via the Equation (2). Although thermodynamic calculations, which are derived by various computational methods based on the available reference data, and experimental methods yield considerable uncertainties [22,24], the calculated thermodynamic values for PGM appear to be in a good agreement with those given in Geosciences 2016, 6, 0002 3 of 14 Although thermodynamic calculations, which are derived by various computational methods based on the available reference data, and experimental methods yield considerable uncertainties [22,24], the calculated thermodynamic values for PGM appear to be in a good agreement with those given in the literature. In addition, to evaluate the accuracy of the method of the calculation of the Gibbs free energy of formation, the (ΔfG) for the rhodium sulfide phases Rh3S4 and Rh2S3were calculated using the HSC program (Tables 2 and 3). The Reaction Equations mode was used to estimate the free energy of Reactions (6) and (7) through Equation (3), combining data from the HSC main database. 3Rh(s) + 2S2(g) = Rh3S4 (6) Geosciences 2016 6 , , 2 4Rh3S4(s) + S2(g) = 6Rh2S3 (7) 3 of 13 These values were compared to those obtained using a solid-state electrochemical technique [25]. The calculated values of ΔfG for these rhodium sulfides (Tables 2 and 3; Figure 1) the literature. In addition, to evaluate the accuracy of the method of the calculation of the Gibbs free were found to be in good agreement with those of temperature in the range from 925 to 1275K. energy of formation, the (DfG) for the rhodium sulfide phases Rh3S4 and Rh2S3were calculated using the HSC programTable 2. Comparison (Tables2 between and3). ΔG Thef valuesReaction of (a) this study Equations and (b) [25]mode for the was reaction: used 3Rh(s) to estimate+ 2S2(g) = Rh the3S4(s). free energy of Reactions (6) and (7) throughT (K) Δ EquationG (a) (kJ/mol) (3), combiningΔG (b) (kJ/mol) data |Δ fromG (b) the− ΔG HSC (a)| main database. 900 −289.89 −273.98 15.92 950 −272.63 −258.75 13.88 3Rhpsq + 2S2pgq = Rh3S4 (6) 1000 −255.46 −243.53 11.93 1050 −238.37 −228.3 10.07 4Rh3S4psq + S2pgq = 6Rh2S3 (7) 1100 −221.37 −213.08 8.29 These values were compared1150 to−204.46 those obtained−197.85 using a solid-state6.60 electrochemical technique [25]. 1200 −187.62 −182.63 5.00 The calculated values of DfG for these rhodium sulfides (Tables2 and3; Figure1) were found to be in 1250 −170.88 −167.4 3.48 good agreement with those1300 of temperature−154.22 in the range−152.18 from 925 to2.04 1275 K. Geosciences(A) 2016, 6, 0002 4 of 14 Figure 1.Cont. (B) Figure 1. ComparisonFigure 1. Comparison of the of calculated the calculated Gibbs Gibbs free free energy (Δ (G)DG) against against temperature, temperature, for two reactions. for two reactions. (A) 3Rh(s)(+A)2S 3Rh2((gs)) += 2S Rh2(g3) S=4 Rh(s)3S in4(s)this in this study study with with values obtained obtained by previous by previous authors authors [25]. Data [ 25for]. Data for Line (a) fromLine (a) Table from2; Table data 2; for data Line for (b):Line (b):D GfΔGf(J(¨J·molmol−´1)1 )= =−548026´548026 + 304.5 + × 304.5 T (K)ˆ fromT (K[25].) from [25].