Prediction of Gibbs free energies of formation of minerals of the alunite supergroup

A method for the prediction of Gibbs free energies of formation for minerals belonging to the alunite family is proposed, based on an empirical parameter Δ_GO⁼ M^z+(c) characterizing the oxygen affinity of the cation M^z+. The Gibbs free energy of formation from constituent oxides is considered as the sum of the products of the molar fraction of an oxygen atom bound to any two cations, multiplied by the difference of oxygen affinity Δ_GO⁼ M^z+(c) between any two consecutive cations. The Δ_GO⁼ M^z+(c) value, using a weighing scheme involving the electronegativity of a cation in a specific site (12-fold coordination site, octahedral and tetrahedral) is assumed to be constant. It can be calculated by minimizing the difference between experimental Gibbs free energies (determined from solubility measurements) and calculated Gibbs free energies of formation from constituent oxides. Results indicate that this prediction method gives values within 0.5% of the experimentally measured values. The relationships between Δ_GO⁼ M^z+(alunite) corresponding to the electronegativity of a cation in either dodecahedral sites, octahedral sites or tetrahedral sites and known as Δ_GO⁼ M^z+(aq) were determined, thereby allowing the prediction of the electronegativity of rare earth metal ions and trivalent ions in dodecahedral sites and highly charged ions in tetrahedral sites. This allows the prediction of Gibbs free energies of formation of any minerals of the alunite supergroup (bearing various ions located in the dodecahedral and tetrahedral sites). Examples are given for hydronium jarosite and hindsalite, and the results appear excellent when compared to experimental values.     

Prediction of Gibbs energies of formation—I. Relationships among Gibbs energies of formation of hydroxides,oxides and aqueous ions

A parameter called ΔO^2? is defined as the difference between the Gibbs energy of formation from the elements of a crystalline oxide and the Gibbs energy of formation from the elements of its cation in aqueous solution (per O^2? in the oxide). Another parameter called Δ hydroxide is defined as the difference between the Gibbs energies of formation of an hydroxide and its constituent oxides, H₂O oxide being considered as ice. A linear equation for 32 hydroxides, using these two parameters is: Δhydroxide = ?0.210 (ΔO^2? cation ? ΔO^2? H⁺). This relation can also be expressed in terms of solution energies. The solution energy of an hydroxide is a linear function of the solution energy of the corresponding oxide. The equation above can be used to predict values for Gibbs energies of formation of hydroxides, oxides or aqueous cations and to test the consistency of existing Gibbs energy values.     

Prediction of Gibbs energies of formation of compounds from the elements—II. Monovalent and divalent metal silicates

A parameter ΔO^2?, defined as the difference between the Gibbs energy of formation of a given oxide and its aqueous cation, was used to obtain linear relationships among Gibbs energies of formation from the elements of hydroxides, oxides and aqueous metallic ions (Tardy and Garrels, 1976). Use of this parameter has now been extended to meta- and orthosilicates for which the Gibbs energies of formation of silicates from their oxides are shown to be linear functions of the ΔO^2? values of their constituent cations. The function obtained for metasilicates is:

$\text{ΔG}{}^{\mathrm{o}}{}_{\mathrm{?}}\text{silicate}\text{? ∑ΔG}{}^{\mathrm{o}}{}_{\mathrm{?}}\text{oxides}\text{= ?}\text{2}\text{3}\text{(ΔO}{}^{\mathrm{2?}}\text{cation}\text{? ΔO}{}^{\mathrm{2?}}\text{silicon}$

and that for orthosilicates is:

$\text{ΔG}{}^{\mathrm{o}}{}_{\mathrm{?}}\text{silicate}\text{? ∑ΔG}{}^{\mathrm{o}}{}_{\mathrm{?}}\text{oxides}\text{= ?}\text{4}\text{4}\text{(ΔO}{}^{\mathrm{2?}}\text{cation}\text{? ΔO}{}^{\mathrm{2?}}\text{silicon}$

in which Δ^o_? silicate is the Gibbs energy of formation from the elements of a silicate of a given cation and ∑ΔG^o_? oxides is the sum of the Gibbs energies of formation from the elements of the constituent oxides of the silicate considered.These functions can be used to test for consistency within and between various sources of thermodynamic data and to estimate free energy of formation values for previously unstudied species.     

含氧酸盐矿物生成自由能的计算

地质科学近年来发展的一个重要方向是热力学理论和热化学方法的应用。在地质领域内应用热力学理论的基础是矿物及有关化合物的热力学性质(或热化学数据)。     

湖相碳酸盐岩元素测试方法研究

湖相碳酸盐岩因形成于大陆环境,通常陆源硅酸盐组分含量较高并影响元素组成特征,不应简单地套用海相碳酸盐岩的方法进行元素测试。对柴西茫东地区红山梁剖面始新统下干柴沟组-中新统下油砂山组湖相碳酸盐岩采用酸溶法、电子探针、LA等多手段进行的地球化学综合研究,结果显示,各种测试方法应用于湖相碳酸盐岩分析时都存在适用性与局限性问题。酸溶法的局限性在于所获得的K等碱金属元素含量不能用于后续分析。而对微区测试方法而言,首先LA与探针两种微区测试方法能否进行数据上的通用需要比较二者的相关性;其次由于光斑大小的限制,对泥晶组分而言,需在判断陆源的干扰程度并进行相应扣除后,才能反映沉积水体的元素组成特征。因此,在分析陆源硅酸盐组分对湖相碳酸盐岩元素含量影响程度的基础上,提出两种排除陆源硅酸盐组分对泥晶组分元素含量影响的方法,可以实现微区测试方法在湖相碳酸盐岩中的有效应用。     

用线性自由能关系预测金属络合物的热力学性质

Sverjensky与Molling提出的线性自由能关系是根据金属阳离子的热力学性质来预测等结构系列中固体相的标准生成自由能。本文研究结果证实,水溶液中金属络合物与简单金属阳离子之间也存在类似的相关关系,预测值与实验值的差异通常小于1．5kcal／mol或小于一个log单位,这一线性自由能关系对于预测自然环境中重金属的水溶物种的配分、迁移和毒性具有非常重要的应用价值。     

Fictive component model of pyroxenes and multicomponent phase equilibria

Pyroxenes are considered as ideal solid solutions of some real components (e.g. diopside or orthoenstatite) and some fictive or hypothetical components (e.g. orthodiopside or orthohedenbergite). Using the reversed experimental data in the CaO-MgO-SiO₂ system, the Gibbs free energy of formation of fictive orthodiopside and of fictive clinoenstatite have been determined in the temperature range of 1,000 to 1,600 °K. The data on free energies of components in the binary system can be used to extend the fictive component model to the ternary CaSiO₃-MgSiO₃-FeSiO₃ system. Using published phase diagrams on the pyroxene quadrilateral, Gibbs free energy of formation of fictive orthohedenbergite has been calculated. Application of the ideally mixing fictive component model to computation of phase equilibria leads to the determination of compositions of coexisting Fe-Mg-Ca pyroxenes at different temperatures.Abbreviations and symbols G _f ⁰ Gibbs free energy of formation from the elements at 1 bar and temperature - G ^Ex excess free energy of mixing in a solution - G molar Gibbs free energy - R gas constant - H enthalpy - S entropy - T absolute temperature - P pressure - KJ/M kilojoules per mole - j joules - Opx orthopyroxene - Cpx clinopyroxene - H hedenbergite - D diopside - E enstatite - F ferrosilite - X mole fraction - K equilibrium constant     

A primer in gibbs energy minimization for geophysicists

Gibbs energy minimization is the means by which the stable state of a system can be computed as a function of pressure, temperature and chemical composition from thermodynamic data. In this context, state implies knowledge of the identity, amount, and composition of the various phases of matter in heterogeneous systems. For seismic phenomena, which occur on time-scales that are short compared to the timescales of intra-phase equilibration, the Gibbs energy functions of the individual phases are equations of state that can be used to recover seismic wave speeds. Thermodynamic properties relevant to modelling of slower geodynamic processes are recovered by numeric differentiation of the Gibbs energy function of the system obtained by minimization. Gibbs energy minimization algorithms are categorized by whether they solve the non-linear optimization problem directly or solve a linearized formulation. The former express the objective function, the total Gibbs energy of the system, indirectly in terms of the partial molar Gibbs energies of phase species rather than directly in terms of the Gibbs energies of the possible phases. The indirect formulation of the objective function has the consequence that although these algorithms are capable of attaining high precision they have no generic means of treating phase separation and expertise is required to avoid local minima. In contrast, the solution of the fully linearized problem is completely robust, but offers limited resolution. Algorithms that iteratively refine linearized solutions offer a compromise between robustness and precision that is well suited to the demands of geophysical modeling.     

挥发份在夕卡岩型和斑岩型矿床形成中的作用

通过总结多年来对夕卡岩型和斑岩型矿床的研究所获得的成果，作者认识到挥发相在这些矿床形成过程中的重要地位和意义。文章系统讨论了在花岗质岩浆中挥发相的形成和时空演化、挥发相的组成及其与硅酸盐熔融体的不相溶性，提供了挥发相在夕卡岩型和斑岩型矿床中存在的证据，提出挥发相对花岗质岩体顶部和邻近围岩的微细裂隙、爆破角砾岩、夕卡岩、碱质硅酸盐交代岩和富含挥发份矿物的形成，以及在矿质的迁移富集等各个过程中都具有十分重要的意义。     

含铝硅酸盐1)吉布斯生成自由能的预测及Y.塔达方法向高温条件下推引的可能性

近几年来,Y.塔达等人^[3-7]建立了一种预测化合物吉布斯生成自由能的经验方法。     

Calculation of Si NMR shifts of silicate complexes with carbohydrates, amino acids, and muhicarboxylic acids: potential role in biological silica utilization

The existence of ether or ester-like complexes of silicate with organic compounds has long been debated in the literature on biological utilization of silicon. Comparison of theoretically calculated ²⁹Si NMR chemical shifts for such complexes with experimentally measured values in biological systems could provide a diagnostic tool for identifying which, if any of these molecules exist under physiological conditions. Results are presented here for ab initio molecular orbital calculations of ²⁹Si NMR shifts and formation energies of silicate complexes with polyalcohols, sugar-acids, pyranose sugars, amino acids and multicarboxylic acids. The effects of functional group and molecular structure including ligand size, denticity, ring size, silicon polymerization and coordination number on calculated ²⁹Si shifts were considered. The potential role of such compounds in biological silica utilization pathways is discussed.²⁹Si NMR shifts and energies were calculated at the HF/6-311+G(2d,p)//HF/6-31G* level. The main result is that only five-membered rings containing penta- and hexa-coordinated Si can explain experimentally observed resonances at ∼ −101 and −141 ppm. Further, the heptet observed in ¹H-²⁹Si coupled spectra can only be explained by structures where Si bonds to oxygens atoms in H-C-O-Si linkages with six symmetrically equivalent H atoms.While compounds containing quadra-coordinated silicon may exist in intracellular silicon storage pools within diatoms, calculated reaction energies suggest that the organism has no thermodynamic advantage in taking up extracellular organ-silicate compounds, instead of silicic acid, from the ambient aqueous environment. Hyper-coordinated complexes are deemed unlikely for transport and storage, though they may exist as transient reactive intermediates or activated complexes during enzymatically- catalyzed silica polymerization, as known previously from sol-gel silica synthesis studies.     

Liquid immiscibility in deep-seated magmas and the generation of carbonatite melts

This paper reviews the results of investigations of melt inclusions in minerals of carbonatites and spatially associated silicate rocks genetically related to various deep-seated undersaturated silicate magmas of alkaline ultrabasic, alkaline basic, lamproitic, and kimberlitic compositions. The analysis of this direct genetic information showed that all the deep magmas are inherently enriched in volatile components, the most abundant among which are carbon dioxide, alkalis, halides, sulfur, and phosphorus. The volatiles probably initially served as agents of mantle metasomatism and promoted melting in deep magma sources. The derived magmas became enriched in carbon dioxide, alkalis, and other volatile components owing to the crystallization and fractionation of early high-magnesium minerals and gradually acquired the characteristics of carbonated silicate liquids. When critical compositional parameters were reached, the accumulated volatiles catalyzed immiscibility, the magmas became heterogeneous, and two-phase carbonate-silicate liquid immiscibility occurred at temperatures of ≥1280–1250°C. The immiscibility was accompanied by the partitioning of elements: the major portion of fluid components partitioned together with Ca into the carbonate-salt fraction (parental carbonatite melt), and the silicate melt was correspondingly depleted in these components and became more silicic. After spatial separation, the silicate and carbonate-silicate melts evolved independently during slow cooling. Differentiation and fractionation were characteristic of silicate melts. The carbonatite melts became again heterogeneous within the temperature range from 1200 to 800–600°C and separated into immiscible carbonate-salt fractions of various compositions: alkali-sulfate, alkali-phosphate, alkali-fluoride, alkali-chloride, and Fe-Mg-Ca carbonate. In large scale systems, polyphase silicate-carbonate-salt liquid immiscibility is usually manifested during the slow cooling and prolonged evolution of deeply derived melts in the Earth’s crust. It may lead to the formation of various types of intrusive carbonatites: widespread calcite-dolomite and rare alkali-sulfate, alkali-phosphate, and alkali-halide rocks. The initial alkaline carbonatite melts can retain their compositions enriched in P, S, Cl, and F only at rapid eruption followed by instantaneous quenching.     

LA-ICP-MS微区原位准确分析含水硅酸盐矿物主量和微量元素

通过描述一种利用LA-ICP-MS准确测定含水硅酸盐矿物主量元素和微量元素含量的多外标、无内标分析方法.总结出该方法基于矿物化学计量式计算含水硅酸盐矿物中挥发分的相对含量,再将全部分析元素归一化到总金属氧化物含量(100%减含水量)的原理,利用多种天然成分的岩石标准玻璃(如MPI-DING玻璃和USGS玻璃)作为外标进行校正计算.利用该方法对角闪石、绿帘石、电气石和透闪石等含水硅酸盐矿物进行了分析,并与利用电子探针和微钻(直径300 μm)取样溶液-ICP-MS分析的结果进行了对比研究.研究结果表明:对于组成均一的主量元素的分析结果与电子探针分析数据一致,相对偏差集中在5%以内.除了那些分布异常不均一的元素(在300 μm尺度上),对微量元素的分析结果与溶液-ICP-MS分析结果具有很好的一致性,二者之间的相对偏差大部分集中在10%以内.研究结论为采用归一化校正策略,选择MPI-DING和USGS玻璃作为外标,利用LA-ICP-MS微区分析方法可以准确测定含水硅酸盐矿物中的主、微量元素含量.      

Relationships among Gibbs energies of formation of sulfates,nitrates, carbonates,oxides and aqueous ions

A parameter _GO^2– is defined as the difference between the Gibbs free energy of formation from the elements of a given oxide and its corresponding aqueous cation. The Gibbs free energies of formation of compounds such as sulfates, nitrates or carbonates, from their constituent oxides, are shown to be linear functions of _GO^2– values of their constituent cations.     

The Earth’s tungsten budget during mantle melting and crust formation

During silicate melting on Earth, W is one of the most incompatible trace elements, similar to Th, Ba or U. As W is also moderately siderophile during metal segregation, ratios of W and the lithophile Th and U in silicate rocks have therefore been used to constrain the W abundance of the Earth’s mantle and the Hf-W age of core formation. This study presents high-precision W concentration data obtained by isotope dilution for samples covering important silicate reservoirs on Earth. The data reveal significant fractionations of W from other highly incompatible lithophile elements such as Th, U, and Ta. Many arc lavas exhibit a selective enrichment of W relative to Th, U, and Nb-Ta, reflecting W enrichment in the sub-arc mantle via fluid-like components derived from subducting plates. In contrast, during enrichment by melt-like subduction components, W is generally slightly depleted relative to Th and U, but is still enriched relative to Ta. Hence, all arc rocks and the continental crust exhibit uniformly low Ta/W (ca. 1), whereas W/Th and W/U may show opposite fractionation trends, depending on the role of fluid- and melt-like subduction components. Further high-precision W data for OIBs and MORBs reveal a systematic depletion of W in both rock types relative to other HFSE, resulting in high Ta/W that are complementary to the low Ta/W observed in arc rocks and the continental crust. Similar to previous interpretations based on Nb/U and Ce/Pb systematics, our Ta/W data confirm a depletion of the depleted upper mantle (DM) in fluid mobile elements relative to the primitive mantle (PRIMA). The abundance of W in the depleted upper mantle relative to other immobile and highly incompatible elements such as Nb and Ta is therefore not representative of the bulk silicate Earth. Based on mass balance calculations using Ta-W systematics in the major silicate reservoirs, the W abundance of the Earth’s primitive mantle can be constrained to 12 ppb, resulting in revised ratios of W-U and W-Th of 0.53 and 0.14, respectively. The newly constrained Hf-W ratio of the silicate Earth is 25.8, significantly higher than previously estimated (18.7) and overlaps within error the Hf-W ratio proposed for the Moon (ca. 24.9). The ¹⁸²Hf-¹⁸²W model age for the formation of the Earth’s core that is inferred from the ¹⁸²W abundance and the Hf/W of the silicate Earth is therefore younger than previously calculated, by up to 5 Myrs after solar system formation depending on the accretion models used. The similar Hf/W ratios and ¹⁸²W compositions of the Earth and the silicate Moon suggest a strong link between the Moon forming giant impact and final metal-silicate equilibration on the Earth.     

Non-Newtonian rheology of homogeneous silicate melts

Several observations of non-Newtonian viscosity of silicate liquids at high stress or strain rates have been published in recent years. However, this phenomenon is not well understood yet. In this paper attention is drawn to the fact that steady state logarithmic values of reduced viscosities of silicate liquids under high stress show a linear dependence on the squared value of the applied stress. This relationship suggests that the elastic work done by the stress on the liquid is related to the observed viscosity decreases. It is shown that the development of non-Newtonian viscosity in silicate melts under high stress can be explained with the Adam and Gibbs (1965) theory, if one accepts that this elastic work generates configurational entropy.     

A simple thermodynamic model for estimating the solubility of H2O in magmas

A symmetrical, strictly regular solution model is used to estimate H₂O solubilities in silicate melts. The standard state chemical potential of dissolved H₂O and the adjustable parameter in the activity coefficient are determined by least squares analyses of data on H₂O solubility in silicate melts. The adjustable parameter in the expression for the activity coefficient (In) is a function only of the anhydrous melt composition and eleven values are provided for melts ranging in composition from picrite to rhyolite. At the 95% confidence level, the model should estimate H₂O contents to within 4.8% of the amount present if the amount present is less than 10 wt.%. This compares to the reproducibility of 2.25% of the amount present for experimental determinations. To apply the model to rocks and magmas estimates ofT, P, and the fugacity of H₂O are required.Variation of the H₂O content of the melt changes the activity of other components. Knowledge of this variation removes the requirement that the fugacity of H₂O be estimated. Application of the properties of exact differentials to the Gibbs function for the hydrous melt provides an expression relating the chemical potential of a feldspar component to the H₂O content of the melt. This expression contains a second adjustable parameter which depends on the anhydrous melt composition. Using this second expression, the H₂O content can be estimated ifT, P, and feldspar composition are known. Data are too meagre to evaluate the quantitative success of the second method.     

Solubility of hydrogen and carbon in reduced magmas of the early Earth’s mantle

The solubility of volatile compounds in magmas and the redox state of their mantle source are the main factors that control the transfer of volatile components from the planet’s interior to its surface. In theories of the formation of the Earth, the composition of gases extracted by primary planetary magmas is accounted for by the large-scale melting of the early mantle in the presence of the metallic Fe phase [1, 2]. The fused metallic Fe phase and the melted silicate material experienced gravitational migration that exerted influence upon the formation of the metallic core of the planet. The large-scale melting of the early Earth should have been accompanied by the formation of volatile compounds, whose composition was controlled by the interaction of H and C with silicate and metallic melts, a process that remains largely unknown as of yet.     

硅酸盐体系的化学平衡:(2)反应热力学

通过具体的应用实例,系统介绍了在矿物材料学研究中硅酸盐体系的多相平衡反应热力学的基本原理。对硅酸盐体系的典型多相平衡反应进行了热力学计算,包括:(1)微晶玻璃制备过程中的硅酸盐熔融反应;(2)霞石正长岩和高铝粉煤灰利用技术中的硅酸盐烧结反应;(3)S iO2-CaO-H2O体系和KA lS i3O8-CaO-H2O体系雪硅钙石、硬硅钙石的水热晶化反应;(4)高铝粉煤灰和霞石正长岩烧结产物的溶解反应;(5)Na[A l(OH)4]-A l(OH)3-H2O体系和Na2SO4-Ca(OH)2-H2O体系中α-A l(OH)3和CaSO4.2H2O的析晶反应。研究成果可望对矿物材料制备实验方案设计、工业生产过程优化及改进产品性能提供理论指导,同时为同类材料学研究提供借鉴。     

Relative contributions of silicate and carbonate rocks to riverine Sr fluxes in the headwaters of the Ganges

Exhumation of the Himalayan-Tibetan orogen is implicated in the marked rise in seawater ⁸⁷Sr/⁸⁶Sr ratios since 40 Ma. However both silicate and carbonate rocks in the Himalaya have elevated ⁸⁷Sr/⁸⁶Sr ratios and there is disagreement as to how much of the ⁸⁷Sr flux is derived from silicate weathering. Most previous studies have used element ratios from bedrock to constrain the proportions of silicate- and carbonate-derived Sr in river waters. Here we use arrays of water compositions sampled from the head waters of the Ganges in the Indian and Nepalese Himalaya to constrain the end-member element ratios. The compositions of tributaries draining catchments restricted to a limited range of geological units can be described by two-component mixing of silicate and carbonate-derived components and lie on a plane in multicomponent composition space. Key elemental ratios of the carbonate and silicate components are determined by the intersection of the tributary mixing plane with the planes Na = 0 for carbonate and constant Ca/Na for silicate. The fractions of Sr derived from silicate and carbonate sources are then calculated by mass-balance in Sr-Ca-Mg-Na composition space. Comparison of end-member compositions with bedrock implies that secondary calcite deposition may be important in some catchments and that dissolution of low-Mg trace calcite in silicate rocks may explain discrepancies in Sr-Ca-Na-Mg covariation. Alternatively, composition-dependent precipitation or incongruent dissolution reactions may rotate mixing trends on cation-ratio diagrams. However the calculations are not sensitive to transformations of the compositions by incongruent dissolution or precipitation processes provided that the transformed silicate and carbonate component vectors are constrained. Silicates are calculated to provide ∼50% of the dissolved Sr flux from the head waters of the Ganges assuming that discrepancies between Ca-Mg-Na covariation and the silicate rock compositions arise from addition of trace calcite. If the Ca-Mg-Na mixing plane is rotated by composition-dependent secondary calcite deposition, this estimate would be increased. Moreover, when ⁸⁷Sr/⁸⁶Sr ratios of the Sr inputs are considered, silicate Sr is responsible for 70 ± 16% (1σ) of the ⁸⁷Sr flux forcing changes in seawater Sr-isotopic composition. Since earlier studies predict that silicate weathering generates as little as 20% of the total Sr flux in Himalayan river systems, this study demonstrates that the significance of silicate weathering can be greatly underestimated if the processes that decouple the water cation ratios from those of the source rocks are not properly evaluated.