Configurational thermodynamics of aluminous pyroxenes: A generalized pair approximation     

Ronald E. Cohen 《Physics and Chemistry of Minerals》1986,13(3):183-197

A pair approximation is used to estimate the effects of short-range order on the thermodynamic properties of aluminous clinopyroxenes on the joins diopside (CaMg-Si₂O₆)-jadeite (NaAlSi₂O₆) and diopside-CaTs (CaAl₂SiO₆). The generalized pair approximation is the simplest model for concentrated solutions which includes short-range order. Short-range order is expected to be especially significant in coupled solid solutions, such as aluminous pyroxenes, since atoms of different valence substitute for each other. The calculations show that the random model, in which the configurational entropy is calculated as if atoms on each crystallographic site mix randomly, is appropriate as a first approximation. The excess entropy relative to the random model behaves regularly, is always negative, and becomes more negative as temperature decreases or the ordering energies increase. The excess entropy relative to the random model can be modeled reasonably well with a simple power series, or Margules-type, formulation. In contrast, the excess entropy relative to a molecular model, in which the ideal activity is assumed to be equal to some mole fraction, is irregular, can be positive or negative, and even changes in sign with variations in temperature and composition. The configurational enthalpy is positive at high temperatures, and becomes negative with decreasing temperature or increasing ordering energy. The mixing enthalpy can have non-configurational contributions, in addition to the effective short-range configurational contributions considered explicitly. The pair approximation predicts an ordering transition from C2/c to P2₁/n for CaTs and diopside-CaTs solutions at moderate to low temperatures, respectively. A field where C2/c orders to C2 is also found. A higher order approximation, different relative ordering energies, or quantitative consideration of strain contributions is required to account for the C2/c to P2/n transition in omphacites. There is no justification for molecular models, in which the configurational entropy is calculated as if endmember “molecules” were mixing in the crystal, in either concentrated or dilute solutions. Molecular models do not represent limiting ordered states for coupled solid solutions.  相似文献   

Calorimetric determination of the enthalpy of Mg-Fe ordering in orthopyroxene     

L. Cemič  W. Kähler 《Physics and Chemistry of Minerals》2000,27(3):220-224

The enthalpy of Mg-Fe ordering in En₅₀Fs₅₀ orthopyroxene was measured using the transposed temperature drop calorimetric method. Heat effects associated with two consecutive drops were recorded. In the first drop, synthetic orthopyroxene samples equilibrated at 823?K, 0.1?MPa and a f?O₂ of the WI buffer were dropped from 823?K into the calorimeter, which was held at 1173?K. The measured heat effect corresponds to the enthalpy change due to the heat capacity of the sample from 823 to 1173?K and to the enthalpy associated with the (dis)ordering of Mg and Fe²⁺. In the second drop, the samples, with an Fe-Mg order corresponding to 1173?K, were dropped again from 823 to 1173?K. From the difference of the heat effects measured in the two experiments, the enthalpy of disordering associated with the temperature change from 823 to 1173?K was calculated to be ?1.73±0.04 J mol^?1. The observed enthalpy corresponds to a change in the mole fraction of iron on the M2 site, ΔX _Fe,M2=?0.096 ± 0.001, which leads to of ΔH ⁰ _exch of 18.0 ± 0.4 kJ mol^?1 for the exchange reaction: The degree of Fe-Mg order was characterized by ⁵⁷Fe Mössbauer resonance spectroscopy. In order to minimize the error due to the thickness of the absorber, the iron concentration of the absorber was reduced step by step from 5 to 1 mg?Fe?cm^?2. The iron distribution extrapolated to zero thickness was used for the calculations of the enthalpy of exchange reaction.  相似文献   

A computational study of Al/Si ordering in cordierite     

S. Thayaparam  V. Heine  M. T. Dove  K. D. Hammonds 《Physics and Chemistry of Minerals》1996,23(2):127-139

The ordering of Al and Si in Mg cordierite Mg₂Al₄Si₅O₁₈ is considered using computer simulation. First the enthalpy of interaction J _ij between sites is derived by computer modelling 101 different Al/Si configurations and analysing their energies. They are compared with similar results for three other minerals and with ab initio calculations to assess the whole approach. Secondly the ordering process is studied using Monte Carlo simulation applied to the J _ij . The ordering phase transition temperature T _c is found as 1800°C in reasonable agreement with the experimental estimate of 1450° C. These are much lower than the estimate T _c(ABW)≈7600°C obtained from Bragg-Williams theory. Strong short-range order sets in below T _c(ABW), and the reasons for much lower temperature T _c of long-range ordering are discussed. Strong short-range also sets in very rapidly in a simulated anneal, in agreement with experiment. Thirdly an attempt is made to compare our calculated enthalpies directly with the results of NMR and calorimetry experiments, not completely successfully. A free energy ΔG≈4.6 eV for the activation barrier for ordering is suggested.  相似文献   

Energetics of water dissolution in trachyte glasses and liquids     

Pascal Richet  Guy Hovis  Jacques Roux 《Geochimica et cosmochimica acta》2004,68(24):5151-5158

Enthalpies of dissolution in HF solutions have been measured at 323 K for a series of hydrous trachyte glasses. Enthalpies of mixing between water and molten trachyte have then been calculated from heat capacity data for the same set of samples and available enthalpy for pure water. The moderately negative enthalpies of mixing suggested at 1 bar by the measurements made on glasses almost disappear when trachyte liquids and water are referred to the same temperature, and particularly so when enthalpies of mixing are calculated for a few kbars pressure. As found for albite and phonolite liquids, trachyte melts thus appear to mix nearly ideally as far as enthalpy is concerned. These results imply that the enthalpy of exsolution of water from magmas is very small or negligible under the P-T-X conditions relevant to trachytic volcanism, even for complete degassing of up to 5 wt% H₂O. Furthermore, the viscosity increase associated with exsolution-driven cooling is negligible compared to the decrease caused directly by water exsolution.  相似文献   

Thermochemistry of glasses and liquids in the systems CaMgSi₂O₆-CaAl₂Si₂O₈-NaAlSi₃O₈, SiO₂-CaAl₂Si₂O₈-NaAlSi₃O₈ and SiO₂-Al₂O₃-CaO-Na₂O     

A. Navrotsky  R. Hon  D.F. Weill  D.J. Henry 《Geochimica et cosmochimica acta》1980,44(10):1409-1423

Enthalpies of solution in 2PbO· B₂O₃ at 712°C have been measured for glasses in the systems albite anorthite diopside, NaAlO₂-SiO₂, Ca_0.5AlO₂-SiO₂ and albite-anorthite-quartz. The systems albite-anorthite and diopside-anorthite show substantial negative enthalpies of mixing, albite-diopside shows significant positive heats of mixing. For compositions up to NaAlO₂ = 0.42 (which includes the subsystem albite-silica) the system NaAlO₂-SiO₂ shows essentially zero heats of mixing. A negative ternary excess heat of mixing is found in the plagioclase-rich portion of the albite-anorthite-diopside system. The join Si₄O₈-CaAl₂Si₂O₈ shows small but significant heats of mixing. In albite-anorthite-quartz. ternary glasses, the ternary excess enthalpy of mixing is positive.Based on available heat capacity data and appropriate consideration of the glass transition, the enthalpy of the crystal-glass transition (vitrification) is a serious underestimate of the enthalpy of the crystal-liquid transition (fusion) especially when the melting point, T_f, is many hundreds of degrees higher than the glass transition temperature, T_g. On the other hand, the same heat capacity data suggest that the enthalpies of mixing in albite-anorthite-diopside liquids are calculated to be quite similar to those in the glasses. The enthalpies of mixing observed in general support the structural models proposed by Taylor and Brown (1979a, b) and others for the structure of aluminosilicate glasses.  相似文献   

Computing Lippmann Diagrams from Direct Calculation of Mixing Properties of Solid Solutions: Application to the Barite-Celestite System     

M. Prieto  A. Fernández-González  U. Becker  A. Putnis 《Aquatic Geochemistry》2000,6(2):133-146

The Lippmann diagram for the system(Ba, Sr)SO₄-H₂O was computed at 25 °Cby determining the solid-phase activity coefficientsfrom first principles calculations. Directcalculations of the mixing properties of thebarite-celestite series indicate this solid solutionbehaves as non-ideal and non-regular. At 25 °C,the enthalpy of mixing shows a minimum around 50 mole% SrSO₄ due to an ordering tendency. Thefree energy of mixing shows two minima that delimit awide and symmetric miscibility gap (from 2.1 to 97.9 mole% SrSO₄) at this temperature. The excessfree energy of mixing requires a Guggenheim expansionseries of 5 terms to be described, where the termswith odd exponents are null as a consequence of thesymmetric distribution of the mixing properties withcomposition. The Lippmann diagram shows a peritecticpoint that corresponds to the composition of an aqueoussolution which is simultaneously at equilibrium withthe two extremes of the miscibility gap. The largedifference between the solubility products of theendmembers involves a strong preferential partitioningof the less soluble endmember towards the solid phase,which explains the extremely Ba-poor composition ofthe aqueous solution (aqueous activity fraction forBa²⁺ = 0.000446 ) at the peritectic point.  相似文献   

Monte Carlo simulation of mixing in Ca3Fe2Ge3O12–Ca4Ge4O12 garnets and implications for the thermodynamic stability of pyrope–majorite solid solution     

Victor L. Vinograd  Bjoern Winkler  Daniel J. Wilson  Andrew Putnis  Julian D. Gale 《Physics and Chemistry of Minerals》2006,33(8-9):533-544

Static lattice energy calculations, based on empirical pair potentials, were performed for a large set of structures differing in the arrangement of octahedral cations within the garnet 2 × 2 × 2 supercell. The compositions of these structures varied between Ca₃Fe₂Ge₃O₁₂ and Ca₄Ge₄O₁₂. The energies were cluster expanded using pair and quaternary terms. The derived ordering constants were used to constrain Monte Carlo simulations of temperature-dependent mixing properties in the ranges of 1,073–3,673 K and 0–10 GPa. The free energies of mixing were calculated using the method of thermodynamic integration. The calculations predict a wide miscibility gap between Fe-rich (cubic) and Fe-pure (tetragonal) garnets consistent with recent experimental observations of Iezzi et al. (Phys Chem Miner 32:197–207, 2005). It is shown that the miscibility gap arises due to a very strong cation ordering at the Fe-pure composition, driven by the charge difference between Ca²⁺ and Ge⁴⁺ cations. The structural and thermodynamic analogies between Ca–Ge and Mg–Si systems suggest that a similar miscibility gap should exist between pyrope and Mg–Si-majorite.  相似文献   

Alternative solution model for the ternary carbonate system CaCO3 - MgCO3 - FeCO3     

Peter L. McSwiggen 《Physics and Chemistry of Minerals》1993,20(1):33-41

The minerals of the ternary carbonate system CaCO₃ - MgCO₃ - FeCO₃ represent a complex series of solid solutions and ordering states. An understanding of those complexities requires a solution model that can both duplicate the subsolidus phase relationships and generate correct values for the activities. Such a solution model must account for the changes in the total energy of the system resulting from a change in the ordering state of the individual constituents. Various ordering models have been applied to binary carbonate systems, but no attempts have previously been made to model the ordering in the ternary system. This study derives a new set of equations that allow for the equilibrium degree of order to be calculated for a system involving three cations mixing on two sites, as in the case of the ternary carbonates. The method is based on the Bragg-Williams approach. From the degree of order, the mole fractions of the three cations in each of the two sites can be determined. Once the site occupancies have been established, a Margules-type mixing model can be used to determine the free energy of mixing in the solid solution and therefore the activities of the various components.  相似文献   

Enthalpies of ordering in the plagioclase feldspar solid solution     

M.A. Carpenter  J.D.C. McConnell  A. Navrotsky 《Geochimica et cosmochimica acta》1985,49(4):947-966

Enthalpies of solution in lead borate at ~700°C have been measured for 36 natural and heat treated plagioclase feldspars. The samples made up two series, as characterised by TEM and XRD. A “low” series contained the natural ordered material and a “high” series the same samples annealed at high temperatures to induce cation disorder. Enthalpy of solution differences between the two series give the enthalpy changes associated with the disordering reactions: low albite → high albite: ~3 kcal/mole “e” structure → Cī high albite structure: ~ 1.4-2.8 kcal/mole Il? structure →- Cl? high albite structure: ~0.7-1.9 kcal/mole Il? structure equilibrated at low temperature → Il? structure equilibrated at high temperature: ~ 1.8?0.8 kcal/mole.ΔH_soln data for the high series overlap with the data of Newtonet al. (1980) for synthetic high structural state plagioclases except in the composition range ~An₉₀–An₁₀₀. They are consistent with an interpretation of the solid solution as being composed, at high temperatures, of two ideal (zero heat of mixing) segments, one with Cl? symmetry and one with Il symmetry, and having a non-first order (continuous) order/disorder transformation between them. The low series can also be separated into two distinct trends, for Il? and “e” structures.Values of the enthalpy change due to disordering (ΔH_ord) also show a number of systematic trends. Firstly, the values for e → Cl? are larger than for Il? → Cl? in the composition range where both e and Il? structures are observed (~An₆₅-An₇₂). Secondly, the enthalpy change on disordering the most ordered e structures at An-rich compositions is larger than for Ab-rich e structures. The apparent change in ΔH_ord, which occurs at ~An₅₀, may be important for the origin of the Bøggild miscibility gap. Thirdly, the large enthalpy change of the e structure, due to ordering, may be sufficient to stabilise it relative even to a mixture of low albite plus anorthite. Values for the enthalpy change on disordering Il? anorthites and bytownites to a Cl? structure have been estimated by assuming that the Cl? solid solution is ideal (non-enthalpic) and then extrapolating a straight line through the data for Ab-rich compositions to pure anorthite.  相似文献   

Equilibrium thermodynamics of Al/Si ordering in anorthite     

M. A. Carpenter 《Physics and Chemistry of Minerals》1992,19(1):1-24

Variations in the equilibrium degree of Al/Si order in anorthite have been investigated experimentally over the temperature range 800-1535° C. Spontaneous strain measurements give the temperature dependence of the macroscopic order parameter, Q, defined with respect to the \(C\bar 1 \rightleftharpoons I\bar 1\) phase transition, while high temperature solution calorimetric data allow the relationship between Q and excess enthalpy, H, to be determined. The thermodynamic behaviour can be described by a Landau expansion in one order parameter if the transition is first order in character, with an equilibrium transition temperature, T _tr, of ～2595 K and a jump in Q from 0 to ～0.65 at T_tr. The coefficients in this Landau expansion have been allowed to vary with composition, using Q=1 at 0 K for pure anorthite as a reference point for the order parameter. Published data for H and Q at different compositions allow the calibration of the additional parameters such that the free energy due to the \(C\bar 1 \rightleftharpoons I\bar 1\) transition in anorthite-rich plagioclase feldspars may be expressed (in cal. mole^-1) as: \(\begin{gathered}G = \tfrac{1}{2} \cdot 9(T - 2283 + 2525X_{Ab} )Q^2 \\ {\text{ + }}\tfrac{1}{4}( - 26642 + 121100X_{Ab} )Q^4 \\ {\text{ + }}\tfrac{1}{6}(47395 - 98663X_{Ab} )Q^6 \\ \end{gathered}\) where X _Ab is the mole fraction of albite component. The nature of the transition changes from first order in pure anorthite through tricritical at ～An₇₈ to second order, with increasing albite content. The magnitude of the free energy of \()\) ordering reduces markedly as X _Ab increases. At ～700° C incommensurate ordering in crystals with compositions ～An₅₀–An₇₀ needs to have an associated free energy reduction of only a few hundred calories to provide a more stable structure. These results, together with a simple mixing model for the disordered ( \()\) ) solid solution, an assumed tricritical model for the incommensurate ordering and published data for ordering in albite have been used to calculate a set of possible free energy relations for the plagioclase system. The incommensurate structure should appear on the equilibrium phase diagram, but its apparent stability with respect to the assemblage albite plus anorthite at low temperatures depends on the values assigned to the mixing parameters of the $$$$ solid solution.  相似文献   

Refinements in a site-mixing model for illites: local electrostatic balance and the quasi-chemical approximation     

Ronald K. Stoessell 《Geochimica et cosmochimica acta》1981,45(10):1733-1741

A quasi-chemical model for illites has been derived, and local electrostatic balance has been added to a random regular solution site-mixing model for illites (Stoessell, 1979). Each model assumes similar order-disorder conditions for both the end-members micas and the solid solution. Thermodynamic properties of illites predicted by the random, electrostatic, and quasi-chemical models are compared as a function of composition. For natural illite compositions, molar entropies of mixing in the electrostatic model are about 1 entropy unit less than those in the random model. Intermediate values are given by the quasi-chemical model. Each model predicts an increased entropy of mixing in dominantly trioctahedral illites as compared to dioctahedral illites. Each model also predicts destabilization of trioctahedral illites using absolute molar exchange energies greater than 2 RT/Z_x, where Z_x is the number of adjacent cation interactions per site in the Xth site class. The most negative free energies of mixing are predicted by the quasi-chemical model. Intermediate values predicted by the random model are apparently the result of error cancellation due to overestimation of both the entropy and enthalpy of mixing.  相似文献   

Atomistic model of diopside-K-jadeite (CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>-KAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>) solid solution     

V. L. Vinograd  O. G. Safonov  D. J. Wilson  L. L. Perchuk  L. Bindi  J. D. Gale  B. Winkler 《Petrology》2010,18(4):447-459

Atomistic model was proposed to describe the thermodynamics of mixing in the diopside-K-jadeite solid solution (CaMgSi₂O6-KAlSi₂O₆). The simulations were based on minimization of the lattice energies of 800 structures within a 2 × 2 × 4 supercell of C2/c diopside with the compositions between CaMgSi₂O₆ and KAlSi₂O₆ and with variable degrees of order/disorder in the arrangement of Ca/K cations in M2 site and Mg/Al in Ml site. The energy minimization was performed with the help of a force-field model. The results of the calculations were used to define a generalized Ising model, which included 37 pair interaction parameters. Isotherms of the enthalpy of mixing within the range of 273–2023 K were calculated with a Monte Carlo algorithm, while the Gibbs free energies of mixing were obtained by thermodynamic integration of the enthalpies of mixing. The calculated T-X diagram for the system CaMgSi₂O₆-KAlSi₂O₆ at temperatures below 1000 K shows several miscibility gaps, which are separated by intervals of stability of intermediate ordered compounds. At temperatures above 1000 K a homogeneous solid solution is formed. The standard thermodynamic properties of K-jadeite (KAlSi₂O₆) evaluated from quantum mechanical calculations were used to determine location of several mineral reactions with the participation of the diopside-K-jadeite solid solution. The results of the simulations suggest that the low content of KalSi₂O₆ in natural clinopyroxenes is not related to crystal chemical factors preventing isomorphism, but is determined by relatively high standard enthalpy of this end member.  相似文献   

Enthalpy effects associated with Al/Si ordering in anhydrous Mg-cordierite     

Michael A Carpenter  Andrew Putnis  Alexandra Navrotsky  J.Desmond C McConnell 《Geochimica et cosmochimica acta》1983,47(5):899-906

Measurements of the heats of solution (ΔH_soln) in molten Pb₂B₂O₅ at 708°C of anhydrous magnesian cordierites, prepared with a range of structural states, show that the enthalpy effect associated with Al/Si ordering is substantial (? 9.76 ± 1.56 kcal mole^?1). Differences in the state of order between synthetic cordierites used in phase equilibrium studies and cordierites in the natural environment could lead to significant errors in the estimation of palaeo-pressures and temperatures. A continuous change of ΔH_soln with annealing time supports the suggestion of putnis (1980) that the hexagonal → orthorhombic transformation in cordierite, which can occur via a modulated structure, is truly continuous under metastable conditions. In addition, a linear relation between ΔH_soln and the logarithm of annealing time has been found, which provides some insight into the nature of the ordering mechanisms at an atomic level. Al and Si exchanges occur continuously between neighbouring tetrahedral sites with a net drift towards increasing order. No kinetic or thermochemical distinction can be made between the development of long range and short range order.The enthalpy of vitrification (~ 12 kcal mole^?1) for a metastable stuffed β-quartz polymorph of cordierite composition is similar to that for pure quartz (on a per two oxygen basis), while the heat of vitrification for even the most disordered cordierite seen in this study is more than a factor of three greater (~40 kcal mole^?1). This is consistent with the view that cordierite glass resembles the quartz structure more closely than the crystalline cordierite structure, and that crystallisation of the glass below ~900°C is controlled by a tetrahedral framework.  相似文献   

Constraints on the thermodynamic mixing properties of plagioclase feldspars     

Michael A. Carpenter  John M. Ferry 《Contributions to Mineralogy and Petrology》1984,87(2):138-148

Taking account of the Cˉ1/Iˉ1 (Al/Si order/disorder) transformation at high temperatures in the albite-anorthite solid solution leads to a simple model for the mixing properties of the high structural state plagioclase feldspars. The disordered (Cˉ1) solid solution can be treated as ideal (constant activity coefficient) and, for anorthite-rich compositions, deviations from ideality can be ascribed to cation ordering. Values of the activity coefficient for anorthite in the Cˉ1 solid solution (γ _An ^Cˉ1 ) are then controlled by the free energy difference between Cˉ1 and Iˉ1 anorthite at the temperature (T) of interest according to the relation: ΔˉG _ord ^Iˉ1 ⇌Cˉ1 =RT ln γ _An ^Cˉ1 . If the Iˉ1⇌Cˉ1 transformation in pure anorthite is treated, to a first approximation, as first order and the enthalpy and entropy of ordering are taken as 3.7±0.6 kcal/mole (extrapolated from calorimetric data) and 1.4–2.2 cal/mole (using an equilibrium order/disorder temperature for An₁₀₀ of 2,000–2,250 K), a crude estimate of γ _An ^Cˉ1 for all temperatures can be made. The activity coefficient of albite in the Cˉ1 solid solution (γ _Ab ^Cˉ1 ) can be taken as 1.0. The possible importance of this model lies in its identification of the principal constraints on the mixing properties rather than in the actual values of γ _An ^Cˉ1 and γ _Ab ^Cˉ1 obtained. In particular it is recognised that γ _An ^Cˉ1 depends critically on ordering in anorthite as well as, at lower temperatures, any ordering in the Cˉ1 solid solution. A brief review of activity-composition data, from published experiments involving ranges of plagioclase compositions and from the combined heats of mixing plus Al-avoidance entropy model (Newton et al. 1980), reveals some inconsistencies. The values of γ _An ^Cˉ1 calculated using the approach of Newton et al. (1980), although consistent with Orville's (1972) ion exchange data, are slightly lower than values derived from experiments by Windom and Boettcher (1976) and Goldsmith (1982) or from ion-exchange experiments of Kotel'nikov et al. (1981). Based on the Cˉ1/Iˉ1 transformation model, values of γ _An ^Cˉ1 <1.0 are unlikely. Discrepancies between the experimental data sets are attributed to incomplete (non-equilibrium) Al/Si order attained during the experiments. It is suggested that the choice of activity coefficients remains somewhat subjective. The development of accurate mixing models would be greatly assisted by better thermodynamic data for ordering in pure anorthite and by more thorough characterisation of the state of order in plagioclase crystals used for phase equilibrium experiments.  相似文献   

Thermodynamics of open networks: Ordering and entropy in NaAlSiO4 glass,liquid, and polymorphs     

Pascal Richet  Richard A. Robie  Jacques Rogez  Bruce S. Hemingway  Philippe Courtial  Christophe Téqui 《Physics and Chemistry of Minerals》1990,17(5):385-394

The thermodynamic properties of carnegieite and NaAlSiO₄ glass and liquid have been investigated through C _p determinations from 10 to 1800 K and solution-calorimetry measurements. The relative entropies S ₂₉₈-S₀ of carnegieite and NaAlSiO₄ glass are 118.7 and 124.8 J/mol K, respectively. The low-high carnegieite transition has been observed at 966 K with an enthalpy of transition of 8.1±0.3 kJ/mol, and the enthalpy of fusion of carnegieite at the congruent melting point of 1799 K is 21.7±3 kJ/mol. These results are consistent with the reported temperature of the nepheline-carnegieite transition and available thermodynamic data for nepheline. The entropy of quenched NaAlSiO₄ glass at 0 K is 9.7±2 J/mol K and indicates considerable ordering among AlO₄ and SiO₄ tetrahedra. In the liquid state, progressive, temperature-induced Si, Al disordering could account for the high configurational heat capacity. Finally, the differences between the entropies and heat capacities of nepheline and carnegieite do not seem to conform to current polyhedral modeling of these properties  相似文献   

Calorimetric study of olivine solid solutions in the system Mg2SiO4-Fe2SiO4     

H. Kojitani  M. Akaogi 《Physics and Chemistry of Minerals》1994,20(8):536-540

Solution enthalpies of synthetic olivine solid solutions in the system Mg₂SiO₄-Fe₂SiO₄ have been measured in molten 2PbO·B₂O₃ at 979 K. The enthalpy data show that olivine solid solutions have a positive enthalpy of mixing and the deviation from ideality is approximated as symmetric with respect to composition, in contrast to the previous study. Applying the symmetric regular solution model to the present enthalpy data, the interaction parameter of ethalpy (W_H) is estimated to be 5.3±1.7 kJ/mol (one cation site basis). Using this W_h and the published data on excess free energy of mixing, the nonideal parameter of entropy (W_s) of olivine solid solutions is estimated as 0.6±1.5 J/mol·K.  相似文献   

Precipitation and mixing properties of the “disordered” (Mn,Ca)CO₃ solid solution     

Dionisis Katsikopoulos  Ángeles Fernández-González  Manuel Prieto 《Geochimica et cosmochimica acta》2009,73(20):6147-455

The enthalpy of mixing of the calcite-rhodochrosite (Ca,Mn)CO₃ solid solution was determined at 25 °C from calorimetric measurements of the enthalpy of precipitation of solids with different compositions. A detailed study of the broadening of powder X-ray diffraction peaks shows that most of the precipitates are compositionally homogeneous. All the experimental enthalpy of mixing (ΔH^m) values are positive and fit reasonably well (R² = 0.86) to a Guggenheim function of three terms: