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چكيده مقاله: 

American  Mineralogist,  Volume  60, pages  667-674,  1975:‌ A Practical  Two-feldspar  Geothermometer

A geothermometer  based  on the  partitioning  of the  albite  component  between  plagioclase and alkali  feldspar,  such  as  the Barth  thermometer,  is of great  practical  value,  particularly since  the  required  analyses  can  be  made  with simple  optical  or X-ray  techniques.‎  Modern  ther-modynamic  data   for the  alkali  feldspars  in the  form of published  Margules  parameters  are used  to  derive a  simple  expression  relating  the composition  of  coexisting  feldspars  to temperature  and  pressure.‎  For convenience,  a set  of curves  has  been  prepared  using  this  ex- pression.‎  This  expression  has  the   following  advantages  over  previous  two-feldspar  geother- mometers:  It takes  into account  a  significant  pressure  dependence;‎  it uses  a much  better  model of alkali  feldspar  solution  behavior;‎  the  calibration  is based  on abundant  experimental  data for the alkali  feldspar  system;‎  and  it agrees  well with existing  experimental  data  for ternary feldspars  as well as  with naturally  occurring  feldspar  pairs

American Mineralogist, Volume 68, pages 398-413, 1983: Calorimetric investigation of the e~cess entropy of mixing in albite-sanidine solid solutions: lack of evidence for Na,K short-range order and implications for two-feldspar thermometry

Heat capacities (5-380 K) have been measured by adiabatic calorimetry for five highly disordered alkali feldspars (Ab990rJ, Ab850rt5, Ab550r45, Ab250r75, and AbtOr99).‎ Positive heat capacity deviations from a linear combination of the end-member heat capacities, which are present mostly at very low  temperatures, result in an excess entropy for intermediate compositions.‎ The excess entropy at 298.‎15 K is well described by the symmetric expression S~~8 = XAt>XolI0.‎3 ::to.‎3 J/mol.‎ K).‎ For practical calculations, the entropy and enthalpy of mixing can be regarded as temperature-independent above room
temperature.‎ The excess entropy and volume of mixing have been combined with solvus determina- tions to obtain a calculated enthalpy of mixing.‎ Because the measured enthalpies of mixing are essentially coincident with those calculated from the solvus determinations, no short- range order for the alkali site could be inferred.‎ The new data for the alkali feldspars have been combined with recent data for plagioclase feldspars to derive an expression for the two-feldspar thermometer that is consistent with present knowledge of the thermodynamics of these solid solutions.‎ (X(jf)2(18810 + 17030 X~b + 0.‎364P) - (XX1n)2(28230 - 39520 XX1b) TK = {( XP1 )2(2 XPl ) } 10.‎3 (X(jf)2 + 8.‎31431n Ab A;‎ Ab Xi\b where the mole fractions refer to the ternary system and P is in bars.‎ Temperatures calculated from this expression tend to be higher than those calculated from previous formulations.‎

American Mineralogist, Volume 73, pages 201-215,1988: Ternary-feldspar modeling and thermometry

A revised thermodynamic model for ternary feldspars-an extension of the approach of Ghiorso (1984)‎- was made possible by (a) inclusion of volume data for  ternary feldspars and (b) adjustment of the compositions (within analytical error) of some of the experi- mental data points (Seck, 1971 a).‎ The excess free-energy expressions of Newton et al.‎ (1980)‎ are used for the plagioclase binary join and those of Haselton et al.‎ (1983)‎ for alkali feldspar.‎ Excess terms for the An-Or join and for ternary interaction were obtained from Seck's experiments by the method of linear least squares.‎ The new model is consistent
with most occurrences of natural ternary feldspars and with experiments on strongly ter- nary feldspars.‎ Most ternary feldspars have negative excess volumes-an important con- straint on pressure corrections in geothermometry.‎ The activity expressions of this model permit yet another formulation of the two-feld- spar geothermometer that fully takes ternary solution into account;‎ it yields three tem-  peratures, one each for Ab, Or, and An equilibria.‎ Few published analyses offeldspar pairs give concordant temperatures, probably because small errors in composition strongly affect the calculated temperatures.‎ However, if the compositions of coexisting feldspars are al- lowed to vary within expected analytical error, three concordant temperatures can be calculated for feldspar pairs that were close to being in equilibrium.‎ The program presented will also indicate pairs that could not have been in equilibrium.‎ This thermometer is more useful than previous two-feldspar thermometers because it (1)‎ fully accounts for ternary solid solution, (2)‎ indicates whether the two feldspars could have been in equilibrium, and (3)‎ gives further information about how the feldspar compositions may have been changed by such postcrystallization  processes as alkali exchange and subsolidus exsolution.‎ Our thermometer yields temperatures similar to those obtained using the formulation of Has- elton et al.‎ (1983)‎ for pairs of feldspars close to binary compositions, and much more reasonable temperatures for strongly ternary compositions than any previous thermometer.‎

American Mineralogist, Volume 75, pages 544-559, 1990
Ternary feldspar experiments and thermodynamic models

This paper reports the results of 20 experiments in which mixes of two or three feldspars were reacted to produce coexisting plagioclase feldspar (PF) and alkali feldspar (AF).‎ Experiments were carried out over the range 700 to 900 °C and 1 to 3 kbar under water- saturated conditions.‎ The compositions of experimental products were determined using the electron microprobe.‎ Starting materials with similar bulk compositions were prepared using different combinations of two and three minerals, and experiments were designed to produce similar AF and PF minerals in the experimental products from different starting binary and ternary compositions.‎ The coexisting AF and PF compositions produced as products define compositional fields that are elongate parallel to the ternary solvus.‎ In 11 experiments reaction was sufficient to produce fields of coexisting AF and PF, or AF, PF,  and melt with a bulk composition close to that of the starting mixture.‎ In six experiments significant reaction occurred in the form of reaction rim overgrowths on seeds of the starting materials, but a tie line connecting AF and PF products lies on the Ab-rich side of the starting bulk composition.‎ In these six experiments some of the An-rich plagioclase starting material was removed from reaction by overgrowth of reaction rims.‎ Three experiments produced AF, PF, and melt from a natural granite starting material.‎ The experiments probably approached stable or metastable exchange equilibrium with respect to Na-K-Ca, but an equilibrium degree of AI-Si order in the rims was most likely not achieved.‎ A thermodynamic model following the approach developed by Ghiorso (1984)‎ and Fuhrman and Lindsley (1988)‎ is applied to these new experimental results.‎ A two-feldspar thermometer is presented in which temperature is constrained by equilibria among all three components-Albite, Orthoclase, and Anorthite-in coexisting ternary feldspars.‎

American Mineralogist, Volume 89, pages 1496–1504, 2004: New developments in two-feldspar thermometry

To a good approximation, feldspars can be considered asThe thermodynamic model of the two-feldspar thermometer has been revised.‎ From recent enthalpy and volume measurements in the (Na,Ca)- and (K,Ca)-feldspar binaries, new interaction parameters have been derived and previous ones have been updated.‎  Entropy parameters have been fi  tted  to the phase equilibrium data of Seck (1971)‎ and Elkins and Grove (1990)‎.‎ The two data sets could be suitably  combined into one.‎ Ideal Ab, Or, and An activities have been expressed in terms of both the molecular mixing and Al-avoidance models.‎ Two-feldspar pairs  from high-grade metamorphic rocks that cooled slowly under dry conditions suffer from a distinct type of retrograde resetting.‎ Whereas the original An content  in both the plagioclase and the alkali feldspar is preserved because the intercrystalline Ca + Al ↔ (Na,K) + Si diffusion is sluggish, Na and K may be  freely exchanged between phases.‎ Mathematical reversal of the Na-K exchange at constant An yields the temperature at which the two feldspars  originally coexisted.‎ The shifts in Ab and Or contents obtained from the reversal refl  ect the relative plagioclase/alkali feldspar proportions observed in thin  sections.‎ Good agreement between calculated and measured ratios was found for feldspar pairs from Sri Lankan granulites.‎ This observation represents a  successful test of the reliability of the calculated Ab-Or shifts.‎ In contrast to dry metamorphic rocks, similar application of chemical constraints is not  indicated in the case of volcanic rocks.‎ Then the two-feldspar thermometer delivers three, usually incongruent temperatures: T(Ab), T(Or), and T(An).‎ From  the abundance of temperatures, Fuhrman and Lindsley (1988)‎ suggested adjusting compositions within assumed chemical uncertainties (e.g.‎, ±2 mol%) so that congruent temperatures could be obtained.‎ However, the result is not unique.‎ Depending on minute variations in the starting compositions, the   temperatures may vary by several tens of degrees.‎ In addition, temperatures vary to a similar extent depending on the type of search algorithm.‎ Therefore, we  advise users to completely abandon this practice.‎ Instead, a statistical procedure is suggested: Two-feldsparcompositions are randomly generated  according to Gaussian distributions with their means at the observed compositions and standard errors chosen according to the quality of the chemical   analysis.‎ This procedure returns normally distributed temperatures [T(Ab), T(Or), T(An)] together with means and standard deviations.‎ From the overlap of the  three Gaussian curves the question of equilibriumor non-equilibrium crystallization of feldspar pairs may be addressed.‎ 

American Mineralogist, Volume 90, no.‎ 2-3, pages 336–346, 2005: :Igneous thermometers and barometers based on plagioclase + liquid equilibria: Tests of some existing models and new calibrations

Although many formulations of plagioclase + liquid equilibria have been calibrated in the last decade, few models specifically address the issue of temperature (T) prediction.‎ Moreover, for those that do, T error is not addressed, greatly limiting their use as geothermometers.‎ Several recent models of plagioclase-liquid equilibria are thus tested for their ability to recover T from their calibration data, and predict T from experiments not used for calibration.‎ The models of Sugawara (2001)‎ and Ghiorso et al.‎ (1995, 2002)‎ outperform earlier calibrations.‎ These models perform reasonably well at T > ۱۱۰۰ °C, though recovery and prediction of T is less precise for hydrous compositions.‎ In addition, these models cannot be integrated with geo-hygrometers, or other mineral-melt thermometers and barometers;‎ the following expression predicts T with up to 40% greater precision:

Formula(۱)

Because these thermometers are pressure (P) sensitive, a temperature-sensitive barometer was also developed

Formula(۲)

In these models, T is in Kelvins and P is in kbar.‎ Anpl and Abpl are the fractions of anorthite and albite in plagioclase, calculated as cation fractions: An = CaO/(CaO + NaO۰.۵ + KO۰.۵) and Ab = NaO۰.۵/(CaO+NaO۰.۵+KO۰.۵). Terms such as Alliq refer to the anhydrous cation fraction of Al in the liquid;‎ H۲O in Equation 1 is in units of wt%.‎ Errors on these models are comparable to those for clinopyroxene thermobarometers: In Equation 1, R = ۰.۹۹ and the standard error of estimate (SEE) is 23 K;‎ for Equation 2, R = ۰.۹۴ and the SEE is 1.‎8 kbar.‎ The models successfully recover mean pressures for experimental data that are not used for calibration, and are furthermore able to recover near-1-atm P estimates for volcanic rocks from Kilauea, Hawaii, which are thought to have crystallized at or very near Earth’s surface.‎


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