Improvement of two-feldspar thermometry

As a result of this project, it will be possible to generate for the first time a complete thermodynamic data set based on measured interaction parameters for the Na-K-Ca-feldspars. For that purpose, the entropic interaction parameters for the Na-Ca-, K-Ca-, and ternary feldspars have to be determined. We will measure, therefore, the heat capacities between 5 K and 1000 K of the end-members and members of the solid solutions to derive the entropies at different temperatures. The applicant has already in his possession synthetic Na-Ca- and K-Ca- feldspars that will be used for the planned study. In addition, ternary feldspars will be prepared from these two binary series. The determined entropy of mixing data, together with recently published enthalpy, configurational entropy and volume data will then be used to formulate a new two-feldspar-thermometer. This thermometer will be checked by a new test and, when necessary, the interaction parameters which are less reliable will be recalibrated. This will significantly improve the thermodynamic mixing model of the ternary feldspars.

The main goal of this project was to improve the thermodynamic description of feldspars with disordered Al/Si distribution (high-temperature feldspars). This was not only important for two-feldspar geothermometry, but an improved thermodynamic description of feldspars is important for many research fields in general, because feldspars are the most abundant minerals in the Earth`s crust. Natural feldspars often form solid solutions (Na-, K-, Ca-feldspar) making a proper description of their mixing properties necessary. This is accomplished by investigating the thermodynamic quantities enthalpy, entropy and volume as a function of composition. Whereas the enthalpy- and volume-composition behaviour of feldspars was already known from the literature, this was not the case for the entropy-composition behaviour. This gap was closed in thermodynamic data sets by fitting data from phase-equilibrium experiments, which were, however, suspected to represent non-equilibrium states. The aim of this project was, therefore, to determine the entropy-composition behaviour of Al/Si disordered feldspars directly by calorimetric measurements. Recently, a PPMS (Physical Properties Measurement System of Quantum Design) has been established by E. Dachs at the University of Salzburg. The PPMS enables the measurement of low temperature heat capacities on milligram-sized samples and consequently the determination of entropies. The results of the measurements on Na-Ca-, K-Ca-, and ternary feldspars allowed the deduction of a mixing model, which was based exclusively on calorimetric and volumetric data. It was found that the new model describes feldspars more reliably than those that are based on phase equilibrium experiments. The new model largely eliminates discrepancies between observed and predicted feldspar compositions that were present in earlier attempts. In the course of this project, further improvements were achieved in the experimental methodology using the PPMS. The uncertainties of PPMS data measured on powdered samples could be reduced and the calculation of the uncertainties improved. Furthermore, the work done in this project sheds new light on the physical nature of the excess entropy of mixing, i.e., the deviation of the entropy of mixing from ideal thermodynamic behaviour. We were able to relate the excess entropy of mixing to the difference in end-member volumes and end-member bulk moduli, a new approach allowing to predict the excess entropy behaviour of solid solutions.