Excess heat capacity of low structural state feldspars

The low- and high temperature heat capacities of low structural state plagioclases and alkali feldspars will be measured. From these measurements, the entropy-composition behaviour of these important mineral systems will be derived improving the thermodynamic description of feldspars. The applicant has already in his possession natural plagioclases and synthetic alkali feldspars. They are well prepared and characterised. Furthermore, the physical nature of the excess heat capacity, i.e., the deviation of the vibrational behaviour of the atoms in a solid solution from that in a mechanical mixture, will be investigated. Benisek and Dachs (2010) provided an approach for this task, which will be tested against the new measurements. The heat capacity of alkali feldspars with a fully ordered Al/Si distribution will be calculated, using density functional theory based computer programs, delivering more details on the excess vibrational behaviour in solid solutions.

The most important results of this project come from the investigations and explanations of the vibrational behaviour of the atoms in solid solutions. The frequencies of the atomic vibrations are often strongly affected by the solid-solution process giving rise to excess vibrational entropies, which are deviations of the vibrational entropy from ideal behaviour. They stabilise (if positive) or destabilise (if negative) these materials and thus play an important role for phase-stability calculations. The vibrational entropies of some solid- solution series were investigated experimentally and by quantum-mechanical calculations. These investigations contributed to the understanding of the vibrational entropy from a macroscopic point of view but also towards an atomic-level understanding. It could be shown that the differences of elasticity of the components building the solid solution are responsible for generating positive or negative deviations from ideal vibrational behaviour. An empirical equation for estimating the excess vibrational entropy, established in a preliminary project, was improved in the course of this project. It can now be applied to several classes of materials, i.e., silicates, chlorides, and metallic alloys. We examined the vibrational entropies of the alkali feldspars, plagioclases, garnets and chlorides as well as silver-palladium, platinum-rhodium, copper-zinc, and copper-gold solid solutions. These investigations brought not only insight into the physics of the vibrational behaviour of the atoms in solid solutions, but they also improved the thermodynamic description of these materials significantly. Beside the research on solid solutions, the determination of the standard entropy of different mineral end-members contributed also to the improvement of the thermodynamic data basis. The investigations on stishovite, dmitryivanovite, TiO2II, starkeyite, almandine, grossular und hydrogrossular are to be mentioned in this context. In addition to the goals of the project, an experimental method for determining the configurational entropy (coming from the disorder of the atomic distribution) was developed by comparing calorimetrically based data with data from phase-equilibrium experiments. The differences could be used to extract the configurational entropy of some solid solutions.