New approaches to strain and elasticity

In the context of the project essentially 3 problem areas were examined, which stand all in a certain connection: elastic behaviour of crystals under extremely high pressures sound propagation in crystals with seismic frequencies influence of microstructures on the macroscopic behavior of crystals These phenomena play a large role inside our earth, where very high temperatures and pressures prevail. It is therefore important to know the elastic behavior of crystals also with very high pressures. We could for the first time set up a model with which one can compute the lattice constants and the elastic constants of arbitrary crystals as a function of pressure. A comparison with X-ray measurements of different minerals in a diamond anvil cell resulted in outstanding agreement between theory and experiment. More than 60 % of our earth consists of minerals with a so-called perovskite structure. On the other hand seismic measurements mainly contribute to our understanding of the physical behavior of our earth. The seismic waves are usually with frequencies of some cycles per second. We measured therefore minerals with perovskite structure with low frequencies, and gained important results for the elastic behavior of minerals at seismic frequencies and different temperatures. In the process of the project we studied among other things a mineral, which is strongly discussed in the geophysical community: Lawsonit is a mineral, which contains 11% water and is stable up to high pressure and temperature. The crystals occur mainly within ranges of the subduction zones, where the continental plates dive deeply into the Earth`s mantle. Lawsonite is thus considered to be a potential candidate for carrying water down into the mantle at subduction zones thereby contributing to the large water circulation of our earth. We examined the phase transition behavior of Lawsonite crystals and found substantial results about the influence of the water molecules on the structural changes with temperature. The results of the project cover ranges of geology, geophysics and mineralogy and surely contribute to a better understanding of the physical properties of our earth.