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The combination of high-pressure X-ray diffraction experiments (HPXRD) on the one hand and ab-initio calculations of the structural parameters as a function of the crystalline volume on the other hand, is a powerful instrument for investigating the structural stability of crystalline materials. One reason for the increased interest in such kind of studies is a continued advancement of the experimental as well as of the theoretical possibilities. The progress concerning HPXRD experiments has mainly been due to the development of new designs of diamond anvil pressure cells (DAC), two dimensional X-ray-detectors and the use of powerful X-ray generators or synchrotron radiation. The improvement of theoretical calculations of the structural stability has been enabled by the increasing computational possibilities, which allow calculations of the total energy, the interatomic forces and stresses from first principles (based on ab-initio calculations of the electronic bandstructure). This makes it possible - to calculate the variation of the structural parameters as a function of the external pressure from first principles and to compare it with the experiment - to find hints at (or even to predict) possible pressure-induced structural transitions - and to analyse experimentally observed structural transitions or other instabilities like for instance an anomalous compressibility behaviour. Since the calculations are based on electronic bandstructure calculations it is possible to analyse the involvement of the electrons in such pressure-induced structural instabilities. The main aim of the present project can be summarised in two points: (1) Establishing a HPXRD facility using diamond anvil pressure cells at the Institute for Applied and Technical Physics of the Vienna University of Technology (TU Vienna). The main component of this facility is a rotating anode X-ray generator, equipped with a 2D wire detector. The purpose of the FWF application is to get financial support for equipment and material, which is necessary for adapting the existing facility so that it is possible to perform HPXRD experiments. A diamond anvil high-pressure cell is available from the FWF project P- 1158 1 - PHY (project leader : E.Gratz). (2) Performing HPXRD experiments and ab-initio calculations for investigating the structural stability of selected intermetallic compounds under pressure. The HPXRD experiments will be performed at the above mentioned facility and also at synchrotron sources (DESY, ESRF). The abinitio calculations will be performed using the program package VASP, which has been developed by the group of Prof. J. Hafner (University of Vienna). Furthermore we also plan the continuation of low and high temperature X-ray diffraction studies for investigating the structural stability with respect to temperature induced effects, like e.g. magnetoelastic effects in compounds with rare earth elements.