The main goal of this proposal is a detailed neutron powder diffraction study on La0.5Ba0.5CoO2.8 to refine relaible the crystal and magnetic structure at 100 K under the action of pressure up to 50 kbar. The obtaned result could provide key insights into most probable model explaining the nature of the anti- and ferromagnetic phase separation observed at the border of the spin state and concomitant ferro-antiferromagnetic transition.The combination of this NPD study with XAFS/XMCD-spectroscopy results at the Co K-edge (ESRF,ID24 beamline) will give us an opportunity to analyze the crystal and magnetic structure changes of lattice parameters as well as local atomic and electronic(spin-state change & magnetic moment of cobalt ions) structure distortions near Co ions in order to establish the correlation between local and long-range order of crystal and magnetic structure changes as well as magnetic and transport properties in a wide temperature range.These NPD experiments plan to perform on the high-intensity(!) two-axis D20 diffractometer with reasonably good resolution at the 1.54 Å using the Paris-Edinburg cell at P = 0, 20, 50 kbar upon increasing and decreasing pressure.