In this article we study the effects of a partial substitution of Ba with the smaller cation Ca in the layered cobaltites YBaCo_2O_{5+delta} for delta approx 0.5. Neutron thermodiffractograms are reported for the compounds YBa_{0.95}Ca_{0.05}Co_2O_{5.5} (x_{Ca}=0.05) and YBa_{0.90}Ca_{0.10}Co_2O_{5.5} (x_{Ca}=0.10) in the temperature range 20 K leq T leq 300 K, as well as high resolution neutron diffraction experiments at selected temperatures for the samples x_{Ca}=0.05, x_{Ca}=0.10 and the parent compound x_{Ca}=0. We have found the magnetic properties to be strongly affected by the cationic substitution. Although the 122 perovskite structure seems unaffected by Ca addition, the magnetic arrangements of Co ions are drastically modified: the antiferromagnetic (AFM) long-range order is destroyed, and a ferrimagnetic phase with spin state order is stabilized below T sim 290 K. For the sample with x_{Ca}=0.05 a fraction of AFM phase coexists with the ferrimagnetic one below T sim 190 K, whereas for x_{Ca}=0.10 the AFM order is completely lost. The systematic refinement of the whole series has allowed for a better understanding of the observed low-temperature diffraction patterns of the parent compound, YBaCo_2O_{5.5}, which had not yet been clarified. A two-phase scenario is proposed for the x_{Ca}=0 compound which is compatible with the phase coexistence observed in the x_{Ca}=0.05 sample.
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