  Neutron powder diffraction measurements, combined with magnetization and
resistivity data, have been carried out in the doped perovskite
La$_{1-x}$Ca$_x$MnO$_3$ ($x=0.47$, 0.50, and 0.53) to elucidate the structural,
magnetic, and electronic properties of the system around the composition
corresponding to an equal number of Mn3+ and Mn4+. At room temperature all
three samples are paramagnetic and single phase, with crystallographic symmetry
Pnma. The samples then all become ferromagnetic (FM) at $T_C\approx 265$ K. At
$\sim 230$ K, however, a second distinct crystallographic phase (denoted A-II)
begins to form. Initially the intrinsic widths of the peaks are quite large,
but they narrow as the temperature decreases and the phase fraction increases,
indicating microscopic coexistence. The fraction of the sample that exhibits
the A-II phase increases with decreasing temperature and also increases with
increasing Ca doping, but the transition never goes to completion to the lowest
temperatures measured (5 K) and the two phases therefore coexist in this
temperature-composition regime. Phase A-II orders antiferromagnetically (AFM)
below a N\'{e}el temperature $T_N \approx 160$ K, with the CE-type magnetic
structure. Resistivity measurements show that this phase is a conductor, while
the CE phase is insulating. Application of magnetic fields up to 9 T
progressively inhibits the formation of the A-II phase, but this suppression is
path dependent, being much stronger for example if the sample is field-cooled
compared to zero-field cooling and then applying the field. The H-T phase
diagram obtained from the diffraction measurements is in good agreement with
the results of magnetization and resistivity.
