  We present a combination of elastic neutron scattering measurements in zero
and 14.5 T and magnetization measurements in zero and 14 T on under-doped
superconducting Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ x=0.17, and the same
measurements in zero field on a non-superconducting crystal with x=0.09. The
data suggest that the under-doped materials may not be electronic phase
separated but rather have slightly inhomogeneous potassium doping. The
temperature dependence of the magnetic order parameter (OP) below the
transition of the sample with x=0.09 is more gradual than that for the case of
the un-doped BaFe$_{2}$As$_{2}$, suggesting that this doping may be in the
vicinity of a tricritical point. We advance therefore the hypothesis that the
tricritical point is a common feature of all superconducting 122s. For the
x=0.17 sample, while T$_{c}$ is suppressed from $\approx$17 K to $\approx$8 K
by a magnetic field of 14 T, the intensity of the magnetic Bragg peaks (1 0 3)
at 1.2 K is enhanced by 10$%$ showing competition of superconductivity (SC) and
antiferromagnetism (AFM). The intensity of the magnetic Bragg peaks (1 0 3) in
the (T$_{c}$, T$_{N}$) temperature interval remain practically unchanged in
14.5 T within a 10$%$ statistical error. The present results are discussed in
the context of the existing literature.
