  Neutron diffraction measurements, performed in presence of an external
magnetic field, have been used to show structural evidence for the kinetic
arrest of the first-order phase transition from (i) the high temperature
austenite phase to the low temperature martensite phase in the magnetic shape
memory alloy Ni37Co11Mn42.5Sn9.5, (ii) the higher temperature ferromagnetic
phase to the lower temperature antiferromagnetic phase in the half-doped charge
ordered compound La0.5Ca0.5MnO3 and (iii) the formation of a glass-like
arrested state (GLAS). The CHUF (cooling and heating under unequal fields)
protocol has been used to establish phase coexistence of metastable and
equilibrium states of GLAS and also to demonstrate the devitrification of the
arrested metastable states in the neutron diffraction patterns. We also explore
the field-temperature (H,T) phase diagram for the two compounds, which depicts
the kinetic arrest line TK(H). TK is seen to increase as H increases.
