  The structural transition at about 1000 {\deg}C, from the hexagonal to the
orthorhombic phase of LuFeO3, has been investigated in thin films of LuFeO3.
Separation of the two structural phases of LuFeO3 occurs on a length scale of
micrometer, as visualized in real space using X-ray photoemission electron
microscopy (X-PEEM). The results are consistent with X-ray diffraction and
atomic force microscopy obtained from LuFeO3 thin films undergoing the
irreversible structural transition from the hexagonal to the orthorhombic phase
of LuFeO3, at elevated temperatures. The sharp phase boundaries between the
structural phases are observed to align with the crystal planes of the
hexagonal LuFeO3 phase. The coexistence of different structural domains
indicates that the irreversible structural transition, from the hexagonal to
the orthorhombic phase in LuFeO3, is a first order transition, for epitaxial
hexagonal LuFeO3 films grown on Al2O3.
