The transmission electron microscopy observations of the charge ordering (CO) which governs the electronic polarization in LuFe2O4-x clearly show the presence of a remarkable phase separation at low temperatures. Two CO ground states are found to adopt the charge modulations of Q1 = (1/3, 1/3, 0) and Q2 = (1/3 + y, 1/3 + y, 3/2), respectively. Our structural study demonstrates that the incommensurately Q2-modulated state is chiefly stable in samples with relatively lower oxygen contents. Data from theoretical simulations of the diffraction suggest that both Q1- and Q2-modulated phases have ferroelectric ordering. The effects of oxygen concentration on the phase separation and electric polarization in this layered system are discussed.
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