The rechargeable lithium-ion cell is an advanced energy-storage system. However, high cost, safety hazards, and chemical instability prohibit its use in large-scale applications. An alternative cathode material, LiFePO(4), solves these problems, but has a kinetic problem involving strong electron/hole localization. One reason for this is believed to be the limited carrier density in the fixed monovalent Fe(3+)PO(4)/LiFe(2+)PO(4) two-phase electrode reaction in LixFePO4. Here, we provide experimental evidence that LixFePO4, at room temperature, can be described as a mixture of the Fe(3+)/Fe(2+) mixed-valent intermediate LialphaFePO4 and Li1-betaFePO4 phases. Using powder neutron diffraction, the site occupancy numbers for lithium in each phase were refined to be alpha=0.05 and 1-beta=0.89. The corresponding solid solution ranges outside the miscibility gap (0<x<alpha,1-beta<x<1) were detected by the anomaly in the configurational entropy, and also by the deviation of the open-circuit voltage from the constant equilibrium potential. These findings encourage further improvement of this important class of compounds at ambient temperatures.