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Structural features responsible for lithium conductivity in Li1+xTi2-xAlx(PO4)3 (x = 0, 0.2, and 0.4) samples have been investigated by Rietveld analysis of high-resolution neutron diffraction (ND) patterns. From structural analysis, variation of the Li site occupancies and atomic thermal factors have been deduced as a function of aluminum doping in the temperature range 100-500 K. Fourier map differences deduced from ND patterns revealed that Li ions occupy M1 sites and, to a lower extent, M3 sites, disposed around ternary axes. The occupation of M1 sites by Li ions is responsible for the preferential expansion of the rhombohedral R3...c unit cell along the c axis with temperature. The occupation of less symmetric M3 sites decreases electrostatic repulsions among Li cations, favoring ion conductivity in Li1+xTi2-xAlx(PO4)3 compounds. The variations detected on long-range lithium motions have been related to variations of the oxygen thermal factors with temperature. The information deduced by ND explains two lithium motion regimes deduced previously by 7Li NMR and impedance spectroscopy. [ABSTRACT FROM AUTHOR]