A systematic study of Li-i+XMXTi2 _ x(PO4)(3) with M = Al, Cr and Fe and 0 <= x <= 1 has been carried out by X-ray and neutron powder diffraction and by impedance spectroscopy. The analysis of the diffraction data allowed us to describe the disposition of the lithium atoms within the structure. They were found to occupy two different positions, the well-known M1 and a new position called M2'. The addition of trivalent metals into the LiTi2(PO4)(3) compound, even in small amount, gives rise to the liberation of the M1 sites and simultaneous occupation of the M2' sites. This situation becomes more pronounced as the substituent content increases, meaning a higher delocalization of lithium atoms within the structure. Moreover, rising temperature also provokes the movement of lithium from M1 to M2'. The impedance spectroscopy measurements allowed us to relate the electrical properties to the observations of the crystal structure. Both dc bulk and grain boundary ionic conductivity show a thermally activated behavior, and their values increase with substituent content until compositions of x= 0.2-0.3. The activation energy for bulk dc conductivity hardly changes with the substitution, and the main factor affecting the variation of the ionic conductivity is the pre-exponential factor. We find indeed a correlation between the pre-exponential factor and the degree of disorder of the lithium atoms in the structure as determined from neutron diffraction data. The highest conductivity was found in the sample Li1.3Al0.3Ti1.7(PO4)(3) with a value of 62 x 10(-3) S cm(-1) at room temperature and activation energy of 0,30 eV, which is comparable with those measured in the best ionic conductors reported to date. (C) 2014 Elsevier B.V. All rights reserved.