Solid state electrolytes are supposed to be key enabling components for the development of the next generation lithium ion batteries. One of the promising materials for Li-ion conduction is Li1+xAlxTi2-x(PO4)(3) (LATP) due to its high ionic conductivity and stability against water, allowing water based production processes. Much effort is made to understand the influence of crystallographic structure and secondary phases on the ionic conductivity, but little is known about the influence of microstructure. This work aims to provide further information about microstructural properties of LATP, including the influence of heat treatment and grain growth as well as the local distribution of secondary phases. Analytics are done by SEM, EDX and EBSD. It turns out that the limitation for Li+ conductivity can most likely be found in the combination of grain growth with highly anisotropic thermal expansion. Ionic conductivity reaching up to 1E-3 S/cm can be achieved by optimized thermal treatment using a conventional air furnace. (C) 2016 Elsevier B.V. All rights reserved.