The origin of phase transition and the usual evolutions of the unit-cell constants of the NASICON structures of the solid solution LiTi$_{2-x}$Ge$_{x}$(PO$_{4}$)$_{3}$

Ge-doped LiTi$_{2}$(PO$_{4}$)$_{3}$ has been synthesized by a conventional solid-state reaction. Compounds LiM$_{2}^{\mathrm{(IV)}}$(PO$_{4}$)$_{3}$ with LTP-type structure present a different behaviour depending on nature of M$^{\mathrm{(IV)}}$. For M$^{\mathrm{(IV)}}$ = Ti and Ge, the structure shows the space group R3c, whereas for M$^{\mathrm{(IV)}}$ = Ge the space group is R3. Differences in behaviour of LiTi$_{2}$(PO$_{4}$)$_{3}$-LiGe$_{2}$(PO$_{4}$)$_{3}$ solid solutions are discussed in relation to the composition. Their structures LiTi$_{2-x}$Ge$_{x}$(PO$_{4}$)$_{3}$ (0 $\le x<$ 2) were determined from X-ray powder diffraction method (XRD) using Rietveld analysis. A sharp change in the lattice parameter $a$ is observed between the compositions with $x$ = 1. The lattice parameter c increases as the Ge content increases in the whole range of composition. The space group R3c becomes R3 for the composition with $x>$ 1. The SEM micrographs of the samples show relative porous microstructures due to the effect of the substitution.