Lattice instabilities near the critical V-V separation for localized versus itinerant electrons in ${\mathrm{LiV}}_{1\mathrm{-}\mathrm{y}}$${\mathrm{M}}_{\mathrm{y}}$${\mathrm{O}}_2$ (M=Cr or Ti) ${\mathrm{Li}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{VO}}_2$

From the compositional dependences of the lattice parameters in the system ${\mathrm{LiV}}_{1\mathrm{-}\mathrm{y}}$Cr ${}_{\mathrm{y}}{}^{}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$, a critical V-V separation ${\mathrm{R}}_{\mathrm{c}}$=2.90±0.01 Å has been determined for an array of octahedral-site ${\mathrm{V}}^{3+}$ ions sharing common octahedral-site edges with six like nearest neighbors. A first-order transition on passing from the itinerant-electron regime R<${\mathrm{R}}_{\mathrm{c}}$ to the localized-electron regime R>${\mathrm{R}}_{\mathrm{c}}$ was also established. In ${\mathrm{LiVO}}_2$, the electron instability associated with an R≈${\mathrm{R}}_{\mathrm{c}}$ is manifest by ${\mathrm{V}}_3$ trimer formation at temperatures T<490 K with R<${\mathrm{R}}_{\mathrm{c}}$ within a trimer and R>${\mathrm{R}}_{\mathrm{c}}$ between trimers. Introduction of a mixed valence in ${\mathrm{Li}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{VO}}_2$ results in a two-phase mixture in the interval 0<x≲0.12; the metastable ${\mathrm{Li}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{VO}}_2$ phase in the interval 0.12≲x≲0.33 disproportionates above a ${\mathrm{T}}_{\mathrm{t}}^{\prime }$≈550 K into ${\mathrm{LiVO}}_2$ and Li[${\mathrm{V}}_2$]${\mathrm{O}}_4$. Comparisons are made between the instabilities associated with a W≈U in the copper oxide superconductors and those in the layered and spinel vanadium oxides. In particular, attention is called to evidences for dynamic charge-density fluctuations that appear to be associated with superconductivity in the coper oxides, but not in the vanadium oxides.