Competition between metal bonding and strain in tetragonal V$_{1-x}$M$_x$O$_2$ (M = Nb, Mo)
Though the effects of metal dopants on the electrostructural transition of rutile VO$_2$ have been studied for many decades, there is still no consensus explanation for the observed trends. A major challenge has been to separate the impact of a dopant's size from other factors such as its electronic configuration, which stems from the difficulty in directly probing the local bonding environment around a dopant atom. This work addresses the special case of larger dopant ions by combining X-ray total scattering experiments on V$_{0.83}$Mo$_{0.17}$O$_2$ and V$_{0.89}$Nb$_{0.11}$O$_2$ single crystals with multiple Monte Carlo method models to simulate local size effects in the high-temperature tetragonal phase (R). We find that sufficiently long apical metal-oxygen bonds (M$-$O$_{ap}$) induce a strain field in the neighboring chains that locally resembles the metal-metal dimer formation present in the low-temperature distorted structure of VO$_2$ (M1). The dimer mode in the M1 structure is antisymmetric along M$-$O$_{ap}$, however, while the strain-induced pseudodimer motif is symmetric. The implied direct competition between motifs is verified experimentally. This finding provides a new mechanistic parameter toward understanding the phase transition. More generally, the work highlights how local strain fields around dopants can lead to complex distortions that are ordinarily attributed to electronic origins.