Real-Space Investigation of Structural Changes at the Metal-Insulator Transition in ${\mathrm{VO}}_2$

Synchrotron x-ray total scattering studies of structural changes in rutile ${\mathrm{VO}}_2$ at the metal-insulator transition temperature of 340 K reveal that monoclinic and tetragonal phases of ${\mathrm{VO}}_2$ coexist in equilibrium, as expected for a first-order phase transition. No evidence for any distinct intermediate phase is seen. Unbiased local structure studies of the changes in V-V distances through the phase transition, using reverse Monte Carlo methods, support the idea of phase coexistence and point to the high degree of correlation in the dimerized low-temperature structure. No evidence for short-range V-V correlations that would be suggestive of local dimers is found in the metallic phase.

Figure 1

(a) The metallic high-temperature tetragonal rutile form of ${\mathrm{VO}}_2$ with a single V-V distance and (b) the insulating low-temperature monoclinic form, showing dimerized chains of alternating short and long V-V distances along the $c$ axis.

Figure 2

Least-squares fits to the PDF of bulk ${\mathrm{VO}}_2$ using (a) the low-temperature monoclinic structure for $T=300\mathrm{K}$ ($R_w$, 11.6%) and (b) the high-temperature tetragonal structure for $T=400\mathrm{K}$ ($R_w$, 9.6%). Circles are experimental data and lines are fits to the average structure. The difference is displayed below each fit. (c) Changes in the $R_w$ fitting parameters, shown for cooling (○) and heating (×) through the transition temperature, show an abrupt transition with good fits at all temperatures outside of $T=340\mathrm{K}$.

Figure 3

(a) Thermal parameters ($U_{ij}$) obtained from PDF least-squares refinement as a function of temperature reveal abrupt changes at the transition temperature. Thermal ellipsoids (99%) for neighboring V polyhedra in the $c$ direction are shown above and below the transition temperature. (b) V-V bond distances from the least-squares refinement (points) overlaid with a map of the V-V distances obtained from RMC modeling.

Figure 4

(a) Experimental x-ray PDFs from ${\mathrm{VO}}_2$ at $T$ below (334 K), equal to (340 K), and above (342 K) the transition temperature. A linear combination of the 334 and 342 K data is shown as points, along with a difference curve to the 340 K data. In (b) the full fitting range is shown—at the transition temperature the sample is comprised of two distinct end-member phases.

Figure 5

(a) The relative probabilities of V atom positions as obtained from RMC modeling are dimerized at four temperatures below and spherical at three temperatures above the transition. At $T=340\mathrm{K}$, the probability distribution is intermediate. In (b), a two-phase model is formed by averaging the experimental maps from $T=334$ and 342 K, both of which resemble the low- and high-temperature end members. This resulting map appears similar to the 340 K data reproduced in (c). Scale bars are 0.2 Å. The color bar indicates minimum and maximum probability.