Nucleation-controlled hysteresis in unstrained hydrothermal $\mathrm{V}{\mathrm{O}}_2$ particles

While nucleation-limited transformation mechanisms are widely implicated in unstrained, undoped $\mathrm{V}{\mathrm{O}}_2$ nanoparticles, a direct link between nucleation barriers and hysteresis widths has not yet been established. Here, we investigate microscopic transformation of structural domains optically in hydrothermally grown $\mathrm{V}{\mathrm{O}}_2$ particles ∼0.5–46 μm in length, which are not elastically clamped to the substrate. We observe abrupt and generally complete transformation in individual particles, consistent with a nucleation-limited transformation mechanism. The forward and reverse transformation temperatures are not correlated, suggesting a range of potency of nucleation sites for both forward and reverse transformation in undoped particles, resulting in a hysteresis of 2.9–46.3 °C. Thus, the macroscopic hysteresis width in bulk $\mathrm{V}{\mathrm{O}}_2$ powders and dispersed particulate films is primarily attributable to a distribution of critical nucleation temperatures between different particles. These findings suggest that as $\mathrm{V}{\mathrm{O}}_2$ volume elements are scaled down for microelectronic applications, manipulation of nucleation sites via defect engineering may be required to control the degree of the $\mathrm{V}{\mathrm{O}}_2$ element reversibility.

Figure 1

Abrupt blue-shift in single $\mathrm{V}{\mathrm{O}}_2$ particles under unpolarized reflected white light and the associated red-difference plots during (a) a heating cycle performed at 1 °C increments (b) the subsequent cooling cycle at 1 °C increments. Difference plots were created by extracting normalized red pixel values, and calculating the difference between a low-temperature reference image and a high-temperature image at each pixel. Reference temperatures were 39.3 °C during heating, and 54.7 °C during cooling.

Figure 2

A single $\mathrm{V}{\mathrm{O}}_2$ particle showing a two-step pinned transition over the course of 2 °C for four cycles in (a) original bright-field images, and (b) difference plots of the red component between the temperature given and 64.3 °C (cycle 1), 63.3 °C (cycle 2), 66.3 °C (cycle 3), and 65.3 °C (cycle 4).

Figure 3

(a) Histogram of the transition temperature (heating and cooling) of 347 individual particles observed in optical microscopy, and the calculated (b) histogram of the hysteresis in the same 347 individual particles showing extreme variations in hysteresis width between 2.9 and 46.8 °C. Notably, large hysteresis particles are composed exclusively of small particles $\left(<2\mu {\mathrm{m}}^3\right)$. (c) A scatter plot of the individual particle heating and cooling transition temperatures shows little correlation between heating and cooling transitions.

Figure 4

(a) Phase transformation from the M1 to R phase upon heating in undoped $\mathrm{V}{\mathrm{O}}_2$ occurs abruptly after nucleation of a domain from a potent site (black dot), where (b) nucleation in different domains is triggered at different transformation temperatures $(T_2,T_3)$, depending on the potency of nucleation sites within that domain, and therefore, the thermodynamic driving force $\left(\mathrm{\Delta }{G}_2,\mathrm{\Delta }{G}_3\right)$ necessary to overcome energetic barriers to nucleation. In general, the facile interface passes through the particle leading to complete transformation. In ∼4% of particles, this interface is hindered by some crystal defect, leading to transformation of the particle in 2–3 distinct domains.

Figure 5

(a) Cumulative fraction of particles that have transformed for each volume bin as a function of temperature. (b) The opposite transect showing the dependence of the fraction of particles that have transformed at each given temperature on particle volume during the heating experiment, and (c) during the cooling experiment. In (a)–(c) solid lines represent the best fit of Eq. (1) on heating (warm colors) or cooling (cool colors), and filled circles or diamonds represent experimentally obtained fractions of particles that have transformed. (d) The calculated potent nucleation site density as a function of driving force according to Eq. (2). Solid lines represent the best fit to Eq. (2) on heating (red) and cooling (blue). Open circles represent the solution to Eq. (1) for ρ using experimentally obtained cumulative transformation fractions ($F$) and volumes (V). Error bars are calculated from error introduced from particle volume and transformation fractions in experimental data.

Figure 6

Dependence of hysteresis width on particle volume of present work as compared with studies in significantly smaller $\mathrm{V}{\mathrm{O}}_2$ volumes [16, 17, 21, 30, 31].