  Vanadium dioxide (VO2) is a model system that has been used to understand
closely-occurring multiband electronic (Mott) and structural (Peierls)
transitions for over half a century due to continued scientific and
technological interests. Among the many techniques used to study VO2, the most
frequently used involve electromagnetic radiation as a probe. Understanding of
the distinct physical information provided by different probing radiations is
incomplete, mostly owing to the complicated nature of the phase transitions.
Here we use transmission of spatially averaged infrared ({\lambda}=1500 nm) and
visible ({\lambda}=500 nm) radiations followed by spectroscopy and nanoscale
imaging using x-rays ({\lambda}=2.25-2.38 nm) to probe the same VO2 sample
while controlling the ambient temperature across its hysteretic phase
transitions and monitoring its electrical resistance. We directly observed
nanoscale puddles of distinct electronic and structural compositions during the
transition. The two main results are that, during both heating and cooling, the
transition of infrared and visible transmission occur at significantly lower
temperatures than the Mott transition; and the electronic (Mott) transition
occurs before the structural (Peierls) transition in temperature. We use our
data to provide insights into possible microphysical origins of the different
transition characteristics. We highlight that it is important to understand
these effects because small changes in the nature of the probe can yield
quantitatively, and even qualitatively, different results when applied to a
non-trivial multiband phase transition. Our results guide more judicious use of
probe type and interpretation of the resulting data.
