  To date, there are very few experimental techniques, if any, that are
suitable for the purpose of acquiring, with nanoscale lateral resolution,
quantitative maps of the thermal expansivity of 2D materials and thin films,
despite huge demand for nanoscale thermal management, for example in designing
integrated circuitry for power electronics. Besides, contactless analytical
tools for determining the thermal expansion coefficient (TEC) are highly
desirable, because probes in contact with the sample significantly perturb any
thermal measurements. Here, we introduce {\omega}-2{\omega} near-field
thermoreflectance imaging, as an all-optical and contactless approach to map
the TEC at the nanoscale with precision. Testing of our technique is performed
on nanogranular films of gold and multilayer graphene (ML-G) platelets. Our
method demonstrates that the TEC of Au is higher at the metal-insulator
interface, with an average of (17.12 +/- 2.30)x10-6 K-1 in agreement with
macroscopic techniques. For ML-G, the average TEC was (-5.77 +/- 3.79)x10-6 K-1
and is assigned to in-plane vibrational bending modes. A vibrational-thermal
transition from graphene to graphite is observed, where the TEC becomes
positive as the ML thickness increases. Our nanoscale method demonstrates
results in excellent agreement with its macroscopic counterparts, as well as
superior capabilities to probe 2D materials and interfaces.
