Quantitative nanoscale modulus measurements and elastic imaging of SnO ₂ nanobelts

A comparative study of the elastic modulus and uniformity of single-crystal Sn O2 nanobelts is presented employing two nondestructive techniques based on atomic force microscopy: differential ultrasonic force microscopy (d-UFM) and atomic force acoustic microcopy (AFAM). In mapping mode both techniques revealed a uniform elastic response across the surface of the nanobelts as expected for single-crystal nanostructures. Comparative analyses of the local indentation modulus (probe area≈100-400 nm2) were undertaken using both techniques at multiple points on the same Sn O2 nanobelt exhibiting a (102) surface crystalline orientation as determined by electron backscatter diffraction. Both d-UFM and AFAM exhibited excellent quantitative agreement yielding indentation moduli of 151±14 and 154±18 GPa, respectively. These values are significantly below the expected value of the (102) indentation modulus of 358 GPa for crystalline Sn O2 determined from the Green's function model of Barnett and Lothe [Phys. Nors. 8, 13 (1975)] adapted by Vlassak [J. Mech. Phys. Solids 51, 1701 (2003)]. This observation is consistent with recent nanoindentation (destructive) measurements of (10 1-) oriented Sn O2 nanobelts that yielded an indentation modulus of 66±10 GPa, well below the expected value of 308 GPa. In addition to confirming the quantitative consistency and overall accuracy of nanoscale modulus measurements using d-UFM and AFAM, the overall trend in these data contradicts recent molecular dynamics studies that call for increased elastic moduli in similar nanobelt structures.