Force modulation microscopy for the study of stiff materials

Force modulation microscopy via sample displacement has been used to image the elastic characteristics of a stiff material - a nickel-based superalloy in which the two phases have close Young's moduli. The experimental operating conditions for obtaining good images are such that the hypothesis of a linear tip - sample interaction is difficult to satisfy when stiff samples are involved, more difficult for a given static load than with compliant materials. To limit the undesirable effects of friction, the cantilever deflection amplitude must be kept small and the modulation frequency must be chosen outside a resonance of the system, but high enough to generate a strong dynamic load able to sufficiently indent the sample. A semiquantitative approach of the elasticity measurement taking into account the nonlinearity of the tip - sample interaction is proposed and described. The semiquantitative term is understood here as the possibility of measuring the elastic modulus of one of the constituents of a material relative to another constituent, the Young's modulus of which is known and used as a reference.