Quantitative elasticity evaluation by contact resonance in an atomic force microscope

We present a local elasticity measurement from the resonance frequency of a cantilever vibrated at its base. A sharp tip on top of the cantilever is in contact with the sample surface at a servo-controlled constant static force. The advantage of a continuum model for the cantilever vibration over the localized-spring model in the elasticity measurement is proved quantitatively. As an application, Young's modulus of soda lime glass was measured and a smooth radial gradient of Young's modulus of about 29% was observed for the first time on a cross section of a carbon fiber of diameter 7 mu m. Further improvement of the independent shear stiffness measurement was proposed by a theoretical analysis of torsional vibration with a boundary condition for the elastically supported tip.