Influence of atomic force microscope cantilever tilt and induced torque on force measurements

Quantitative force measurements performed using the atomic force microscope (AFM) inherently rely on calibration of the AFM cantilever spring constant to convert the measured deflection into a force. Here, we examine the effect of cantilever tilt and induced torque on the effective normal spring constant resulting from variable placement of the tip probe, as is frequently encountered in practice. Explicit general formulas are presented that account for these combined effects for both sharp tips and spherical probes. In contrast to previous studies, we find that induced tip torque can act to either enhance or reduce the effective normal spring constant of the cantilever. The implications of this study to practical force measurements are discussed. c 2008 American Institute of Physics.