Phase image contrast mechanism in intermittent contact atomic force microscopy

A model is presented showing that phase variations in intermittent contact atomic force microscopy (IC-AFM) (tapping mode) result from variations in both conservative and dissipative forces. It is shown that when operating with constant cantilever oscillation amplitude, however, conservative forces drive the phase contrast. The equations of cantilever tip-sample surface contact are solved analytically for constant amplitude IC-AFM operation. Solutions are obtained for the tip-sample contact time, maximum sample indentation depth, and phase shift in the cantilever oscillations. The model equations are applied to the calculation of the phase contrast, defined as the difference in phase shift between two points in the image, for a diamond-graphite nanocomposite sample having a heterogeneous variation in graphite porosity ranging from approximately 30 vol % to roughly 60 vol %. The phase contrast predicted from the model equations, using only conservative forces in the model, is calculated to be approximately 69 degrees for 30 vol % porosity and roughly 79 degrees for 60% porosity. The model predictions are in very good agreement with the measured range of values from 69.4 degrees to 78.5 degrees obtained from a IC-AFM phase image of the sample. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3503478]