  The quantitative interatomic force measurements open a new pathway to
materials characterization, surface science, and chemistry by elucidating the
force between 'two' interacting atoms as a function of their separation. Atomic
force microscope is the ideal platform to gauge interatomic forces between the
tip and the sample. For such quantitative measurements, either the oscillation
frequency or the oscillation amplitude and the phase of a vibrating cantilever
are recorded as a function of the tip-sample separation. These experimental
measures are subsequently converted into the interatomic force laws. Recently,
it has been shown that the most commonly applied mathematical conversion
techniques may suffer a significant deviation from the actual force laws. To
avoid assessment of unphysical interatomic forces, either the use of very small
(i.e., a few picometers) or very large oscillation amplitudes (i.e., a few
nanometers) has been proposed. However, the use of marginal oscillation
amplitudes gives rise to another problem as it lacks the feasibility due to the
adverse signal to noise ratios. Here we show a new mathematical conversion
principle that confronts interatomic force measurements while preserving the
oscillation amplitude within the experimentally achievable and favorable
limits, i.e. tens of picometers. We anticipate that our findings will be the
nucleus of reliable evaluation of material properties with a more accurate
measurement of interatomic force laws.
