Crls

2a res res

6RFz

We have used the term ''ideal'' quite ambiguously to describe LsCsRcaLnS, the most appropriate scan size for defect generation. It is expected and empirically validated that the generated defects will be more uniformly (relative to overlapping trials) distributed over the wear area before the advent of other varieties of defects. This allows for the design of experiments to probe these low-density species (typically <1 defect within the tip-sample contact).[14]

To evaluate the effects of scan overlap we must account for the additional history overlap imparts to the surface; achieved by estimating a scan correction

(scancor) for overlapping studies. The scancor determines the additional number of scans contributed by overlap to the contact history and therefore can be used to estimate the number of scan cycles required to achieve an equivalent degree of wear, under identical loads, without scan overlap. The scancor is arrived at naturally by association to the force of overlap within overlapping contacts. The Hertz model defines the pressure distribution p(r) in terms of r, the distance from the center of contact via Eq. (8).[144]

2n na2 o o

2pona2 3

Here po is the maximum Hertz pressure within the contact. Once the boundary of the overlapping area is defined (Fig. 5), the force of overlap can be calculated. The scancor is collectively calculated in terms of F^ta1, the total force within all successive overlapping contact areas. F^p is formulated from a geometric breakdown of overlapping circles of radii a (Fig. 5) and leads to the three integrals in Eq. (9), which have been converted to Cartesian coordinates. The (Fz x res) term normalizes each experimental scan and the functions A, B, and C are given in Fig. 5.

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