  Surface topography strongly modifies adhesion of hard-material contacts, yet
roughness of real surfaces typically exists over many length scales. This
investigation aims to determine which scales of topography have the strongest
effect on macroscopic adhesion. Adhesion measurements were performed on
technology-relevant diamond coatings of varying roughness using spherical ruby
probes that are large enough ($0.5$-mm-diameter) to sample all length scales of
topography. For each material, more than $2000$ measurements of pull-off force
were performed in order to investigate the magnitude and statistical
distribution of adhesion. Using sphere-contact models, the roughness-dependent
effective values of work of adhesion were measured, ranging from $0.08$ to
$7.15$ mJ/m$^2$ across the four surfaces. The data was more accurately fit
using numerical analysis, where an interaction potential was integrated over
the AFM-measured topography of all contacting surfaces. These calculations
revealed that consideration of nanometer-scale plasticity in the materials was
crucial for a good quantitative fit of the measurements, and the presence of
such plasticity was confirmed with AFM measurements of the probe after testing.
This analysis enabled the extraction of geometry-independent material
parameters; the intrinsic work of adhesion between ruby and diamond was
determined to be $46.3$ mJ/m$^2$. The range of adhesion was $5.6$ nm, which is
longer than is typically assumed for atomic interactions, but is in agreement
with other recent investigations. Finally, the numerical analysis was repeated
for the same surfaces but this time with different length-scales of roughness
included or filtered out. The results demonstrate a critical band of
length-scales between $43$ nm and $1.8$ nm in lateral size that has the
strongest effect on the total adhesive force for these hard, rough contacts.
