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The surface topography of diamond coatings strongly affects surface properties such as adhesion, friction, wear, and biocompatibility. However, the understanding of multi-scale topography, and its effect on properties, has been hindered by conventional measurement methods, which capture only a single length scale. Here, four different polycrystalline diamond coatings are characterized using transmission electron microscopy to assess the roughness down to the sub-nanometer scale. Then these measurements are combined, using the power spectral density (PSD), with conventional methods (stylus profilometry and atomic force microscopy) to characterize all scales of topography. The results demonstrate the critical importance of measuring topography across all length scales, especially because their PSDs cross over one another, such that a surface that is rougher at a larger scale may be smoother at a smaller scale and vice versa. Furthermore, these measurements reveal the connection between multi-scale topography and grain size, with characteristic scaling behavior at and slightly below the mean grain size, and self-affine fractal-like roughness at other length scales. At small (subgrain) scales, unpolished surfaces exhibit a common form of residual roughness that is self-affine in nature but difficult to detect with conventional methods. This approach of capturing topography from the atomic- to the macro-scale is termedcomprehensive topography characterization, and all of the topography data from these surfaces has been made available for further analysis by experimentalists and theoreticians. Scientifically, this investigation has identified four characteristic regions of topography scaling in polycrystalline diamond materials.

 

The failure of roughness parameters to predict surface properties stems from their inherent scale-dependence; in other words, the measured value depends on how the parameter was measured. Here we take advantage of this scale-dependence to develop a new framework for characterizing rough surfaces: the Scale-Dependent Roughness Parameters (SDRP) analysis, which yields slope, curvature, and higher-order derivatives of surface topography at many scales, even for a single topography measurement. We demonstrate the relationship between SDRP and other common statistical methods for analyzing surfaces: the height-difference autocorrelation function (ACF), variable bandwidth methods (VBMs) and the power spectral density (PSD). We use computer-generated and measured topographies to demonstrate the benefits of SDRP analysis, including: novel metrics for characterizing surfaces across scales, and the detection of measurement artifacts. The SDRP is a generalized framework for scale-dependent analysis of surface topography that yields metrics that are intuitively understandable. 

Background: Surface topography strongly modifies adhesion of hard-material contacts, yet roughness of real surfaces typically exists over many length scales, and it is not clear which of these scales has the strongest effect. Objective: This investigation aims to determine which scales of topography have the strongest effect on macroscopic adhesion. Methods: 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. Results: 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. Conclusions: The results demonstrate a critical band of length-scales—between 43 nm and 1.8 µm in lateral size—that has the strongest effect on the total adhesive force for these hard, rough contacts. 

A mechanistic understanding of adhesion in soft materials is critical in the fields of transportation (tires, gaskets, and seals), biomaterials, microcontact printing, and soft robotics. Measurements have long demonstrated that the apparent work of adhesion coming into contact is consistently lower than the intrinsic work of adhesion for the materials, and that there is adhesion hysteresis during separation, commonly explained by viscoelastic dissipation. Still lacking is a quantitative experimentally validated link between adhesion and measured topography. Here, we used in situ measurements of contact size to investigate the adhesion behavior of soft elastic polydimethylsiloxane hemispheres (modulus ranging from 0.7 to 10 MPa) on 4 different polycrystalline diamond substrates with topography characterized across 8 orders of magnitude, including down to the angstrom scale. The results show that the reduction in apparent work of adhesion is equal to the energy required to achieve conformal contact. Further, the energy loss during contact and removal is equal to the product of the intrinsic work of adhesion and the true contact area. These findings provide a simple mechanism to quantitatively link the widely observed adhesion hysteresis to roughness rather than viscoelastic dissipation. 

In atomic force microscopy (AFM) and metrology, it is known that the radius of the scanning tip affects the accuracy of the measurement. However, most techniques for ascertaining tip radius require interruption of the measurement technique to insert a reference standard or to otherwise image the tip. Here we propose an inline technique based on analysis of the power spectral density (PSD) of the topography that is being collected during measurement. By identifying and quantifying artifacts that are known to arise in the power spectrum due to tip blunting, the PSD itself can be used to determine progressive shifts in the radius of the tip. Specifically, using AFM images of an ultrananocrystalline diamond, various trends in measured PSD are demonstrated. First, using more than 200 different measurements of the same material, the variability in the measured PSD is demonstrated. Second, using progressive scans under the same conditions, a systematic shifting of the mid-to-high-frequency data is visible. Third, using three different PSDs, the changes in radii between them were quantitatively determined and compared to transmission electron microscopy (TEM) images of the tips taken immediately after use. The fractional changes in tip radii were detected; the absolute values of the tip radii could be matched between the two techniques, but only with careful selection of a fitting constant. Further work is required to determine the generalizability of the value of this constant. Overall, the proposed approach represents a step towards quantitative and inline determination of the radius of the scanning tip and thus of the reliability of AFM-based measurements.