Scanning white light interferometry (SWLI) is a large area imaging technique that measures the 3D height profile of a surface with nanometer-level accuracy. It can be used
to measure the height of the debris and worn areas on the film surface. In addition to being a fast and reproducible, SWLI is a non-contact measurement method. This is especially important for tribological experiments because it means the height
characterization will not affect the sample surface topography or chemistry, which would reduce the value of subsequent chemical measurements. The vertical resolution for this method is high (< 1 nm), but the lateral resolution is dependent on the optics and charge- couple device (CCD) camera used. For typical lens settings (20x objective, 0.5x internal magnification), one pixel encompasses ~1.1 x ~1.1 µm2. This relatively large pixel size, combined with the smoothness of ta-C and UNCD, means that SWLI cannot accurately measure the surface roughness of these films below a ~1 µm lateral dimension. Wear tracks are typically ~50 µm wide (determined by the applied load and corresponding amount of contact area and wear) and ~600 µm long (determined by the stroke of the reciprocating wear tests). The optical objectives available allow measurements of the entire wear track in one FOV. Plotting the height profile in 3D shows the track profile (Fig. 2.8). From this, the average and maximum wear depth of different tracks can be compared. Additionally, by summing the volume of every pixel that has depth below the initial height, one can calculate the wear volume.
Fig. 2.8: Profilometry image of a UNCD wear track created at 1.0N, 1.0% relative humidity. The height scaling is amplified by a factor of 40 compared to the lateral
dimensions.
The SWLI technique obtains height information as follows. An interference pattern is produced between light reflected from the test surface and the reflected light from a flat reference surface. This summed image is measured by a camera as a series of fringes caused by the constructive or destructive interference of light from the two surfaces. The technique is referred to as 'white light' because it is a light source with center wavelength of 546 nm, but has a 120 nm full width, so it emits a range of
frequencies. Because of this, the beam has a finite coherence length. As the piezo motor ramps the objective and reference surface through a range of distances from the test surface, each point on the surface will have several heights with constructive interference (fringe maxima). However, due to the coherent nature of the beam, only one height will
give the brightest maximum. The software finds the height at which each pixel has a calculated maximum coherent interference with the light from the reference mirror, and then backs out a relative height value for that point. Because this technique relies on the intensity of the interference signal, sections of the surface that have poor reflection due to roughness or extreme geometry, such as a debris particle or the sidewall of a wear track, can sometimes produce dropped pixels.
To find the wear volume removed for each track, optical profilometry measurements are performed using a Zygo New View 6300 SWLI profilometer. An analysis routine with a graphical user interface (GUI) was designed as part of this thesis to convert the raw height data into a wear rate for the track. Data from a SWLI image are loaded in ASCII format, with the x- and y-dimension of the matrix representing CCD camera pixels, and the matrix value representing height in nm. The header file contains the conversion factors from pixel value to lateral dimensions. The images are then processed to remove artifacts and enable analysis of the wear volume. The first
processing step is a plane fit. Due to the flatness and low roughness of the substrate, as well as the low roughness of these coatings, the as-grown film surrounding the wear track is treated as a plane. The user selects a region that includes all points in the image inside the wear track, and then these values are excluded from the plane fit. This fit is then subtracted from the data set, leaving the surface with the average of all non-wear track pixels centered at zero height. Any errant or missing points anywhere in the image are then flagged. Nonsensical data is identified by finding any pixel that is different in height by more than three times the standard deviation of the average of the surrounding pixels
in a 25x25 grid (excluding the center point itself). If a point is dropped during the initial measurement, meaning the Zygo output software sets the height value to be
'2147483640', the Matlab code sets the value to not-a-number (NaN).
Then all of the flagged points are replaced by values determined from an
interpolation using a spline fit curve (one for each orthogonal direction of the data set) to find the best estimate for the actual height. Only the heights of non-flagged data points are used in the interpolating fit. The two values from the interpolation are compared. If they are similar, the average of the two is used for the height. If they are very dissimilar, the one that is closer to the neighboring average is used. This may not be the most
rigorous way to fix dropped data points, but the bulk of these errant points occur on areas of debris where the true height is above the zero plane. Profilometry analysis is mostly used for wear volumes and wear rates, and thus is only concerned with points below the zero plane. Finally, the user inputs the load used during tribometry, the track length, and the number of cycles.
Wear rate is then calculated using Archard’s law, which states,
· (1)
where K is the wear rate, V is the volume removed (in mm3), N is the normal load (in Newtons), and d is the sliding distance (in meters). The wear volume of the track is calculated by summing the depths of every pixel inside the track that is below the plane of the surrounding surface, and then multiplying those depths by the area of a pixel.
For a wear track that is 600 μm long and 50 μm wide, assuming the uncertainty in the height of every pixel is 1 nm, the number of pixels is determined by finding the total
area of the wear track. The shape is assumed to be a 600x50 μm2 rectangle with two hemispherical ends with radius 25 μm. Then, using the 1.1x1.1 µm2 pixel size with uncertainty of 3%, the total number of pixels in the wear track is found by dividing the wear track area by the pixel area. Finally, the uncertainty in the volume is calculated by multiplying the number of pixels in the wear track by the area of a pixel and the 1 nm uncertainty in height, giving 3.2 x 10-8 mm3. Considering a track with the tribometry parameters that would give the highest uncertainty in the wear rate (ta-C with a minimum load of 0.05 N) for 5000 cycles and a 600 µm track length, this would be an uncertainty in the wear rate of 1.1 x 10-7 mm3N-1m-1.
We also use the calibrated profilometry data to ascertain the worn area of the sphere. Wear scar diameter is found from a sphere height profile across the center of the scar. A good approximation for the wear scar is a circular shape. Assuming this, the wear volume for the sphere is calculated from the diameter of the wear scar and using basic geometry to calculate the removed volume. Since the sphere and the films are not ductile materials, plastic deformation is considered unlikely and the change in volume is entirely attributed to wear (removed volume).
Since the volume measurements are performed only once, at the end of the tribometer test, they are referred to as ‘single point’ wear rate values. As the majority of wear occurs in the first few cycles (typically the first 10 – 100), single point
measurements do not provide steady-state wear rate information. Instead, they provide only an upper-bound value.