The distribution and characteristics of surface cracking (i.e. sub-surface damage or SSD) formed during standard grinding processes has been investigated on fused silica glass. The SSD distributions of the ground surfaces were determined by: 1) creating a shallow (18-108 μm) wedge/taper on the surface by magneto-rheological finishing; 2) exposing the SSD by HF acid etching; and 3) performing image analysis of the observed cracks from optical micrographs taken along the surface taper. The observed surface cracks are characterized as near-surface lateral and deeper trailing indent type fractures (i.e., chatter marks). The SSD depth distributions are typically described by a single exponential distribution followed by an asymptotic cutoff in depth (c max ). The length of the trailing indent is strongly correlated with a given process. Using established fracture indentation relationships, it is shown that only a small fraction of the abrasive particles are being mechanically loaded and causing fracture, and it is likely the larger particles in the abrasive particle size distribution that bear the higher loads. The SSD depth was observed to increase with load and with a small amount of larger contaminant particles. Using a simple brittle fracture model for grinding, the SSD depth distribution has been related to the SSD length distribution to gain insight into 'effective' size distribution of particles participating in the fracture. Both the average crack length and the surface roughness were found to scale linearly with the maximum SSD depth (c max ). These relationships can serve as useful rules-of-thumb for nondestructively estimating SSD depth and to identify the process that caused the SSD. In certain applications such as high intensity lasers, SSD on the glass optics can serve as a reservoir for minute amounts of impurities that absorb the high intensity laser light and lead to subsequent laser-induced surface damage. Hence a more scientific understanding of SSD formation can provide a means to establish recipes to fabricate SSD-free, laser damage resistant optical surfaces.

Various ceria and colloidal silica polishing slurries were used to polish fused silica glass workpieces on a polyurethane pad. Characterization of the slurries' particle size distribution (PSD) (using both ensemble light scattering and single particle counting techniques) and of the polished workpiece surface (using atomic force microscopy) was performed. The results show the final workpiece surface roughness is quantitatively correlated with the logarithmic slope of the distribution function for the largest particles at the exponential tail end of the PSD. Using the measured PSD, fraction of pad area making contact, and mechanical properties of the workpiece, slurry, and pad as input parameters, an Ensemble Hertzian Gap (EHG) polishing model was formulated to estimate each particle's penetration, load, and contact zone. The model is based on multiple Hertzian contact of slurry particles at the workpiece-pad interface in which the effective interface gap is determined through an elastic load balance. Separately, ceria particle static contact and single pass sliding experiments were performed showing~1-nm depth removal per pass (i.e., a plastic type removal). Also, nanoindentation measurements on fused silica were made to estimate the critical load at which plastic type removal starts to occur (P crit~5 3 10 À5 N). Next the EHG model was extended to create simulated polished surfaces using the Monte Carlo method where each particle (with the calculated characteristics described above) slides and removes material from the silica surface in random directions. The polishing simulation utilized a constant depth removal mechanism (i.e., not scaling with particle size) of the elastic deformation zone cross section between the particle and silica surface, which was either 0.04 nm (for chemical removal) at low loads (

P crit ). The simulated surfaces quantitatively compare well with the measured rms roughness, power spectra, surface texture, absolute thickness material removal rate, and load dependence of removal rate.

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