Surface and sub-surface damage

Generally surface or sub-surface damage (SSD) of fused silica optics are created during grinding and/or polishing processes. Many researchers indicated that a Beilby layer, also referred to as the redeposition layer, commonly covers the polished optical surface [3-6]. Beneath the Beilby layer, a defect layer consisting of micro cracks is usually found.

The defect layer is also known as the SSD layer and not detectable by visual methods.

Above the defect-free bulk, a deformed layer, which contains compressive stresses or tensile stresses, is found below the defect layer. Figure 4.3 shows the surface and sub-surface morphology of polished fused silica.

In order to reduce the depth of the defect layer, a common method is used that the subsequent process removes the overall amount of SSD generated by the preceding process. This method is illustrated in Figure 4.4. However, surface and sub-surface damage are still found usually even after fine polishing.

The creation of SSD is commonly believed as a moving indentation process. In other words, when the mechanically loaded hard indenters (abrasives) are sliding on the optical surface during manufacturing processes, SSD occurs. Figure 4.5 shows the sequence of a static indentation process with the increasing indention load on a sharp indenter. Plastic deformation, median crack, and lateral crack are generated with the increasing load (though lateral crack occurs during unloading) in the static indentation process. For a blunt indenter, the situation is a little different in that the Hertzian cone

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Figure 4.2 The steps of the conventional optics production process

Figure 4.3 Schematic of surface/sub-surface morphology of polished fused silica[6]

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Figure 4.4 The depth evolutions of SSD from grinding to polishing processes, after [7]

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Figure 4.5 Sharp indenter impact into surface of brittle glass under increasing force (top to bottom), and the corresponding unloading events. P, plastic

deformation; I, indentation mark; M, median crack; L, lateral crack [8, 9]

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crack rather than lateral crack initiates and propagates in isotropic materials (such as fused silica) beyond the load under which only plastic deformation occurs. The Hertzian cone crack is shown in Figure 4.6.

Figure 4.5 and Figure 4.6 are the situations for static indentations, i.e. non-moving indenters penetrate into a frictionless interface. When considering polishing processes, sliding/rolling and frictions between abrasive particles and work-piece surface become important and must be taken into account. For a sliding abrasive particle, the movement results in a change in the stress distribution that the peak stress is at the tailing edge of the particle. Therefore fracture occurs as an arc-shape rather than trailing ring-shape which is observed in frictionless Hertzian cone contact [10, 11]. The trailing crack on fused silica surface is shown in Figure 4.7.

It is believed that a critical load, 𝑝_𝑐, which is the initiation load for fracture (i.e., scratch and sub-surface crack), does exist. The critical load varies with the local shape of polishing particle and mechanical properties of both work-piece and particles[11, 12].

If the normal load acting on a polishing particle, 𝑝, is greater than the critical load (𝑝_crit), fracture occurs. The fracture initiation condition is written as

p pcrit (4.1)

During an ideal polishing process, the normal load acting on each polishing particle is quite low (10^-9-10^-6N), which is well below the critical fracture initiation load that is on the order of 0.001N for plastic and 0.1 N for brittle fracture[11, 13, 14].

Assume (1) only a very small fraction (less than 0.5), 𝑓_𝑙,of abrasive particles that loaded between the polishing pad and work-piece surface are actually involved in polishing [15]; and (2)abrasive particles between polishing pad and work-piece surface are mechanically loaded evenly. Therefore normal load per polishing particle can be calculated by

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Figure 4.6 Section view of Hertzian cone crack [16]

Figure 4.7 A crack on fused silica surface produced by a sliding ceria particle

125 total number of abrasive particles between the polishing pad and work-piece surface.

It is commonly assumed that the polishing pad is a purely elastic material, and therefore according to elastic contacting theory, the load applied on each particle is proportional to the depth of penetration for a fixed gap which is the mean particle size in the vertical direction. In other words, loads on particles actually vary with the size of particles, i.e. greater load is applied on larger particle. Therefore Equation (4.2) is true only if the polishing particles between the polishing pad and work-piece surface have the same sizes.

Figure 4.8 shows the tested (by Cilas Particle Size Analyzer) size distribution of the ceria particles, which we used in the experiments, with nominal diameter of 2.5 μm. In other words, the sizes of particle involved in polishing process are various. So the modified load on a polishing particle with diameter of, 𝑑, is given by

( ) ^{T T}

L c l T c

P d P d

p d N d f N d ^(4.3)

here, assume the polishing particles are sphere in shape, 𝑑_𝑐 is mean diameter of polishing particles. According to the Equation (4.3), as shown in Figure 4.9, d₃ > d₁ >

d₂, leads to p₃ > p₁ > p₂.

The variation of load on particle could possibly induce fracture on the work-piece surface if loads on some bigger particles are greater than the critical fracture initiation load. Especially when some rogue particles (such as dust or glass debris which are much bigger than the polishing particles) are involved in the polishing process due to

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Figure 4.8 Size distribution of ceria particles with nominal diameter of 2.5 μm measured using Cilas Particle Size Analyzer. The histogram stands for the

numerical ratio of abrasive versus sizes; and the red line stand for the cumulative percentage of abrasive versus sizes.

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Figure 4.9 Mechanisms of damage generation in polishing process (after [12])

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poorly maintained polishing conditions and environment. Therefore, surface scratches and sub-surface damage are generated in the polishing processes. Figure 4.7 is a typical scratch created in the polishing process.