John C. Lambropoulos

Thermal conductivity of dielectric thin films

A direct reading thermal comparator has been used to measure the thermal conductivity of dielectric thin‐film coatings. In the past, the thermal comparator has been used extensively to measure the thermal conductivity of bulk solids, liquids, and gases. The technique has been extended to thin‐film materials by making experimental improvements and by the application of an analytical heat flow model. Our technique also allows an estimation of the thermal resistance of the film/substrate interface which is shown to depend on the method of film deposition. The thermal conductivity of most thin films was found to be several orders of magnitude lower than that of the material in bulk form. This difference is attributed to structural disorder of materials deposited in thin‐film form. The experimentation to date has primarily centered on optical coating materials. These coatings, used to enhance the optical properties of components such as lenses and mirrors, are damaged by thermal loads applied in high‐power las...

Subsurface damage in some single crystalline optical materials

We present a nondestructive method for estimating the depth of subsurface damage (SSD) in some single crystalline optical materials (silicon, lithium niobate, calcium fluoride, magnesium fluoride, and sapphire); the method is established by correlating surface microroughness measurements, specifically, the peak-to-valley (p-v) microroughness, to the depth of SSD found by a novel destructive method. Previous methods for directly determining the depth of SSD may be insufficient when applied to single crystals that are very soft or very hard. Our novel destructive technique uses magnetorheological finishing to polish spots onto a ground surface. We find that p-v surface microroughness, appropriately scaled, gives an upper bound to SSD. Our data suggest that SSD in the single crystalline optical materials included in our study (deterministically microground, lapped, and sawed) is always less than 1.4 times the p-v surface microroughness found by white-light interferometry. We also discuss another way of estimating SSD based on the abrasive size used.

Surface microroughness of optical glasses under deterministic microgrinding

Deterministic microgrinding of precision optical components with rigid, computer-controlled machining centers and high-speed tool spindles is now possible on a commercial scale. Platforms such as the Opticam systems at the Center for Optics Manufacturing produce convex and concave spherical surfaces with radii from 5 mm to ∞, i.e., planar, and work diameters from 10 to 150 mm. Aspherical surfaces are also being manufactured. The resulting specular surfaces have a typical rms microroughness of 20 nm, 1 μm of subsurface damage, and a figure error of less than 1 wave peak to valley. Surface roughness under deterministic microgrinding conditions (fixed infeed rate) with bound abrasive diamond ring tools with various degrees of bond hardness is correlated to a material length scale, identified as a ductility index, involving the hardness and fracture toughness of glasses. This result is in contrast to loose abrasive grinding (fixed nominal pressure), in which surface microroughness is determined by the elastic stiffness and the hardness of the glass. We summarize measurements of fracture toughness and microhardness by microindentation for crown and flint optical glasses, and fused silica. The microindentation fracture toughness in nondensifying optical glasses is in good agreement with bulk fracture toughness measurement methods.

Removal rate model for magnetorheological finishing of glass

Magnetorheological finishing (MRF) is a deterministic subaperture polishing process. The process uses a magnetorheological (MR) fluid that consists of micrometer-sized, spherical, magnetic carbonyl iron (CI) particles, nonmagnetic polishing abrasives, water, and stabilizers. Material removal occurs when the CI and nonmagnetic polishing abrasives shear material off the surface being polished. We introduce a new MRF material removal rate model for glass. This model contains terms for the near surface mechanical properties of glass, drag force, polishing abrasive size and concentration, chemical durability of the glass, MR fluid pH, and the glass composition. We introduce quantitative chemical predictors for the first time, to the best of our knowledge, into an MRF removal rate model. We validate individual terms in our model separately and then combine all of the terms to show the whole MRF material removal model compared with experimental data. All of our experimental data were obtained using nanodiamond MR fluids and a set of six optical glasses.

The isotropic assumption during the Czochralski growth of single semiconductors crystals

Abstract The finite element method is used in order to determine the validity of the commonly made assumption that crystals grown by the Czochralski method may be modeled as elastically isotropic. Using elastic constants typical of Si, GaAs, InP, and GaSb, we calculate the stresses and dislocation densities under the isotropic assumption, and also by fully accounting for the elastic anisotropy of crystals grown along the or directions. Comparison of the two calculations determines the extent of the validity of the isotropic assumption. We also address the question of whether or not it is possible to suppress the dependence of the stresses on the circumferential coordinate, thus reducing the original three-dimensional problem (dependence on r , θ, z ) to a two-dimensional problem (dependence on r, z only) involving fewer unknowns, while still accounting (in an approximate manner) for the anisotropy of the grown crystal in a satisfactory way. Under these circumstances, the Navier-Stokes equations for the radial u ( r, z ) and axial displacement w ( r, z ) are derived. These equations involve the Poisson ratio as well as a measure of the anisotropy of the crystal, but they are independent of the circumferential coordinate θ.

Shear stress in magnetorheological finishing for glasses

We report in situ, simultaneous measurements of both drag and normal forces in magnetorheological finishing (MRF) for what is believed to be the first time, using a spot taking machine (STM) as a test bed to take MRF spots on stationary parts. The measurements are carried out over the entire area where material is being removed, i.e., the projected area of the MRF removal function/spot on the part surface, using a dual force sensor. This approach experimentally addresses the mechanisms governing material removal in MRF for optical glasses in terms of the hydrodynamic pressure and shear stress, applied by the hydrodynamic flow of magnetorheological fluid at the gap between the part surface and the STM wheel. This work demonstrates that the volumetric removal rate shows a positive linear dependence on shear stress. Shear stress exhibits a positive linear dependence on a material figure of merit that depends upon Youngs modulus, fracture toughness, and hardness. A modified Prestons equation is proposed that better estimates MRF material removal rate for optical glasses by incorporating mechanical properties, shear stress, and velocity.

Process parameter effects on material removal in magnetorheological finishing of borosilicate glass

We investigate the effects of processing parameters on material removal for borosilicate glass. Data are collected on a magnetorheological finishing (MRF) spot taking machine (STM) with a standard aqueous magnetorheological (MR) fluid. Normal and shear forces are measured simultaneously, in situ, with a dynamic dual load cell. Shear stress is found to be independent of nanodiamond concentration, penetration depth, magnetic field strength, and the relative velocity between the part and the rotating MR fluid ribbon. Shear stress, determined primarily by the material mechanical properties, dominates removal in MRF. The addition of nanodiamond abrasives greatly enhances the material removal efficiency, with the removal rate saturating at a high abrasive concentration. The volumetric removal rate (VRR) increases with penetration depth but is insensitive to magnetic field strength. The VRR is strongly correlated with the relative velocity between the ribbon and the part, as expected by the Preston equation. A modified removal rate model for MRF offers a better estimation of MRF removal capability by including nanodiamond concentration and penetration depth.

Twyman effect mechanics in grinding and microgrinding

In the Twyman effect (1905), when one side of a thin plate with both sides polished is ground, the plate bends: The ground side becomes convex and is in a state of compressive residual stress, described in terms of force per unit length (Newtons per meter) induced by grinding, the stress (Newtons per square meter) induced by grinding, and the depth of the compressive layer (micrometers). We describe and correlate experiments on optical glasses from the literature in conditions of loose abrasive grinding (lapping at fixed nominal pressure, with abrasives 4-400 μm in size) and deterministic microgrinding experiments (at a fixed infeed rate) conducted at the Center for Optics Manufacturing with bound diamond abrasive tools (with a diamond size of 3-40 μm, embedded in metallic bond) and loose abrasive microgrinding (abrasives of less than 3 μm in size). In brittle grinding conditions, the grinding force and the depth of the compressive layer correlate well with glass mechanical properties describing the fracture process, such as indentation crack size. The maximum surface residual compressive stress decreases, and the depth of the compressive layer increases with increasing abrasive size. In lapping conditions the depth of the abrasive grain penetration into the glass surface scales with the surface roughness, and both are determined primarily by glass hardness and secondarily by Youngs modulus for various abrasive sizes and coolants. In the limit of small abrasive size (ductile-mode grinding), the maximum surface compressive stress achieved is near the yield stress of the glass, in agreement with finite-element simulations of indentation in elastic-plastic solids.

Loose abrasive lapping hardness of optical glasses and its interpretation

We present an interpretation of the lapping hardness of commercially available optical glasses in terms of a micromechanics model of material removal by subsurface lateral cracking. We analyze data on loose abrasive microgrinding, or lapping at fixed nominal pressure, for many commercially available optical glasses in terms of this model. The Schott and Hoya data on lapping hardness are correlated with the results of such a model. Lapping hardness is a function of the mechanical properties of the glass: The volume removal rate increases approximately linearly with Youngs modulus, and it decreases with fracture toughness and (approximately) the square of the Knoop hardness. The microroughness induced by lapping depends on the plastic and elastic properties of the glass, depending on abrasive shape. This is in contrast to deterministic microgrinding (fixed infeed rate), where it is determined from the plastic and fracture properties of the glass. We also show that Prestons coefficient has a similar dependence as lapping hardness on glass mechanical properties, as well as a linear dependence on abrasive size for the case of brittle material removal. These observations lead to the definition of an augmented Preston coefficient during brittle material removal. The augmented Preston coefficient does not depend on glass material properties or abrasive size and thus describes the interaction of the glass surface with the coolant-immersed abrasive grain and the backing plate. Numerical simulations of indentation are used to locate the origin of subsurface cracks and the distribution of residual surface and subsurface stresses, known to cause surface (radial) and subsurface (median, lateral) cracks.

Anisotropic thermal conductivity of rare earth--transition metal thin films

Thermal conductivity measurements were performed on several amorphous rare earth transition metal thin films of varying microstructure. The thermal conductivity perpendicular to the plane of the film, measured by the thermal comparator method, was compared with the thermal conductivity value measured parallel to the plane of the film. The latter value was obtained by converting electrical conductivity values to thermal conductivity via the Wiedemann--Franz relationship. As expected, the columnar microstructure induced during the sputter deposition of the thin films causes an anisotropy in the thermal conductivity values, with the in-plane values consistently lower than the out-of-plane values. The effect is most pronounced for the more columnar films deposited at higher pressure, for which the in-plane thermal conductivity, 0.3 W/mK, is an order of magnitude lower than the out-of-plane thermal conductivity, 4.3 W/mK. The thermal conductivity out of the plane of the film decreased with increasing deposition pressure, due to the decreasing film density.