Abstract

Magnetorheological finishing (MRF) is a deterministic subaperture polishingprocess. Theprocess 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.

© 2007 Optical Society of America

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    [CrossRef]
  2. D. Golini, S. D. Jacobs, W. I. Kordonski, and P. Dumas, "Precision optics fabrication using magnetorheological finishing," in Advanced Materials for Optics and Precision Structures, M. A. Ealey, ed., Proc. SPIE CR67, 251-274 (1997).
  3. S. D. Jacobs, S. A. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, "An overview of magnetorheological finishing (MRF) for precision optics manufacturing," in Ceramic Transactions, R. Sabia, V. A. Greenhut, and C. Pantano, eds. (ACERS, 1999).
  4. W. I. Kordonski and S. D. Jacobs, "Model of magnetorheological finishing," in Sixth International Conference on Adaptive Structures, C. A. Rogers, J. Tani, and E. J. Breitbach, eds. (Technomic, 1996), pp. 63-74.
  5. A. B. Shorey, S. D. Jacobs, W. I. Kordonski, and R. F. Gans, "Experiments and observations regarding the mechanisms of glass removal in magnetorheological finishing," Appl. Opt. 40, 20-33 (2001).
    [CrossRef]
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    [CrossRef]
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  17. F. Sugimoto, Y. Arimoto, and T. Ito, "Simultaneous temperature measurement of wafers in chemical mechanical polishing of silicon dioxide layer," Jpn. J. Appl. Phys. , Part 1 34, 6314-6320 (1995).
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  18. H. Matsuo, A. Ishikawa, and T. Kikkawa, "Role of frictional force on the polishing rate of Cu chemical mechanical polishing," Jpn. J. Appl. Phys. , Part 1 43, 1813-1819 (2004).
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  20. J. C. Lambropoulos, S. D. Jacobs, and J. Ruckmann, "Material removal mechanism from grinding to polishing," Ceram. Trans. 102, 113-128 (1999).
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  23. J. E. DeGroote, A. E. Marino, J. P. Wilson, K. E. Spencer, and S. D. Jacobs, "Effects of nanodiamond abrasive friability in experimental MR fluids with phosphate laser glass LHG-8 and other optical glasses," in Optical Manufacturing and Testing VI, H. P. Stahl, ed., Proc. SPIE 5869, 121-132 (2005).
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    [CrossRef]
  38. W. C. Oliver and G. M. Pharr, "Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology," J. Mater. Res. 19, 3-20 (2004).
    [CrossRef]
  39. R. H. Doremus, Y. Mehrotra, W. A. Lanford, and C. Burman, "Reaction of water with glass--influence of a transformed surface-Layer," J. Mater. Sci. 18, 612-622 (1983).
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  40. S. Nakashima, H. Matayoshi, T. Yuko, K. Michibayashi, T. Masuda, N. Kuroki, H. Yamagishi, Y. Ito, and A. Nakamura, "Infrared microspectroscopy analysis of water distribution in deformed and metamorphosed rocks," Tectonophysics 245, 263-276 (1995).
    [CrossRef]
  41. M. Maaza, B. Farnoux, F. Samuel, C. Sella, and P. Trocellier, "Effect of mechanical polishing on the surface-structure of glasses studied by grazing angle neutron reflectometry," Opt. Commun. 100, 220-230 (1993).
    [CrossRef]
  42. P. Baillif, B. Chouikhi, L. Barbanson, and J. C. Touray, "Dissolution kinetics of glass fibers in saline solution: in vitro persistence of a sparingly soluble aluminum-rich leached layer," J. Mater. Sci. 30, 5691-5699 (1995).
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2005 (1)

J. E. DeGroote, A. E. Marino, J. P. Wilson, K. E. Spencer, and S. D. Jacobs, "Effects of nanodiamond abrasive friability in experimental MR fluids with phosphate laser glass LHG-8 and other optical glasses," in Optical Manufacturing and Testing VI, H. P. Stahl, ed., Proc. SPIE 5869, 121-132 (2005).

2004 (3)

H. Matsuo, A. Ishikawa, and T. Kikkawa, "Role of frictional force on the polishing rate of Cu chemical mechanical polishing," Jpn. J. Appl. Phys. , Part 1 43, 1813-1819 (2004).
[CrossRef]

W. C. Oliver and G. M. Pharr, "Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology," J. Mater. Res. 19, 3-20 (2004).
[CrossRef]

M. Schinhaerl, E. Pitschke, R. Rascher, P. Sperber, R. Stamp, L. Smith, and G. Smith, "Temporal stability and performance of MR polishing fluid," in Current Developments in Lens Design and Optical Engineering, P. Z. Mouroulis, W. Smith, and R. B. Johnson, eds., Proc. SPIE 5523, 273-280 (2004).
[CrossRef]

2001 (2)

T. Hoshino, Y. Kurata, Y. Terasaki, and K. Susa, "Mechanism of polishing of SiO2 films by CeO2 particles," J. Non-Cryst. Solids 283, 129-136 (2001).
[CrossRef]

A. B. Shorey, S. D. Jacobs, W. I. Kordonski, and R. F. Gans, "Experiments and observations regarding the mechanisms of glass removal in magnetorheological finishing," Appl. Opt. 40, 20-33 (2001).
[CrossRef]

2000 (1)

U. Mahajan, M. Bielmann, and M. Singh, "Abrasive effects in oxide chemical mechanical polishing," Mater. Res. Soc. Symp. , Proc. 566, 27-32 (2000).
[CrossRef]

1999 (1)

J. C. Lambropoulos, S. D. Jacobs, and J. Ruckmann, "Material removal mechanism from grinding to polishing," Ceram. Trans. 102, 113-128 (1999).

1998 (2)

V. H. Bulsara, Y. Ahn, S. Chandrasekar, and T. N. Farris, "Mechanics of polishing," Trans. ASME , J. Appl. Mech. 65, 410-416 (1998).
[CrossRef]

A. Kaller, "Properties of polishing media for polishing optics," Glass Sci. Technol. 71, 174-183 (1998).

1997 (2)

D. Golini, S. D. Jacobs, W. I. Kordonski, and P. Dumas, "Precision optics fabrication using magnetorheological finishing," in Advanced Materials for Optics and Precision Structures, M. A. Ealey, ed., Proc. SPIE CR67, 251-274 (1997).

J. C. Lambropoulos, S. Xu, and T. Fang, "Loose abrasive lapping hardness of optical glasses and its interpretation," Appl. Opt. 36, 1501-1516 (1997).
[CrossRef] [PubMed]

1995 (6)

S. D. Jacobs, "Nanodiamonds enhance removal in magnetorheological finishing," Finer Points 7, 47-54 (1995).

F. Sugimoto, Y. Arimoto, and T. Ito, "Simultaneous temperature measurement of wafers in chemical mechanical polishing of silicon dioxide layer," Jpn. J. Appl. Phys. , Part 1 34, 6314-6320 (1995).
[CrossRef]

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Puchebner, D. Strafford, W. I. Kordonski, I. V. Prokhorov, E. Fess, D. Pietrowski, and V. W. Kordonski, "Magnetorheological finishing: a deterministic process for optics manufacturing," in Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE 2576, 372-383 (1995).
[CrossRef]

M. J. Cumbo, D. Fairhurst, S. D. Jacobs, and B. E. Puchebner, "Slurry particle size evolution during the polishing of optical-glass," Appl. Opt. 34, 3743-3755 (1995).
[CrossRef] [PubMed]

P. Baillif, B. Chouikhi, L. Barbanson, and J. C. Touray, "Dissolution kinetics of glass fibers in saline solution: in vitro persistence of a sparingly soluble aluminum-rich leached layer," J. Mater. Sci. 30, 5691-5699 (1995).
[CrossRef]

S. Nakashima, H. Matayoshi, T. Yuko, K. Michibayashi, T. Masuda, N. Kuroki, H. Yamagishi, Y. Ito, and A. Nakamura, "Infrared microspectroscopy analysis of water distribution in deformed and metamorphosed rocks," Tectonophysics 245, 263-276 (1995).
[CrossRef]

1993 (3)

M. Maaza, B. Farnoux, F. Samuel, C. Sella, and P. Trocellier, "Effect of mechanical polishing on the surface-structure of glasses studied by grazing angle neutron reflectometry," Opt. Commun. 100, 220-230 (1993).
[CrossRef]

M. Buijs and K. Korpel-van Houten, "A model for lapping of glass," J. Mater. Sci. 28, 3014-3020 (1993).
[CrossRef]

M. Buijs and K. Korpel-van Houten, "Three-body abrasion of brittle materials as studied by lapping," Wear 166, 237-245 (1993).
[CrossRef]

1992 (1)

W. C. Oliver and G. M. Pharr, "An Improved Technique for Determining Hardness and Elastic-Modulus Using Load and Displacement Sensing Indentation Experiments," J. Mater. Res. 7, 1564-1583 (1992).
[CrossRef]

1991 (1)

H. Dunken, "Surface chemistry of optical glasses," J. Non-Cryst. Solids 129, 64-75 (1991).
[CrossRef]

1990 (1)

L. M. Cook, "Chemical processes in glass polishing," J. Non-Cryst. Solids 120, 152-171 (1990).
[CrossRef]

1983 (1)

R. H. Doremus, Y. Mehrotra, W. A. Lanford, and C. Burman, "Reaction of water with glass--influence of a transformed surface-Layer," J. Mater. Sci. 18, 612-622 (1983).
[CrossRef]

1977 (1)

W. A. Lanford, "Glass hydration--method of dating glass objects," Science 196, 975-976 (1977).
[CrossRef] [PubMed]

1971 (1)

T. Izumitani and S. Harada, "Polishing mechanism of optical glasses," Glass Technol. 12, 131-135 (1971).

1947 (2)

K.-H. Sun, "Fundamental condition of glass formation," J. Am. Ceram. Soc. 30, 277-281 (1947).
[CrossRef]

K.-H. Sun and M. L. Huggins, "Energy additivity in oxygen-containing crystals and glasses, II," J. Phys. Colloid Chem. 51, 438-443 (1947).
[CrossRef] [PubMed]

1927 (1)

F. W. Preston, "The theory and design of plate glass polishing machines," J. Soc. Glass Technol. 11, 214-256 (1927).

Appl. Opt. (3)

Ceram. Trans. (1)

J. C. Lambropoulos, S. D. Jacobs, and J. Ruckmann, "Material removal mechanism from grinding to polishing," Ceram. Trans. 102, 113-128 (1999).

Finer Points (1)

S. D. Jacobs, "Nanodiamonds enhance removal in magnetorheological finishing," Finer Points 7, 47-54 (1995).

Glass Sci. Technol. (1)

A. Kaller, "Properties of polishing media for polishing optics," Glass Sci. Technol. 71, 174-183 (1998).

Glass Technol. (1)

T. Izumitani and S. Harada, "Polishing mechanism of optical glasses," Glass Technol. 12, 131-135 (1971).

J. Am. Ceram. Soc. (1)

K.-H. Sun, "Fundamental condition of glass formation," J. Am. Ceram. Soc. 30, 277-281 (1947).
[CrossRef]

J. Mater. Res. (2)

W. C. Oliver and G. M. Pharr, "An Improved Technique for Determining Hardness and Elastic-Modulus Using Load and Displacement Sensing Indentation Experiments," J. Mater. Res. 7, 1564-1583 (1992).
[CrossRef]

W. C. Oliver and G. M. Pharr, "Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology," J. Mater. Res. 19, 3-20 (2004).
[CrossRef]

J. Mater. Sci. (3)

R. H. Doremus, Y. Mehrotra, W. A. Lanford, and C. Burman, "Reaction of water with glass--influence of a transformed surface-Layer," J. Mater. Sci. 18, 612-622 (1983).
[CrossRef]

P. Baillif, B. Chouikhi, L. Barbanson, and J. C. Touray, "Dissolution kinetics of glass fibers in saline solution: in vitro persistence of a sparingly soluble aluminum-rich leached layer," J. Mater. Sci. 30, 5691-5699 (1995).
[CrossRef]

M. Buijs and K. Korpel-van Houten, "A model for lapping of glass," J. Mater. Sci. 28, 3014-3020 (1993).
[CrossRef]

J. Non-Cryst. Solids (3)

H. Dunken, "Surface chemistry of optical glasses," J. Non-Cryst. Solids 129, 64-75 (1991).
[CrossRef]

L. M. Cook, "Chemical processes in glass polishing," J. Non-Cryst. Solids 120, 152-171 (1990).
[CrossRef]

T. Hoshino, Y. Kurata, Y. Terasaki, and K. Susa, "Mechanism of polishing of SiO2 films by CeO2 particles," J. Non-Cryst. Solids 283, 129-136 (2001).
[CrossRef]

J. Phys. Colloid Chem. (1)

K.-H. Sun and M. L. Huggins, "Energy additivity in oxygen-containing crystals and glasses, II," J. Phys. Colloid Chem. 51, 438-443 (1947).
[CrossRef] [PubMed]

J. Soc. Glass Technol. (1)

F. W. Preston, "The theory and design of plate glass polishing machines," J. Soc. Glass Technol. 11, 214-256 (1927).

Jpn. J. Appl. Phys. (2)

F. Sugimoto, Y. Arimoto, and T. Ito, "Simultaneous temperature measurement of wafers in chemical mechanical polishing of silicon dioxide layer," Jpn. J. Appl. Phys. , Part 1 34, 6314-6320 (1995).
[CrossRef]

H. Matsuo, A. Ishikawa, and T. Kikkawa, "Role of frictional force on the polishing rate of Cu chemical mechanical polishing," Jpn. J. Appl. Phys. , Part 1 43, 1813-1819 (2004).
[CrossRef]

Mater. Res. Soc. Symp. (1)

U. Mahajan, M. Bielmann, and M. Singh, "Abrasive effects in oxide chemical mechanical polishing," Mater. Res. Soc. Symp. , Proc. 566, 27-32 (2000).
[CrossRef]

Opt. Commun. (1)

M. Maaza, B. Farnoux, F. Samuel, C. Sella, and P. Trocellier, "Effect of mechanical polishing on the surface-structure of glasses studied by grazing angle neutron reflectometry," Opt. Commun. 100, 220-230 (1993).
[CrossRef]

Proc. SPIE (4)

M. Schinhaerl, E. Pitschke, R. Rascher, P. Sperber, R. Stamp, L. Smith, and G. Smith, "Temporal stability and performance of MR polishing fluid," in Current Developments in Lens Design and Optical Engineering, P. Z. Mouroulis, W. Smith, and R. B. Johnson, eds., Proc. SPIE 5523, 273-280 (2004).
[CrossRef]

S. D. Jacobs, D. Golini, Y. Hsu, B. E. Puchebner, D. Strafford, W. I. Kordonski, I. V. Prokhorov, E. Fess, D. Pietrowski, and V. W. Kordonski, "Magnetorheological finishing: a deterministic process for optics manufacturing," in Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE 2576, 372-383 (1995).
[CrossRef]

D. Golini, S. D. Jacobs, W. I. Kordonski, and P. Dumas, "Precision optics fabrication using magnetorheological finishing," in Advanced Materials for Optics and Precision Structures, M. A. Ealey, ed., Proc. SPIE CR67, 251-274 (1997).

J. E. DeGroote, A. E. Marino, J. P. Wilson, K. E. Spencer, and S. D. Jacobs, "Effects of nanodiamond abrasive friability in experimental MR fluids with phosphate laser glass LHG-8 and other optical glasses," in Optical Manufacturing and Testing VI, H. P. Stahl, ed., Proc. SPIE 5869, 121-132 (2005).

Science (1)

W. A. Lanford, "Glass hydration--method of dating glass objects," Science 196, 975-976 (1977).
[CrossRef] [PubMed]

Tectonophysics (1)

S. Nakashima, H. Matayoshi, T. Yuko, K. Michibayashi, T. Masuda, N. Kuroki, H. Yamagishi, Y. Ito, and A. Nakamura, "Infrared microspectroscopy analysis of water distribution in deformed and metamorphosed rocks," Tectonophysics 245, 263-276 (1995).
[CrossRef]

Trans. ASME (1)

V. H. Bulsara, Y. Ahn, S. Chandrasekar, and T. N. Farris, "Mechanics of polishing," Trans. ASME , J. Appl. Mech. 65, 410-416 (1998).
[CrossRef]

Wear (1)

M. Buijs and K. Korpel-van Houten, "Three-body abrasion of brittle materials as studied by lapping," Wear 166, 237-245 (1993).
[CrossRef]

Other (33)

D. C. Cornish and I. M. Watt, The Mechanism of Glass Polishing (SIRA Institute, Ltd., 1963).

MetroPro Reference Guide (Zygo Corporation, 2001).

A. B. Shorey, "Mechanisms of material removal in magnetorheological finishing (MRF) of glass," Ph.D. dissertation (University of Rochester, 2000).

S. D. Jacobs, S. A. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, D. Golini, W. I. Kordonski, P. Dumas, and S. Hogan, "An overview of magnetorheological finishing (MRF) for precision optics manufacturing," in Ceramic Transactions, R. Sabia, V. A. Greenhut, and C. Pantano, eds. (ACERS, 1999).

W. I. Kordonski and S. D. Jacobs, "Model of magnetorheological finishing," in Sixth International Conference on Adaptive Structures, C. A. Rogers, J. Tani, and E. J. Breitbach, eds. (Technomic, 1996), pp. 63-74.

A. S. Birks and R. E. Green, Jr., "Material characterization methods," in Nondestructive Testing Handbook, P.McIntyre, ed. (American Society for Nondestructive Testing, 1991), pp. 386-402.

A. G. Evans, Fracture Toughness: The Role of Indentation Techniques (American Society for Testing and Materials, 1979), pp. 112-135.

Mark IV xp Interferometer, Zygo Corporation, Middlefield, Conn. 06455.

Taylsurf CCI 3000 noncontact 3D surface profiler. Taylor Hobson Inc., Rolling Meadows, IL 60008. The 50× objective (0.37 × 0.37 mm2) and four phase averages were used for each measurement.

J. C. Lambropoulos, "What mechanics and materials science can do for the modern optical workshop," in Fall 1999 Workshop (APOMA, 1999).

J. C. Lambropoulos, F. Yang, and S. D. Jacobs, "Toward a mechanical mechanism for material removal in magnetorheological finishing," in Optical Fabrication and Testing Workshop (Optical Society of America, 1996), pp. 150-153.

S. D. Jacobs, W. I. Kordonski, I. V. Prokhorov, D. Golini, G. R. Gorodkin, and T. D. Strafford, "Magnetorheological fluid composition," U.S. patent 5,804,095 (8 September 1998).

UK Abrasives Inc., 3045 Mac Arthur Boulevard, Northbrook, Ill. 60062.

J. E. DeGroote, "Surface interactions between nanodiamonds and glass in magnetorheological finishing (MRF)," Ph.D. dissertation (University of Rochester, 2007).

pH meter, Beckman Coulter, Inc., 4300 North Harbor Boulevard, Fullerton, Calif. 92834.

Combination pH Electrode, Sensorex, Garden Grove, Calif. 92841.

Computrac Max-1000 Moisture Analyzer, Arizona Instrument, 4114 East Wood Street, Phoenix, Ariz. 85040.

Nano Indenter XP and Testworks 4 software, MTS Nano Instruments, 1001 Larson Drive, Oak Ridge, Tenn. 37830.

American Society for Testing and Materials, "Standard test method for Vickers indentation hardness of advanced ceramics," ASTM International C 1327-03 (American Society for Testing and Materials, 2003), pp. 462-469.

M. J. Cumbo, "Chemo-mechanical interactions in optical polishing," Ph.D. dissertation (University of Rochester, 1993).

Schott North America, Inc., 555 Taxter Road, Elmsford, N.Y. 10523 (2001 version).

Hoya Corporation, 572 Miyazawa-cho, Akishima-shi, Tokyo, Japan (1998 version).

D. C. Brown, S. D. Jacobs, J. A. Abate, O. Lewis, and J. Rinefierd, "Figures of merit and correlations of physical and optical properties in laser glasses," in 9th Annual Symposium on Optical Materials for High Power Lasers, in Laser Induced Damage in Optical Materials, A. J. Glass and A. H. Guenther, eds. National Bureau of Standards (U.S.), Spec. Publ. 509 (National Bureau of Standards, 1977), pp. 416-433.

Kistler single axis slim line shear load cell measuring system, model 9143B21 (www.kistler.com), Maxwell Bennett Associates, P.O. Box 401, West Henrietta, N.Y. 14586.

National Instruments Corporation, 11500 N Mopac Expressway, Austin, Tex. 78759-3504.

MRF force sensor program was written while Jason Keck was employed at The Laboratory for Laser Energetics. Keck is now employed at Semrock, Inc. 3625 Buffalo Road, Suite 6, Rochester, N.Y. 14624.

The force sensor setup was designed by Andrew Dillenbeck of The Laboratory for Laser Energetics, 250 East River Road, Rochester N.Y. 14623.

"Ohara Optical Glass Catalogue," 7 (Ohara Corporation, 2005).

T. S. Izumitani, "Cold working of optical glasses," in Optical Glass (American Institute of Physics, 1986).

A. Wheeler and A. Ganji, Introduction to Engineering Experimentation (Prentice-Hall, 1996), pp. 145-149.

J. C. Lambropoulos, Rochester, N.Y. (personal communication, 2005).

NSL Analytical, 7650 Hub Parkway, Cleveland, Ohio 44125; phone: (216) 447-1550, e-mail: nsl@nslanalytical.com; http://www.nslanalytical.com.

R. C. Weast, ed. CRC Handbook of Chemistry and Physics, 68th ed. (CRC, 1986), pp. F169-F172.

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Figures (13)

Fig. 1
Fig. 1

Schematic of the MRF contact zone (not to scale).

Fig. 2
Fig. 2

Interferometric image of an MRF spot. Maximum removal in the region of deepest penetration (ddp) is indicated with an arrow in the figure. Typical spotting time is 2 s to achieve approximately 0.2 μm deep spots.

Fig. 3
Fig. 3

Pictures of STM during spot formation.

Fig. 4
Fig. 4

Photograph of the piezoelectric force sensor used to measure drag force, mounted on the STM.

Fig. 5
Fig. 5

Percent weight loss, D s , versus testing solution pH for all six optical glasses. The D s relationships that are used in our MRF material removal model are located on the right-hand side of the figure.

Fig. 6
Fig. 6

Bulk and near surface mechanical FOM values plotted with peak removal rate data for MRF spots taken with 0.01 vol. % UK-medium A nanodiamond MR fluid.

Fig. 7
Fig. 7

Peak removal rate plotted versus drag force for our six optical glasses in MR fluids with increasing concentrations of NDP nanodiamonds.

Fig. 8
Fig. 8

Peak removal rate versus drag force for four 0.01 vol . % nanodiamond MR fluids. Spots were taken on all six glasses with each fluid. The glass types are identified for the NDP points only to make the figure easier to read. The glass order is the same for the other nanodiamond fluids.

Fig. 9
Fig. 9

Peak removal rate versus F d / H s for four 0.01 vol. % nanodiamond MR fluids. Spots were taken on all six glasses with each fluid. The glass types are identified for the NDP points only to make the figure easier to read. The glass order is the same for the other nanodiamond fluids.

Fig. 10
Fig. 10

Peak removal rate data versus the third term of the MRF material removal rate model. The experimental data for this plot includes the increasing nanodiamond concentration for the 29, 35, 44, and 54 nm nanodiamond experiments. CI size and concentration are constant as described in the text. The confidence levels are all greater than 99%.

Fig. 11
Fig. 11

Peak removal rate versus term 4 of our MRF material removal model. The 0.01 vol . % UK-medium A nanodiamond fluid was allowed to naturally age for nine days in the STM. All spots were made using the same operating conditions. The confidence levels for all of the linear trend lines drawn in the figure are greater than 99%.

Fig. 12
Fig. 12

Peak removal rate versus term 5 with the average single bond strength for five MR fluids.

Fig. 13
Fig. 13

Experimental peak removal rate data for six glasses with various MR fluids versus our MRF material removal rate model, incorporating mechanics, polishing particle properties, and chemistry. The terms A, v, B n d , ϕ CI , C CI , B CI , b, R, and T are all constant.

Tables (6)

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Table 1 Optical Glass Mechanical Properties Rank Ordered by Increasing Mechanical FOM

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Table 2 Young's Modulus Data Measured on the Bulk Glass (Pulse-Echo Method) and at a Depth of 60 nm Into the Surface (Nanoindentation) in Three Different Fluid Environments

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Table 3 Microhardness Data Measured on the Bulk Glass (Vickers) and Nanohardness Measured at a Depth of 60 nm Into the Surface (Nanoindentation) in Three Different Fluid Environments

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Table 4 Mechanical FOM Values Calculated From Young's Modulus and Hardness Values Measured for the Bulk (B), the Dry Near Surface (D), the Near Surface in DI Water (W), and the Near Surface in MR Fluid Supernatant (S)

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Table 5 Composition Data for Our Glass Set a

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Table 6 Calculated Average Single Bond Strength and Term 5, b is a Unitless Coefficient Empirically Equal to 1000

Equations (13)

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Amount of polishing p v t ,
MRR = C p p v ,
w = μ A p v t .
MRR = C p , B 1 n P i 3 / 4 L m , c E 5 / 4 K c H v 2 p v .
MRR e E A / R T .
MRR = C p , M F f v .
MRR A c 1 / 3 ϕ 1 / 3 .
MRR A c 1 / 3 ϕ 4 / 3 .
MRR = C p p v = C p L A v = C p , S μ L A v = C p , S F d A v = C p , S τ v .
MRR peak [ E S K c H S 2 ] Term 1 [ F d A v ] Term 2 × [ B n d ϕ n d 1 / 3 C n d 1 / 3 + B CI ϕ CI 4 / 3 C CI ] Term 3 × [ D s ( pH MRF ) 3 / 10 ] Term 4 [ e sbs / bRT ] Term 5 .
MRR vol E B 7 / 6 K c H k 23 / 12 .
MRR peak E B K c H V 2 ,
MRR peak E S K c H S 2 ,

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