WO2013019875A1

WO2013019875A1 - Method and system for polishing solid hollow spheres

Info

Publication number: WO2013019875A1
Application number: PCT/US2012/049184
Authority: WO
Inventors: Tayyab I. SURATWALA; William A. Steele; Michael D. Feit; Michael Stadermann; Jim E. FAIR; Kuang Jen Wu; Kari MORENA; Kuo-Chun Chen; Abbas KIKROO; Kelly YOUNGBLOOD
Original assignee: Lawrence Livermore National Security, Llc
Priority date: 2011-08-02
Filing date: 2012-08-01
Publication date: 2013-02-07

Abstract

A method of polishing an object includes placing the object in a container and placing a load bearing media different than the object in the container. The method also includes placing a polishing compound in the container and rotating the container about an axis of rotation.

Description

METHOD AND SYSTEM FOR POLISHING SOLID HOLLOW

SPHERES

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No.

61/514,430, filed on August 2, 201 1 , entitled "Method and System for Polishing Solid Hollow Spheres," the disclosure of which is hereby incorporated by reference in its entirety for all purposes. STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER

FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

[0002] The United States Government has rights in this invention pursuant to Contract No. DE-AC52-07NA27344 between the U.S. Department of Energy and Lawrence Livermore National Security, LLC, for the operation of Lawrence Livermore National Laboratory.

BACKGROUND OF THE INVENTION

[0003] Plastic shells are used in Inertial Confinement Fusion (ICF) laser targets. During the laser firing, the capsule absorbs energy and compresses/implodes, causing the hydrogen isotope fuel within the capsule to greatly increase in density. In order to provide an efficient implosion process, the surface quality of the capsules is controlled. As-made capsules have bumps and dimples (as high as several microns and tens of microns wide) as a consequence of the deposition process for making the capsules. These bumps greatly degrade the ability for the capsule to compress uniformly. Therefore, there is a need in the art for improved methods and systems for improving capsule surface quality.

SUMMARY OF THE INVENTION

[0004] According to the present invention, techniques related to optical components are provided. More particularly, embodiments of the present invention relate to methods and systems for polishing solid or hollow spheres, for example, hollow plastic spheres. Merely by way of example, the invention has been applied to a tumble finishing process in which local planarization of surface non-uniformities on an external surface of an object is performed. The methods and systems described herein are applicable to the processing and fabrication of a wide variety of optical materials suitable for use with high power laser and amplifier systems.

[0005] According to an embodiments of the present invention, a new method for polishing and achieving local planarization on precision spherical, plastic capsules is provided. Such capsules have various applications, such as ablators used in high-peak-power laser targets for fusion energy research. The as-manufactured ablators contain many shallow domes (many 100's of nm high and a few l O's of μπι wide) on the outer surface which are undesirable due to their contribution to instabilities during implosion. These capsules were polished (i.e., Tumble Finished) by rotating a cylindrical vial containing the capsule, many borosilicate glass or zirconia media, and an aqueous-based colloidal silica polishing slurry. During Tumble Finishing, the relative media/capsule motions cause multiple, random sliding spherical-spherical Hertzian contacts, resulting in material removal, and possibly plastic deformation, on the capsule. As a result, the domes were observed to locally planarize (i.e., converge to lower heights). Utilizing the correct kinematics (i.e., the characteristics of the media/capsule motions), as controlled by the vial rotation rate and the fill fraction of media and slurry, high velocity downward circumferential media motions were avoided, preventing fracturing of the fragile capsules. Also, the resulting post-polished surface roughness on the capsule was found to scale with the initial media surface roughness. Hence, pre-polishing the media greatly reduced the roughness of the media and thus the roughness of the polished capsule. A material removal model is described based on the Preston model and spherical- spherical Hertzian contacts which shows reasonable agreement with measured average removal rates of 35±1 5 nm/day and which serves as a valuable tool to scale the polishing behavior with changes in process variables. Narrow domes were observed to planarize more rapidly than wider domes. A local planarization convergence model is also described, based on the concept of workpiece-lap mismatch where the local pressure, and hence removal, varies with the gap at the interface contact. The calculated rate and shape evolution of various size isolated domes compares well with the experimental data. [0006] According to an embodiment of the present invention, a method of polishing an object is provided. The method includes placing the object in a container and placing a load bearing media different than the object in the container. The method also includes placing a polishing compound in the container and rotating the container about an axis of rotation. [0007] According to another embodiment of the present invention, an apparatus for polishing an object is provided. The apparatus includes a generally cylindrical container characterized by an internal volume and the object disposed in the container. The apparatus also includes a plurality of load bearing media disposed in the container. The plurality load bearing media are different from the object. The apparatus further includes a polishing compound disposed in the container and a rotation device operable to rotate the container about an axis of rotation.

[0008] In an embodiment, the present invention provides methods for polishing and smoothing hollow and solid plastic spheres by tumbling in a cylindrical container in the presence of media and slurry. The media (typically solid glass spheres) acts as a load bearing medium against the shell or sphere being polished and the aqueous slurry contains polishing particles (typically colloidal silica), which remove material from the surface of the shell. This technique has been optimized to remove local bumps and dimples (with heights or depths as high as several microns and widths of tens of microns) reducing the overall roughness on plastic shells. Also, this polishing method and process has been specifically tailored: 1 ) not to cause significant scratching, 2) not to modify the overall roundness of the shell/sphere, 3) not to fracture the shell/sphere, and 4) not to embed polishing particles into the sphere surface. The smoothness of these plastic shells is an important parameter for plastic shells used in targets for high power fusion lasers. These plastic shells are designed to compress and implode during the laser firing. Increasing the surface smoothness can dramatically reduce the asymmetry of the capsule compression/implosion. Symmetric capsule

compression/implosion is a critical criterion for creating a target with a high probability of achieving ignition. This polishing method can also be applied to polishing or smoothing of plastic shells or spheres used for a wide variety sphere manufacturing.

[0009] The present invention has applications and uses for polishing capsules for fusion laser targets and well as commercial/industrial sphere manufacturing, such as bearings or hollow spheres, especially for cases when the spheres are fragile and surface smoothness requirements are high.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 is a photo of a capsule shell (2 mm diameter) used as an ablator in high- peak-power laser targets for fusion energy research;

[0011] FIGS. 2A - 2C illustrate SEM micrographs of the capsule surface as-deposited, after conventional polishing, and after Tumble Finishing performed according to an embodiment of the present invention, respectively; [0012] FIG. 3 is a photo of an acrylic vial cylinder (60 mm long) containing colloidal silica slurry, glass media, and a single capsule according to an embodiment of the present invention;

[0013] FIG. 4A is a schematic diagram of an AFM spheremapper for characterizing capsule surface and shape; [0014] FIG. 4B is a schematic of a PSDI scanning interferometer for characterizing isolated defects (i.e., domes);

[0015] FIG. 5 is a schematic diagram illustrating characteristic motions of the capsule and media during Tumble Finishing according to an embodiment of the present invention;

[0016] FIG. 6 is a plot illustrating circumferential motion fraction (f_m) as function of vial rotation rate (R_v), media fill fraction (f,), and slurry fill fraction (f_s) according to an embodiment of the present invention;

[0017] FIGS. 7A and 7B are SEM images of a capsule surface after Tumble Finishing without a pre-polished media/vial and with a pre-polished media/vial according to an embodiment of the present invention, respectively; [0018] FIG. 8 is a plot illustrating measured areal pit density as function of media roughness according to an embodiment of the present invention;

[0019] FIGS. 9A and 9B are optical micrographs of the capsule surface before and after Tumble Finishing according to an embodiment of the present invention, respectively. [0020] FIGS. 9C and 9D are plots of the isolated defect distribution on the same capsule as measured by PSDI before and after Tumble Finishing according to an embodiment of the present invention, respectively;

[0021] FIG. 9E is a plot showing comparison of capsule roughness before and after Tumble Finishing as function of mode number (i.e., Power Spectral Density) from the average of 3 full circumference AFM lines scans according to an embodiment of the present invention.

[0022] FIG. 1 OA is a PSDI image and a corresponding line scan of a capsule surface before (left) and after (right) Tumble Finishing of an isolated, narrow dome on the capsule.

[0023] FIG. 1 OB is a PSDI image and a corresponding line scan of a capsule surface before (left) and after (right) Tumble Finishing of an isolated, wide dome on the capsule.

[0024] FIGS. 1 1A and 1 IB are schematic diagrams illustrating relevant parameters and dynamics of the media and capsule for a cascading motion during approach and at contact during Tumble Finishing according to an embodiment of the present invention, respectively.

[0025] FIG. 12 is a plot illustrating the calculated load at contact (P), the contact zone diameter (2a), and the removal rate (dh/dt) for a range of possible relative velocities and values according to an embodiment of the present invention;

[0026] FIGS. 13 A - 13D are x-lineouts of 3D simulations of the surface evolution of various dome and dimple defects during Tumble Finishing according to an embodiment of the present invention; [0027] FIG. 14 is a plot of calculated post-Tumble Finishing heights of various measured domes and dimples (using Eq. l i b and initial measured heights (h₀) and width (w₀)) cross plotted with the measured final height of the same corresponding domes and dimples. The dashed line corresponds to a 1 -to-l correlation between calculated and measured values; and

[0028] FIG. 1 5 is a simplified flowchart illustrating a method of polishing an object according to an embodiment of the present invention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

[0029] Typical ablators are hollow, spherical plastic capsules (~2 mm in diameter) used on ignition targets in high-peak-power laser systems such as the National Ignition Facility (NIF). During their fabrication, isolated defects (typically bumps which are 100's of nm high and 10's of μπι in width) are present on the outer surface which can have a negative impact on target performance due to their contributions to instability or mix during implosion.

[0030] According to embodiments of the present invention, methods and systems for polishing and achieving local planarization on hollow plastic spheres, which can be referred to as Tumble Finishing are provided. In some embodiments, tumble finishing is performed by rotating a cylindrical vial (-25 mm in diameter) containing the capsule, glass media (~2 mm in diameter), and an aqueous-based colloidal silica (-50 nm) slurry. The isolated defect distribution and the shape and roughness of the capsules were characterized before & after polishing using PSDI (phase shifting diffractive interferometry) and AFM (atomic force microscopy). Successful polishing (i.e. achieving bump removal and planarization without fracturing, scratching, or causing impact damage) is provided by embodiments of the present invention. Parameters utilized herein include use of the appropriate media (e.g., material, size & surface roughness), kinematics, and fill fraction of media & slurry. Taller, wider bumps were found to planarize and converge more slowly than shorter, narrow bumps. Using the Preston model applied to small tool polishing and an isolated defect convergence model, the rate of local planarization can be quantitatively computed and compared with the experimental data. The Tumble Finishing process can be implemented as a standard production process for making ablators and contributes to improved ablator production yield by reducing Mixed Mass (a metric used to describe the degree of contribution of the isolated defects to the instability of the implosion).

[0031] Specifications for the NIF include the specification that ignition capsules are characterized by a small number of large surface defects in order to minimize the amount of ablator material mixed into the hot spot at ignition. The inventors have quantified contributing isolated defects using a phase shifting diffraction interferometer (PSDI) technique and process the ignition capsules as described herein to reduce these features.

[0032] Capsules are tumble finished in a process developed for ablator targets (also referred to as capsules) but applicable to a wider variety of objects including a variety of optical elements. Typically, capsules may have a number of defects with widths larger than thirty microns and heights greater than 600 nm. In an embodiment, capsules are polished in four day increments based on the largest twenty-five isolated defects, individual domes, and clusters of domes. These processes have improved the capsule yields. Embodiments of the present invention are also useful in removing residual debris, minimizing scratches, and increasing production rates.

[0033] According to some embodiments of the present invention, methods and systems are provided for locally planarizing spherical surfaces in which the surface roughness is reduced without substantially modifying the initial shape of the object being polished. Although some embodiments are discussed in terms of locally planarizing spherical surfaces, the surfaces do not need to be spherical and other surfaces including elliptical surfaces are included within the scope of the present invention, which provides for local planarization of a variety of media.

[0034] Precision plastic, spherical capsules are needed for some applications, such as ablators used in targets in high-peak-power laser systems for fusion energy research, such as the NIF. As an example, FIG. 1 is a photo of a capsule shell (2 mm diameter) used as an ablator in high-peak-power laser targets for fusion energy research. These ablators, which can have dimensions on the order of millimeters (e.g., 2 mm in diameter and -190 μηι thick) are injected with isotopes of hydrogen that are frozen as a layer on the inner surface, which compress through laser inertial confinement. The capsules are fabricated using plasma- assisted chemical vapor deposition (PA-CVD), where hydrogen and trans-2-butene are broken down to form an amorphous polymer coating on a pre-fabricated spherical poly-a- methylstyrene (PAMS) substrate (called mandrels) produced by micro-encapsulation. Later, the mandrels are removed through thermal decomposition.

[0035] In some applications such as inertial confinement fusion, the capsules have stringent surface roughness and isolated defect requirements, since these can contribute to

hydrodynamic instabilities leading to non-uniform implosions. Despite having good overall roughness (e.g., <10 nm rms), the capsules can have many isolated surface defects (which can be referred to as domes) that are hundreds of nanometers in height and tens of microns in width. FIGS. 2A - 2C illustrate SEM micrographs of the capsule surface as-deposited, after conventional polishing of the as-deposited capsule, and after Tumble Finishing of the as- deposited capsule performed according to an embodiment of the present invention, respectively. The inventors believe, without limiting embodiments of the present invention, that these domes are caused by small particle or asperity precursors present on the mandrel which grow into a dome during PA-CVD. Recently, conventional polishing techniques have been used to remove domes, usually at the expense of scratching the surface and increasing overall roughness as illustrated in FIG. 2B. Other existing techniques of polishing spheres were insufficient due to the capsule's small size and fragility. [0036] Tumble Finishing offers several advantages over conventional polishing techniques for planarization: 1 ) since the polishing system is hermetically sealed, the capsule is less prone to scratching (as long as incoming materials are free of rogue particles and surface asperities), 2) unlike conventional polishing, capsule mounting is not needed, thereby minimizing capsule deformation and mounting-interface-induced scratching and 3) the process is relatively simple and low cost. In some Tumble Finishing systems, the tumble finishing process does not modify the overall shape (i.e., sphericity) of the items being polished, which can occur with some conventional polishing techniques. However, as described herein, capsules used in some applications of interest are largely spherical and thereby, only local planarization is performed. [0037] Embodiments of the present invention utilize a Tumble Finishing process suitable for the polishing of hollow capsules, providing process improvements associated with the kinematics and media roughness. Utilizing the processes described herein, including optimized processes, the domes can be locally planarized with minimal degradation to the overall capsule roughness as illustrated in FIG. 2C. Without limiting embodiments of the present invention, a material removal model is described (based on the Preston material removal concept and sliding spherical-spherical Hertzian contact) along with a dome convergence model (based on workpiece-lap mismatch contribution to non-uniform pressure distribution) that compare well with experimental data.

[0038] As discussed above, ablators or capsules can be made using the micro-encapsulation method for the mandrel (used as the substrate) and PA-CVD deposition for the capsule. In one method, media to be polished (e.g., a capsule) is placed in a chamber with polishing media, a polishing compound, and a lubricant. As an example, a solution of colloidal silica (50 nm; Blue colloidal silica suspension available from Allied High Tech Products, Inc., Rancho Dominguez, CA) serving as the polishing compound is diluted l Ox with de-ionized water ( 18 ΜΩ) with the addition of a lubricant (e.g., 0.25 wt% Micro-90^® soap solution available from International Products Corp, Burlington, NJ). The solution is prepared and prefiltered using a 0.45 μηι point-of-use filter. The capsule, solution, and polishing media (e.g., 2.4 mm diameter, Grade 48 borosilicate glass available from Winstead Precision Ball Comp.) or zirconia (Grade 3) available from Grainger, Inc. of Lake Forest, IL, were then placed in a chamber, for example, an acrylic vial cylinder (25 mm diameter x 60 mm long x 20 radius ends) with a pre-polished interior surface. FIG. 3 is a photo of an acrylic vial cylinder (60 mm long) used as a container 310, also referred to as a chamber, to contain one or more objects (e.g., one or more capsules), load bearing media (e.g., glass polishing media), and a polishing compound (e.g., colloidal silica slurry) according to an embodiment of the present invention. [0039] The acrylic vial is inserted into a cylindrical sleeve (e.g., 1 10 mm in diameter). The unit is placed on a tumbler (e.g., a C&M Topline three bar tumbler) and rotated at various rotation rates for a predetermined period, for example, 96 hours. The media material, media surface finish, and the fill fraction of the media (ft,) and slurry (f_s) varied depending on the tumbling processing conditions, f is defined as the normalized vertical height of media in the vial and f_s is defined as the normalized vertical height of the slurry meniscus after the addition of the media. At f_b=0.8, the vial contains ~1700 media. The vial, media and capsule were cleaned pre- and post- polishing by soaking them in de-ionized water under ultrasonic agitation and aggressively rinsing with de-ionized water and air drying. In some of the Tumble Finishing processes, the media was pre-polished by Tumble Finishing at 100 rpm in cerium oxide slurry (Hastilite PO at Baume 9 available from Universal Photonics of

Hicksville, NY) for several weeks to improve the surface morphology (i.e., reduction in surface asperities) of the media before use in the polishing process for the capsule. In some embodiments, the surface roughness (i.e., peak to valley) of the polishing media (e.g., an initial surface roughness of 0.22 μιη RMS) is reduced using pre-polishing to provide polishing media having a surface roughness less than 100 nm RMS, less than 50 nm RMS, or less than 40 nm RMS.

[0040] In a study to evaluate the media motions, some of the Tumble Finishing processes were performed in a glass vial (25 mm diameter) with a flat end to allow for ease of viewing during rotation. The average media velocity, general media direction of motion, and capsule survivability as a function of media fill fraction, slurry fill fraction, slurry surface tension, and vial rotation rate can be studied. [0041] In some embodiments, the surface morphology of the capsule is characterized pre- and post- Tumble Finishing using various techniques to characterize the material removal properties. The capsule mass was measured gravimetrically (±0.0005 gm) after equilibrating to fixed relative humidity and temperature to determine material removal rate. FIG. 4A is a schematic diagram of an AFM spheremapper for characterizing capsule surface and shape. FIG. 4B is a schematic of a PSDI scanning interferometer for characterizing isolated defects (i.e., domes). Bright field optical microscopy using a Nikon Optiphot was performed to obtain general surface characteristics of the capsule surface. A spheremapper, an Atomic Force Microscope configured for characterizing spherical surfaces, was used to determine circumferential roughness lineouts and create power spectral density curves of the capsule surface. Additionally, Phase Shifting Diffractive Interferometry (PSDI) was performed to image the whole capsule surface and determine the isolated defect counts, locations, and size characteristics. In addition, the media were characterized using white light interferometry (Veeco Wyko NT9800) to determine their average surface roughness. [0042] Utilizing embodiments of the present invention, the inventors have analyzed the media kinematics to study the motions of the media (e.g., number of collisions, velocities, media path, and the like), i.e., the kinematics, during Tumble Finishing. The media kinematics may 1) influence the overall material removal rate on the capsule and 2) influence the randomness of contact with the capsule surface. Several specific issues that were addressed relating to the polishing of low density, fragile capsules are: 1 ) the capsule will float, requiring specific kinematic conditions to overcome, 2) the capsule is prone to liquid surface tension adhesion particularly with the walls of the vial, and 3) the capsule is more prone to breakage during impact. The first two issues can be addressed by keeping fill fraction of the media and slurry equal (f_b=f_s) in a particular embodiment and by adding a surfactant to the slurry (e.g., Micro-90^® soap) to reduce the liquid surface tension. In some embodiments, the addition of the surfactant, also referred to as a lubricant, reduces or minimizes the motion of the polishing media from the path 510 followed by polishing media in FIG. 5.

[0043] To address the latter, a simple kinematic study of the media-capsule motions was performed by viewing the edge of the vial during tumble finishing. The resulting general characteristic motions of the media and capsule were observed for different vial rotation rates (R_v) and fill fractions (f_b,f_s). The kinematics are described in Table 1 and shown

schematically in FIG. 5.

[0044] Table 1 illustrates the measured characteristics of media motions and of capsule survivability as function of the media fill fraction (¾), slurry fill fraction (f_s), and vial rotation rate (R_v) during ten runs according to an embodiment of the present invention.

Table

[0045] FIG. 5 is a schematic diagram illustrating characteristic motions of a single capsule being polished and the polishing media during Tumble Finishing according to an embodiment of the present invention. FIG. 5 illustrates the container 310, which can also be referred to as a chamber or polishing vial. The container contains one or more capsules 1 10 and a plurality of load bearing media 505, which can also be referred to as polishing media. In the illustrated example, the load bearing media are solid glass spheres. In other embodiments, a plurality of metallic spheres or glass, ceramic, or metallic shells (i.e., hollow spheres) are utilized. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. A polishing compound 530 in solution, also referred to as a slurry, such as colloidal silica in an aqueous solution is also illustrated in FIG. 5. The polishing compound facilitates polishing of the object by the load bearing media. Although a single object to be polished, i.e., a single capsule, is illustrated in FIG. 5, embodiments of the present invention are not limited to the polishing of a single object, but can be applied to multiple objects to be polished. [0046] The polishing media 505, also referred to as the load bearing media, can have a range of sizes and material characteristics. In an embodiment, the polishing media are substantially the same size as the object being polished, for example, a diameter ranging from about 200 μηι to 4 mm, more particularly, between 200 μηι and 2 mm. In a particular embodiment, the diameter of the polishing media are within a predetermined percentage of the diameter of the object being polished, for example, within 100%. In a particular embodiment, the capsule is 2 mm in diameter and the polishing media are 2 mm in diameter. One of ordinary skill in the art would recognize many variations, modifications, and alternatives. As the media size increases, the probability of fracturing the capsule increases, which can adversely affect throughput. Additionally, modification of the size of the polishing media changes the size of the contact zone during polishing, which is a factor affecting the rate at which surface features such as bumps are removed.

[0047] Referring to FIG. 5, the polishing process can be analyzed in terms of various layers of polishing media (illustrated by arrows indicating the direction and velocity of motion of the polishing media and the capsule). On the left side of the chamber, the polishing media adjacent the wall of the chamber are moving upward with high velocity. The next layer of polishing media farther from the wall is still moving upward, but with a reduced velocity. Near the center of the chamber, the polishing media are moving downward with a high velocity. The capsule is illustrated as surrounded by polishing media moving in a downward direction with an intermediate velocity. The contact between the polishing media and the capsule is a function of these directions and velocities and results in removal of material through polishing.

[0048] As illustrated in FIG. 3, ends 320 of the vial are curved into a rounded shape, which the inventor believe, without limiting embodiments of the present invention, prevent the media and/or slurry from sticking in squared off corner regions. Thus, the container can be fabricated using an acrylic material having a generally cylindrical shape, with the end portions of the container being characterized by a curvature as illustrated in FIG. 3. The curvature can have elements that are spherical, hyperbolic, or the like.

[0049] As illustrated in Table 1 and FIG. 5, two characteristic types of motions and corresponding velocities were observed: 1 ) a cascading motion (v_casc) where the media slides down after moving only part way up the internal circumference of the vial, or 2) a circumferential motion (v_up & Vd_0Wn) where the media adheres to the vial's inner

circumference all the way around, particularly accelerating with gravity during descent and resulting in a collision with media at the bottom of vial. In some embodiments, the cascading velocities are increased (e.g., maximized) without any direct collisions due to the capsule's fragile nature. This can be contrasted with ball milling, which strives to maximize the collisions from circumferential motions and impact energy. The circumferential motion occurs at a critical velocity given by:

where r_v is the inner radius of the vial and r_m is the media radius. For the results shown in Table 1 , r_v = 10.5 mm and r_m = 1 .2 mm, and hence R_cr = 3 10 rpm. Therefore, in the kinematic study, rotation rates were kept well below this value.

[0050] The other characteristic motion, cascading motion, generally occurred in layers (n^) with characteristic angles (Θ) and velocities (v_casc) at each vial rotation rate (R_v) and fill fraction (¾, f_s). The velocity was lowest in the center of layers and increased outwards (see FIG. 5). The maximum cascading velocity (v_casc) is noted for each of the kinematic conditions explored in Table 1 . The fill fractions for the polishing media fill fraction (ft,) and the fill fraction for the slurry (f_s) are not additive, but are measured including both media and slurry.

[0051] For the kinematic conditions where ¾ = f_s < 0.5 (see Table 1 ), some circumferential motion was still observed, despite the fact that R_v « R_cr, as characterized by f_m (fraction of the media travelling around the circumference), v_up (velocity of the media going up the circumference of the vial), and Vd_0Wn (velocity of the media traveling down the circumference of the vial). This is likely due to surface tension of slurry leading to greater adhesion of the media with the ID of the vial. v_up was significantly lower than Vd_0Wn due to the force of gravity, and Vd_0Wn values were amongst the highest velocities observed (200 mm/sec).

[0052] In addition, when the fill fraction was low (fb = f_s < 0.5), the capsules were observed to fracture, as described in the last column of Table 1 . Without limiting embodiments of the present invention, the inventors believe that high velocity motions of down lead to greater probability of high load, normal collisions between the capsule and media, leading to catastrophic failure.

[0053] FIG. 6 is a plot illustrating circumferential motion fraction (f_m) as function of vial rotation rate (R_v), polishing media fill fraction (ft), and slurry fill fraction (f_s) according to an embodiment of the present invention. Increasing the fill fraction to ft = f_s = 0.8 resulted in f_m = 0 (i.e., no circumferential motion as illustrated by polishing media 510, only cascading motion) and no catastrophic fracturing of the capsule for all rotation rates. Because higher fill fractions resulted in catastrophic failures, this configuration was used as the baseline Tumble Finishing process. Without limiting embodiments of the present invention, the higher fill fraction is believed to increase surface tension induced pull from the nearest neighbor media, overcoming the surface tension between the media and vial wall, and thus preventing the circumferential motion of the media. Additionally, the inventors believe, without limiting the present invention, that the addition of a surfactant or lubricant contributes to the reduction of circumferential motion of the polishing media as a result of decreased surface tension between the walls of the container and the polishing media.

[0054] Embodiments of the present invention contrast with conventional ball milling processes in which the fill fraction of the media and slurry is small (e.g., less than 50%) to encourage circumferential motion of the media and resulting high velocity impact between the media. As described herein, the process regime utilized by embodiments of the present invention differs greatly from conventional polishing processes since high fill factors are utilized to reduce or prevent circumferential motion of the media and utilize cascading motion to provide a low impact polishing process.

[0055] An issue that is addressed by embodiments of the present invention is providing a Tumble Finishing process in which isolated surface defects (i.e., domes) are planarized without introducing undesirable surface features, such as pits and scratches, due to rogue particles or asperities from external contamination, from corrosion products of the media/vial, and/or from the roughness of the media and vial. The rogue particles were minimized using stringent cleaning or filtering processes of the media, slurry, and vial, and selecting media materials that would not corrode (i.e., glass, ceramic, or the like). The roughness of the media was shown to significantly affect the amount of pitting and scratching observed on the capsule surface. [0056] Additionally, embodiments of the present invention utilize a closed system illustrated by the sealed container 3 10 in FIG. 3. By sealing the vial, the humidity inside the polishing system can be maintained at a value higher than the ambient humidity, for example, higher than 80%, higher than 85%, higher than 90%, higher than 95%, higher than 97%, higher than 98%, higher than 99% and up to 100%. In some embodiments, the humidity is provided at a high level to prevent substantial drying of the slurry in the system. The lack of drying in the environment prevents the formation of the hard agglomerates and the associated scratching. Additional discussion related to the use of sealed and/or high humidity environments to prevent damage from rogue particles and agglomerates is provided in International Patent Application No. PCT/US2012/029837, filed on March 20, 2012, the disclosure of which is hereby incorporated by reference in its entirety for all purposes.

[0057] FIGS. 7A and 7B are SEM images of a capsule surface after Tumble Finishing without a pre-polished media/vial and with a pre-polished media/vial according to an embodiment of the present invention, respectively. As shown in FIG. 7A, some examples of the observed pits and scratches are shown as measured by scanning electron microscopy. The pits were typically ~10 μιη wide and several hundred nm deep. Using image analysis, the areal density of scratches or pits on a series of Tumble Finished capsules, polished with media of varying amounts of roughness, was determined and the results are shown in FIG. 8, which is a plot illustrating measured areal pit density as function of media roughness according to an embodiment of the present invention. In FIG. 8, the line represents a linear regression fit to the data. In addition to borosilicate glass spheres, other high modulus media characterized by suitable density and beneficial corrosion properties, including stainless steel, tungsten carbide, other oxide-based media including other glasses, zirconium oxide, zirconia, aluminum oxide, silicon nitride, or the like can be utilized according to alternative embodiments.

[0058] The higher roughness media (e.g., as received borosilicate glass) led to capsules with the highest areal pit densities (producing results as shown in FIG. 7A). in contrast, the lower roughness media, either polished or purchased at a higher grade, led to capsules with lower pit areal densities (producing results as shown in FIG. 7B). [0059] As described herein, the average removal rate was determined from the mass loss before and after Tumble Finishing. The mass loss due to polishing was complicated by the fact that the capsule has the ability to uptake Oxygen. Hence the spatial and time average thickness removal rate was determined using: dh _ m, - m_f + Am₀

dt p_CH r_s ²t (2) where mj is the initial mass before polishing after equilibration to 45% RH, m_f is the mass after polishing and equilibration to 45% RH, t is the polishing time, PCH is the density of the capsule material, Am₀ is the mass uptake of a control capsule from storage in liquid water for time t, and r_s is the radius of the capsule shell. After Tumble Finishing under the baseline conditions (t = 96 hrs, R_v = 100 rpm, f_¾ = f_s = 0.8), mj - m_f- Am₀= 4 μg and the average removal rate was determined as 35±15 nm/day. [0060] As described above, a useful application of Tumble Finishing is to locally planarize ablator capsules. FIGS. 9A-9E compare the results for a pre- and post- Tumble Finished capsule shell using the baseline process described above (i.e., pre-polished borosilicate glass media and vial; R_v = 100 rpm, f_b = f_s = 0.8; t = 96 hrs). FIGS. 9A and 9B are optical micrographs of the capsule surface before and after Tumble Finishing according to an embodiment of the present invention respectively. FIGS. 9C and 9D are plots of the isolated defect distribution on the same capsule as measured by PSDI before and after Tumble Finishing according to an embodiment of the present invention, respectively. FIG. 9E is a plot showing comparison of capsule roughness before and after Tumble Finishing as function of mode number (i.e., Power Spectral Density) from the average of 3 full circumference AFM lines scans according to an embodiment of the present invention, respectively.

[0061] Referring to FIGS. 9A and 9B, optical microscope images are shown of a portion of the capsule surface, illustrating the removal of the majority of the pre-existing domes on the capsule surface. FIGS. 9C and 9D show the height and width distribution of each of the domes over the whole 4π capsule surface pre- and post- Tumble Finishing, as analyzed by PSDI. The lines in the figures are contour lines representing a fixed severity in contribution of these domes to instability of the ablator implosion (referred to a "mix mass") for fusion energy applications. In other words, taller and wider domes have a larger mix mass. It is desirable to have domes within the two (positive and negative) contour lines. The capsule had over 15,000 identified domes before Tumble Finishing and only 1 1 8 after, illustrating the high degree of local planarization achieved. The peak to valley roughness (RMS) was measured as 7.2 μηι for the data presented in FIG. 9C and was reduced to a peak to valley roughness (RMS) of only 1.5 μηι after polishing as shown in FIG. 9D.

[0062] FIG. 9E compares the power spectral density (PSD) as a function of mode number for the same capsule pre- and post- Tumble Finishing, as measured by the AFM

Spheremapper. Mode number is defined as the spatial scale length across the circumference of the capsule (i.e., mode 1 is a full circumference (~6.3.1 mm) and mode 1000 is a scale length 1/1000 of the circumference (6.3 μιη)). The dashed line in FIG. 9E represents a target specification for the PSD, derived based on minimizing the instability of the implosion when such a capsule is used in ICF applications. No observable change in the capsule low mode shape occurred, confirming that the Tumble Finishing process is gentle enough not to change the overall sphericity of the capsule. Also, due to the reduction of the domes, the high mode roughness is improved. Finally, the mid modes are slightly degraded after Tumble Finishing under some conditions, likely due to slight variations in the random contacts during polishing resulting in small removal variations at the spatial scale lengths greater than the contact size.

[0063] FIG. 1 OA is a PSDI image and a corresponding line scan of a capsule surface before (left) and after (right) Tumble Finishing of an isolated, narrow dome on the capsule. FIG. 10B is a PSDI image and a corresponding line scan of a capsule surface before (left) and after (right) Tumble Finishing of an isolated, wide dome on the capsule. As illustrated in FIGS. 10A-10B, 2D profiles and lineouts of two isolated specific domes (one narrow and one wide) are shown pre- and post- Tumble Finishing as measured by PSDI. Both domes decreased in height. However, the narrow dome converged much further to planarity than the wider dome. In both FIGS. 10A and 10B, the cross hairs identify the same location pre- and post- Tumble Finishing. [0064] According to embodiments of the present invention colloidal silica is used as a polishing compound, but other polishing compounds can be utilized, including alumina, diamond abrasives, combinations thereof, or the like. Without limiting embodiments of the present invention, the inventors have studied the chemical and/or mechanical removal mechanism by modifying the Preston model as employed in relation to material removal on glass, silicon, and other ceramic materials to extend the model to describe removal on plastic. In the general form, material removal is described as: dh

dt (3) where dh/dt is the time average removal rate at some given time t and position x,y on the workpiece, μ is the friction coefficient which is a function of the relative velocity (v_r) at the workpiece/lap interface, and σ is the pressure distribution resulting from the applied pressure (σ₀) and the nature of the workpiece/lap contact. k_p is the Preston constant, which is the value that describes the amount of material removal per unit velocity and pressure. In other words, the Preston constant describes the relative rate of removal of a given polishing particle on the workpiece and houses all the complex microscopic/molecular level interactions during polishing. [0065] During Tumble Finishing, the contact area, number of contacts, and contact time between the media and capsule are also considered. We assume that material removal is governed by the cascading motions as described above between the media and capsule which load the polishing particles against the capsule surface.

[0066] FIGS. 1 1 A and 1 IB are schematic diagrams illustrating relevant parameters and dynamics of the media and capsule for a cascading motion during approach and at contact during Tumble Finishing according to an embodiment of the present invention, respectively. This mechanism is analogous to small tool polishing, which is often used for fabricating optical components. The Preston equation for the spatial and time average removal rate can be re-written for Tumble Finishing in the following form:

where v,. cos# is the tangential velocity component of relative velocity vector

(v, = v„ - v„_, ) between the media and capsule. f_c is fraction of the capsule surface area in contact with media for each media/capsule contact, and f, is the fraction of time the media is in contact with the capsule. Note that the contacts are assumed to be perfectly random over the surface of the capsule, removing the spatial dependence shown in Eq. (3).

[0067] Hertzian sphere-on-sphere contact mechanics can be used to quantitatively evaluate material removal (described by Eq. (4)). As illustrated by FIG. 1 I B, the peak load (P) at contact is due to two contributions: 1 ) the force at impact when a single media contacts and the capsule, and 2) the effective weight of the media in the layers above. The former can be determined by equating the kinetic energy of media with that of elastic strain energy at maximum penetration into the capsule. The latter can be estimated by the weight of the average number of media above the capsule. Hence, the peak load at contact can be described as:

p_m is the mass density of the media, |v,.| sin 6> is the normal component of the relative velocity v_r at contact, g is the gravitation constant (9.80 m²/s), nL is the number of layers, r_m is the media radius, and r_c is the composite radius of the capsule shell and media (defined below). k' is material constant given by:

*.₌ ⁽Iz ₊ ⁽!z (6) where E_S and E_M are elastic modulus of the capsule shell and media, respectively, and v_s and v_m are the Poisson's ratio of the capsule shell and media, respectively. Because the capsule is a shell, the capsule shell effective modulus (E_S) is given by:

where ECH is the modulus of the raw CH material of the capsule, t_s is the shell thickness, and r_s is the shell radius.

[0068] Using Hertzian contact mechanics expanded to sphere-on-sphere contact where one of the spheres is a shell, the contact zone radius (a) is given by:

[0069] The material constant (k), the composite modulus (E_C), and composite radius (r_c) are given by:

(9a)

[0070] From the load (P) and contact zone radius (a) determined above, one can determine the pressure (σ), fraction of area making contact (f_c), and the fraction of time media is making contact with capsule (f_t), which are given by:

P

σ =

7i a²

(10a)

(10b) r...

(10c)

[0071] Note that the normal velocity (]v_r | sin Θ) influences the pressure at contact and the tangential velocity (|v_r| cos#) is directly proportional to material removal (see Eqs. (4)-(5)). From the kinematic measurements, the maximum cascading velocity at R_v = 100 rpm was casc = 1 12 mm/sec (see Table 1 ). However, the relative velocity (|v,.|) would be noticeably less due to that fact the relative velocity is the difference in velocity between layers. An estimate of the average relative velocity can be made assuming that the velocity profile between cascading layers is roughly linear, and the capsule is randomly located within each layer as a function of time. For R_v = 100 rpm and f, = f_s = 0.8, n_L = 10 and Θ = 70°; hence, the relative velocity is estimated as 2x1 12 mm/sec/(10- l layers) or ~25 mm/sec. For the configuration and materials used in some embodiments, Ecu ⁼ 2.2 GPa, v_s = 0.4, r_s = 1 .0 mm, t_s = 190 μιη, E_m = 70 GPa, v_m = 0.20, r_m = 1 .2 mm, and p_m = 2.2 gm/cm^J.

[0072] FIG. 12 is a plot illustrating the calculated load at contact (P), the contact zone diameter (2a), and the removal rate (dh/dt) for a range of possible relative velocities and values according to an embodiment of the present invention. Using literature values for the

Preston Coefficient for colloidal silica on glass (k = 1 .6 x 10^"5 μηι m N) and for the friction coefficient (μ = 0.7), the calculated load (P), contact diameter (2a), and average thickness removal rate (dh/dt) are plotted as a function of various relative velocities in FIG. 12. At a relative velocity of 25 mm/sec, the calculated removal rate is 33 nm/day, which is similar to the measured values of 35±15 nm/day. Correspondingly, this suggests that the average contact zone diameter (2a) is -39 μηι and the average load at contact ~3xl 0^"3 N. Note that if a relative velocity of 200 mm/sec is used for Vd_0Wn when capsule was observed to

catastrophically fail, P = 0.03 N. The this model serves as a framework for developing insight to the impact for changes in Tumble Finishing conditions (e.g., media material, size, rotation rates, geometry, and convergence). [0073] As described above, the Tumble Finishing process performs well in locally planarizing the domes on the surface as illustrated in FIGS. 9A - 10B. Accordingly, a model has been developed for describing the polishing convergence or planarization rate of such features. For any removal process from a surface, one method to change the surface profile stems from the concept of workpiece-lap mismatch. When a tool or lap makes contact with the workpiece, the physical mismatch at the interface will cause a pressure differential, and, hence, according to the Preston's equation, a spatial removal rate differential. Since the tool typically wears much slower than the workpiece, the workpiece surface will converge to the shape of tool because material is removed faster where the workpiece-lap mismatch is small.

[0074] As material is removed, the mismatch at the interface will go to zero and the pressure, and hence the removal rate, will become spatially uniform. The rate of convergence will depend greatly on the stiffness of the tool, where for high stiffness tools convergence is fast (often called non-conformal or convergent polishing) and where for compliant tools there is no pressure differential and uniform material removal occurs (called conformal polishing).

[0075] The Preston Equation can be rewritten in a simple form to account for the instantaneous spatially dependent removal rate due to workpiece-lap mismatch effects in the form:

where dh/dt is the spatial and time average thickness removal rate defined in Eq. (4), hj(x,y,t) is the surface height on a given point on the surface, and L is a characteristic length. The second term in the parenthesis describes the workpiece-lap mismatch effect on the material removal in terms of the local curvature of the surface of the workpiece. In other words, a negative curvature feature on the surface (i.e., a peak) will see enhanced removal, and a positive curvature feature on the surface (i.e., a valley) will reduce removal. The L term incorporates the effect of both the size of the contact zone and relative stiffness of the tool. The formalism described by Eq. (11 ) has also been used to describe material removal on surface from chemical etching processes.

[0076] FIGS. 13 A - 13D are x-lineouts of 3D simulations of the surface evolution of various dome and dimple defects during Tumble Finishing according to an embodiment of the present invention. Referring to FIGS. 13A - 13D, results are shown for the numerical solution of Eq. (1 1) for various 3D isolated defects (i.e., a narrow dome, a wide dome, two intersecting domes, and a narrow dimple). For these computations, L=820 μπι, r_ave=35 nm/day, and t=96 hours. As observed experimentally, the narrow domes converged more quickly than the wider domes (see FIGS. 13A and 13B in comparison with FIGS. 10A and 10B). The intersecting domes have a more complicated behavior; with removal, the domes merge and the resulting dome has an effective width which is larger than that of either initial dome and which slows down the convergence rate as shown in FIG. 13C. Finally, a dimple feature (i.e. a valley) will also converge by widening and reducing is relative depth as shown in FIG. 13D.

[0077] Additional values and scenarios used in the computations are as follows. FIG. 13A is for a Narrow Gaussian dome (600nm high; 16.5 μηι wide). FIG. 13B is for a Wide Gaussian dome (600 nm high; 50 μιη wide). FIG. 13C is for Multiple domes. FIG. 13D is for a Narrow Dimple (600 nm deep; 16.5 μηι wide).

[0078] Eq. (1 1 ) can also be solved analytically by approximating the shape of the domes as Gaussian with initial height h₀ and full width half maximum (FWHM) width w₀. The solution for the height relative to the average baseline surface height at time t at distance r from the dome center is given by:

where

and dh

16 1n 2 L t

w(t) = W( 1 + dt

o 2 (12c)

[0079] Eq. (12b) demonstrates that the convergence rate will decrease as width of the dome increases. FIG. 14 is a plot of calculated post-Tumble Finishing heights of various measured domes and dimples (using Eq. (l i b) and initial measured heights (h₀) and width (w₀)) cross plotted with the measured final height of the same corresponding domes and dimples. The dashed line corresponds to a 1 -to- l correlation between calculated and measured values.

[0080] According to some embodiments, the time to polish is determined using the above equations and measurements of the topology, including surface features, prior to polishing, computing a polishing time as a function of the widths and heights of the features. In some implementations, the largest features are used to compute the polishing time.

[0081] As illustrated in FIG. 14, the effectiveness of the analytical solution to the convergence model is compared in predicting the final height of isolated domes after polishing using a single value for the characteristic length (L = 820 μιη). The measured final height of the dome after polishing is cross plotted against the predicted final height of the dome after polishing. The dashed line represents a 1 -to-l correspondence between measured and calculated heights. The model shows a reasonably good agreement with experimental results over a wide range of isolated dome heights and even some dimples. [0082] As described herein embodiments of the present invention provide a novel method, which can be referred to as Tumble Finishing, for polishing and planarizing isolated features (domes) on spherical capsules. Using the kinematics described herein (typically controlled by fill fraction and rotation rate) and reducing rogue particles and asperities in the system, Tumble Finishing successfully removes material and locally planarizes domes on the surface. A material removal model developed by the inventors (based on the Preston material removal concept and sliding spherical-spherical Hertzian contact) predicts an average thickness removal rate values similar to that measured. In addition, a local planarization rate convergence model, based on the concept of workpiece-lap mismatch where the local pressure, and hence removal, varies with the gap at the contact interface was developed by the inventors and is described herein. The calculated rate and shape evolution of various sized isolated domes compare well with the experimental data. The Tumble Finishing process is well suited for treating capsule ablators used in Targets for High-Peak-Power laser systems for fusion energy research such as National Ignition Facility to improve local surface planarization and to help in reducing instabilities during implosion.

[0083] FIG. 15 is a simplified flowchart illustrating a method of polishing an object according to an embodiment of the present invention. The method 1500 includes placing the object in a container ( 1510) and placing a load bearing media different than the object in the container (1512). As an example, the object can be a hollow plastic media, for instance, a hollow plastic sphere. The load bearing media can include a plurality of oxide-based spheres (e.g., glass spheres) having similar size to the object, i.e., the diameter of the load bearing media is substantially equal to the diameter of the object. [0084] In an alternative embodiment, the method includes pre-polishing the load bearing media prior to placing the load bearing media in the container with the object. As an example, the pre-polished load bearing media can be characterized by a surface roughness less than 100 nm RMS. Thus, in the embodiment illustrated in FIG. 1 5, the load bearing media can also be pre-polished, with the term load bearing media including pre-polished load bearing media. One of ordinary skill in the art would recognize many variations, modifications, and alternatives.

[0085] The method also includes placing a polishing compound in the container (1514) and rotating the container about an axis of rotation ( 1516). In a specific embodiment, the method also includes placing a surfactant in the container. In some embodiments, the container is an acrylic material having a generally cylindrical shape. The end portions of the container are characterized by a curvature. During some implementations, the container is characterized by an internal volume and the object, the load bearing media, and the polishing compound fill greater than 50% of the internal volume, for example, greater than 55% of the internal volume, greater than 60%o of the internal volume, greater than 65% of the internal volume, greater than 70% of the internal volume, greater than 75% of the internal volume, greater than 80% of the internal volume, greater than 85% of the internal volume. In some implementations the method contains sealing the container.

[0086] It should be appreciated that the specific steps illustrated in FIG. 15 provide a particular method of polishing an object according to an embodiment of the present invention. Other sequences of steps may also be performed according to alternative embodiments. For example, alternative embodiments of the present invention may perform the steps outlined above in a different order. Moreover, the individual steps illustrated in FIG. 15 may include multiple sub-steps that may be performed in various sequences as appropriate to the individual step. Furthermore, additional steps may be added or removed depending on the particular applications. One of ordinary skill in the art would recognize many variations, modifications, and alternatives.

[0087] It is also understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to persons skilled in the art and are to be included within the spirit and purview of this application and scope of the appended claims.

Claims

WHAT IS CLAIMED IS: L A method of polishing an object, the method comprising: placing the object in a container;

placing a load bearing media different than the object in the container;

placing a polishing compound in the container; and

rotating the container about an axis of rotation.

2. The method of claim 1 wherein the object comprises hollow plastic media.

3. The method of claim 2 wherein the hollow plastic media comprises a sphere.

4. The method of claim 1 wherein the load bearing media comprises a plurality of oxide-based spheres.

5. The method of claim 4 wherein the oxide-based spheres comprise glass spheres.

6. The method of claim 1 further comprising pre-polishing the load bearing media prior to placing the load bearing media in the container.

7. The method of claim 6 wherein the pre-polished load bearing media are characterized by a surface roughness less than 100 nm RMS.

8. The method of claim 1 wherein a diameter of the load bearing media is substantially equal to a diameter of the object.

9. The method of claim 1 wherein the container comprises an acrylic material having a generally cylindrical shape.

10. The method of claim 9 wherein end portions of the container are characterized by a curvature.

1 1 . The method of claim 1 wherein the container is characterized by an internal volume and the object, the load bearing media, and the polishing compound fill greater than 50% of the internal volume.

12. The method of claim 1 1 wherein the object, the load bearing media, and the polishing compound fill greater than 80% of the internal volume.

13. The method of claim 1 further comprising placing a surfactant in the container.

14. The method of claim 1 further comprising sealing the container.

15. An apparatus for polishing an object, the apparatus comprising: a generally cylindrical container characterized by an internal volume;

the object disposed in the container;

a plurality of load bearing media disposed in the container, wherein the plurality load bearing media are different from the object;

a polishing compound disposed in the container; and

a rotation device operable to rotate the container about an axis of rotation.

16. The apparatus of claim 15 wherein a fill factor associated with the plurality of load bearing media and the polishing compound is greater than 50% of the internal volume.

17. The apparatus of claim 15 wherein the object comprises a hollow plastic sphere.

18. The apparatus of claim 15 wherein the plurality of load bearing media comprise a plurality of borosilicate glass spheres.

19. The apparatus of claim 18 wherein the plurality of borosilicate glass spheres are characterized by a surface roughness less than 100 nm RMS.

20. The apparatus of claim 15 wherein the polishing compound comprises an aqueous solution of colloidal silica.

21 . The apparatus of claim 15 wherein the generally cylindrical container comprises an acrylic vial having curved internal end portions.