Strength-Limiting Surface Damage in Single-Crystal SapphireImaged by X-ray Topography

David Black

National Institute of Standards and Technology, Gaithersburg, Maryland 20899

X-ray topography was used in an effort to understand therelationship between microstructure and fracture strength insingle-crystal sapphire bend bars. The bars were indistinguish-able using standard optical characterization techniques, butX-ray diffraction topography revealed that they could beseparated into two distinct types. The first type had anoriented microstructure consisting of a pattern of linear fea-tures parallel to the long axis of the bars. This microstructurewas attributed to fabrication damage. The second type waswell-polished, nearly damage-free sapphire. Fracture strengthdata showed that the damaged bars had strengths less than70% of the bars without damage.

I. Introduction

BECAUSE of its high strength at elevated temperatures, single-crystal sapphire is the material of choice for many high-

technology applications including photolithography and high-power laser optics, and as window material for antiballisticmissiles.1 However, the high fracture strength of perfect sapphirecan be severely compromised by surface flaws.2 When surfacedamage reduces strength, components designed for demandingin-service conditions may not survive. The appearance of somesurface flaws is unavoidable since fabrication involves damagingthe surface as it is shaped. The damage can be in the form ofcracks, crystallographic defects, and/or compositional changes.3–5

If the fabrication route is not properly understood, damage (flaws)introduced early in the manufacturing process may not be removedcompletely in subsequent steps. The degree to which surfacedamage affects strength depends on the magnitude of residualstrains, the number and sizes of flaws, and their location on thepart with respect to the areas of maximum stress. One criticallylocated flaw can lead to the failure of the entire part.

Thermomechanical models have been applied to the design ofsapphire optics and to the prediction of in-service performance.The success of these models depends on having accurate values forthe strength. This raises two questions. First, what is the actualstrength of sapphire for a given or specified surface condition orfabrication process? Second, can one detect the occasional flawoutside the expected distribution that may limit strength?

To answer these questions one needs to understand the relation-ship between fabrication, surface damage, and fracture strength.An effective study of the relationship between surface and subsur-face damage and strength requires characterization techniques thatare sensitive to the relevant microstructure and can distinguishmicrostructural changes in the surface and near-surface region as itrelates to fabrication and/or postfabrication processes. This paperoffers results from one technique, X-ray diffraction topography,

and correlates specific microstructural features that are observedwith fracture strength results.

II. X-ray Diffraction Topography

X-ray topography is a characterization technique for studyingthe defect microstructure of single crystals.6–9 The basis for thetechnique is that the diffracted X-ray intensity from any point ona crystal is determined by the local crystalline perfection at thatpoint. Thus, the intensity diffracted from a perfect region of acrystal will be different from that from an imperfect region.Imperfect regions exist around crystallographic defects such asdislocations, stacking faults, inclusions, and voids and long-rangeinhomogeneously strained regions. The spatial distribution ofintensity diffracted from a sample surface is a one-to-one map ofthe distribution of defects and strains. This map is the X-raytopographic image. The experimental geometry for recording asurface-sensitive topograph is shown in Fig. 1. A monochromaticand nearly parallel X-ray beam is prepared from synchrotronradiation by a double crystal monochromator using asymmetricallycut silicon crystals.10 This beam illuminates the sample crystal,and a specific set of crystallographic planes is oriented withrespect to the incident beam at the Bragg angle according to theequation

E � hc/�2d sin �)

where E is the incident X-ray energy, h is Planck’s constant, c isthe speed of light, d is the lattice spacing of the selected set ofplanes, and � defines the Bragg angle. The diffracted beam isrecorded on high-resolution film and/or viewed in real time on anX-ray sensitive video camera. The diffraction may be symmetric,incident angle equal to diffracted angle, for planes parallel to thesurface or asymmetric for planes inclined to the surface. The bestspatial resolution of a topograph is about 1 �m and the depth ofpenetration into the sample is from several tens of micrometers toa few nanometers depending on the diffraction conditions. De-pending on the diffraction conditions, an area up to 100 cm2 can beimaged in a single exposure.

III. Experimental Procedure

The samples for this study consisted of a single set of 39sapphire bending bars. These bars were part of the SapphireStatistical Characterization and Risk Reduction (SSCARR) pro-gram,11 an interservice program to develop a fracture strengthdatabase for sapphire. The bars were manufactured from plates cutfrom a boule grown by the heat exchanger method12 and werenominally 3 mm � 4 mm � 45 mm with chamfered edges, ASTMtype B.13 The tensile surface of the bars was parallel to the basalplane, (0001), and was specified to be of optical quality, torepresent a specific fabrication process. The long axis of 34 of thebars was oriented parallel to the m-axis and in the remaining 5 barsthe long axis was parallel to the a-axis. Fracture testing wasperformed by researchers at the University of Dayton ResearchInstitute (Dayton, OH) under contract to the SSCARR program.

D. R. Clarke—contributing editor

Manuscript No. 188126. Received November 27, 2000; approved June 11, 2001.

J. Am. Ceram. Soc., 84 [10] 2351–55 (2001)

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The bars were fractured in four-point bending using conditionssimilar† to those specified in ASTM Standard C116113 using fullyarticulated fixtures. Testing was performed at 500 K in air with aconstant crosshead displacement rate of 0.5 mm/min, an inner spanof 10 mm, and an outer span of 40 mm.

X-ray diffraction topographs were recorded from the surface ofthe bars before fracture testing. The topographs were taken at theNIST Materials Science Beam Line, X23A3, at the NationalSynchrotron Light Source at Brookhaven National Laboratory. Anincident energy of 8 keV was used and the symmetric 0006diffracted beam was recorded from the tensile surface of the bars.The surface was also examined using an optical microscope witha typical magnification of 50� and Nomarski contrast to enhancesurface details. The surface finish of the bars was measured tocompare to the topographs and to serve as another standardinspection method. The surface finish measurements were madeusing a noncontact surface profiler (TOPO-3D, Wyko Corp.,Tucson, AZ‡). The numerical data for surface finish were recordedusing a 10� objective so that the root mean square (rms)roughness values were area-averaged over 0.94 mm2. The rmsroughness was measured at three positions on each bar and thesevalues were averaged. The uncertainty is estimated by the standarddeviation.

IV. Results

Since all of the bars were fabricated to the same specification,one would not expect large variations in the quality of the surfaces.The results from the standard optical inspection methods con-formed to this expectation. Optical microscopy data indicated thatthe surfaces were all nearly identical with only occasionalscratches and/or digs (small gouges) on an otherwise high-qualitysurface. Similarly, the surface finish data had an average value of�0.7 nm rms roughness, confirming the optical quality of thesurfaces. There was, however, a distribution of roughness valuesfrom about 0.6 to about 1.2 nm. To determine whether thisvariation in roughness had any effect on fracture strength, weattempted to correlate surface finish to strength. A plot of surfaceroughness values versus fracture strength for 15 randomly selectedbars is shown in Fig. 2. From the scatter in the data, it appears thatthere is no correlation between roughness and strength. However,several of the bars with the smallest surface roughness had thelowest strength, suggesting that a factor other than roughness waslimiting strength. Using the standard optical characterization

methods, no specific features of the bars could be related to thefracture strength. This situation changed dramatically when thebars were examined by X-ray topography.

The topographs revealed that instead of a single microstructure,expected for nominally identical surfaces, there were two distinctmicrostructures, with 14 bars designated Type 1 and 25 barsdesignated Type 2. Figure 3 shows representative topographs ofthe two types. The microstructure of the Type 2 bars is typical ofwell-polished, high-quality sapphire. The absence of surface dam-age is demonstrated by the visibility of individual dislocations asindicated. When the surface is sufficiently damaged, the underly-ing dislocation structure becomes obscured. This is the case for theType 1 bars. In Type 1 bars, the microstructure consists of a seriesof diffuse linear features running the length of the bars. Theamount of surface damage is so large that no contrast fromdislocations is visible.

As an example, consider the topographs in Fig. 4. The image inFig. 4(A) shows part of a topograph from a sapphire disk whereonly minor residual scratches have been left from the polishingprocess. The damage immediately under the scratches dominatesthe contrast from the dislocations, but in between the scratches, thedislocation structure is also visible. The image in Fig. 4(B) showsanother bend bar where the surface was prepared by a differentfabrication process. In Fig. 4(B) the number of residual scratcheshas increased to the point where the underlying microstructure isobscured.

Generally, the microstructure resulting from an abrasive fabri-cation process can be identified by the nature of the residualscratches. The scratches are randomly oriented for polishingprocesses, and linear, or slightly curved, parallel lines for lappingand grinding processes. The microstructure of the Type 1 bars is anextreme case where grinding-induced damage dominates andcharacteristic polishing features are not evident. Surface grindingis usually performed by a linear translation of the part relative tothe grinding wheel. The damage from a grinding operationpenetrates into the surface much more deeply than the damagefrom polishing processes. If enough material is not removed, thisgrinding damage can remain throughout all subsequent fabricationsteps. The resulting part may have a smooth, flat, and polishedsurface but considerable subsurface damage remains. The linearnature of the microstructure in the Type 1 bars is consistent witha grinding operation and leads to the conclusion that the Type 1bars were not undercut sufficiently in the subsequent polishingprocesses.

In addition to fabrication-related features, an additional type ofdamage was observed on both types of bars as indicated in Fig. 3.This type of damage has been observed on many other sapphiresamples and has been identified as resulting from inadvertentmishandling of the samples. It is generally characterized by anonlinear, sometimes quite serpentine, family of large scratches;an example is shown in Fig. 5. The structure of this damage isconsistent with human intervention, such as placing the sample

†C1161 is intended primarily for polycrystalline ceramics and glasses. The smallerinner span (10 mm) used by UDRI is a major departure from the C1161 procedure.The smaller span increases the moment arm in the flexure test and thus reduces theload at failure and the contact stresses at the load points.

‡Certain commercial equipment, instruments, or materials are identified in thispaper in order to specify the experimental procedure adequately. Such identificationis not intended to imply recommendation or endorsement by the National Institute ofStandards and Technology, nor is it intended to imply that the materials or equipmentidentified are necessarily the best available for the purpose.

Fig. 1. Schematic of the geometry for recording a surface topograph.Fig. 2. Plot of fracture strength versus average surface roughness for 15randomly selected bars.

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into alignment or clamping fixtures, or picking up the sample froma dirty surface. The sensitivity of X-ray topography can highlightthese features even when they are difficult if not impossible to findby standard optical characterization.14

The fracture data can now be interpreted in light of thedifferences between the two types of bars to ascertain to whatdegree the surface damage is a significant factor in fracturestrength. Table I shows the fracture data for all bars. Opticalfractography was performed as part of the fracture testing. Failurelocations were determined, but not specific flaws, and independentof the topographic analysis; these data are analyzed as a group of

identical specimens. Performing the analysis per ASTM Standard123915 gives an unbiased Weibull modulus§ of m � 4 (�1, �0.7)(90% confidence bounds). The Weibull characteristic strength is0 � 655 MPa (�46, �44 MPa). If we now use the topographicanalysis to segregate the data into two separate (exclusive)

§The Weibull modulus and characteristic strength were determined using linearregression rather than maximum likelihood. The probability estimator was (i � 0.5)/Nwhere N is the number of data points and i is the ith data point when ranked byincreasing strength.

Fig. 3. Representative topograph from Type 1 and Type 2 bars. Dislocations (D) are visible as indicated and damage from inadvertent handling (HD) wasobserved on both types of bars. The long axis of the specimens is vertical in both images.

Fig. 4. Topographs showing varying degrees of residual polishing scratches on a sapphire surface.

October 2001 Strength-Limiting Surface Damage in Single-Crystal Sapphire 2353

populations, we get the following results. For the Type 2 bars theunbiased Weibull modulus is m � 6 (�1.9, �1.4) and thecharacteristic strength is 0 � 725 MPa (�44, �41 MPa). For theType 1 bars the unbiased Weibull modulus is m � 3.9 (�1.7,�1.2) and the characteristic strength is 0 � 499 MPa (�66, �57MPa). These results clearly show that the observed surface damageis correlated to strength. The Type 1 bars have a characteristicstrength more than 30% below that of the Type 2 bars. It should benoted that the effect of handling damage has been ignored. Withoutfractographic data to identify specific failures from the handlingdamage there is no basis to evaluate handling damage and so it hasbeen assumed to be randomly distributed among both types ofbars.

The topographs can also be used to aid in the interpretation ofthe fractography results. Of the 39 bars examined, surface failureswere identified in 18 bars and edge failures in the remaining 21bars. Segregating the strength data by failure location yields asurprising result. The average strength for the surface failures,551 190 MPa (one standard deviation), is about 10% lower thanthe average strength for the edge failures, 617 134 MPa.Generally, it is the other way around.16,17 This result can beunderstood by using the topographs to examine the segregated datafor the distribution of each type of bar. Doing so reveals that morethan 80% (17 of 21) of the edge failures were in Type 2 bars. Thetopographs have shown that the surface of the Type 2 bars is less

damaged, and therefore stronger, and so the failures occur at theedges. It should be noted that the data in Fig. 2 were determinedbefore the bars could be segregated into types. Figure 6 shows thedata replotted using the information from the topographs todesignate each bar as Type 1 or Type 2. Of the 15 randomlyselected bars, six were Type 2 and nine were Type 1.

V. Summary

X-ray diffraction topography has been used to aid in theinterpretation of strength data and fractographic analysis. Topog-raphy data were used to uncover microstructural damage, whichcan limit fracture strength. Topographs from 39 nominally identi-cal sapphire bend bars showed that the bars could be divided intotwo separate populations, one damaged and one not damaged. Thefracture strength of the damaged bars was more than 30% belowthe undamaged bars. The microstructure observed in the topo-graphs was not observed by standard optical characterizationmethods. While the topograph is recorded at unity magnification,detail in the image results from much smaller structures. A minordisruption of the surface, which would otherwise be very difficultto identify optically or with a SEM, can be a pronounced featurein the topograph.

Acknowledgments

It is a pleasure to acknowledge Mr. George Quinn for his critical reading of themanuscript and patient explanations of the intricacies of fracture and Ms. KatherineMedicus for providing surface finish data.

References

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Fig. 5. Example of handling damage that can be found on polishedsurfaces.

Fig. 6. Data from Fig. 2 are replotted using the topographic results todifferentiate between the Type 1 and Type 2 bars.

Table I. Fracture Strength Data for 39 Bend Bars

Strength(MPa) Type

Failurelocation

Strength(MPa) Type

Failurelocation

301 1 Surface 367 1 Edge304 1 Surface 436 1 Edge318 1 Surface 477 2 Edge338 1 Surface 491 2 Edge412 1 Surface 516 1 Edge454 1 Surface 524 2 Edge481 1 Surface 531 1 Edge490 1 Surface 548 2 Edge510 1 Surface 601 2 Edge581 2 Surface 601 2 Edge591 2 Surface 633 2 Edge614 2 Surface 642 2 Edge617 1 Surface 669 2 Edge664 2 Surface 672 2 Edge676 2 Surface 678 2 Edge729 2 Surface 679 2 Edge904 2 Surface 688 2 Edge942 2 Surface 688 2 Edge

698 2 Edge811 2 Edge

1007 2 Edge

Average 551 617

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