Cracking and fracturing behaviors of industrial diamond plates

R.W. Armstrong a,*, K.L. Jackson b, D.L. Thurston b, J.L. Fitz b, P.J. Boudreaux b,C.Cm. Wu c

a Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USAb Laboratory for Physical Sciences, College Park, MD 20740, USA

c Naval Research Laboratory, Washington, DC 20375, USA

Received 9 March 1998; accepted 25 November 1998

Abstract

Ring cracking measurements have been made on millimeter thick industrial diamond plates by performing a reverse type of

hardness test with a conventional steel ball indenter system. Cathodoluminescence (CL) measurements at the ring crack edges

provided evidence of associated deformation. Follow-on fracture strength measurements were made by three-point bend testing of

beams laser-cut from two materials to probe both microstructural in¯uences and the e�ect of laser-drilled ``via holes'' (for electrical

application). Expanded autographic records of the bend tests allowed estimation of elastic modulus values. The bend tests were

modeled satisfactorily with an ANSYS ®nite element description. Fracture surface topography measurements made on the failed

bend specimens of one material also provided indication of plastic deformation being associated with the diamond material cracking

behavior. Ó 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction

Evaluation of the mechanical properties of millimeterthick industrial diamond plates are of concern for theiruse as thermally-e�cient, necessarily perforated, sub-strates in a three-dimensional cube architecture involv-ing an interconnected network of multichip modules(MCMs) [1]. Figure 1 gives a schematic illustration of adesign concept that has been put forward. Typically,eight silicon chips are distributed on a 10 cm ´ 10 cm´ 0.1 cm MCM stacked into a 10 cm cube designed toachieve nanosecond computational performance. Nu-merous laser-drilled and metal-®lled ``via holes'' are putthrough each substrate for electrical connections. Thevia patterns were presumed to be detrimental to requiredstrength properties, including concern about damagefrom the laser-drilling. Also, correlation of the strengthproperties with obvious di�erences in growth structuresof plates obtained from di�erent suppliers was of inte-rest. Thermal conductivities for the plates, measured to

be in the range of 10±13 W/K cm, were deemed to beacceptable.

2. Material and test conditions

2.1. Materials

Two diamond plate materials, designated A and B,were obtained with di�erent microstructural character-istics [2]. Both materials exhibited a columnar grainstructure through the plate thickness, beginning with theinitiation of smaller grains on the nucleation surface andexpanding to larger grains on the ®nal growth surface.Material A showed a grain size of approximately 0.02mm on the nucleation surface spreading by preferentialgrowth to 0.20 mm on the top growth surface alsoshowing a relatively unconnected ®lamentary pattern ofcrack ®ssures, apparently due to grain separations oc-curring during the growth process. Material B containeda smaller grain structure, say, 0.01 mm on the nucleationsurface, enlarged to 0.04 mm on the growth surface, inthis case, free of any microscopic crack structure, butgiving the appearance of textured grains on the growthsurface through larger regions of enhanced re¯ectivitybeing observed at clusters of grains (see, for example,Fig. 6 of Ref. [2]).

International Journal of Refractory Metals & Hard Materials 17 (1999) 1±10

* Corresponding author.

0263-4368/99/$ ± see front matter Ó 1999 Elsevier Science Ltd. All rights reserved.

PII: S 0 2 6 3 - 4 3 6 8 ( 9 8 ) 0 0 0 6 9 - 9

2.2. Test conditions

Strength measurements were determined, ®rst, byexploratory hardness testing, with a steel ball indentersystem, of the crack-associated growth surfaces of ma-terial A specimens and then by three-point bend testingof both laser-cut A and B specimen beams, with nucle-ation or growth surfaces in tension, and with or withoutlaser-drilled via holes. The unimportance of via hole orbeam edge damage for the laser-cut beam specimens wasdemonstrated through una�ected hole-free beam testresults being obtained on specimens with or withoutsubsequent laser-polished edges. Optical, scanning elec-tron and acoustic microscopy techniques were employedto characterize the material specimens before, and after,laser-drilling or bend testing, including use of the tech-niques of fracture surface topography analysis (FRAS-TA) for examining the separations of broken specimens[3]. The FRASTA results for B material beam failures,coupled with cathodoluminescence (CL) measurementsobtained at ring crack edges of indenter-loaded materialA specimens, gave surprising evidence of plastic ¯owhaving occurred in association with the cracking be-haviors.

3. (Reverse) indentation tests

Initially, it was thought that the diamond materialsmight be so brittle, particularly on the growth surfacesof material A specimens such that ring-type or conecracking might occur during elastic loading with a steelball indenter on a conventional indentation tester. Infact, ring cracks were produced at the circumference ofnear millimeter-dimension contact diameters that re-sulted after appreciable deformation of either the 1.588or 3.175 mm steel balls employed in what proved to be areverse type of hardness test. The steel ball deformationand diamond ring cracking results have been interpretedon an e�ective indentation hardness stress±strain basisthat follows the combination of elastic, plastic andcracking behaviors [4] that a material (or test ball) mightpotentially exhibit.

3.1. Steel ball deformation

Figure 2 shows the schematic indentation test alongwith optical interference patterns of a ``¯attened'' ballindenter face, say, as shown below after testing with the3.175 mm ball indenter. The interference pattern traces

Fig. 1. Schematic view of three-dimensional computer concept employing thermally e�cient, diamond-based, multichip modules.

2 R.W. Armstrong et al. / International Journal of Refractory Metals & Hard Materials 17 (1999) 1±10

the larger (longitudinal) radius of curvature associatedwith elastic unloading of the ball after prior strainhardening to the ¯attened contact diameter. The hard-ness strain is speci®ed by the contact diameter, d, di-vided by ball diameter, D, ratio that was found to beapproximately 0.3 for the measurements to be described.Reported measurements for the quasi-static compres-sion, between tungsten carbide platens, of 3.0 mm di-ameter martensitic chrome alloy steel ball bearings haveshown that plastic deformation of the balls was initiated

at loads as small as 50 kgf, as was true here, and thatcontinued loading of the balls eventually producedlongitudinal cracking in them at an indentation strain ofapproximately 0.4, corresponding to a stress of ap-proximately 7 GPa [5]. This stress exceeds the experi-mental stress level found in the present study forcracking of the diamond plates with a 3.175 mm ball,but is below the stress level associated with diamondcracking at smaller ball diameters. The steel balls em-ployed here did not crack.

Fig. 2. Steel ball indenter system for producing ring cracks in diamond at the ¯attened circumference of the plastically strained ball indenter; the

interferograms give indication at two magni®cations of the surface curvature caused by the elastic unloading displacement of the otherwise ¯attened

ball surface.

R.W. Armstrong et al. / International Journal of Refractory Metals & Hard Materials 17 (1999) 1±10 3

3.2. Hardness stress±strain curve

Figure 3 shows on a hardness stress±strain basis [4]the interpretation of measurements made in the presentstudy. The shaded circle points, for a 3.175 mm ball, andshaded square points, for a 1.588 mm ball, are shown atthe respective experimental strain (d/D) and stress (load/residual contact area) values indicated in the graph at thevertical ``steel data'' arrow. The long inclined straightline shown in the graph represents the predicted Hertzianelastic behavior for a steel ball indentation on diamond,employing diamond and steel elastic constants, E and m,for ball (b) and specimen (s), in the relation [4]

rH � �4=3p���1ÿ m2b�=Eb � �1ÿ m2

s �=Es�ÿ1�d=D�: �1�The open circle and square points on the Hertzian elasticcurve are thus shown as the matching elastic stressessupported by the diamond plates, in counterpart to theelastically supported steel hardness stresses achieved byprior strain hardening during loading.

The higher black circle and square points on theHertzian elastic loading curve are the minimum theo-retical stresses computed for ring cracking on an inden-tation fracture mechanics basis from the relationship [6]

rc P �4Esc=pD�1ÿ m2s ��K2

1 � K22 ��1=2�d=D�ÿ1=2

; �2�where c is the crack surface energy and the K's representa numerical integration factor for the indenter stressstate. The diamond material parameters in Eqs. (1) and

(2) were taken from reported values [7]. A highercracking stress is required theoretically for a smaller balldiameter, in agreement with normal experimental ob-servations. As shown, the measured ring crackingstresses at the larger ball diameter are far below thetheoretical stress value, presumably because of the crack®ssures present on the A material surface, while theexperimental stresses for the smaller, less a�ected balldiameter approach closer to the theoretical value.

Also shown in Fig. 3 are the upper Hertzian elasticcurve for diamond on diamond and two diamond-shaped points for experimental diamond pyramid mic-rohardness indentation test results plotted at an e�ective(d/D) value of 0.375; ®rst, a higher value from reportedindentation hardness measurements [8], and secondly, alower value determined in the present study by indentingat a ®ssure-free region of material A.

3.3. Ring crack observations

Figure 4 shows a relatively well-de®ned, nearlycomplete ring crack produced in the growth surface ofan A material plate with a 1.588 mm diameter ball. Thecrack intersects a larger ring crack produced withthe larger ball, both cracks being on a larger scale thanthe material grain size. The crack ®ssures mentionedearlier for the growth surfaces of material A are revealedin the background pattern as unconnected wavy linesegments. Examination of the ring crack patterns here,and in other cases, shows linkage in a number of placesbetween the smaller crack segments and the encom-passing discontinuous ring cracks. Fig. 4, on the mac-roscale, may be compared with a reported example ofmultiple segmented overlapping of ring cracks obtained

Fig. 3. Hardness stress±strain basis for interpreting steel ball and di-

amond elastic, plastic, and cracking behaviors, including theoretical

stress values for ring cracking at two ball sizes and, also, experimental

diamond pyramid microhardness results; D is the ball diameter and d is

the contact diameter between ball and specimen.

Fig. 4. Ring cracks in diamond exhibiting linkages with a surface

growth structure of segmented crack ®ssures.

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on the microscale by erosive silica particle impactdamage of diamond material [9].

4. Cathodoluminescence (CL) measurements

Recombination of electrons and holes at separated(multiple nitrogen) donor±(boron) acceptor pair impu-rities in diamond is apparently responsible for the ob-servation of (blue) emission A-band CL measurements,that are also associated with dislocations in natural andindustrial diamond materials [10]. A vibronic spectrumwith a zero-phonon line, that is reportedly sensitive tostrain and/or plastic deformation, is also normally ob-served at the upper A-band end of the diamond CLspectra [11].

4.1. Crack edge versus unstressed material

Figure 5 shows a split micrographic match between asecondary electron image of an indenter-loaded surfaceregion containing a ring crack edge and a correspondingmonowave-length CL image obtained at 438 nm from thesame region. Strong A-band emission is shown at the ringcrack edges. The CL image was obtained at 5.1 K usingan Oxford MonoCL system [12]. Consistently higherA-band emission was obtained from such ring crack edgeregions. Otherwise, the localized nature of emission fromthe individual grains, because of their di�erent orienta-tions, provides a background of varying texture.

4.2. A-band spectra

Relative comparison of CL measurements obtainedat 5.1 K is shown in Figure 6: for the upper curve, of

signi®cantly enhanced A-band emission at a ring crackedge region; and, for the lower curve, emission from aregion of the nearby indentation-free surface area. TheA-band results are in line with a previous comparison ofCL spectra obtained with the transmission electron mi-croscope of cleavage-damaged diamond material con-taining dislocations and, separately, of otherwiseidentical defect-free material [10]. Also notable in eachspectrum in Fig. 6 is the emitted 500 nm zero-phononline that is substantially stronger from the crack edgeregion, also in agreement with previous measurementsof zero-phonon line enhancement achieved by priorstraining [10,11].

5. Three-point bend test conditions

The bend tests were conducted on an Instron testingmachine with silicon nitride anvils and beam specimenslaser-cut to dimensions of 28 mm ´ 2 mm ´ 1 mm, asprescribed for previously calibrated tests of ceramicmaterials. For this case, autographic records were ob-tained at a full chart load scale of 10 kgf and slowestcrosshead velocity of 0.5 mm/min that, coupled with achart speed of 500 mm/min, provided for 1 cm of chartdisplacement correspond to a beam displacement of 10lm. With separate determination of the specimen-freeforce constant of the testing machine, chart records gaveforce±displacement traces of su�cient extent to allowestimates of Young's modulus (E) values [2].

5.1. Nucleation/growth and hole considerations

Figure 7 shows an example of the type of load±de-¯ection curves obtained, in this case, for hole-free ma-terial A specimens tested, ®rst, with the growth surfacein tension and, then, with the nucleation surface intension. As mentioned, evaluation of the reasonably

Fig. 5. At a ring crack edge in diamond, matched (split screen) SEM

micrographs of: left, a secondary electron image; right, a CL image at

438 nm.

Fig. 6. A-band spectra from diamond: an upper spectrum at the ring

crack edge; and, lower spectrum away from the ring crack edge.

R.W. Armstrong et al. / International Journal of Refractory Metals & Hard Materials 17 (1999) 1±10 5

linear relationship that is shown for the applied forcedependence on displacement provided Young's modulus(E) estimates that were found to be in agreement withexpected diamond values [2]. Also, in agreement withthe deformation curves shown in Fig. 7, the nucleationsurface of specimens exhibited generally a fracture stresslevel approximately two times greater than that requiredto cause fracture initiation beginning from the growthsurface.

Figure 8 shows a summary chart of reported A andB material fracture results, including polishing con-siderations and drilled-hole in¯uences [2]. Hole-freematerial A specimens exhibited lower fracture stressesthan material B specimens, especially for tensilestresses applied across the growth surface, but also forthe comparison of nucleation surface results, presum-ably because of the e�ect of ®ssures and larger grainsizes generally being present in the A material. Thehighest fracture stresses measured here of 950 and 980MPa for hole-free material B compare with a recentestimate of 2000 MPa for <0.5 lm thick diamond®lms prepared by a microwave plasma chemical vapordeposition technique [13].

The e�ect of via holes was investigated for the sameoverall beam dimensions by laser-drilling ®ve 0.1 mmdiameter holes in the beams spaced either 0.5 or 1.0mm apart along the length of the beam and centeredat the midway position of the beam. Holes taperedfrom 0.2 mm diameter at the nucleation surface to 0.1mm at the growth surface were drilled into the mate-rial B specimens. The larger diameter holes on thenucleation surface of B material produced a signi®cant

reduction in fracture stresses, though now establishedat a level approximately equal to that of A materialwithout drilled holes, while the smaller diameter holesat the growth surface of the material B specimensproduced essentially no change in the measured frac-ture stresses. The fracture surfaces of all material Bspecimens appeared to exhibit relatively well-de®nedcleavage facets in local regions.

Fig. 7. Autographic load±(crosshead) displacement curves for diamond beams in a three-point bend test: (a) growth surface in tension; and,

(b) nucleation surface in tension.

Fig. 8. Chart of comparative nucleation versus growth surface strength

measurements from three-point bend tests on two diamond materials,

with and without, laser-drilled via holes. Material conditions are: (A)

Material A, no holes, polished sides, (B) Material A, no holes, un-

polished sides; (C) Material A, with holes, 1.0 mm apart; (D) Material

A, with holes, 0.5 mm apart; (E) Material B, no holes; (F) Material B,

with holes, 1.0 mm apart; (G) Material B, with holes, 0.5 mm apart.

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5.2. ANSYS modeling

The ANSYS ®nite element program was applied tomathematical modeling of the stress±strain behavior tobe expected for the tested beams, employing Young'smodulus and Poisson ratio values appropriate for dia-mond [7]. Good agreement between computed and ex-perimental measurements was obtained for surfacestresses and beam de¯ections corresponding to test re-sults of the type shown in Fig. 7. The model computa-tions have been carried over to provide usefulassessment of limiting stresses and de¯ections that canbe tolerated by possible misalignment of an MCM plateat larger, corner guidance, holes used in assembling thethree-dimensional computer unit.

6. Fractographic observations

Scanning electron microscopy (SEM) observationswere made of the matching fracture surfaces of the failedbeam specimens, ®rst, for hole-free A and B materials.The fracture surfaces of material A specimens wererougher, particularly, across the width of the beams,perhaps, appearing surprisingly so because of lowerfracture stresses being measured for material A. How-ever, it was concluded that the greater roughness waspossibly attributed to linking-up of the crack ®ssurespermeating the A material. Material B fracture surfaceswere relatively ¯at and included, near to the growthsurfaces, local regions of cleavage-facet-like appearancesspanning several grains, thought to be associated withthe textured orientations of multiple grain clusters, asmentioned earlier.

6.1. FRASTA observations

The matching fracture surfaces of hole-free specimenswere examined in detail [3,14] by utilizing the twoFRASTA methods of fracture±area-projection plots(FAPPs) and cross-section plots (XSPs). An areal-typeFAPP is obtained by superposing matched surface areasat small displacements along the direction of projectionnormal to the average fracture surface so as to spatiallyresolve early regions of separations in depth. In thissense, the serial FAPPs provide pictures of areas ofcrack formation and enlargement analogous to staticX-ray radiographs in transmission. An XSP shows across-sectional plane perpendicular to the matchedfracture surfaces at small displacements, generally takennormal to a presumed crack growth direction, alsoproviding valuable information on the sequential pro-cesses of fracturing.

Both methods of examination applied to the presentdiamond materials gave complementary results: mate-

rial A separations occurred with much less evidence ofsequential steps of crack opening, in agreement withlower fracture stresses being measured for more brittlematerial; whereas, material B showed strong evidence ofcrack growth through the beam thickness requiring anincreased (bend-type) separation from the tensile (back)side of the beam, thus being associated with a greatermaterial strength and toughness. Figure 9 gives tworepresentative XSPs in each case, with the applied sep-aration forces directed horizontally, for A and B mate-rial specimens, also with crack growth beginning fromthe top of the ®gures. The open (crack) separations formaterial A are attributed to the ®ssures detected ongrowth surfaces; and, the signi®cantly overlapped im-ages for material B show the exceptional crack openingdisplacement necessarily required for (the downward)growth of fracturing (see Fig. 8 in Ref. [3b]).

6.2. SEM view of hole fractures

The essential appearances of A and B material frac-ture surfaces were unchanged by the failure at lowerstresses of specimens containing laser-drilled via holes.Figure 10(a) and (b) show comparative views ofmatching fracture surfaces produced through holes in Aand B material specimens, respectively. In each case, thespecimen halves are in contact along their failed tensilesurface edges, which, for Fig. 10(a) is the A materialnucleation surface. Figure 10(b) shows the counterpartfracture through a tapered hole in B material, also withfracture initiated at the nucleation surface.

The summary chart in Fig. 8 shows that fracturingthrough the central holes from the nucleation surfaces inB material was accomplished at a greater degradation instrength compared to the A material, still leaving the Bmaterial with a strength level signi®cantly greater thanthat associated with the nucleation surfaces of drilled Amaterial specimens. The drilled holes had a negligiblee�ect on the growth surface strength of A material be-cause of the more signi®cant crack ®ssures alreadypresent. A substantial part of the greater strength of Bmaterial is accounted for by its smaller grain size, inagreement with other results recently presented [15]. Ona comparative grain size basis, the nucleation surface ofA material is also comparatively weak, perhaps, indi-cative of crack-like ®ssure initiations even at the earlieststages of material fabrication?

7. Summary

Indentation hardness loading and three-point bendtest results are presented for the cracking behaviors andstrength properties of two diamond materials that arecandidates for employment in a three-dimensional

R.W. Armstrong et al. / International Journal of Refractory Metals & Hard Materials 17 (1999) 1±10 7

computer architecture. Ring cracking was achieved inone diamond material by a reverse type of hardness testfor the steel ball indenter system; and, CL measurementsat the ring crack edges provided evidence of permanentdeformation having been associated with cracking.Three-point beam tests of laser-cut beam specimens ofboth materials, with and without drilled via holes, es-tablished reference fracture stress levels for the materi-als; and, fracture surface topography analysis of thefailure surfaces of the second candidate material also

provided evidence of plastic deformation being associ-ated with its fracturing behavior.

Acknowledgements

Sincere appreciation is expressed to a number ofcolleagues for valuable contributions to this project, asfollows: at the Laboratory for Physical Sciences, A.Leyendecker and W.T. Beard; at the University of

Fig. 9. Matched pairs of fracture surface XSPs for assessing diamond material separation behaviors in three-point bend test, via FRASTA.

8 R.W. Armstrong et al. / International Journal of Refractory Metals & Hard Materials 17 (1999) 1±10

Maryland, N. Strifas, X.J. Zhang, D. Evans, and S.Merritt; at the Naval Research Laboratory, J. Butlerand D. Vestyck; and, at SRI International, T. Koba-yashi.

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