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Scripta Materialia 62 (2010) 839–842

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Slip-line spacing in ZrB2-based ultrahigh-temperature ceramics

Dipankar Ghosh,a Ghatu Subhasha,* and Nina Orlovskayab

aDepartment of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USAbDepartment of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA

Received 21 January 2010; revised 3 February 2010; accepted 5 February 2010Available online 10 February 2010

Macroscopic manifestation of microscale plasticity at room temperature in the form of slip-lines has been elusive in brittle solids.Recently, such a phenomenon has been reported in ZrB2 ceramics and ZrB2–SiC composites, where slip-lines were detected in room-temperature deformation. Here we show that the slip-line spacing increases with grain size in these ceramics and their composites.Such behavior has been rationalized on the basis of geometrically necessary dislocations and the role of grain boundaries andinterfaces.� 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Ultrahigh temperature ceramics; Slip-line spacing; Geometrically necessary dislocations; Interface

Isolated dislocation activity in ceramics duringroom-temperature mechanical deformation has been welldocumented in the literature [1,2]. However, macroscopicmanifestation of microscale dislocation plasticity is rarein ceramics, especially in those which have an extremelyhigh melting point (m.p.), due to limited or almost zerodislocation mobility [3–5]. Recently, it has been shownthat readily detectable slip-line patterns form duringroom-temperature mechanical deformation in an ultra-high-temperature zirconium diboride–silicon carbide(ZrB2–SiC) composite (m.p. > 3000 �C) [4], suggestingmacroscale dislocation mobility in this ceramic. However,it is also known that plastic flow in polycrystalline mate-rials is highly heterogeneous and occurs as intermittentbursts, sometimes referred to as “slip avalanches” [6,7],eventually leading to highly localized deformation in theform of surface slip-steps or slip-lines. Such strain locali-zation is known to reduce ductility and often acts as a pre-cursor to material failure. Therefore, it is important toinvestigate whether such plastic strain localization isinfluenced by any microstructural length scale such asgrain size in these ceramics. Although studies on grain sizeand slip-line spacing relationships are available for somemetals and alloys [8–15], to the best of our knowledgeno such literature exists for ceramics due to the difficultyassociated with the slip-line formation at room tempera-ture. Thus, the current study attempts to shed light on

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* Corresponding author. Tel.: +1 352 392 7005; e-mail: subhash@ufl.edu

grain-size dependence of slip-line spacing in ZrB2 ceram-ics and composites.

For the current work, four ceramics with differentaverage ZrB2 grain sizes were chosen: two polycrystal-line ZrB2 ceramics (grain sizes of 20 and 41 lm), oneZrB2–5 wt.% SiC composite (grain size 5 lm) and oneZrB2–10 wt.% SiC composite (grain size 2 lm). TheZrB2–10 wt.% SiC composite and one of the ZrB2

ceramics were processed employing spark plasma sinter-ing (SPS) method, while the other ZrB2–5 wt.% SiCcomposite was sintered through the plasma pressurecompaction technique (P2C�) [4]. The other ZrB2 cera-mic was produced through the hot press (HP) technique.Both P2C� and SPS have similar sintering mechanisms,by which consolidation involves plasma activation andlocalized resistive heating (i.e., Joule heating) of a pow-der compact through the application of a low voltage di-rect current (DC) [4]. The ZrB2 ceramics processedthrough SPS and HP are referred to in the following dis-cussions as SPS-ZrB2 and HP-ZrB2, respectively. Vick-ers indentations at a load of 1000 g were conducted onmetallographically polished surfaces. A field emissionscanning electron microscope (JEOL 6335F) was em-ployed to image the induced slip-line patterns in thevicinity of indentations, and then the spacings were mea-sured from the scanning electron microscopy (SEM)micrographs.

Figure 1 presents SEM and optical micrographs(in Nomarski illumination) of fractured and metallo-graphically polished surfaces revealing the grain

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Figure 1. Microstructure of fractured surfaces of (a) ZrB2–10 wt.% SiCand (b) ZrB2–5 wt.% SiC composites, and polished surfaces of (c) HP-ZrB2 and (d) SPS-ZrB2 ceramics. Note the increase in grain size fromZrB2–10 wt.% SiC to ZrB2–5 wt.% SiC to HP-ZrB2 to SPS-ZrB2.

840 D. Ghosh et al. / Scripta Materialia 62 (2010) 839–842

morphology and relative grain sizes in all of the fourceramics investigated in this study. Variation in averageZrB2 grain sizes among the pure ZrB2 ceramics and theZrB2–SiC composites is clearly evident from these micro-graphs. For illustration purposes, slip-line patterns in thevicinity of indentations are shown only for HP-ZrB2 inFigure 2(a), while a magnified view of the deformationpatterns within a ZrB2 grain are shown in Figure 2(b).In ZrB2–SiC composites, slip-lines were evolved onlywithin the ZrB2 matrix phase, not in the SiC particulatephase. Our intent here was to investigate the changes inslip-line spacing with ZrB2 grain size variation amongthe pure ZrB2 ceramics and the ZrB2–SiC composites

BrZ-PH)b( 2

Slip-lines

(a)

0

200

400

600

800

1000

1200

1400

Slip

-lin

e sp

acin

g (n

m)

Average ZrB2 grain size ( )

SPS-ZrB2

HP-ZrB2

ZrB2-5wt%SiC

ZrB2-10wt%SiC

2 5 21 41

(c)

Figure 2. (a) Optical micrograph (Nomarski illumination) revealingslip-lines in the vicinity of an indentation and (b) within a ZrB2 grain inHP-ZrB2. (c) Slip-line spacing in all the ceramics revealing the increasein average spacing with increasing average grain size.

and to develop a scientific rationale. Since the presenceof SiC particulate phase can influence the slip-line spacingwithin the matrix phase, we also conducted a transmissionelectron microscopy (TEM) analysis to identify the influ-ence of these particles on dislocation generation along theZrB2–SiC interface (discussed later).

In this investigation, slip-lines were limited to within15–25 lm of the edges of the indentations. Slip-line spac-ing measurements were made in the surrounding regionsof indentations where slip-lines were clearly visible fromthe SEM micrographs. On average, at least 40–50 slip-linespacings were measured. Slip-line spacing measurementsrevealed that the spacing was not constant within thegrains; rather, a large variation was observed. This is be-cause the slip-line spacing can vary from grain to graindepending on the spatial location, the orientation of agrain with respect to the local stress axis and the magni-tude of strain. In spite of these variations, the currentstudy clearly revealed that, for both the pure ZrB2 ceram-ics and the ZrB2–SiC composites, the average slip-linespacing increased with average grain size (see Fig. 2(c)),and thus a definite trend between slip-line spacing andgrain size was established.

The observed grain-size dependence of slip-line spac-ing can be rationalized from different viewpoints. First,the effect of grain size on slip-line spacing is argued onthe basis of plastic strain accommodation in polycrystal-line materials in contrast to a single crystal. Secondly, theconcept of geometrically necessary dislocations (GNDs)is invoked to correlate both strain gradient and disloca-tion density with slip-line spacing. Thirdly, the role ofinterface boundaries on slip-line spacing in ZrB2–SiCcomposites is discussed.

In polycrystalline materials, plastic strain is largelylocalized within those grains that are favorably orientedfor easy slip. Note in Figure 2(a) that slip-lines wereformed within only a few ZrB2 grains surrounding theindentations. Let us consider an indentation process in asingle crystal and in a polycrystal, where both the singlecrystal and some grains in the polycrystalline materialhave similar orientations for easy slip. As the indentationprogresses, the strain at a given spatial position within theindentation process zone will be uniformly distributed in asingle crystal, whereas for polycrystalline material thestrain will be concentrated in those grains that are favor-ably oriented for easy slip, resulting in the non-uniformdistribution of plastic strain in the polycrystal. Also,localized strain within these favorably oriented grainscan exceed the average strain level in a single crystal.Therefore, total deformation is accommodated only in afew grains and results in an increased number of slipbands at a finer spacing. Such behavior has been well doc-umented in metals [16]. Due to this nature of plastic strainaccommodation in polycrystals, for the same materialwith different grain sizes, slip will be more intense in asmaller grain than in a larger grain. Eventually, as thegrain size reduces, slip will tend to become uniformthroughout the smaller grains and strain homogenizationwill occur. Thus, slip-line spacing is expected to decreasewith decreasing grain size in polycrystalline materials, asobserved in Figure 2(c).

Conceptually, dislocations are classified into statisti-cally stored dislocations (SSDs) and GNDs [17–22].

D. Ghosh et al. / Scripta Materialia 62 (2010) 839–842 841

While the former are associated with homogeneousstrain, the latter are considered to be additional defectsand are required to accommodate the strain gradientdue to non-uniform plastic strain [18,19]. GNDs donot contribute directly to the plastic strain [19]; however,their density scales with the magnitude of non-uniformplastic strain (i.e., strain gradient) [17]. Nix and Gao[18] attributed these GNDs to the formation of slip-lineson the indented surfaces where large strain gradients ex-ist. However, in our studies, it is seen that slip-lines (andslip-steps) are not only limited to the indented surfacebut also extend to the surrounding regions in the vicinityof indentation (see Fig. 2(a)).

In Figure 3, the idealized slip-line spacing on the in-dented surface has been indicated as S and the spacingon the surface outside the indent is shown as S1. If his the angle between the surface of the indenter andthe specimen plane, then S can be expressed as [18]

S ¼ Bah¼ nba

hð1Þ

where h is the indentation depth, a is the contact radius,B is the apparent Burgers vector, expressed as B = nb (nis the number of “real” planer dislocations that haveslipped on the glide plane as a result of a Frank–Readprocess [15]), and b is Burgers vector. Thus, slip-linespacing is related to indentation depth. Similarly, itcan be shown that S1 is also related to indentationdepth. The ratio between apparent Burgers vector B1

(B1 = mb, m is the number of “real” planer dislocationsslipped on the glide plane similar to n and m – n) and S1

is expressed as

tan h1 ¼B1

S1

ð2Þ

Therefore,

S1 ¼mh

na tan h1

� �S ð3Þ

Although, S and S1 are idealized slip-line spacings ina continuum, in polycrystalline materials they are as-sumed as average slip-line spacing. In this work, S wasextremely fine and difficult to measure. However, S1,the slip-line spacing outside the indent (shown in

a – contact radius h – indentation depth,

- angle between surface of indenter and specimen plane S – slip-line spacing on indented surface S1 – slip-line spacing on surface outside of indent B1 – apparent Burgers vector

– ratio of B1 and S1

B1θ1

S1Indenter

a

h

S

S1

θ

Slip-lines on indented surface

Slip-lines on outside of indentation

Elastic region

Plastic region Low-dislocation

density

High-dislocation density

Figure 3. Schematic of a conical indentation in a crystalline solid. Inthe plastic zone, the dislocation density is higher near the indentercompared to regions away from it [18].

Fig. 2(a)), was more readily detectable and measurable.From Eq. (3), it is seen that the slip-line spacing S1 isalso related to indentation depth h, similar to S.

The total dislocation density (qT), in the presence of astrain gradient, is expressed as

qT ¼ qG þ qS ð4Þwhere the density of SSDs is qS and the density ofGNDs is qG. However, qS depends on the average strainof indentation, which is related to the indenter type(tan h) [18]. In contrast, qG is inversely related to inden-tation depth as

qG ¼3

2bh

� �tan2 h ð5Þ

Also, qG is known to scale with the reciprocal ofgrain size [23]. Therefore, at a given indentation load,although the average strain may remain the same, qG

will increase with decreasing grain size. Again, this pro-vides another rational explanation for the observed in-crease in density of slip-lines (or decrease in slip-linespacing) with decreasing grain size.

The roles of grain boundaries and interface bound-aries in slip localization also need to be considered be-cause they act as sources for dislocations. The fractionof grain boundaries within a given material volume in-creases with decreasing grain size, which may help toproduce a greater number of dislocations (i.e., an in-crease in dislocation density), leading to the homogeni-zation of strain with decreasing ZrB2 grain size. ForZrB2–SiC composites, as well as the ZrB2 grain size var-iation, the presence of SiC can also play a role inenhancing the dislocation density and influence theslip-line spacing. Figure 4 shows a bright-field TEM im-age revealing several dislocations within a ZrB2 grain,probably nucleated from the nearby ZrB2–SiC interface.This TEM specimen was extracted from a region of ascratch groove containing slip-lines in the ZrB2–5 wt.%SiC composite [4,24]. In addition, due to the strainincompatibility across a ZrB2–SiC interface, strain gra-dients are expected to exist along these boundaries.Therefore, a higher fraction of ZrB2–SiC interfaces canalso increase the dislocation density, which in turn re-sults in a reduction in the slip-line spacing to accommo-date these excess defects.

All the above viewpoints support the observed trendbetween the grain size and the slip-line spacing, i.e., a de-crease in spacing with decreasing grain size. As

Figure 4. A bright-field TEM image revealing dislocations within theZrB2 matrix near the ZrB2–SiC interfaces.

842 D. Ghosh et al. / Scripta Materialia 62 (2010) 839–842

discussed, plastic strain localization within the grains inpolycrystalline materials increases with decreasing grainsize, which leads to finer slip-line spacing. An increase inthe plastic strain at the local level requires additional de-fect generation compared to that for a homogeneousglobal strain. This leads to the concept of GNDs, whichcan explain the inhomogeneous deformation and associ-ated slip localization in indentation process. As also dis-cussed, qG increases with the magnitude of the non-uniform plastic strain and with decreasing grain size.qG is also inversely related to h (see Eq. (5)), which isa function of grain size. Due to the variation in grainsizes, the possible influence of grain boundaries andinterfaces on dislocation density and slip-line spacingwere also addressed.

A number of other contributing factors, such as pro-cessing induced residual stress and defects, which mayalso influence the observed results, have not been con-sidered here. All of the four ceramics were sintered atdifferent processing conditions, which may result in dif-ferent levels of defect density and residual stresses inthese materials. Such variations in defect density andresidual stresses can influence the deformation-induceddislocation density, and hence the slip-line spacing.

In summary, the present study clearly reveals that theaverage slip-line spacing within the ZrB2 phase increaseswith increasing ZrB2 grain size for pure ZrB2 ceramics aswell as for ZrB2–SiC composites. This observation isrationalized in the context of (i) the plastic deformationin single and polycrystalline materials; (ii) the role ofgeometrically necessary dislocations; (iii) the roles ofgrain boundaries and interfaces in materials.

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