High-temperature plastic deformation of Er 2O 3-doped ZrO 2 single crystals

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Acta Materialia 54 (2006) 2195–2204

High-temperature plastic deformation of Er2O3-dopedZrO2 single crystals

J. Martınez Fernandez a,*, A.R. Pınto Gomez a, J.J. Quispe Cancapa a,A.R. de Arellano Lopez a, J. Llorca b, J.Y. Pastor b, S. Farmer c, A. Sayir c

a Department of Physics of Condensed Matter-ICMSE, University of Seville-CSIC, P.O. Box 1065, 41080 Seville, Seville, Spainb Department of Materials Science, Polytechnic University of Madrid, ETS de Ingenieros de Caminos, 28040 Madrid, Spain

c NASA Glenn Research Center, Cleveland, OH 44135-3191, USA

Received 10 June 2005; received in revised form 9 January 2006; accepted 10 January 2006Available online 9 March 2006

Abstract

The high-temperature plastic deformation of 5 mol% Er2O3-doped ZrO2 monofilaments and rods processed by the laser-heatedfloating-zone method was studied using tensile and compression tests. The microstructure of the as-fabricated and plastically deformedcrystals was characterized by scanning and transmission electron microscopy. The crystals were formed by a fine distribution of nano-meter-sized tetragonal variants with the c-axes mutually perpendicular, this particular microstructure being a consequence of the fastquenching associated with the fabrication process. A model is proposed to analyze the interaction between dislocations gliding in themultiple {100}Æ011æ slip planes and the interaction of dislocations with the tetragonal variants, taking into account the peculiar micro-structure of the material. The model explains the high work hardening observed in the system, the formation of unique plasticity-induceddefects, and the high-temperature fracture mechanisms. These issues are discussed in comparison with previous studies of yttria-dopedpartially stabilized zirconia.� 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Plastic deformation; Zirconia; High-temperature mechanical properties; Dislocations; Scanning/transmission electron microscopy

1. Introduction

Considerable efforts have been made to understand themicrostructure and mechanical properties of ZrO2-basedceramics. These efforts have mainly been concerned withthe CaO–ZrO2 [1], MgO–ZrO2 [1], and Y2O3–ZrO2 [2–9]systems.

Plastic deformation and microstructural evolution ofY2O3 partially stabilized ZrO2 crystals grown by skull melt-ing have been previously studied [6–8]. These crystals showa cubic matrix and well-defined tetragonal precipitates withan internal structure formed by lamellae of two tetragonalvariant perpendicular c-axes. Hardening is related to thedislocation–precipitate interaction. Mechanisms to explain

1359-6454/$30.00 � 2006 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2006.01.012

* Corresponding author. Tel.: +34 954 552 894; fax: +34 954612097.E-mail address: [email protected] (J.M. Fernandez).

the decrease of flow stress in this system with an increase oflamella size have been proposed. When the crystals aredeformed along the Æ1 12æ direction, age softening is dueto dislocation bow-out in the softer, unfaulted lamella vari-ants. When the deformation occurs along the Æ100æ direc-tion, the activation of multiple dislocation slip planesresults in a higher flow stress of the as-fabricated crystalsin respect to the deformation along the Æ1 12æ direction.This flow stress also decreases with aging, due to the for-mation of Æ100æ dislocations that are perfect in two tetrag-onal variants and move more easily in larger lamellae.

In this work, Er2O3 doping was selected for several rea-sons. The optical application of this alloy has been previ-ously demonstrated [10,11]. The structural properties mayalso be important because a strong interaction of disloca-tions with point defects is expected, associated with the dif-ference in ionic radius between Er and Zr, and the high

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1 Electron Microscopy Service, University of Seville, Spain.2 NASA Glenn Research Center, OH, USA.

2196 J.M. Fernandez et al. / Acta Materialia 54 (2006) 2195–2204

stability of the tetragonal phase [12–14]. Furthermore, thisstability does not impede the martensitic transformation atroom temperature that is induced by crack propagation[15].

In this study, the mechanisms of plastic deformation athigh temperature are analyzed in partially stabilized5 mol% Er2O3–ZrO2 single crystals (Er-PSZ) processed bythe laser-heated floating-zone method. The results are dis-cussed in comparison with previous investigations ofY2O3–ZrO2.

2. Experimental

Monofilaments and crystals in a rod form with a compo-sition 5 mol% Er2O3–ZrO2 were grown by the laser-heatedfloat-zone method in air. The source rods were prepared byextrusion of 99.999% pure (Alpha Easer) paste. A detaileddescription of source rod preparation and single-crystalgrowth conditions can be found in previous publications[16,17]. To initiate directional solidification a seed of sin-gle-crystal Y2O3–ZrO2 was used, oriented in the Æ11 1ædirection. The pulling rates of the monofilaments and rodcrystals were 38 and 10 cm/h, respectively. The monofila-ments’ diameters ranged from 150 to 230 lm with lengthsup to 20 cm. Rod diameters ranged from 1.3 to 2 mm.The crystallographic orientation of the rods was deter-mined using the Laue X-ray back-reflection technique.

Compression tests were carried out in air at 1400 �C ata constant strain rate of 2 · 10�5 s�1 (sample length of4 mm). Testing was performed using a screw-driven univer-sal testing machine (Microtest EM1/50/FR, Madrid,Spain) with a furnace mounted on its frame (the wholesample was located in the furnace hot zone). Single-crystalPSZ pads were used between the alumina compression rodsand the sample to avoid indentation. Strain was measuredwith two linear variable-displacement transducers(LVDTs) connected to alumina rods, inserted into thehot zone, in contact with the zirconia pads located on bothsides of the sample.

Tensile tests of the monofilaments were carried out usinga servohydraulic testing machine (Instron Limited, UK).The monofilament ends were deposited in a longitudinalgroove (whose radius was close to the fiber radius)machined in an aluminum plate, and gripped by screwinganother aluminum plate on top. The aluminum plates wereconnected to the frame through two perpendicular hinges,respectively, to remove bending and torsion stress on themonofilaments, and the central length of the fiber wasintroduced in a clamp furnace with a hot zone length of19 mm. The tests were run at 1400 �C at constant strainrates of 4.4 · 10�5 and 4.4 · 10�4 s�1.

High-temperature tensile creep was measured usingdead-weight loads and cold grips. The experiments wererun in air with the central part of the fiber being placedin a clamp furnace with a 25 mm hot zone. The test tem-peratures ranged from 1350 to 1570 �C and the stressesfrom 140 to 250 MPa. The variation in monofilament

length during the high-temperature tensile tests (creepand constant strain rate) was measured with two LVDTsconnected to flags attached to the cold portions of themonofilaments.

Microstructural observations were performed on as-fabricated and deformed samples by scanning electronmicroscopy (SEM) using Philips XL-30 1 and HitachiS-4700 2 instruments, and by transmission electron micros-copy (TEM) using a Philips CM200 instrument.1,2 Sam-ples for SEM observations were carbon coated to avoidcharging. Disks for TEM observations were cut fromthe samples and thinned to electron transparency bymechanical polishing, dimpling, and ion milling, and car-bon coated.

3. Results

3.1. Microstructure

The growth direction of the crystals was determined tobe Æ111æ (crystallographic direction of the seed crystal)within a 10� scatter, using the Laue X-ray back-reflectiontechnique.

The microstructure of the as-fabricated crystals is shownin Fig. 1. The TEM foil is oriented in the Æ11 1æ zone axis asshown by the diffraction pattern. The three families oftetragonal {112} reflections are present in the diffractionpattern, which indicates that the microstructure consistsof a distribution of three tetragonal variants with the c-axesmutually perpendicular, because each of the {112} reflec-tions was originated univocally by one of these tetragonalvariants (due to the small difference in the lattice parame-ters between the cubic and tetragonal structure, splittingon the former cubic spots cannot be observed and thetetragonal phase is detected by the presence of extra spots).Dark-field images taken with the {112} reflections showthat the tetragonal regions are complementary and havenanometer size.

3.2. Mechanical behavior

Stress–strain plots of constant compression rate experi-ments performed at 1400 �C are shown in Fig. 2. The yieldstresses at 0.2% strain offset were in the range 250–270 MPa for this loading configuration (strain rate of2 · 10�5 s�1). Following plastic yield, there was a regionof strong strain hardening (hardening rate of Dr/De =l/30, where l is the shear modulus was taken as 36 GPaand obtained by extrapolating the elastic moduli fromRef. [18]) accompanied by ‘‘serrated’’ flow. Failure initi-ated typically around 3% strain.

Fig. 2 also includes stress–strain curves corresponding totensile tests at constant strain rates of 4.4 · 10�5 and4.4 · 10�4 s�1. The yield stresses were in the range 225–

0

100

200

300

400

500

600

700

0 0.01 0.02 0.03 0.04 0.05 0.06

Tension. 4.4 x 10-4 s-1

Tension, 4.4 x 10-4 s-1

Tension, 4.4 x 10-5 s-1

Compression, 2.0 x 10-5 s-1

Str

ess

(MP

a)

Strain

1400˚C

Fig. 2. Stress versus strain curves for compression and tension testsperformed at 1400 �C at constant strain rate. The strain rate used is asindicated (filled and open circles are used to differentiate the curves but donot correspond to data points).

Fig. 1. TEM images showing the microstructure of the as-fabricatedcrystals. The presence of three tetragonal variants can be inferred from the{112} extra spots in the diffraction pattern. The bright-field micrographshows the distribution of the nanometer-size domains.

J.M. Fernandez et al. / Acta Materialia 54 (2006) 2195–2204 2197

325 MPa, similar to the ones obtained in compression (asignificant increase in the yield stress with strain rate wasnot detected). Some of the tests failed at low strain(1–2%, Fig. 2). Other monofilaments, however, underwentplastic deformation for larger strains (3–5%) and showed acontinuous increase of the hardening rate up to failure athigh stresses (up to 525 MPa, with a hardening rate up tol/4) as shown in Fig. 2.

Results of a typical monofilament tensile creep test areshown in Fig. 3A. There was measurable primary creepstrain for temperatures over 1500 �C. Following an exter-nal modification, either an increase in the stress level or

temperature, additional strain is produced but saturationis reached readily. This behavior indicates that a truestationary state is not reached, as would be expected in asystem without mechanisms to allow dislocation recovery.The strain rates measured after the primary creep areplotted with previous data for cubic yttria-stabilizedzirconia (Y-FSZ) [6], normalized at 100 MPa using a stressexponent of 4. Er-PSZ clearly has a superior creep resis-tance (Fig. 3B).

3.3. Microstructure after the mechanical tests

The serrated flow observed in the constant strain rateexperiments correlates with the activation of Luders bandsas observed by SEM (Fig. 4). The crystallographic analysisindicates that the traces of the Luders bands correspond to{100} slip planes, which have the highest possible Schmidtfactor in this orientation (0.47). The geometry of the stepsin the Luders bands caused by their intersections givesadditional evidence of the shear deformation along thesebands (Figs. 4 and 5A). The density of Luders bandsincreases with strain as shown in the sequence of micro-graphs corresponding to plastic deformations of 1% and3% (Figs. 5A and B). When the crystals are compresseduntil a stress decrease is detected as a sign of failure initia-tion (Fig. 5B), two interesting observations arise: (a) con-trast probably associated with the activation of a thirdfamily of Luders bands (arrowed at both sides of themicrograph); (b) defects with well-defined geometricalshapes associated with the intersection of Luders bands.These defects have a square shape when they are associatedwith the intersection of two Luders bands (indicated as 1 inFig. 5B) and hexagonal shapes when associated with theintersection of three Luders bands (indicated as 2 inFig. 5B). Depth profiles of these defects, obtained by laserscanning confocal microscopy (Fig. 5B), indicated thatthere is a loss of material associated with these defects.These stress concentrations are further proven by theobservation by SEM of crack incitation in the corners ofsuch defects, and the formation of macroscopic cracks bytheir coalescence (Fig. 5C).

The TEM observations of the crystals after plasticdeformation show important changes to the microstructuredue to the thermal treatment associated with the tests.Fig. 6 shows a bright-field micrograph taken in the Æ013æzone axis. The distribution of the tetragonal variants isnow very regular, forming a texture with traces that corre-spond to {110} planes, where the boundaries between vari-ants are not well defined. The same microstructure wasobserved in samples oriented in the Æ012æ and Æ001æ zoneaxis.

The TEM observations of the plastically deformed crys-tals also show systematic defects consisting of elongatedregions with slightly different contrast (Fig. 7A). Two-beancondition observations indicated that these defects areregions slightly tilted from the surrounding crystal, proba-bly associated with the formation of Luders bands.

Fig. 4. SEM images of a deformed sample showing details of the displacement associated with the Luders bands depending of the sample surfaceorientation. See text for further discussion.

0

50

100

150

200

250

300

350

0 10000 20000 30000 40000 50000

Time (s)

Elo

ng

atio

n (m

m)

T = 1550 Cσ = 170 MPa

1,E-11

1,E-10

1,E-09

1,E-08

1,E-07

1,E-06

1,E-05

1,E-04

1,E-03

4,5 5 5,5 6 6,5

104/T (k-1)

Cre

ep r

ate

(s-1

)

9.4 mol%YSZ [9]

21 mol%YSZ [9]

5mol% Er2O3 doped ZrO2 fibers

B

A

Fig. 3. Strain versus time curve of a typical tensile creep test. (A) Primary creep at first loading; (B) comparison with the creep rates of Y-FSZ [9](the arrows indicate that the creep rate was under the detection limit).


Fig. 5. SEM images showing the Luders bands in crystals plasticallydeformed at 1400 �C. (A) 1% plastic strain (detail shown in inset). (B) 3%plastic strain. Plasticity-induced defects are originated. The depth profileof a defect (marked B) was obtained using scanning laser confocalmicroscopy and it is shown in the inset. (C) Coalescence of plasticity-induced defects that originate a crack. The detail of crack generation in thecorners of a plasticity-induced defect is shown in the inset.


Dislocations were also observed in the deformed crys-tals, although the large strain contrast associated with thetetragonal phase makes these observations very difficult.

Strong dislocation–dislocation and dislocation–precipitateinteractions are evident from observations as shown inFig. 7B. It is interesting to note how the dislocationcontrast changes in the dislocation segments shearing dif-ferent tetragonal domains, which may be an indication ofstacking fault formation.

4. Discussion

4.1. Dislocation slip systems activated and yield stress

When zirconia is compressed along the [111] direction,three equivalent {10 0}Æ011æ slip systems will be likely tobe activated, as they have the highest Schmidt factor(0.47) followed closely by the {111}Æ011æ slip systems. Itis interesting to note that a small deviation of �10� fromthe [111] crystal orientation will further increase theSchmidt factor of some of the {100}Æ011æ slip systemsup to 0.5, favoring their activation. This sensitivity to devi-ation of a few degrees of the crystal orientation explains thesequential activation of the {100}Æ0 11æ slip systems.

The traces expected from the activation of {100}Æ011æLuders bands shows a clear similitude with the actualexperimental observation. Detailed observations of the sur-face steps originated by the Luders bands (Fig. 4) are alsoin agreement with the activation of {100}Æ011æ slip sys-tems. In the regions where the Burgers vector ð~bÞ and sur-face normal ð~nÞ have a parallel component, a step is formedgoing inward (top region) or outward (bottom region) ofthe crystal surface. When ~b and ~n are perpendicular, thestep is formed within the fiber surface (note that some ofthe steps present in the micrograph corresponding to thissituation are due to a second family of Luders bands).The steps originated have a typical size of 2–3 lm, whichindicates that a slip of about 104 dislocations was necessaryto create them. Dislocation traces observed by TEM alsosupport the activation of {100}Æ011æ slip systems(Fig. 7B).

The values of the yield stresses in the tension and com-pression tests are quite similar, with values in the range225–325 MPa. This similar behavior is expected, as theonset of plastic deformation is in both cases due to disloca-tion generation and glide in the same crystallographic ori-entation. When the strain rate is increased one order ofmagnitude (Fig. 2), a significant increase in the yield stresswas not detected, probably due to a high power depen-dence of strain rate with stress.

The yield stress of Er-PSZ is greater than that of Y-FSZtested under the same conditions [4], and similar to that ofas-received Y-PSZ with dopant composition approximatelyin the same position of the two-phase region of the phasediagram (4.7 mol% Y2O3), and deformed in the Æ110æand Æ112æ directions [6,8]. Both orientations share somesimilarities with the multiple {100} slip planes activationof our system; in the first case multiple slip planes are acti-vated, and in the second case a single slip plane of the same{100} type is activated.

Fig. 6. TEM bright-field image (Æ013æ zone axis) showing the microstructure after the mechanical tests.


The tetragonal nuclei are a barrier for dislocationmotion as the dislocation Burgers vector will not be a lat-tice displacement in them. The precipitates are finely dis-tributed and cannot be avoided by dislocation bow out,because this will require a very high stress:

s � lb=R ð1ÞConsidering the small precipitate size (<10 nm) and separa-tion (R), these stresses would be well over 1 GPa, clearlyhigher than the ones measured.

The precipitates will then act as a friction force becausethey have to be sheared during the dislocation movementassociated with the initiation of the plastic behavior. Thisis clear in TEM images, like the ones in Fig. 7B wherethe dislocation lines appear to form steps following the pre-cipitates contour.

The yield stress follows the equations [19]

ssd ¼fmax

b2

cf max

2T

� �1=2

ð2Þ

ssc ¼fmax

2b2

c2fmaxr4Tb

� �1=3

ð3Þ

for the limit cases of strong-dilute (Eq. (2)) and soft-concentrated (Eq. (3)) obstacles, where r is the precipitateradius, T = 1/2lb2 is the line tension, fmax = cr is the forcenecessary to shear the precipitates (c is the stacking faultenergy), and c is the concentration of precipitates on thegliding plane (defined as fpb2/r2, where fp is the fractionof tetragonal phase). Eqs. (2) and (3) indicate that the yieldstress increases with precipitate size and concentration. Thevalues of the yield stress obtained from these situations,assuming a staking fault energy of 0.3 J/m2 [6], fp = 1,and r = 10 nm, range between 100 MPa (Eq. (3)) and

250 MPa (Eq. (2)). These calculations show that theprocesses of pure particle shear are easier than the disloca-tion bow out around the tetragonal variants (dislocation–dislocation interactions are not considered in the first stageof plasticity); the stresses obtained are in reasonableagreement with the experimental ones. The yield behaviorof Er-PSZ and Y-PSZ as-fabricated crystals [8] is similar(in as-fabricated Y-PSZ, yield stresses of 250 MPa arereached for precipitate sizes of 100 nm). The smaller pre-cipitates in Er-PSZ cause an increase of c and a decreaseof fmax, so the effect on the yield stress of these two param-eters tends to cancel out. The movement of fairly isolateddislocations and the onset of plastic deformation are notaffected then in a significant way by the microstructural dif-ferences between these as-fabricated systems.

4.2. Work hardening

The work hardening after plastic yield presents a uniquebehavior in this system; it continuously increases in magni-tude with strain, starting from l/30 and reaching values upto l/4 (Fig. 2). There is no precedent for this ‘‘accelerated’’work hardening for these systems in the literature; the max-imum values measured in this study were well over themaximum values for Y-PSZ (�l/20) [8]. This high harden-ing correlates well with the high density of Luders bands(Figs. 4, 5A and B) and the plasticity-induced defects(Fig. 5B) originated from their strong interaction (seeSection 4.3). These experimental observations strongly sug-gest that the interaction between dislocations (Ludersbands) plays a major role in the mechanical behavior,and its effect must be added to the ‘‘background friction’’of the fine tetragonal precipitation. The plastic behaviormust then be explained in terms of the interaction between

Fig. 7. (A) TEM bright-field image (Æ100æ zone axis) showing a typical ‘‘band’’ observed on the plastically deformed crystals. (B) TEM image showingdislocation–tetragonal domain interaction (g = 200).


the different slip systems activated, immersed in a crystalstructure that presents a considerably high volume fractionof three types of tetragonal variants with nanometer size.

A model to explain the plastic behavior is proposed inFig. 8. The superficial defects act as dislocation sources,once the stress level is high enough. The dislocations gener-ated move relatively rapidly in a localized zone (Ludersband), initiating the plastic deformation. Let us considera source of dislocations with b1 ¼ a=2½�11 0� gliding on a(001) plane (Fig. 8A). The dislocations will move initiallywithout interaction, requiring a moderate external stressto shear the tetragonal precipitates (yield stress discussedin Section 4.1). As the dislocation density increases in that

plane, another equivalent slip system may be activated, forexample a (01 0) plane with b2 ¼ a=2½�101� dislocationsgliding on it (Fig. 8B). When these two families of disloca-tions interact, several types of events may occur, all of themimpeding dislocation glide.

These two slip planes intersect along [100], so two dislo-cations with dislocation lines in that direction can react toform superdislocation segments with Burgers vectora/2[112]. Although the formation of such superdisloca-tions involves an increase of the elastic energy

jb3j2 ¼3

2a2 > jb1j2 þ jb1j2 ¼ a2 ð4Þ

Fig. 8. Dislocation interaction model. See text for further discussion.


they are likely to be formed to produce an overall decreaseof energy of the system under compression. These superdis-locations would have an energy that is still lower than thea[110] superdislocations considered to be responsible forthe averaging in Y-PSZ deformed in the Æ112æ direction[6]. These superdislocations have a Burgers vector almostparallel to the compression direction, which does notcorrespond to a perfect translation in any of the threetetragonal variants, and is out of any of the possible slipplanes. Therefore, they will be very effective obstacles,causing dislocation pileup and strong hardening.

If the dislocations intersect at an angle, dislocation seg-ments will be created in each dislocation, along the direc-tion of the other dislocation Burgers vector. Thesedislocation steps cannot glide in the slip plane, being anadditional source of hardening. The activation of a third{10 0}Æ011æ slip system, as the applied stress increases, will

produce additional dislocation reactions that furtherimpede dislocation glide.

There are important microstructural differences betweenEr-PSZ and the previously studied Y-PSZ that make thehardening process discussed above more effective. Thesedifferences are associated with particularities of the fabrica-tion techniques. Y-PSZ crystals were fabricated by skullmelting, a slow cooling technique, while the laser-heatedfloat-zone fabrication technique used in the present workinvolved a fast quenching of the system. The effect of thedifferent thermal history after solidification is clear whenmicrostructures are compared: the as-received crystals ofY-PSZ [7] contain tetragonal precipitates with sizes of100 nm that already show the twinned internal microstruc-ture, immersed in a cubic matrix (the volume fraction ofthe tetragonal precipitates ranges from 15% to 35% forY2O3 concentrations of 5.8–3.4 mol%, respectively [7]).However, as fabricated Er-PSZ crystals consist of a finerdistribution of tetragonal variants with dimensions under10 nm, that can hardly be discerned, do not have internaltwinned microstructure, and comprise most of the volumefraction. The strong quenching from the melt through thecubic region of the phase diagram for the laser-heatedfloat-zone method does not allow diffusion processes toform tetragonal precipitate nuclei, which results in a micro-structure that is probably formed by metastable t 0 phase.This microstructure can be considered to some extent asa modulation of the tetragonal parameters consisting ofsmall precipitates, as all the cubic phase transforms tometastable tetragonal phase during rapid quenching. Thisfact is further confirmed by the microstructural observa-tions of the deformed samples: a texture that seems tocover all the volume, formed probably by reorganizationof the t 0 variants during the short thermal treatment asso-ciated with the tests (Fig. 6).

In this unique microstructure the mechanisms of agesoftening observed for Y-PSZ crystals cannot be active.In Y-PSZ deformed along the Æ10 0æ direction, in whichmultiple {110}Æ110æ are activated, particle shear was con-sidered to occur by a/2Æ100æ dislocations, themselves pro-duced by the reaction of a/2Æ110æ dislocations. The Æ100ædislocations can shear both lamellae of some tetragonalprecipitates, being responsible for the decrease of flowstress with aging. This mechanism is less effective thesmaller the precipitate variants are, being inoperative forthe Er-PSZ microstructure. In the same way, the age soft-ening observed in aged Y-PSZ crystals deformed in theÆ11 2æ direction, for lamellae size over 60 nm, does notapply to the Er-PSZ crystals, where the precipitate micro-structure of twined lamellae is not formed. As a result ofthese processes impeding dislocation motion, and the lackof mechanisms to release the stress at the dislocationpileup front, the dislocation density increases at a higherrate, causing the ‘‘accelerated hardening’’ observed. Figs.5B and C show evidence of strong dislocationinteractions, high density of interacting Luders bandsand plasticity-induced defects (see Section 4.3), followed


by failure occurring just after the third {100}Æ01 1æ slipsystem is activated.

4.3. Plasticity-induced surface defects

The dislocation density increases in these crystals up tofailure, due to the lack of mechanisms to release disloca-tions at the pileup front. The dislocations are confined inplanar regions (Luders band), approximately equallyspaced, being the spacing between bands inversely propor-tional to the strain/applied stress (Figs. 5A and B). Twosets of interacting Luders bands create a parallelepiped-shaped surface with high dislocation density (Fig. 8C),whose edges are the fronts of the dislocation pileup, thestresses being very high there. A three-dimensional regionwith high density of dislocations in four of the six faces iscreated. As one of the faces is the external surface, onlyone face remains with relatively low defect density, thisarea being what initially prevents the chip out of theenclosed material.

As stress and strain increase, this unique microstructurefinally leads to the chip out of the material enclosed in this‘‘dislocation cell’’. Laser confocal microscopy studies con-firm that the depth of these dimples is approximately0.5 lm (Fig. 5B). The depth profile shows how the dimpleis shallower in the center, confirming that the fracture orig-inates in the lateral surfaces. The remnant material in thecenter of the back surface indicates that this surface waspreventing the cell from chipping out.

The morphology of these defects is also in good agree-ment with the traces expected from the slip planes. Withthe compression direction parallel to [111], the{10 0}Æ011æ and {001}Æ110æ Luders bands will intersectin an external surface perpendicular to ½�12�1� forming arhomb, as observed (defect marked 1 in Fig. 5B). If thethird {010}Æ10 1æ Luders band is active, it will have tracesperpendicular to the compression direction and will createplasticity-induced defects with hexagonal shape, asobserved (marked 2 in Fig. 5B). The lack of mechanismsto release stresses in Er-PSZ, associated with its particularmicrostructure, leads to very high internal stresses at thefront of the dislocation pileup, causing the unique localizedplasticity-induced defects that to our knowledge have notbeen reported before.

4.4. Failure mechanism

The process that originated the defects referred to abovecan also generate cracks in the remaining material(Fig. 5C), and will play an important role in the final fail-ure. It is interesting to note that these defects do not appearrandomly. When a certain density of them is created, thenewly formed defects tend to align with the existing onesin the compression direction (Fig. 5B). This distinct behav-ior can be understood as a response to the existence of anadditional free surface (the dimple due to material chipout). This surface will create additional attractive image

forces on the dislocations gliding nearby. The componentof these forces in the compression direction will favor addi-tional dislocation concentration and the easier generationof defects. The alignment of these defects will be responsi-ble for crack formation and finally failure, as observed(Fig. 5C).

5. Conclusions

A model to explain the plastic deformation behavior of5 mol% Er-PSZ single crystals fabricated using the laser-heated floated-zone method is proposed. This model isbased in the interaction between dislocations from the mul-tiple {100}Æ01 1æ slip systems, and of these dislocationswith the tetragonal phase. These interactions involve theformation of dislocation segments out of the slip planes,superdislocations with Burgers vectors close to the com-pression direction, and stacking faults associated with theprecipitate shear. All these processes impede dislocationmovement. The microstructure of these crystals, consistingof a fine distribution of three types of nanometer-sizetetragonal variants originating from the fast cooling inher-ent to the fabrication process, does not allow mechanismsto release the stresses at the dislocation pileup front to beactive. The model explains:

� The ‘‘accelerated’’ work hardening, not reported beforefor these systems.� The formation of plasticity-induced defects, associated

with the interaction of Luders bands.� The high-temperature fracture mechanism, in which

cracks are generated by coalescence of such a defects.

Acknowledgments

This investigation was supported by the Spanish Minis-try of Science and Technology through Grants MAT2000-1533 and MAT2003-6085. The research in the USA wasfunded by AFOSR Grant #49620-01-1-0500.

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High-temperature plastic deformation of Er 2O 3-doped ZrO 2 single crystals

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