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Cation Segregation in an Oxide Ceramic with Low Solubility: Yttrium

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  • INTERFACE SCIENCE 10, 99110, 2002c 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.

    Cation Segregation in an Oxide Ceramic with Low Solubility:Yttrium Doped -Alumina

    M.A. GULGUN, R. VOYTOVYCH, I. MACLAREN AND M. RUHLEMax Planck Institut fur Metallforschung, Heisenbergstr. 3, 70569, Stuttgart, Germany

    R.M. CANNONEvans Hall (MC 1760), Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

    Abstract. The segregation behaviour of a cation (yttrium) with a low solubility in the polycrystalline oxide host(-Al2O3) has been investigated at temperatures between 1450 and 1650C using analytical scanning transmissionelectron microscopy. Three distinct segregation regimes were identified. In the first, the yttrium adsorbs to all grainboundaries with a high partitioning coefficient, and this can be modelled using a simple McLean-Langmuir typeabsorption isotherm. In the second, a noticeable deviation from this isotherm is observed and the grain boundaryexcess reaches a maximum of 9 Y-cat/nm2 and precipitates of a second phase (yttrium aluminate garnet, YAG) startto form. In the third regime, the grain boundary excess of the cation settles down to a value of 67 Y-cat/nm2 thatis in equilibrium with the YAG precipitates. In a material (accidentally) co-doped with Zr, the Zr seems to behavein a similar way to the Y and the Y + Zr grain boundary excess behaves in the same way as the Y grain boundaryexcess in the pure Y-doped system. In this latter system, Y-stabilised cubic zirconia is precipitated in addition toYAG at higher Y + Zr concentrations.

    Keywords: -alumina, grain boundary, segregation, adsorption, precipitation

    1. Introduction

    Segregation of impurity atoms or intentionally addeddopants has a strong influence upon the microstructuraldevelopment [16] and properties [712] of materials.For this reason, it has been widely studied in manyclasses of materials including metals [13, 14], semi-conductors [15], ceramics [1618] and metal ceramiccomposites [19].

    Polycrystalline -alumina is one of the most widelystudied ceramics in terms of the link between seg-regation behaviour, microstructure and properties [1,2025]. In this material, impurities and dopants havea particularly strong influence on the microstructure

    Present address: Sabanci University, FENS, Tuzla, Istanbul 81474,Turkey.Present address: LTPCM INPG, BP. 75, 38402 Saint-Martin-DHeres Cedex, France.

    and high temperature properties of the ceramic since-alumina (-Al2O3) has a very limited solubility formost cations except for trivalent iron, chromium andtitanium or for cosolubility with charge compensationsuch as MgTiO3 [26]. For instance, in one case the sol-ubility of Y in -alumina has been estimated in onestudy to be less than 10 ppm even at the melting point[27], although it may be noted that some other studiesshow a somewhat higher solubility as will be discussedlater. Thus, most dopants or impurities are forced to re-side primarily at grain boundaries or are precipitated[2, 2831]. Such grain boundary segregated cations,together with precipitates located at grain boundariesor multiple grain junctions, may have a strong effect ona variety of processes including sintering, grain growthand creep.

    A classic example of the influence of dopants onthe -alumina microstructure is the Lucalox processin which MgO inhibits grain growth even when no

  • 100 Gulgun et al.

    second phase is present [32]. More recently, yttriumhas been identified as an element that dramatically en-hances the creep properties of the ceramic [9, 3336].Other rare-earth dopants [33, 3537] or codoping [38]have similar positive effects on the creep resistance.It has been shown that these improved creep proper-ties of yttrium doped -alumina are closely related tothe grain boundary segregation and/or precipitation be-haviour [2, 9, 34, 35, 3941]. In fine grained -alumina,grain boundary sliding accommodated by diffusion isbelieved to be the main mechanism of creep at tempera-tures above 1200C [42, 43]. Yttrium segregating to thegrain boundaries must be interfering with one or bothof these processes and therefore increase the resistanceof the material to deform at high temperatures. Severalatomistic mechanisms have been suggested to explainthis improvement in creep resistance [3437, 40].

    Quantification of Y grain boundary segregation in-Al2O3 was first performed by Gruffel and Carry[23]. They showed using EDXS in the TEM that as thegrain size increased, the Y level at the boundary firstincreased monotonically and then saturated at a fixedlevel, in conjunction with the precipitation of yttriumaluminate garnet (YAG) crystals in the microstructure.This saturation was correlated with an anomalousplateau in the curve of the creep rate as a functionof grain size by Priester et al. [40]. They showed thata temporary increase in creep rate during the plateauregime occurs at the average grain size which corre-sponds to the approach of the grain boundary yttriumconcentration to the saturation value. More recentlyGulgun et al. [2] and Wang et al. [28] proposed thatsome supersaturation could occur prior to nucleationand precipitation of the YAG. The purpose of presentpaper is to study the segregation and precipitation be-haviour of Y systematically. This is done both for verypure samples and for cases where Zr impurities arepresent.

    2. Experimental Procedure

    The -alumina ceramics which are the subject of thiswork were prepared from high purity (99.995% purity)-alumina powders (AKP-3000) Sumitomo ChemicalCo., Osaka, Japan) with a 0.30.7 m particle size andfollowing impurity content:

  • Cation Segregation in an Oxide Ceramic with Low Solubility 101

    Grinstead, U.K.) operated at 100 kV and equippedwith an energy dispersive X-ray spectrometer (EDXS,Model 5500, Noran-Tracor Northern, Middleton, WI).In order to obtain a statistically realistic picture of thesegregation of yttrium at the interfaces in each sample,1015 grain boundaries were analysed usually with atleast 3 measurements on each grain boundary. The ex-cess concentration of the segregant was calculated us-ing the box method from the formula of Ikeda et al.[44]:

    excess = [(Y/Al)GB (Y/Al)bulk] w (1)

    where excess is the excess concentration of the segre-gant per unit area of the boundary, Y/Al is the cation ra-tio of Y to Al, is the aluminium site density in cat/nm3

    (47.1 Al cat/nm3 for -alumina), and w is the width ofthe electron beam scan area perpendicular to the bound-ary in nanometres. The cation ratios Y/Al were calcu-lated from experimental X-ray intensity ratios using anexperimentally determined k-factor of 1.36 (for cat.%,[45]). This differs significantly from the theoreticallycalculated value from the EDXS software of 2.109. Ingeneral, a scan area size of 10 13 or 20 26 nmwas used to minimize the uncertainty stemming frombeam broadening within the sample. Measurementswith smaller scan-box sizes suffer from inaccuraciesdue to beam broadening especially in thicker regions[46] and can also fail to enclose the whole boundarywidth if the boundary is not exactly edge on. Grainboundary excess measurements were done in regionsof the sample where the thickness varied between 0.51.5 Al2O3 , where Al2O3 is the mean free path for in-elastic scattering of electrons in -alumina at 100 kV(Al2O3 is approximately 105 nm [47, 48]). The widthof the scan area, w, was not corrected for beam broad-ening or X-ray absorption within the sample [46]. Thisis unlikely to lead to large errors as the two effectsare opposite to one another, beam broadening reducingthe apparent Y concentration, but absorption reducingthe Al counts. For wider box widths the effects almostcancel each other out and the variability from one mea-surement to another is significantly larger than any errorarising from beam broadening.

    The detection limit of the spectrometer for Y is de-pendent on the exact conditions used for each measure-ment (in particular on the total number of Y counts inthe spectrum, which is dependent on box width, beamcurrent and specimen thickness). In the best case thiscan be of the order of 0.3 yttrium cat/nm2, but more

    typically with the experimental parameters used here,it would be of the order of 12 cat/nm2.

    In the case of quantification of Zr boundary con-centrations, the same method was used with a semi-empirical k-correction factor, k(Zr/Al)k for determiningthe Zr concentrations. This was based on the measuredk-factor for Y/Al [45], multiplied by a calculated Zr/Yk-factor from the EDXS spectrometer software of 1.08,giving a value of k(Zr/Al)k = 1.455. This is likely to befar more accurate than using a theoretically calculatedZr/Al value since calculations of k-factors betweenneighbouring elements in the periodic table should bemuch more accurate than those calculated for widelyseparated elements.

    Attempts were also made to quantify other possibleimpurities from the EDXS spectra including Si, Ca,Mg, Fe and Ti. None of these elements except Si couldbe reliably detected within the detection limits of ourexperimental procedure, thus showing that if present,their concentrations are certainly below 11.5 cat/nm2,and from some spectra, lower than 0.5 cat/nm2. Si wasdetected in some grain boundaries but was also oftendetected in EDXS spectra from the bulk at comparablelevels. This has previously been noted in similar sam-ples [41] and probably arises from contamination inspecimen preparation or from diffusion pump vapourin the vacuum system during observation of the samplein conventional TEMs. Nevertheless there was clearlya small quantity of Si at some grain boundaries afterbackground subtraction. Due to the lack of data, fullquantification of Si at grain boundaries will not be re-ported in this paper. As for other elements a detectionlimit for Si of about 12 cat/nm2 was found.

    3. Results

    3.1. Sample Purity

    It is feasible that some impurities could have been in-troduced into the samples in the preparation of the ce-ramics in a number of ways. Firstly, ball milling mayhave introduced impurities by wear of the milling me-dia. In the experiments of Howorth et al. [49] on wetmilling of alumina with Y-stabilised tetragonal zirco-nia (5 wt% Y2O3) milling media contamination ratesfor the milled powder of about 0.01 wt% per hour werefound, and similar loss rates were reported for millingof quartz. According to the data sheet for the YTZ zir-conia balls [50] (also approximately 5% Y2O3), theweight loss rates for the zirconia balls were an order

  • 102 Gulgun et al.

    of magnitude lower than this with quartz (with aboutequal weights of balls and powder). This would thensuggest that one hours milling with these balls wouldleave about 10100 ppm zirconia impurities in the alu-mina. The manufacturers of the YTZ balls also quoteda wear rate for alumina balls of about 0.040.06 wt%per hour [50]. This would then suggest that any trans-fer of impurities from the alumina balls (present at the0.3% level) would be negligible in one hour of milling.

    Secondly, some impurities could have conceivablybeen introduced in the use of the pestle and mortar,most likely SiO2, although the crushing was very gen-tle and it is likely that the contamination was very low.The chances of significant contamination in the press-ing stages by anything non-volatile are believed to bevery low. The main source of Si contamination is likelyto have occurred during sintering due to the evapora-tion of Si (possibly as SiO) from the MoSi2 furnace el-ements and re-deposition on the sample, although thisshould have been reduced by the insertion of the sam-ple in a powder bed, covered with a second crucible.Nevertheless, contamination by Si during sintering onthe sample surfaces, and especially at higher sinteringtemperatures has been noted.

    Table 1 lists the bulk chemical compositions as de-termined by ICP/OES and grain sizes of the two setsof samples investigated in this work. The G-Y sam-ples were doped only with varying amounts of yttrium.

    Table 1. Grain sizes after 2 and 12 h sintering together with Y andZr contents for the samples used in this study.

    GS GS Y ZrSample (m) 2 h (m) 12 h (at. ppm.) (at. ppm.)

    Pure Y-doped

    Y0 2.9 5.6

  • Cation Segregation in an Oxide Ceramic with Low Solubility 103

    Figure 1. SEM micrographs of polished and thermally etched sec-tions of G-Y samples sintered at 1550C: (a) Y0 sintered for 2 h; (b)Y500 sintered for 2 h; and (c) Y1000 sintered for 2 h.

    behaviour of yttrium doped -alumina is treated in anupcoming publication [51].

    The segregation behaviour of yttrium in polycrys-talline -Al2O3 was investigated as a function of the

    total amount of yttrium added to the ceramic. In con-trast to previous studies in the literature, a statisticalapproach to quantification of grain boundary segrega-tion was taken whereby the measured grain boundaryexcess concentration of yttrium is plotted as a cumu-lative frequency versus the grain boundary excess forevery measurement point. Such plots provide a visualway of seeing the median value of grain boundary seg-regation for the total added dopant concentration aswell as the width of the distribution. This distributionwidth may in part reflect variations from boundary toboundary owing to differences in boundary orientation,dynamics of grain boundary migration, as well as com-positional inhomogeneities inherited from the originalgreen body. Figure 2 shows the grain boundary excessconcentration of Y, Y, for the G-Y samples dopedwith different levels of Y2O3 and sintered at 1550Cfor 2 hours. The spread of grain boundary yttrium ex-cess from one measurement to another in each samplewas fairly narrow and spanned about 5 cat/nm2.

    In Fig. 3(a) and (b), the average values of grainboundary yttrium excess in different samples are plot-ted against the total amount of dopant in the poly-crystal (represented in cation ppm) that are sintered at1550C for 2 and 12 h, respectively. Hypotheticalcurves of the grain boundary excess assuming 100% ad-sorption to the grain boundary are also shown on theseplots (dashed lines). These curves are computed forthe measured grain size, assuming that all the impuritycations that are introduced to the polycrystal segregate

    Figure 2. Cumulative frequency chart for measured Y grain bound-ary excesses for 6 different G-Y compositions all sintered at 1550Cfor 2 hours.

  • 104 Gulgun et al.

    (a)

    (b)

    Figure 3. Y excesses at grain boundaries in G-Y samples as mea-sured using analytical STEM, together with lines for 100% segrega-tion and for a Langmuir-McLean adsorption isotherm with parame-ters described in the text: (a) 2 hours sintering at 1550C; (b) 12 hourssintering at 1550C. The three segregation regimes may be clearlyseen of (I) undersaturated, (II) supersaturated, and (III) equilibriumsegregation after precipitation.

    to all available grain boundaries equally and that thereis negligible dissolution of the cation in the bulk ofthe -alumina crystals (see Eq. (3) later in the Discus-sion section). The dotted lines in the graphs are plot-ted assuming a Langmuir-McLean adsorption isothermmodel, which will be discussed in detail later in thistext.

    Three regimes can be seen on these plots. At low totalconcentrations of yttrium (region I, dilute regime), themeasured yttrium excess for both sintering times fol-lows the calculated hypothetical curves and it appearsthat the yttrium cations had partitioned themselves tothe internal interfaces as adsorbates. At slightly higherconcentrations (regime II), a noticeable deviation fromboth the hypothetical perfect adsorption curve and thesimple Langmuir-McLean behaviour is observed andthe yttrium excess at the grain boundaries reaches amaximum of about 9 cat/nm2. In this regime, precip-itation of YAG begins. In the third regime, precipi-tation of YAG crystals is widespread throughout the

    microstructure [2, 42]. In this regime, the yttrium grainboundary excess is stable at an equilibrium value ofabout 6 to 7 cat/nm2. Further addition of more dopantto the polycrystal only increased the number of YAGprecipitates but did not affect the grain boundary excessconcentration. This grain boundary excess concentra-tion of yttrium in the presence of second phase precip-itates, the plateau-value, was investigated at differenttemperatures and is reported later in this work.

    3.3. Segregation and Precipitation in Y and ZrCo-Doped -Alumina

    Figure 4 shows the Zr grain boundary concentration,Zr, in the G-YZr samples sintered at 1550C for2 hours. The average Zr concentrations in these sam-ples were about 13 cat/nm2, and corresponded well tothe bulk Zr concentration, as measured by ICP-OES.The spread in Zr excess distribution among the grainboundaries was rather narrow (3 Zr-cat/nm2) for allthe samples.

    In Fig. 5(a) and (b), the average values of grainboundary excess concentration for Y and Y + Zr, areplotted against the total amount of yttrium in the sam-ples that were sintered at 1550C for 2 and 12 h, respec-tively. When the grain boundary excesses for yttriumand zirconium are added together for these G-YZr sam-ples, a segregation behaviour is observed similar tothe segregation of yttrium alone in the Zr-free G-Ysamples.

    Figure 4. Cumulative frequency chart for measured Zr grain bound-ary excesses for 5 different G-YZr compositions, all sintered at1550C for 2 hours.

  • Cation Segregation in an Oxide Ceramic with Low Solubility 105

    (a)

    (b)

    Figure 5. Y and Y + Zr concentrations at grain boundaries in G-YZr samples as measured by analytical STEM, together with a the-oretical line for 100% segregation to the boundary and no precip-itation: (a) 2 hours sintering at 1550C; (b) 12 hours sintering at1550C. Square symbols denote Y grain boundary concentrations,and diamonds indicate Y + Zr concentrations.

    Figure 6(a) shows a bright field TEM micrographof two YAG particles in a G-YZr sample doped with3000 wt. ppm Y2O3 (sintered at 1550C for 12 hours),one at a multiple grain junction and one on the grainboundary nearby. Most YAG particles were found insuch locations, although some are found isolated in theinterior of grains. It appears that the YAG particles areformed at the grain boundaries but may be left behindby these boundaries as the grains continue to grow andbecome stranded in the grains.

    Figure 6(b) shows a micrograph of a ZrO2 precipitatein the same sample, located at a multiple grain junction.Such precipitates were very infrequently found and ap-peared almost exclusively at multiple grain junctions.The morphology of these particles was generally dif-ferent from those of the YAG precipitates, and theyseemed to display a lower dihedral angle with respectto the -alumina than the YAG. There was, however,

    Figure 6. TEM images of precipitates: (a) YAG precipitates in aY1000 G-YZr specimen sintered at 1550C for 12 hours; (b) c-ZrO2precipitate at a 4 grain junction in a Y3000 G-YZr specimen sinteredat 1550C for 12 hours.

    still some evidence of slightly positive curvature at thefaces for ZrO2 precipitates at 4-grain junctions and thusthe dihedral angle is probably slightly higher than 108.The cation composition of the zirconia particles wasestimated from EDXS measurements (using a conven-tional TEM) of 13 particles to be 65 3% Zr, 35 3%Y. This should lie in the phase field for cubic zirconia[52] and close to a triple point in the ternary Al2O3-ZrO2-Y2O3 phase diagram between cubic ZrO2, Al2O3and YAG [53, 54]. Three diffraction patterns recordedfrom the particle shown in Fig. 6(b) at different go-niometer orientations were also consistent with the cu-bic zirconia phase.

    4. Discussion

    As noted in the introduction, Gruffel and Carry [25]were the first to show that the concentration of yttrium

  • 106 Gulgun et al.

    at -alumina grain boundaries increased with increas-ing doping up to a point, beyond which the bound-ary concentration was constant. This trend was laterconfirmed by Gulgun et al. [2] and Wang et al. [28],where evidence was presented that a Y supersaturationat the grain boundary may occur before the plateauvalue is reached implying some nucleation barrier tothe formation of YAG. The present work has unam-biguously shown that the segregation behaviour of yt-trium in very pure -alumina can be divided into threedistinct regimes: (I) a dilute adsorption regime in whichthe yttrium coverage of the grain boundaries (/o) in-creases with the total amount of yttrium in the ceramic,(II) a supersaturated regime where the adsorption risesto a maximum, and (III) a regime in which the yttriumcoverage at boundaries falls to a lower plateau level,with the remainder present in YAG precipitates. Thesethree regimes are discussed in detail below in the con-text of a simple adsorption isotherm of Langmuir andMcLean [55]. This is based on the following equation:

    /o = K (Xt Sv) (2)

    where is the planar density of yttrium at the boundary,o is the planar density of available grain boundarysites for adsorption, K is the partition coefficient, Xtis the total concentration of yttrium in the -alumina,Sv is the total grain boundary area per unit volume,and is the volume per cation in -alumina (0.0212nm3/cat). The grain boundary area per unit volume canbe calculated from the grain size as Sv = 3/G.

    The observed aspects of segregation of yttrium inpolycrystalline -alumina are prototypical for the ad-sorption behaviour of a surface-active impurity withvery low bulk solubility. Most cation impurities in-alumina with the exception of chromium and ironfall into this category. Thus, the segregation behaviourof other surface active cations could be effectivelymodelled with the analysis developed in the followingparagraphs.

    In addition to this, it is clear that the excess concen-tration in the boundaries will not be strongly affectedby external parameters like cooling rate. Nearly all theyttrium is at the grain boundaries or in the YAG pre-cipitates. In the dilute regime Y will not change easilyduring cooling since there is a very low Y concentra-tion in the lattice. In the equilibrium regime, a changein the excess requires diffusion from the YAG precip-itates and not just from the nearby lattice. Thus, it iskinetically hindered.

    4.1. Regime I. Dilute Coverage

    In this regime, the yttrium coverage increases with in-creasing Xt . Although the total Y-content, Xt , is wellabove the lattice solubility limit, Xl (10100 ppm, asdiscussed later), no second phase is observed. Thusmost of the yttrium is adsorbed at the grain bound-aries. At very low Y content this corresponds to thesituation where Xl Sv and therefore:

    Xt /Sv = Xt G/3 (3)

    In this approximation should increase linearly withgrain size, G.

    From the first few points of the versus Xt plotsin Fig. 3 (including the first data points in the super-saturation regime), it should be possible to fit the fullLangmuir-McLean equation to the data and thus esti-mate plausible values of o and K . Estimating thesetwo parameters from the segregation plots is rather im-precise, however, since the fit to the equation is non-linear. Hence the results should be approached withsome caution. Such an analysis gives o values in therange of 1013 cat/nm2 and a partitioning coefficientof K in the range 420 104. The preferred valueschosen and used in graph plotting are o = 11 andK = 7 104. Using these parameters, then, it seemsquite possible in this dilute regime to calculate the yt-trium coverage from the total amount of impurity usingthis Langmuir-McLean model and a good fit betweenexperimental data and calculated curves is shown forthe regime in the graphs of Fig. 3(a) and (b).

    This very high K value corresponds to an extremelystrong segregation of Y to grain boundaries in Al2O3and is in accord with recent computational simulationsof the segregation of Y in Al2O3. These first principlescalculations based on density functional theory showeda high segregation energy. In this case, the reduction ofthe grain boundary energy due to segregation was cal-culated to be 1.2 J/m2 for 3 cat/nm2 and roughly doublethis for 6 cat/nm2 [56], i.e. the segregation energy peratom is approximately constant for low to intermediatecoverage at the GB.

    Using these parameters discussed above, the ex-pected adsorption behaviour versus grain size can alsobe plotted as is shown in Fig. 7 for low bulk concen-trations of Y, where the majority of the Y remains atthe boundaries and does not precipitate (not quite truefor Y500/12 hours). A reasonable agreement is foundbetween the predicted and the observed grain boundary

  • Cation Segregation in an Oxide Ceramic with Low Solubility 107

    Figure 7. Plot of yttrium grain boundary concentration versus grainsize for the three G-Y samples with the lowest doping, with calcu-lated Langmuir-McLean adsorption curves for each Y content super-imposed (calculated using the parameters given in the text).

    Y excesses for the measured grain sizes for these 3 low-est Y levels, further demonstrating the reliability of theL-M model with the parameters given above.

    4.2. Regime II. Grain Boundary Supersaturation

    From plots of Y versus Xt it is clear that the tran-sition between the dilute and equilibrium regimes isnot monotonic. There exists a supersaturation regionwhere Xl > Xl and Y >

    Y. At 1550

    C Y is about6 Y cat/nm2 at the plateau value whereas in regimeII, Y reaches a peak at 9 Y/nm2. Statistical analysisof the experimental data (with 95% confidence limits)reveals that this supersaturation peak in the Y versusbulk composition graphs is statistically significant withrespect to the plateau value for both the 2 h sintered and12 h sintered samples.

    This supersaturation prior to precipitation clearly in-dicates that there is a nucleation barrier for YAG pre-cipitate formation. Moreover, this can in principle beconfirmed by observing the morphology of YAG par-ticles. In general if the dihedral angle of a precipitateis zero (i.e. perfect wetting) then precipitation occurswithout energy barriers at any GB. If the dihedral angleis less than 60 then precipitation may occur at tripleline junctions without any nucleation barrier, and ifthe dihedral angle is less than 108 then the nucleationbarrier free precipitation may occur at 4 grain junctionpoints. Observation of precipitates in TEM will in gen-eral underestimate the dihedral angle of a non-sphericalparticle since the highest observed dihedral angles willoccur when a particle is sectioned through the centre,but a range of different sections will be made in the

    preparation of a thin TEM specimen. Thus, the largestdihedral angles observed are likely to be the best indi-cation of the true dihedral angle. In micrographs suchas that shown in Fig. 6(a), the highest dihedral anglesfor YAG are clearly greater than 108 and the particlesgenerally have a fairly rounded or ovoid appearance.This morphology is therefore quite consistent with theproposition that the precipitation process has energybarrier to nucleation.

    4.3. Regime III. Equilibrium Segregation

    At high levels of impurity content, Xt , or at larger grainsizes for a fixed amount of total impurity content, theY-excess concentration at the grain boundaries levelsoff at a constant value of about Y = 67 cat/nm2 at1550C, accompanied by the precipitation of YAG. Onthis plateau, Y is dictated by the activity of yttrium atthe solubility limit in the lattice, which is proportionalto the solubility limit in the lattice, Xl , so the followingrelation holds:

    Xl exp(Gppt/kT) (4)

    Any additional Y added to the ceramic will form moreYAG particles. Most of the Y is in YAG particles and theactivity of yttrium at the GBs is fixed by the precipitates.

    The equilibrium value of the boundary concentrationwould be expected to be temperature dependent andwould vary according to:

    exp[{(Gad) (Gppt)}/kT] (5)

    where Gad and Gppt are the energies for adsorptionand precipitation. The actual value at the plateau wouldthen scale as:

    Y exp{[(Sad) (Sppt)]/kT}/[1 + exp{[(Sad) (Sppt)]/kT}] (6)

    Then if [(H ad) (H ppt)] > 0, the plateaulevel increases as temperature decreases, and oppositeis true for [(H ad)(H ppt)] < 0. Figure 8 showsa graph of the value of the plateau level against inversetemperature for three different sintering temperatures(1450, 1550 and 1650C). It is clear that the temper-ature variation of this plateau value is small but theplateau value does decrease slightly with temperature.Thus the two enthalpy terms are of similar magnitudeswith the adsorption entropy being the smaller of thetwo.

  • 108 Gulgun et al.

    Figure 8. Graph of the yttrium grain boundary concentration on theequilibrium segregation plateau versus the reciprocal temperature.

    4.4. Determination of the Lattice Solubility of Y

    The direct evaluation of the extremely low lattice sol-ubility of Y is impossible using currently availableelectron microscope based analytical techniques. Nev-ertheless, it may be possible to estimate the amountof Y dissolved in the lattice from Xl = Xt Sv.Figure 9 shows a plot of versus calculated Xl , to-gether with the L-M adsorption isotherm for the aboveparameters overlaid. One can then estimate the latticesolubility Xl at

    Y by finding the point at which the

    L-M isotherm reaches the Y plateau level of 6. In asimilar manner, the non-equilibrium lattice solubilityof Y at the supersaturation peak, X supl , can be estimatedfrom the point at which the adsorption curve reaches

    Figure 9. Plot of Y grain boundary concentration against calcu-lated lattice composition assuming no precipitation, with the bestfit Langmuir-McLean isotherm superimposed. Values of the latticecomposition are indicated where Y is at the plateau composition,X soll , and at the supersaturated peak level, X

    supl .

    the peak gamma value of 9. These results will be subjectto large errors, however, since they are calculated fromthe (small) difference of two large numbers (and thuserrors will be greatly magnified). Moreover, the pre-cise results depend on the details chosen for the fitparameters of the L-M equation, which are difficult todetermine precisely. Nevertheless, this approach wasused with the data collected at 1550C and values ofXl 17 10 ppm and X supl 65 30 were gained.

    It may be noted that other estimates have also beenmade of yttrium solubility in -alumina. As noted inthe introduction, Cawley and Halloran [27] determineda solubility of

  • Cation Segregation in an Oxide Ceramic with Low Solubility 109

    zirconium and yttrium behave in quite a similar wayto those doped with yttrium alone. Although Zr4+ ionsare significantly smaller than Y3+ ions (0.72 A as com-pared to 0.90 A), both are significantly larger than Al3+

    (0.51 A) and Zr shows a low solubility in the Al2O3 lat-tice in a similar way to Y. Thus Zr ions are also forcedto reside mostly at grain boundaries.

    In the case of Y and Zr codoping, the combinedY+Zr value showed a similar dependence on the to-tal Y + Zr concentration to the dependence of the Yon Y concentration in samples just doped with Y. Thatis to say, the same, undersaturated, supersaturated andplateau regions are also seen on the plots. For this rea-son, it seems likely that Y and Zr behave similarly at theboundaries and probably compete with one another forsimilar sites at the boundaries despite their differencein ionic radius. Moreover, samples beyond the super-saturation peak display precipitates of Y-doped ZrO2,in addition to YAG precipitates.

    There is, however, a question as to whether the nucle-ation barriers for the precipitation of ZrO2 and YAG aresimilar or not, as this may affect which is precipitatedfirst, or more readily. It was noted above in Section 3that the zirconia particles clearly had a lower dihedralangle than the YAG particles. Exact measurements aredifficult to make but it appeared likely that the anglewas larger than 108. Thus, it would seem that thereis some nucleation barrier to the precipitation of ZrO2,but that the nucleation barrier is lower than for YAG.

    It may be noted that YAG particles were nucleatedat grain boundaries, as well as at triple or higher or-der grain junctions, the most energetically favourablepoints in the microstructure for nucleation, whereasZrO2 was only nucleated at multiple grain junctions.The reason for this is probably related to the relativeconcentrations of Zr and Y ions. Y grain boundary con-centrations can reach high values above 9 cat/nm2 asthe grains grow during sintering, such that precipita-tion is forced to occur directly at grain boundaries, aswell as at energetically more favourable sites. In thecase of Zr, however, the grain boundary concentrationswill never reach these high levels, and therefore precip-itates will only be nucleated at the most energeticallyfavourable places.

    5. Conclusions

    The adsorption behaviour of yttrium in -alumina hasbeen studied using a detailed analytical STEM tech-nique. At low concentrations the yttrium level at the

    grain boundaries increases with bulk concentration, asecond regime is then found where the yttrium levelrises to a maximum, before a final regime in whichthe yttrium level falls off to a plateau value and theexcess yttrium is precipitated as yttrium aluminate gar-net (YAG). The early stages of this adsorption curvehave been shown to fit well to a McLean-Langmuiradsorption isotherm with a very high partition coeffi-cient for grain boundary adsorption. It was shown thatthe supersaturation prior to precipitation is associatedwith an energy barrier to precipitation, and this is alsoconsistent with the precipitate morphology.

    The adsorption behaviour in a second system inwhich -alumina is co-doped with Y and Zr has alsobeen studied and it was found that similar behaviourhappens in this system, where the relevant quantity isthe sum of Y + Zr at the boundary. This suggests thatboth cations behave similarly at boundaries and com-pete for similar sites. In this combined system, precip-itation of ZrO2 was observed in the plateau concentra-tion range, in addition to the precipitation of YAG.

    Acknowledgments

    The generous support provided in the form of fellow-ships to R.V. and I.M. by the Alexander von HumboldtFoundation and to M.G. and R.V. by the Max PlanckGesellschaft is gratefully acknowledged. We are verygrateful to Mrs. M. Sycha and Mrs. M. Kallfass forpreparing samples for TEM observation and to Mrs.S. Kuhnemann for assistance with the operation of theSEM.

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