Dietrich Hesse, Stephan SenzMax-Planck-Institut für Mikrostrukturphysik, Halle (Saale), Germany

Interfacial reaction mechanisms and thestructure of moving heterophase boundariesduring pyrochlore- and spinel-forming solid statereactions

If bulk or thin-film ceramics consisting of more than onecomponent are subjected to a high temperature during pro-cessing or use, interfacial solid– solid reactions occur be-tween the components. To understand this type of reactions,the atomic structure of various reactive oxide/pyrochloreand oxide/spinel model interfaces is studied by high-resolu-tion transmission electron microscopy. Kinetics of the pyro-chlore- and spinel-forming reactions at these interfaces areshown to depend on the atomic structure of the interface,in particular on that of the interfacial dislocations. Duringthe reaction, these dislocations have to move together withthe advancing interface. Accordingly, reaction kinetics aredetermined by the mode of dislocation movement and, thus,by the Burgers vector geometry of the interfacial disloca-tions. The type of interfacial dislocations is, in turn, influ-enced by the stress conditions during the initial stage ofthe solid state reaction.

Keywords: Solid state reactions; Reactive interfaces; Spi-nels; Pyrochlores; Electron microscopy

1. Introduction

Solid state reactions in ceramic materials have been investi-gated for many years and are still the subject of intensive re-search [1– 8]. Studying such reactions, one can learn aboutthe influence of thermodynamic potentials, crystal defects,interfaces, and their interactions, on phase formation pro-cesses during solid state reactions. If bulk or thin-film ceram-ics consisting of more than one component are subjected tohigh temperature during processing or in use, interfacialsolid – solid reactions may occur between the components.Even if these reactions extend only a few nanometers intothe adjacent phases, they may affect the desired propertiesof the ceramics. Investigating the interfacial reaction mech-anisms and the structure of the moving heterophase bound-aries will improve the understanding of such solid state re-actions. Spinel- and pyrochlore-forming topotaxial solidstate reactions as

AO + B2O3! AB2O4 (1)

2 AO + BO2! A2BO4 (2)

2 AO2 + B2O3! A2B2O7 (3)

are prototypes of chemical reactions in complex oxides, cf.[1, 3]. As will be shown, interfacial dislocations may playan important role in these reactions. This role has beeninvestigated experimentally, using (high-resolution) trans-mission electron microscopy (TEM), scanning forcemicroscopy (AFM), and X-ray diffraction.

2. Experimental

Reactive MgO/spinel and ZrO2/pyrochlore interfaceswere prepared in a high-vacuum environment or in air,using commercial MgO(100) and Y2O3-stabilized cubicZrO2(100) (YSZ) single-crystal surfaces of different micro-topography. The MgO or YSZ substrates were heated to ahigh temperature (1100 to 1300 °C) and then subjected tothe vapour of a binary oxide (TiO2, Cr2O3, SnO2, In2O3,La2O3, etc.). The vapour was generated by electron-beamevaporation (5 kV; 100 mA) of a pressed or sintered powdertarget, or – in case of SnO2 and In2O3 – by thermal evapora-tion of an oxide powder. The evaporation/deposition rate ofabout 0.2 nm/s was controlled by a quartz microbalance. Inthis way, crystallographically well-defined reactive inter-faces between the initial substrate and a certain productphase – a spinel or a pyrochlore in the form of a thinfilm, or of thin islands – were prepared, in particularMgO/Mg2TiO4, MgO/MgCr2O4, MgO/MgIn2O4, MgO/Mg2SnO4, and ZrO2/La2Zr2O7 reactive interfaces.

The initial MgO and YSZ surfaces, the spinel and pyro-chlore phases, and the reactive interfaces were investigatedby scanning force microscopy (AFM), X-ray diffractometry(XRD), and particularly by high-resolution transmissionelectron microscopy (HRTEM) of cross sections. The elec-tron microscope investigations were performed in the trans-mission electron microscopes Philips CM20T (at 200 kV),and JEM 4000 EX (at 400 kV). The samples were thinnedby standard grinding, gluing and ion-beam methods. Detailsof the experiments are described, e. g., in Refs. [9– 14].

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Table 1. Lattice parameters (in Å) of the involved phases.

MgO ZrO2 MgAl2O4 Mg2GeO4 MgCr2O4

4.213 5.1 8.08 8.246 8.33

MgFe2O4 Mg2TiO4 Mg2SnO4 MgIn2O4 La2Zr2O7

8.39 8.44 8.64 8.83 10.8

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3. Results

3.1. Lattice misfit and orientation relationship

The structure of reactive interfaces depends on the crystal-lography and on the mutual orientation of the phases sepa-rated by the interface. Depending on the lattice parameters,a, of these phases, a lattice misfit, f (in %), is present alongthe BO/PS reactive interface (PS – pyrochlore or spinel;BO – binary oxide, i. e., MgO or ZrO2)

f = 200 · (aPS/2 – aBO)/(aPS/2 + aBO) (4)

Sign and amount of the lattice misfit, in turn, determine thegeometry of the misfit dislocation network forming. All thephases investigated (MgO, ZrO2, spinels, pyrochlores) havea cubic crystal structure. Table 1 gives an overview of thelattice parameters of the phases involved in our experi-ments. In a first approximation, the prepared BO/PS reac-tive interfaces turned out to be characterized by cube-on-cube orientation relationships between the binary oxideand the spinel or pyrochlore, respectively:

(001)BO || (001)PS; [100]BO || [100]PS (5)

This was established by XRD, electron diffraction, andhigh-resolution electron microscopy [9– 14]. As an exam-ple, Fig. 1 shows the TEM overview (a) and a high-resolu-tion micrograph (b) of a cross section of the MgO/Mg2TiO4

reactive interface formed due to a reaction of type Eq. (2),with A = Mg and B = Ti. The cube-on-cube orientation re-lationship between MgO and Mg2TiO4 is clearly revealedby the HRTEM image.

3.2. The network of misfit dislocations

Depending on sign and amount of the lattice misfit, misfitdislocation networks of different Burgers geometries werefound at the reactive interfaces. The network spacing, andthe Burgers geometry (Burgers vector b and line vector <)of the dislocations constituting the network were analysedin detail applying diffraction contrast methods to plan-viewsamples and also Burgers circuit analyses of HRTEM crosssection images. As an example, Fig. 2 shows the plan-viewdiffraction contrast analysis of the misfit dislocation net-work at the MgO/MgCr2O4 interface, and Fig. 3 shows acorresponding cross-sectional HRTEM image of this inter-face. The analysis yields a spacing of (25 � 5) nm, and aBurgers geometry characterized by the Burgers vectors

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Fig. 1. Cross-sectional TEMmicrographs of the MgO/Mg2TiO4 reactive hetero-phase boundary.

Fig. 2. Plan-view diffraction contrast analysis of the Burgers vectors of the misfit dislocations at the MgO/MgCr2O4 reactive heterophase bound-ary. (a) Bright field (BF) image. (b)– (e) Dark field (DF) images. g is the diffracting vector.

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b1 = 1/2 aMgO [110] and b2 = 1/2 aMgO [110] for the two setsof dislocations, and by the corresponding line vectors<1 = [110] and <2 = [110]. This shows that the dislocationsare of pure edge type, and that the Burgers vector lies inthe plane of the interface. The MgO/MgCr2O4 orientationrelationship was shown to exactly correspond to Eq. (5).

In other cases, however, well-defined small deviationsfrom this orientation relationship occur, with the crystal lat-tice of the spinel or pyrochlore phase, respectively, beingtilted away from Eq. (5) by a few degrees. This tilt may oc-cur into four directions, in correspondence with the fourfoldcrystal symmetry of the BO (001) crystal surface, resultingin a split-up of the (00<) spinel and pyrochlore reflectionsin XRD pole figures into four sub-reflections (Fig. 4). Ac-cordingly, tilt domains of four types appear in the spineland pyrochlore phase, which can be visualized by AFMand TEM in the initial reaction stages, when individual spi-nel or pyrochlore islands are formed (see Figs. 8 and 9 be-low). Moreover, in the cases of deviations from Eq. (5),out-of-plane Burgers vectors of the misfit dislocations werefound (Fig. 5) instead of in-plane vectors. Sense andamount of the tilt of the spinel (or pyrochlore) lattice arecorrelated to the Burgers vector geometry of the disloca-tions of the corresponding misfit dislocation network. Ta-ble 2 presents a summary of the experimental findings atthe different reactive interfaces investigated, viz. the mor-phology (p – plane; r – rough), the amount of the deviationfrom Eq. (5) in terms of tilt angle, the absence ( – ) or pres-ence (+) of a dislocation network, and the Burgers vectorgeometry (b; <) of the dislocations constituting this net-work. Also shown are sign (+; – ) and amount (in %) of thelattice misfit, f, involved.

From Table 2, the following phenomenological summarycan be deduced. In cases of very low misfit (MgO/Mg2TiO4; MgO/MgFe2O4) no dislocation network and notilt occur. The reactive interface is coherent (cf. Fig. 1b),which can be explained by the inert f.c.c. oxygen sublatticeof MgO simply being taken over by the spinel due toWagner’s cation counterdiffusion reaction mechanism [15](cf. Ref. [16] for thin-film reactions). At negative misfit(e. g., MgO/MgCr2O4), a network of misfit edge disloca-tions with in-plane Burgers vectors is present at the reactiveinterface, while at positive misfit (e. g., MgO/MgIn2O4 andZrO2/La2Zr2O7), a network of misfit edge dislocations with

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Fig. 3. HRTEM image of a cross section of the MgO/MgCr2O4 reac-tive heterophase boundary, seen along the [110] direction of MgO andspinel. ‘B’ marks a coherent region of the boundary, whereas ‘C’ marksa misfit dislocation with an in-plane Burgers vector b = 1/2 aMgO [110].

Fig. 4. Part of an X-ray pole figure of a sample containing a MgO/Mg2SnO4 reactive heterophase boundary. The (008) spinel peak is splitinto four sub-peaks. The polar angle ranges from 0 (centre) to 3° (rim).

Fig. 5. HRTEM image of a MgO/MgIn2O4 re-active heterophase boundary. (a) Unfiltered,(b) (200) Fourier-filtered, and (c) (002) Four-ier-filtered images, indicating two sets of extrahalf-planes, and accordingly two Burgers vec-tor components b|| and b?, respectively.

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out-of-plane Burgers vectors occurs, the perpendicularcomponent b? = 1/2 aBO [001] of which is the reason forthe observed small tilt of the spinel and pyrochlore latticeoff the orientation Eq. (5). No correlations of these observa-tions with the morphology of the interface were found.

3.3. Burgers geometry, mode of misfit dislocationmovement, and reactivity

As a consequence of these findings, two principal Burgersgeometries are found: One with in-plane Burgers vectors(at negative misfit), the other with out-of-plane ones (atpositive misfit). These two principal geometries result intwo different modes of the unidirectional misfit dislocationmovement into the [001] direction. The latter occurs be-cause the misfit dislocation network has to move togetherwith the advancing interface due to the interfacial solidstate reaction proceeding into the [001] direction, i. e., intoan overall direction perpendicular to the interface plane.The two modes are(i) diffusional climb in the case of in-plane Burgers vec-

tors (Fig. 6), and(ii) conservative glide in the case of out-of-plane Burgers

vectors (Fig. 7).While the glide mechanism (Fig. 7) can proceed easily andquickly, the climb mechanism (Fig. 6) is a slow and energeti-

cally unfavourable process, because it requires the diffusionof lattice molecules (in particular oxygen ions) to the misfitdislocations in order to add them to the extra spinel latticeplanes at the interface [9, 10]. Since oxygen ions are ratherslowly diffusing in a dense-packed oxide lattice, the reac-tivity of those interfaces where out-of-plane Burgers vec-tors are present should be higher than that of those wherein-plane Burgers vectors constitute the network of misfitdislocations. The zero-misfit interfaces should be evenmore reactive than the former two, because the conservativeglide process suffers from an additional resistance due tothe Peierls stress experienced by gliding dislocations. Thesepredictions were qualitatively confirmed by our observa-tions. The three different principal structures of the reactiveinterfaces – without dislocations, with dislocations of in-plane Burgers vector, and with dislocations of out-of-planeBurgers vector – thus result in three different values of in-terface mobility, or reactivity.

3.4. Initial microtopography, stresses, and the Burgersgeometry

In view of the above findings, the questions arise, when andby which processes the misfit dislocations form, whethertheir Burgers vector is univocally determined by the signof the lattice misfit or not, and if not, which other factors de-

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Table 2. Determined characteristics of the reactive interfaces prepared on flat MgO and YSZ (001) substrate surfaces, respectively, byreactions with binary oxide vapours.

Interface Misfit f (%) Morphology Tilt angle Disloc. network Burgers vector Line vector

MgO/MgAl2O4 – 4.2 p 0 + 1/2 aMgO [110] [110]MgO/Mg2GeO4 – 2.0 r 0 + 1/2 aMgO [110] [110]MgO/MgCr2O4 – 1.1 r 0 + 1/2 aMgO [110] [110]MgO/MgFe2O4 – 0.4 p 0 – – –MgO/Mg2TiO4 + 0.2 p 0 – – –MgO/Mg2SnO4 + 2.5 p 0.8° + 1/2 aMgO [101] [010]MgO/MgIn2O4 + 4.7 p 3.5° + 1/2 aMgO [101] [010]ZrO2/La2Zr2O7 + 5.5 p 2.5° + 1/2 aZrO2 [101] [010]

Fig. 6. Scheme of the diffusive climb mechanism of the misfit disloca-tion movement at the MgO/MgCr2O4 boundary. Open circles designateoxygen ions, black arrows Burgers vectors. Open arrows indicate thedirection of movement of the reactive heterophase boundary.

Fig. 7. Scheme of the conservative glide mechanism of the misfit dis-location movement at the MgO/MgIn2O4 boundary. For the meaningof the arrows, see Fig. 6.

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termine the Burgers vector. To study these questions, the in-itial reaction stages were investigated by AFM and TEM,using BO (001) crystal surfaces of different microtopogra-phies [12 – 14]. Fig. 8 shows an AFM image and a TEMplan-view image of La2Zr2O7 islands that have grown on aflat YSZ(001) substrate during the initial stage of reactionEq. (3), with A = Zr and B = La. Each island consists of

four tilt domains, as demonstrated by the XRD pole figure(Fig. 9a). Fig. 9b shows the internal structure of an islandtogether with the network of misfit dislocations at theZrO2/La2Zr2O7 interface. These dislocations, running along<100> directions at a spacing of about 8 nm, were analysedby TEM [13,14]. They turned out to be edge dislocationswith Burgers vectors b1 = 1/2 aZrO2 [101] and b2 = 1/2 aZrO2

[011], i. e., out-of-plane Burgers vectors. The interface-par-allel component of the Burgers vector accommodates thelattice mismatch, while the perpendicular componentcauses a tilt of the La2Zr2O7 lattice around the <110> axesby about 2.5° (cf. Fig. 9a). A different picture occurs whenthe reaction is performed on YSZ (001) surfaces containinga large number of pits of about 20 to 30 nm in diameter.(The origin of the pits is not clear. They might be due tosmall precipitates of tetragonal ZrO2 that were removedfrom the surface during surface polish.) On these surfaces,the islands grow around the pits, leaving a central hole,and, in addition to four tilted domains of trapezoidal shape,they always contain between one and four stripe domainstilted around <100> (Fig. 10). The latter have misfit dislo-cations with an in-plane Burgers vector of type b =1/2 aZrO2

[100], as was revealed by Fourier-filtered HRTEM images[12].

The observed structural and morphological differencesbetween the case of a flat YSZ surface and the one with pitscan be explained considering the generation mechanisms ofmisfit dislocations (Fig. 11). On flat surface areas, misfitdislocations of a Burgers vector b =1/2 aZrO2 ½101] are gen-erated at the corners of the growing islands, where the epi-taxial stress has a maximum. They subsequently move tothe ZrO2/La2Zr2O7 interface by glide on {101} planes, thus

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Fig. 8. (a) AFM and (b) TEM plan-viewimages of La2Zr2O7 islands on a flat YSZ(001) surface. Inset: Greyscale indicating thevertical coordinate (height).

Fig. 9. (a) Part of an X-ray pole figure and (b)TEM plan-view image of La2Zr2O7 islandsgrown on a flat YSZ (001) surface. In the polefigure shown, the polar angle ranges from 0(centre) to 5° (rim). The TEM image showsfour tilt domains, and dislocation networks.

Fig. 10. Plan-view TEM image of a La2Zr2O7 island grown around asurface pit on a YSZ (001) substrate. Four <110>-tilted domains(Nos. 1 to 4) and two <100>-tilted stripe domains (Nos. 5 and 6) arevisible.

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forming the <110>-tilted domains (Fig. 11a). Near a pitrim, however, part of the stresses arising in the growing is-land can certainly relax by deformation of the pit rim. (De-tails of the mechanism still remain open.) The remainingstress components result in the generation of dislocationswith Burgers vector b =1/2 aZrO2 [100] at the pit rim on thelevel of the ZrO2/La2Zr2O7 interface. The dislocations sub-sequently move under the island by glide on the (001) planeforming the <100>-tilted stripe domains (Fig. 11b). For de-tailed models, see Refs. [12 – 14].

Considering the previously established relation betweenreactivity and the mode of movement of misfit dislocations– given by the Burgers geometry – it is suggested that thereactivity of a plane ZrO2/La2O3 interface is higher thanthat of an interface providing many sites of stress relaxa-tion, like pit rims of a high density. This is a somewhat sur-prising result, because usually plane interfaces are believedto be less reactive than rough interfaces.

4. Conclusions

Crystallography and atomic-scale structure of a reactive in-terface play an important role in determining the reactivityof this interface. The reactivity (or reaction kinetics) de-pends on the mobility of the interfacial dislocation network,because the misfit dislocations have to move together withthe advancing reaction front. The mobility of the disloca-tions, in turn, depends on the mode of dislocation move-ment (conservative glide or diffusive climb), so that, finally,interface mobility and reactivity depend on the Burgersvector geometry of the misfit dislocations. The Burgersvector geometry, in turn, depends on the sign and amountof the lattice misfit, but also on the stress conditions initi-ally prevailing at the reactive interface. Structure and chem-istry of reactive interfaces in ceramics are, thus, closely in-terrelated.

The authors are thankful to Drs. W. Blum, A. Graff, C. J. Lu, H. Sieber,P. Werner, N. D. Zakharov, and M. Zimnol for their respective experi-mental contributions to this work. Thanks are due to Professors U. Gö-sele and J. Heydenreich for continuous support, and to ProfessorH. Schmalzried for many fruitful discussions.

Work supported by DFG via SFB 418 at Martin-Luther-UniversitätHalle –Wittenberg.

References

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[3] H. Schmalzried: Chemical kinetics in solids, VCH, Weinheim(1995).

[4] U. Gösele, K.N. Tu: J. Appl. Phys. 53 (1982) 3252.[5] M. Backhaus-Ricoult, H. Schmalzried: Ber. Bunsenges. Phys.

Chem. 89 (1985) 1323.[6] M. Martin, in: V.V. Boldyrev (Ed.), Reactivity of solids – past,

present and future, Blackwell Science, Oxford (1996) 91.[7] D. Hesse: Solid State Ionics 95 (1997) 1.[8] M. Backhaus-Ricoult: Annu. Rev. Mater. Res. 33 (2003) 55.[9] H. Sieber, D. Hesse, P. Werner: Phil. Mag. A 75 (1997) 889.

[10] D. Hesse, A. Graff, S. Senz, N.D. Zakharov: Ceram. International26 (2000) 753.

[11] St. Senz, W. Blum, D. Hesse: Phil. Mag. A 81 (2001) 109.[12] C.J. Lu, S. Senz, D. Hesse: Phil. Mag. A 81 (2001) 2705.[13] C.J. Lu, S. Senz, D. Hesse: Phil. Mag. Letters 82 (2002) 167.[14] C.J. Lu, S. Senz, D. Hesse: Surface Science 515 (2002) 507.[15] C. Wagner: Z. Phys. Chem. B 34 (1936) 309.[16] D. Hesse: J. Vac. Sci. Technol. A 5 (1987) 1696.

(Received October 29, 2003; accepted February 3, 2004)

Correspondence address

Priv.-Doz. Dr. Dietrich HesseMax-Planck-Institut für MikrostrukturphysikWeinberg 2, D-06120 Halle (Saale), GermanyTel.: +49 345 5582 741Fax: +49 345 5511 223E-mail: hesse@mpi-halle.de

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Fig. 11. Cross-sectional scheme of two mech-anisms of dislocation generation, (a) on flatYSZ surface areas, and (b) near a pit rim.Tilted black dislocation symbols “T” denoteout-of-plane Burgers vectors, non-tilted greysymbols in-plane ones.

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