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INTERFACE SCIENCE 8, 279–294, 2000 c 2000 Kluwer Academic Publishers. Manufactured in The Netherlands. The Crystallography of Interphase Boundaries Between Silicon Carbide and Silicon Nitride in Silicon Nitride— Silicon Carbide Particulate Composites S. TURAN Anadolu University, Department of Ceramic Engineering, Iki Eyl¨ ul Kamp ¨ us¨ u, 26470 Eskis ¸ehir, Turkey K.M. KNOWLES * Universityof Cambridge, Department of Materials Science and Metallurgy, Pembroke Street, Cambridge, CB2 3QZ, UK [email protected] Abstract. Interphase boundaries between 3C SiC grains and two different β -Si 3 N 4 morphologies in Si 3 N 4 SiC composites have been studied by transmission electron microscopy. In general, boundaries between small β -Si 3 N 4 intragranular precipitates and surrounding SiC grains were relatively free of intergranular films, whereas bound- aries between large β -Si 3 N 4 grains and adjacent SiC grains were invariably covered with thin intergranular films. Orientation relationships approximating to [110] 3C SiC k [0001] β -Si 3 N 4 and (001) 3C SiC k (10 ¯ 10) β -Si 3 N 4 were found to dominate between 3C SiC grains and the intragranular β -Si 3 N 4 precipitates, but there was no ev- idence of any favoured orientation relationship between the large β -Si 3 N 4 grains and adjacent SiC grains. The rationale for ‘special’ orientation relationships arising when there is no intergranular film present at 3C SiC β - Si 3 N 4 interfaces is explored geometrically using the near-coincidence site lattice model, with the significant result that the dominant orientation relationships between 3C SiC grains and the intragranular β -Si 3 N 4 precipitates have low misfits relative to all other possible orientation relationships between 3C SiC and β -Si 3 N 4 . Keywords: crystallography, engineering ceramics, interphase boundaries, silicon carbide, silicon nitride 1. Introduction Ceramics such as silicon nitride (Si 3 N 4 ), silicon car- bide (SiC) and Si 3 N 4 SiC composites are candidate materials for high temperature applications because of their strength, relative chemical stability and good cor- rosion resistance. Over the last two decades, a variety of Si 3 N 4 SiC composites have been produced using whiskers, fibres, particulates and platelets with either SiC or Si 3 N 4 as the reinforcing agent. The addition of these reinforcing agents has generally achieved a modest increase in the fracture toughness of the ma- trix at the expense of other properties such as strength, * Author to whom all correspondence should be addressed. although recent work on self-reinforced β -silicon ni- tride-based ceramics shows that strengths of 1 GPa and fracture toughness values of more than 10 MPa m 1/2 can be achieved by careful processing with the addi- tion to α-Si 3 N 4 powder mixtures of β -Si 3 N 4 rodlike seeds and yttria and alumina as sintering aids [1, 2]. In contrast to these ‘conventional’ composites, re- cently developed Si 3 N 4 SiC ceramic nanocomposites, in which nanosized SiC particles have been dispersed in a matrix of Si 3 N 4 , have been claimed to have bet- ter fracture toughness, strength and high temperature mechanical properties than conventionally processed monolithic Si 3 N 4 ceramics with equiaxed grain struc- tures [3, 4]. These latter composites are also reported to show superplastic elongation, related to the presence

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Page 1: The Crystallography of Interphase Boundaries Between Silicon Carbide and Silicon Nitride in Silicon Nitride—Silicon Carbide Particulate Composites

INTERFACE SCIENCE 8, 279–294, 2000c© 2000 Kluwer Academic Publishers. Manufactured in The Netherlands.

The Crystallography of Interphase Boundaries BetweenSilicon Carbide and Silicon Nitride in Silicon Nitride—

Silicon Carbide Particulate Composites

S. TURANAnadolu University, Department of Ceramic Engineering, Iki Eylul Kampusu, 26470 Eskis¸ehir, Turkey

K.M. KNOWLES∗

University of Cambridge, Department of Materials Science and Metallurgy, Pembroke Street, Cambridge,CB2 3QZ, UK

[email protected]

Abstract. Interphase boundaries between 3C SiC grains and two differentβ-Si3N4 morphologies in Si3N4 SiCcomposites have been studied by transmission electron microscopy. In general, boundaries between smallβ-Si3N4

intragranular precipitates and surrounding SiC grains were relatively free of intergranular films, whereas bound-aries between largeβ-Si3N4 grains and adjacent SiC grains were invariably covered with thin intergranular films.Orientation relationships approximating to [110] 3C SiC‖ [0001] β-Si3N4 and (001) 3C SiC‖ (1010) β-Si3N4

were found to dominate between 3C SiC grains and the intragranularβ-Si3N4 precipitates, but there was no ev-idence of any favoured orientation relationship between the largeβ-Si3N4 grains and adjacent SiC grains. Therationale for ‘special’ orientation relationships arising when there is no intergranular film present at 3C SiCβ-Si3N4 interfaces is explored geometrically using the near-coincidence site lattice model, with the significant resultthat the dominant orientation relationships between 3C SiC grains and the intragranularβ-Si3N4 precipitates havelow misfits relative to all other possible orientation relationships between 3C SiC andβ-Si3N4.

Keywords: crystallography, engineering ceramics, interphase boundaries, silicon carbide, silicon nitride

1. Introduction

Ceramics such as silicon nitride (Si3N4), silicon car-bide (SiC) and Si3N4 SiC composites are candidatematerials for high temperature applications because oftheir strength, relative chemical stability and good cor-rosion resistance. Over the last two decades, a varietyof Si3N4 SiC composites have been produced usingwhiskers, fibres, particulates and platelets with eitherSiC or Si3N4 as the reinforcing agent. The additionof these reinforcing agents has generally achieved amodest increase in the fracture toughness of the ma-trix at the expense of other properties such as strength,

∗Author to whom all correspondence should be addressed.

although recent work on self-reinforcedβ-silicon ni-tride-based ceramics shows that strengths of 1 GPa andfracture toughness values of more than 10 MPa m1/2

can be achieved by careful processing with the addi-tion to α-Si3N4 powder mixtures ofβ-Si3N4 rodlikeseeds and yttria and alumina as sintering aids [1, 2].

In contrast to these ‘conventional’ composites, re-cently developed Si3N4 SiC ceramic nanocomposites,in which nanosized SiC particles have been dispersedin a matrix of Si3N4, have been claimed to have bet-ter fracture toughness, strength and high temperaturemechanical properties than conventionally processedmonolithic Si3N4 ceramics with equiaxed grain struc-tures [3, 4]. These latter composites are also reportedto show superplastic elongation, related to the presence

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280 Turan and Knowles

of an intergranular liquid phase at high temperature[5].

The mechanical performance of Si3N4 SiC com-posites prepared either through a conventional or ananocomposite route will depend critically on the be-haviour of the interfaces in the composites. For exam-ple, the bonding at interfaces will determine whetherinterfaces inhibit or promote crack formation and crackgrowth. If interfaces contain thin films of remnant vis-cous phases, undesirable creep growth at elevated tem-peratures can arise even if there are property enhance-ments at low temperatures. Nanoparticles located atgrain boundaries can either strengthen such boundariesor act themselves as crack initiators, depending on themechanism of bonding between the nanoparticles andthe adjacent grains.

Thus, it is important to be able to characterise in-terfaces such as Si3N4 SiC interfaces at or near theatomic level. Such studies have been relatively few innumber. Niihara et al. [3] suggested on the basis of theirtransmission electron microscopy (TEM) evidence thatlow energy interfaces develop preferentially in Si3N4

grains containing small SiC precipitates, without speci-fying uniquely the orientation relationships and inter-face planes that they observed. A more detailed two partTEM study by Unal et al. [6] and Unal and Mitchell[7] on chemically vapour deposited Si3N4 grown onsingle crystal SiC found two characteristic orientationrelationships between the Si3N4, which deposited it-self asα-Si3N4,1 and the substrate SiC which, near thesurface of the crystal, was twinned 3C SiC# rather thanα-SiC,2 which constituted the bulk of the substrate. Thedominant orientation relationship they observed can bedescribed approximately as [101] 3C SiC‖ [0001] α-Si3N4 with (111) 3C SiC‖ (1010)α-Si3N4. This orien-tation relationship has also been reported between 3CSiC andβ-Si3N4 by Pan et al. [8] between their ‘type A’SiC nanoparticles and the surroundingβ-Si3N4 ma-trix. It is significant that intergranular films were notreported by Niihara et al. [3], nor by Unal et al. [6] andUnal and Mitchell [7], and that, of these four studies,the presence of any amorphous intergranular film be-tween SiC and Si3N4 is only reported by Pan et al. [8].Even in Pan et al.’s study, amorphous films were onlyseen in some parts of the SiCβ-Si3N4 interfaces fortheir ‘type A’ particles.

Other studies on conventionally produced hotpressed and hot-isostatically pressed SiCSi3N4 com-posites have reported clear evidence of intergranularfilms [9–13]. For example, More et al. [10] investigated

the microstructure of hot pressed 30 vol% SiC whisker-reinforced Si3N4 matrix composites with 6 wt% Y2O3

and 1.5 wt% Al2O3 added as sintering aids and founda film thickness of 1–2 nm at SiCSi3N4 interphaseboundaries. Unal et al. [12] showed the existence ofvery thick intergranular films (5–10 nm thick) at inter-phase boundaries in 10 vol% SiC whisker reinforcedand hot isostatically pressed material produced withoutdensification aids. Chowdhury et al. [13] reported thepresence of relatively thin films (∼1 nm thick) at in-terphase boundaries between Huber SiC whiskers andSi3N4 matrix grains in a hot isostatically pressed mate-rial. However, in contrast to such observations, Braueet al. [14] claimed that most of the interphase bound-aries were free from intergranular films in their TokaiSiC whisker-reinforced and hot pressed Si3N4 matrixcomposites. Chowdhury et al. [13] reported that theinterphase boundaries in SiCSi3N4 composites madeusing American Matrix SiC whiskers were free of inter-granular films when examined by high-resolution TEM(HRTEM), but high oxygen concentrations at theseinterphase boundaries could be detected by position-resolved electron energy-loss spectroscopy. None ofthese researchers reported any ‘special’ or ‘favoured’orientation relationship between SiC and Si3N4 crys-tals, although one of the micrographs from [14] isclearly taken at an orientation which, from an inspec-tion of the diffraction pattern, can be described as(111) 3C SiC‖ (1010) β-Si3N4 with [101] 3C SiCclose to, but some way from, [0001]β-Si3N4, becauseonly theh0h0 β-Si3N4 systematic reflections are ap-parent when the electron beam direction is along [101]3C SiC. Pan et al. [8] also found random orienta-tions of their ‘type B’ 3C SiC nanoparticles embed-ded inβ-Si3N4 matrices for which there was evidenceof substantial amorphous phase at the SiCβ-Si3N4

interfaces.During the course of our work on Si3N4 SiC com-

posites, two types of interphase boundaries were foundas a consequence of the bimodal size distribution ofthe Si3N4 grains [15, 16]. The first type of interphaseboundary was formed between intragranularβ-Si3N4

precipitates and surrounding 3C SiC grains. The secondtype was between largeα- or β-SiC grains and Si3N4

grains of a similar size. In this paper, we report details ofthese two types of interphase boundaries and compareour results with previously published work in this area.The objectives of our work were to ascertain whetheror not there was evidence for the adoption of preferredorientation relationships between Si3N4 and SiC, and

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if so under what circumstances, and to ascertain theextent of remnant amorphous material at Si3N4–SiCinterfaces, with the aim of establishing which types ofinterfaces occurred as a result of random processes andwhich occurred by non-random processes, such as, forexample, those which arise in thin films during epitax-ial growth processes.

2. Experimental Procedure

Si3N4 SiC composites were prepared by first mixingcommercially availableα-SiC andα-Si3N4 powderswithout the addition of any sintering aids and then sub-jecting powder compacts to hot isostatic pressing intantalum cans at 2373 K for an hour under 200 MPaargon pressure to achieve composite densification.Prior to hot-isostatic pressing, two of the green com-pacts containing 10 and 20 wt% Si3N4 were deoxidisedbriefly for 10 min in a graphite furnace at 1900◦C bythe addition of carbon resin to eliminate surface sil-ica [15, 16]. Theα-SiC was Lonza UF15 powder witha surface area of 15 m2/g and major impurities of 0.8wt% oxygen, 0.4 wt% carbon and residual Al, Fe and Titotalling together 1200 ppm. Theβ-Si3N4 was StarckLC10 powder with a surface area of 15 m2/g and majorimpurities of 1.5 wt% oxygen and 0.2 wt% carbon.

Transmission electron microscope specimens pre-pared by conventional ion-beam thinning were exam-ined at 200 kV in a JEOL 2000FX and at 400 kV in aJEOL 4000EX-II which has a spherical aberration co-efficient,Cs, of 1 mm and a point-to-point resolutionof ≈1.7 A.

3. Experimental Results and Interpretation

3.1. Interphase Boundaries Between SiC Grainsand Si3N4 Precipitates

Typical examples ofβ-Si3N4 precipitates within 3CSiC grains are shown in Figs. 1–3. The appearance ofthese fine 100–200 nm diameter precipitates when im-aged with the electron beam direction parallel to [0001]β-Si3N4 was variable—some precipitates, such as theones in Figs. 1 and 3 were hexagonal or elongated withrounded ends and{1010} facets, whereas others, suchas the one in Fig. 2, were seen by comparison to berelatively circular in projection.

There are clear moir´e fringes at theβ-Si3N4 SiCinterfaces in the dark field images in Fig. 2(a) and (b),

Figure 1. Examples of (a) an hexagonal shapedβ-Si3N4 precipitateand (b) an elongated shapedβ-Si3N4 precipitate in 3C SiC matrixgrains. In both cases the facets are{1010} β-Si3N4. The insets to (a)and (b) show the [0001]β-Si3N4 electron diffraction patterns, rotated90◦ with respect to the images. The 3C SiC matrix spots arrowed inthe inset to (b) are 111 type spots.

indicative of planes in the two phases which are almostparallel. This also shows that the Si3N4 SiC interfaceswhere the moir´e fringes are visible are inclined at asmall angle to the incident electron beam, which inthis case was parallel to [110] 3C SiC. The electrondiffraction patterns in Fig. 2(c) and (d) demonstratethat the [110] 3C SiC and [0001]β-Si3N4 directionsare not parallel. In fact, in this case, there is a 9◦ ro-tation between these two zones. More significantly, itis evident from Fig. 2(c) that the (002) SiC and (3030)β-Si3N4 planes are parallel. These planes have almostthe same interplanar spacing (2.179A and 2.195A,respectively), and it is interference between reflectionsfrom these two sets of planes which gives rise to therelatively coarse moir´e fringes seen in Fig. 2(a) and (b).Unfortunately, because no part of the interphase bound-ary between this Si3N4 precipitate and the surroundingSiC grain was parallel to the electron beam for either

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Figure 2. (a) and (b), dark field images of interphase boundariesbetween aβ-Si3N4 precipitate and a surrounding SiC grain when the3C SiC grain was aligned parallel to [110]. (c) Electron diffractionpattern from the SiC grain and precipitate when the electron beamis parallel to [110] 3C SiC. (d) As (c), but with the electron beamparallel to [0001]β-Si3N4. The SiC spots in both the diffractionpatterns are indicated with arrows and the two spots used to form thedark field images in (a) and (b) are labelled in white on (c) as (a) and(b) respectively.

the [110] 3C SiC zone or the [0001]β-Si3N4 zone, itwas not possible to determine without ambiguity byHRTEM whether or not there was a thin intergranularfilm present at this particular interphase boundary.

In the example in Fig. 3, the [110] 3C SiC and [0001]β-Si3N4 directions were only 4◦ apart. The image inFig. 3(a) was taken when the electron beam was paral-lel to [0001]β-Si3N4. While once again it was evidentfrom Fig. 3(b) and (c) that the (001) 3C SiC and (1010)β-Si3N4 planes were almost parallel, there was a defi-nite measurable small rotation of∼2◦ between thesetwo sets of planes about the ‘common’ zone axes. In-terfaces IB1 and IB4 between the precipitate and thesurrounding grain in Fig. 3(a) were parallel to the elec-tron beam within experimental uncertainty, while in-terfaces IB2, IB3, IB5 and IB6 were almost parallel tothe electron beam. The SiC grain in Fig. 3(a) does notshow any lattice fringes since the interplanar spacingof the 1.54A (220) SiC planes which give rise to themost prominent SiC reflections at this electron beamorientation is below the microscope resolution. How-ever, the thin white band of contrast evident in Fig. 3(a)

Figure 3. (a) Low magnification high resolution image with the[0001] β-Si3N4 direction parallel to the electron beam showing across section of a{1010} facetedβ-Si3N4 precipitate embedded in a3C SiC grain. (b) Electron diffraction pattern from (a) with the SiCspots arrowed. There is a relative rotation of 90◦ with respect to theimage in (a). (c) Electron diffraction pattern from SiC and theβ-Si3N4 precipitate after tilting 4◦ away from (b) to make the electronbeam close to [110] SiC.

along the SiC Si3N4 interface indicates that the Si3N4

precipitate is probably surrounded with a thin band ofamorphous phase.

In order to clarify the nature of the different parts ofthe interphase boundary in Fig. 3(a), edge-on HRTEMimages were obtained by tilting away from [0001]β-Si3N4. These images showed that parts of the in-terphase boundary were faceted on the SiC side andthat there was evidence for thin intergranular films. Inparticular, it is interesting that interfaces IB1 and IB4in Fig. 3(a) were similar in character, in that they areboth faceted on the SiC side and they both contain in-tergranular films, despite the non-random orientationrelationship between the precipitate and the surround-ing grain. An HRTEM image of interface IB1 when theelectron beam is parallel to [110] 3C SiC demonstrat-ing these features of interface IB1 is shown in Fig. 4(a).By comparison, HRTEM images of interface IB6 and

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Figure 4. (a) HRTEM image of the region denoted in Fig. 3 as IB1formed with the electron beam parallel to [110] SiC. (b) HRTEMimage of interface IB6 when the electron beam was 2◦ away from boththe [110] SiC and [0001] Si3N4 directions. (c) the interface regionbetween IB1 and IB6 imaged using the same conditions as in (b).

the interface between IB1 and IB6 shown in Fig. 4(b)and (c) respectively appeared to be free of intergran-ular film to a resolution defined by the (111) 3C SiCinterplanar spacing, realistically∼5 A.

Schematics of the electron diffraction patterns fromFigs. 2 and 3 are shown in Fig. 5(a) and (b) respectively.For simplicity, we have taken the beam directions to be[110] 3C SiC‖ [0001]β-Si3N4 for both these schemat-ics. It is apparent that there is a rotation between thesetwo zones about the common 00l 3C SiC andh0h0 β-Si3N4 sets of systematic reflections in going from theschematic in Fig. 5(a) to the actual electron diffractionpattern in Fig. 2(b), and that in going from Fig. 5(b) toFig. 3(b), there is a small rotation about thehh0 set of3C SiC reflections.

The approximate orientation relationship of [110]3C SiC‖ [0001] β-Si3N4 and (001) 3C SiC‖ (1010)β-Si3N4 was the dominant orientation relationshipseen between particles and the surrounding matrices.Of the tenβ-Si3N4 particles whose crystallographywe established, nine had this approximate orientationrelationship.

Figure 5. Schematic overlapping diffraction patterns for (a) Fig. 2and (b) Fig. 3 showing the orientation relationships between SiCgrains and intragranular Si3N4 precipitates. For simplicity, the beamdirections have been taken to be [110] 3C SiC‖ [0001]β-Si3N4 forboth these schematics.

The exception was found during HRTEM imaging,for which the general procedure was to align either a〈110〉 3C SiC zone or the [0001]β-Si3N4 zone parallelto the electron beam. The electron diffraction pattern inthe inset to Fig. 6 shows that for this particularβ-Si3N4

particle, the 3C SiC grain is close to a [110] orienta-tion and that there is a 1210 systematic set ofβ-Si3N4

reflections parallel to 220 type 3C SiC reflections. Thefaint arrowedβ-Si3N4 reflections show that the beamdirection is close to [2027] β-Si3N4, with the rows offaint 4132 typeβ-Si3N4 reflections making an angle of81.4◦ with the 1210 systematic set of reflections. Evenallowing for slight angular variations in the orientationrelationship between the precipitates and the surround-ing grains from one particle to the next, it is clear thatthis orientation relationship is substantially differentfrom those seen in Figs. 2 and 3, simply because thisis the only〈110〉 3C SiC zone to contain these particu-lar 220 type 3C SiC reflections. Hence this diffraction

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Figure 6. An example of an interphase boundary between an intra-granularβ-Si3N4 precipitate and a surrounding 3C SiC grain facetedon a{111} plane with an intergranular film having a varying thick-ness along the interface. The electron diffraction pattern shown inthe inset (not orientated with respect to the image) is [110] 3C SiC‖[2027] β-Si3N4.

pattern is not obtainable by tilting 60◦ or 90◦ away to a〈110〉 3C SiC zone from a symmetry-related〈110〉 3CSiC zone approximately parallel to [0001]β-Si3N4.Instead, we shall show in §4 that this orientation re-lationship is in essence a variant for 3C SiCβ-Si3N4

interfaces of the second orientation relationship for 3CSiC β-Si3N4 interfaces reported by Unal et al. [4, 5]which they also only observed on one occasion.

The HRTEM image in Fig. 6, taken when the elec-tron beam is parallel to [110] 3C SiC, shows that herethe interphase boundary contains an intergranular film,the thickness of which varies significantly. It is mostthin (∼10A thick) where theβ-Si3N4 particle abuts the{111} 3C SiC facet. The image has similarities withwidely reported observations of film thinning whenmoving from pockets of amorphous material found attriple junction regions to grain boundaries in engineer-ing ceramics. These similarities can be accounted forin terms of the particle morphology.

3.2. Interphase Boundaries Between SiC Grainsand Si3N4 Grains

The character of interphase boundaries between SiCand the Si3N4 grains of a similar size (the meangrain size of both types determined from optical mi-croscopy was≈5µm) was different from that of inter-phase boundaries between SiC grains and intragranularSi3N4 precipitates. All interphase boundaries observedeither by HRTEM or Fresnel defocus imaging tech-niques were seen to be covered with thin intergranu-lar films in compacts which were not deoxidised priorto hot isostatic pressing. No characteristic orientation

Figure 7. (a) Underfocus and (b) overfocus Fresnel fringe profilesindicating the existence of intergranular films at three different in-terfaces connected to the same triple junction formed between a 3CSiC grain, anα-SiC grain and a Si3N4 grain.

relationships between SiC and Si3N4 were evident. Themicrographs from a typical Fresnel through-focus se-ries shown in Fig. 7 demonstrate that both interphaseboundaries betweenβ-Si3N4 andα-SiC andβ-Si3N4

and 3C SiC are wetted by thin films.The HRTEM image of the interphase boundary be-

tweenα-SiC and aβ-Si3N4 grain in Fig. 8 clearlyshows the existence of a∼12 A thick intergranularfilm. In this case, the SiC grain is oriented parallel to[1120], whereas the Si3N4 grain is oriented parallel to[1, 5, 4, 12] ([134] in the three index notation). Athird example, but this time between a 3C SiC grainand two adjacentβ-Si3N4 grains is shown in Fig. 9(a).The enlarged views of the interphase boundaries (IB(b)and IB(c)) in Fig. 9(a) shown in Fig. 9(b) and (c) res-pectively demonstrate that here the two film thick-nesses are noticeably different, despite their meetingat the same triple junction. From enlargements of thesemicrographs, the film thicknesses at interfaces IB(b)and IB(c) were found to be 19± 1 A and 14± 1 A,respectively.

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Figure 8. (a) An HRTEM image of an interphase boundary between a largeα-SiC grain and aβ-Si3N4 grain containing a∼12 A thickintergranular film imaged when the electron beam was parallel to [1120] α-SiC and [1, 5,4, 12]β-Si3N4. (b) Diffraction pattern obtained fromthe interface in (a), with selectedβ-Si3N4 spots indexed. The elliptical ‘spot’ arrowed, but unindexed, is a superposition of the4041 diffractionspot from theβ-Si3N4 grain and the 0,0,0,11 spot in the 000l systematic from the 6Hα-SiC polytype.

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Figure 9. (a) An HRTEM image of two interphase boundaries between a 3C SiC grain and twoβ-Si3N4 grains attached to the same triplejunction. (b) and (c) are the enlarged views from the interfaces labelled as IB(b) and IB(c) in (a), showing clear differences in the film thickness.

3.3. Interphase Boundaries Between SiC and Si3N4

in Composites Made from Deoxidised Powders

In these composites no intragranular Si3N4 precipitateswere observed within SiC grains, and there was littleevidence for substantial volumes of liquid phase avail-able during processing at high temperature. Thus, notsurprisingly, interphase boundaries betweenα-SiC andSi3N4 grains were free from intergranular films, suchas the one shown in Fig. 10 where the Si3N4 grain isoriented parallel to [0001] and theα-SiC is orientedclose to [1010]. This observation is consistent withour earlier reports on SiCSiC grain boundaries andBN SiC interphase boundaries in these deoxidisedcompacts [15–17].

4. Discussion

A number of issues emerge from the experimental ob-servations reported in §3. For example, how do ourobservations with respect to orientation relationshipsbetween SiC and Si3N4 compare with previous work?Could we have envisaged that orientation relationships

Figure 10. (a) An HRTEM image of an interphase boundary be-tween anα-SiC grain and aβ-Si3N4 grain from a composite madefrom deoxidised powders showing the absence of any intergranularfilm.

approximating to [110] 3C SiC‖ [001] β-Si3N4 and(001) 3C SiC‖ (100)β-Si3N4 between 3C SiC grainsand the intragranularβ-Si3N4 precipitates would domi-nate? To what extent are boundaries wet by amorphousthin films, assuming that at high temperatures suffi-cient liquid is available to wet all available boundaries?

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How can strong local variation in film thickness beexplained? We will examine answers to each of theseissues in turn.

4.1. Orientation Relationships at SiCSi3N4

Interphase Boundaries

The dominant approximate orientation relationship of[110] 3C SiC ‖ [0001] β-Si3N4 and (001) 3C SiC‖ (1010) β-Si3N4 betweenβ-Si3N4 precipitates andthe surrounding 3C SiC grains is the same as oneof the orientation relationships reported by Pan et al.[18] between 3C SiC particles and a surroundingβ-Si3N4 grain. It is also closely related to the dominantorientation relationship between 3C SiC andα-Si3N4

(essentially very similar in structure toβ-Si3N4, butwith twice thec lattice repeat) found by Unal et al.[6, 7] and the orientation relationship between 3C SiCandβ-Si3N4 reported by Pan et al. [8]. A small rota-tion of 5.26◦ about [110]β-SiC is all that is required tobring (0110)β-Si3N4 parallel to (111) 3C SiC. A sig-nificant difference between our observations and thoseof Unal et al. is that we have found unambiguous evi-dence for thin amorphous intergranular film at parts ofthese boundaries, as for example in Fig. 4(a), althoughother boundaries appeared to be relatively free of suchfilms, such as those in Fig. 4(b) and (c). However, thisaccords with observations made by Pan et al. [8, 18] onthe ‘type A’ 3C SiC particles they observed which haddistinct orientation relationships with the surroundingβ-Si3N4 matrix.

Since Unal et al. made their observations onα-Si3N4

deposited on (111) 3C SiC surfaces by chemical vapourdeposition, they were able to consider atomic models oftheα-Si3N4 SiC interfaces to account for their obser-vations. They proposed that matching of SiN4 and SiC4

tetrahedra dominated the tendency for (1010)α-Si3N4

to be parallel to{111} 3C SiC, accounting qualitativelyfor small rotations away from the ideal orientation re-lationship of [110] 3C SiC‖ [0001]β-Si3N4 that theyobserved experimentally in terms of the relief of struc-tural mismatch arising from the large misfit betweencorresponding crystal planes of the two structures, asshown in Table 1 of [7].

Pan et al. [8, 18] accounted for what they consid-ered to be special orientation relationships between 3CSiC andβ-Si3N4 by proposing that during sintering thesmall SiC particles are able to rotate in the vicinity ofthe liquid-solid interface during sintering in order toform interfaces with low mismatching energy before

being consumed totally by growingβ-Si3N4 grains. Asimilar process, but with growing 3C SiC grains con-suming smallβ-Si3N4 particles occurred in the com-posites made from as-received powders, so in principlewe can invoke the same argument to account for theoccurrence of the approximate orientation relationshipof [110] 3C SiC‖ [0001]β-Si3N4 and (001) 3C SiC‖(1010)β-Si3N4 that we see.

The explanations by Pan et al. and Unal et al. havetheir limitations. One obvious question to consider iswhy the approximate [110] 3C SiC‖ [0001] β-Si3N4

and (001) 3C SiC‖ (1010) β-Si3N4 orientation rela-tionship dominates our experimental observations onthe Si3N4 precipitates and is close to the orientationrelationships reported by Unal et al. and Pan et al. Itis clearly instructive to examine crystallographic andatomic bonding aspects ofβ-Si3N4 SiC interfaces freeof amorphous phases, to see if there is any rationale forthe selection of any characteristic orientation relation-ships which might be presumed, or be shown by anappropriate computer simulation procedure, to be ‘lowenergy’.

While obvious caution must be exercised in the useof geometric criteria for low interfacial energies (see,for example, Sutton and Balluffi [19] who concludethat no geometric criterion for low interfacial energycan be regarded as wholly reliable), there is at presentno suitable atomistic modelling algorithm which canbe used to examine structures and energies of inter-faces between crystalline phases where one or morephase is covalently bonded [20]. Instead, a useful start-ing point in determining crystallographic features ofheterophase interfaces is the near-coincidence concept[21] to try and determine what orientation relationshipsmight arise on the basis of low misfits. In this approach,the details of atomic bonding at the interfaces are nec-essarily of secondary importance, although ultimatelythe adoption of any particular three-dimensional orien-tation relationship and the energetics of the interfacewill be determined by the way in which atoms bond atthe interfaces.

We have therefore used the Bonnet and Cousineaucomputation method for near-coincident cell genera-tion [22] to search for near-coincidence cells in 3C SiCand β-Si3N4. For these calculations, we have takenthe lattice parameter of 3C SiC to be 4.358A andthe lattice parameters ofβ-Si3N4 to bea= 7.6044Aand c= 2.9075 A. We have further chosen lattice 1to be 3C SiC and lattice 2 to beβ-Si3N4. Possiblenear-coincident cellsM1 andM2 for lattices 1 and 2

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288 Turan and Knowles

Table 1. Near-coincident cells for 3C SiC (lattice 1) andβ-Si3N4 (lattice 2).

NCSLPair no. 61 62 M1 M2 ε1, ε2, ε3 N [U ]F1 (×N)

−2 −1 1 6 −1 −3 −0.040 −2 −8 01 11 6 7 −2 −3 0 1 0 0.024 6 7 −5 3

−7 2 4 0 0 1 0.060 −7 5 3

−4 −1 2 6 0 −3 −0.040 −4 −6 02 11 6 7 −1 −3 0 1 0 0.024 6 7 −6 3

−7 1 4 0 0 1 0.060 −7 6 3

1 −3 −1 1 0 0 −0.082 4 −6 −13 12 8 1 1 −1 0 2 0 −0.064 4 4 2 −1

1 −1 2 0 0 4 −0.007 4 −2 2

2 −2 −2 4 −2 −2 −0.180 2 −4 −24 12 8 −3 3 1 0 1 0 −0.007 4 −3 6 −1

6 −3 −3 0 0 2 0.047 6 0 0

−7 6 4 4 −2 −3 −0.156 −7 5 05 13 8 −1 −1 2 0 2 −1 0.033 4 −1 −3 2

1 1 −1 0 0 1 0.060 1 3 2

1 −2 0 4 −2 0 −0.083 1 −6 06 14 8 5 −3 1 0 1 0 0.024 4 5 −2 2

−5 3 1 0 0 2 0.060 −5 2 2

−3 −1 0 4 0 0 −0.083 −3 −4 07 14 8 4 −1 1 0 1 0 0.024 4 4 −4 2

−4 1 1 0 0 2 0.060 −4 4 2

3 −5 2 4 −2 0 −0.106 3 −7 18 14 8 4 −3 0 0 2 −1 −0.012 4 4 −2 −2

5 −2 0 0 0 1 0.099 5 1 1

0 −3 0 4 0 −2 −0.055 0 −6 09 15 8 5 −1 2 0 2 0 0.060 4 5 −2 2

−5 1 2 0 0 1 0.064 −5 2 2

0 −3 0 4 −3 −2 −0.007 0 −12 010 15 8 5 −5 −2 0 2 0 0.013 8 10 −5 4

−5 5 3 0 0 1 0.060 −10 5 4

−6 −1 3 8 0 −4 −0.007 −6 −8 011 15 8 9 −1 −4 0 1 0 0.013 8 9 −8 4

−9 1 5 0 0 1 0.060 −9 8 4

1 −5 1 1 0 0 −0.025 4 −5 212 15 8 1 −4 −1 0 4 0 −0.007 4 4 −4 −2

1 3 0 0 0 2 0.101 4 3 0

7 −1 0 4 0 0 −0.027 7 −4 013 16 8 1 1 1 0 1 0 0.060 4 1 4 2

−1 −1 1 0 0 2 0.103 −1 −4 2

3 −4 2 3 0 −1 −0.135 3 −4 114 13 9 4 −1 −1 0 3 −2 −0.026 3 4 −1 −1

1 3 −2 0 0 1 −0.026 1 3 1

5 −3 0 3 −1 0 −0.064 5 −4 015 16 9 1 1 0 0 1 0 0.000 3 1 4 0

0 0 2 0 0 3 0.081 0 0 2

−8 −1 4 10 0 −5 −0.016 −8 −10 016 19 10 11 −1 −5 0 1 0 0.035 10 11 −10 5

−11 1 6 0 0 1 0.060 −11 10 5

3 −3 −3 6 −4 −4 −0.110 3 −6 −317 18 12 −4 4 2 0 1 0 −0.035 6 −4 8 −2

9 −6 −6 0 0 2 −0.007 9 0 0

(Continued on next page.)

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Crystallography of Interphase Boundaries 289

Table 1. (Continued).

NCSLPair no. 61 62 M1 M2 ε1, ε2, ε3 N [U ]F1 (×N)

1 −2 0 6 −3 0 −0.064 1 −9 018 20 12 7 −4 1 0 1 0 −0.045 6 7 −3 3

−7 4 1 0 0 2 0.060 −7 3 3

0 −3 0 6 −4 −3 −0.076 0 −9 019 21 12 7 −6 −3 0 2 0 0.015 6 7 −4 3

−7 6 4 0 0 1 0.060 −7 4 3

1 −7 1 1 0 0 −0.066 6 −7 320 21 12 1 −6 −1 0 6 0 −0.007 6 6 −6 −3

1 4 0 0 0 2 0.073 6 4 0

0 3 0 3 −2 −2 −0.035 0 9 021 21 12 −1 1 2 0 2 0 −0.007 6 −2 1 4

5 −5 −3 0 0 2 0.038 10 −5 1

−3 2 3 3 0 −2 −0.038 −6 6 322 22 12 1 −3 0 0 2 0 0.032 6 2 −9 2

4 0 −2 0 0 2 0.050 8 0 2

1 −6 −1 1 0 0 −0.028 6 −6 −323 23 12 1 5 0 0 6 0 0.025 6 6 5 0

1 −7 1 0 0 2 0.094 6 −7 3

9 −3 0 6 −1 0 −0.007 9 −9 024 24 12 4 0 1 0 1 0 0.060 6 4 4 3

−4 0 1 0 0 2 0.081 −4 −4 3

−5 −1 0 6 0 0 −0.007 −5 −6 025 24 12 7 −1 1 0 1 0 0.060 6 7 −6 3

−7 1 1 0 0 2 0.081 −7 6 3

24 −1 −12 14 0 −7 −0.041 24 −14 026 25 14 1 1 0 0 1 0 −0.002 14 1 14 7

−1 1 1 0 0 1 0.060 −1 −14 7

3 0 −2 4 0 −2 −0.101 3 0 −227 25 16 1 5 −4 0 4 −3 −0.024 4 1 5 1

6 −5 1 0 0 1 0.013 6 −5 1

−5 5 3 4 −2 −2 −0.139 −5 5 128 25 16 −1 −2 1 0 2 0 −0.031 4 −1 −5 1

4 −2 −1 0 0 2 0.064 4 0 2

Computations performed for61 max = 25,62 max = 17,1L = 0.5 A, Smax= 0.25,1u = 0.4 and1θ =0.003 rad in the NCSL notation used by Bonnet and Cousineau (1977). The columns ofM1 andM2 definebase vectors of possible near-coincident cells for lattices 1 and 2 respectively.ε1, ε2, andε3 are the principalstrains which when applied to the near-coincident cell for lattice 2 produce the shape of the near-coincidentcell for lattice 1. [U ]F1 relates the components of vectors referred to lattice 2 to components referred to lattice1 through Eq. (1) in the text.

respectively and other related crystallographic quanti-ties are given in Table 1 using the three index nota-tion for planes and vectors forβ-Si3N4 rather than the4-index Miller-Bravais notation. These twenty eightcrystallographically distinct relationships were deter-mined using the calculation parameters61 max= 25,62 max= 17,1L = 0.5 A, Smax= 0.25,1u = 0.4 and1θ = 0.003 rad using the notation of [22]. Here,61

is the ratio of the volume of the near-coincident cellof 3C SiC to the volume of the conventional cubicF

unit cell of 3C SiC,62 is the ratio of the volume of thenear-coincident cell ofβ-Si3N4 to the volume of theconventional unit cell ofβ-Si3N4,1L is the maximumallowed mismatch in length between two correspond-ing vectorsV1 andV2 in lattices 1 and 2 which can bechosen to be parallel for computational purposes,Smax

is the maximum allowed sum of the magnitudes of theprincipal strainsε1, ε2 andε3 involved in relating for-mally the near-coincident cells of the two lattices,1uhas to take a value less than 0.5 and is related to the

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290 Turan and Knowles

formalism describing mathematically the slight mis-match of corresponding near-coincident cells, and1θ

is a suitably small angular increment used in the com-putation method to generate rotations about suitableV1 ‖V2.

For each relationship in Table 1, the matrix [U ]F1

relates components of vectorsv2 referred to lattice 2 tocomponents of vectorsv1 referred to lattice 1 throughthe formula

v1 = [U ]F1v2 (1)

and similarly three-index plane normal descriptions,n, represented as row vectors, are related through theformula

n2 = n1[U ]F1 (2)

Thus, for NCSL Pair No. 10, where61= 15 and62= 8, and whereS, the sum of the magnitudes of theprincipal strainsε1, ε2 andε3 = 0.080, less thanSmax,the column vectors of the near-coincident cellM2 arerelated to the column vectors of the near-coincident cellM1 through Eq. (1). In addition for this pair, [011]1

is related to [002]2 (i.e., [0002]2 in the four indexnotation) and (200)1 is related to (030)2 ((0330)2 infour indices). A comparison of this with the approx-imate orientation relationship exhibited betweenβ-Si3N4 precipitates and surrounding 3C SiC matricesin Figs. 1–4 shows that in principle this NCSL pairdescribes a variant of the approximate experimentallyobserved orientation relationship. NCSL Pair Nos. 9and 19 can also do this, but with noticeably higherSvalues of 0.179 and 0.151 respectively.

Most of the NCSL pairs in the Table match [011]1 to[002]2. The misfit between these two vectors, definedas{(|011|1/|002|2)− 1} is 0.060, which accounts forthe frequent occurrence of this as a principal strain inTable 1. It also turns out that NCSL Pair No. 10 has thesamevalue ofS as Pair No. 11, slightly less than PairNo. 21 when the strains are computed to more than 3significant figures. These three pairs have the lowestvalues ofS in the Table.

Further consideration of these three NCSL pairsshows that for No. 10, the principal strainsε1, ε2 andε3 are defined by the misfits between the correspond-ing vector pairs [300]1 and [120]2, [055]1 and [400]2,and [011]1 and [002]2. For Pair No. 11, these sameprincipal strains correspond to misfits between the cor-responding vector pairs [111]1 and [010]2, [10, 5,5]1and [840]2, and [011]1 and [002]2. The essential dif-ference between these two NCSLs is a large rotation

of 35.26◦, half the angle between〈111〉 vectors in the[011] 3C SiC zone, so that whereas NCSL Pair No.10 can be used as a first description of the orienta-tion relationships seen experimentally, Pair No. 11 can-not. However, for Pair No. 11, it is also apparent that(111)1 corresponds to (310)2. This NCSL Pair there-fore describes in terms of low misfits a variant of theorientation relationship between Si3N4 and intergran-ularβ-SiC reported recently in Si3N4 20 vol%β-SiCnanocomposites by Cheong et al. [23].

On the basis of this geometric analysis, the [U ]F1

matrix for NCSL Pair No. 10 can be taken to be acorrespondence matrix (in the terminology used byMacKenzie and Bowles [24]) analogous to the Baincorrespondence shown to be useful for f.c.c. – b.c.c. in-terfaces [25]. It is then straightforward mathematicallyto accommodate small angular misorientations awayfrom the ‘ideal’ correspondence and enable a formaldescription of any orientation relationship in terms ofmisfits and determine what misfits will arise for vari-ous interface planes, as for example shown by Knowlesand Smith [25] in their discussion of the Nishiyama-Wasserman and Kurdjumov-Sachs orientation relation-ships for epitaxial (111) f.c.c. – (110) b.c.c. interfaces.

Turning now to the orientation relationship with thesurrounding SiC matrix shown by theβ-Si3N4 particlein Fig. 6, it follows that since there is a 1210 systematicset ofβ-Si3N4 reflections parallel to 220 type 3C SiCreflections, [0001]β-Si3N4 has to be parallel to a 3CSiC vector lying in the (220) 3C SiC plane. The beamdirection in Fig. 6 is close to [2027] β-Si3N4, whichmakes an angle of tan−1(2

√3a/7c) = 52.31◦ with

[0001] β-Si3N4. Since the beam direction in Fig. 6 isalso close to [110] 3C SiC, it follows that [0001]β-Si3N4 must make an angle of 2.43◦ with either [112] or[112] 3C SiC. Either way, it follows from a comparisonof this orientation relationship and the orientation rela-tionship of [0001]α-Si3N4 ‖ [121] 3C SiC and [1210]α-Si3N4 ‖ [101] 3C SiC observed on a single occasionby Unal et al. [7] that these are essentially describingthesameorientation between Si3N4 and 3C SiC, albeitfor different structural forms of Si3N4.

Of the NCSL Pairs in Table 1 only four (Nos. 3, 8,27 and 28) have [U ]F1 matrices which enable the threeindex direction [001]β-Si3N4 to correspond to a〈112〉3C SiC direction, and of these only Nos. 27 and 28also enable [010] β-Si3N4 (i.e., [1210]β-Si3N4 in thefour-index system), or a direction related by symmetryto this, to correspond to a〈110〉 3C SiC direction. Fur-thermore, (500)2 is related to (222)1 through Eq. (2)

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Crystallography of Interphase Boundaries 291

for NCSL Pair No. 27, while for NCSL Pair No. 28,(500)2 is related to (222)1. Thus, both NCSL pairs areplausible candidates for correspondence matrices de-scribing interfacial misfits for the orientation relation-ship shown in Fig. 6, although No. 27 would appearto be the more promising because it has a lower valueof S.

NCSL Pairs Nos. 10 and 27 could also be used toaccount for the orientation relationships observed be-tweenχ -Si3N4 and 3C SiC by Unal et al. [6, 7]. Sincethere is a 3.3% contraction along thec-axis and a 2.0%linear expansion in the (0001) plane between the crystalstructures ofβ-Si3N4 andα-Si3N4, the principal strainsε1, ε2 andε3 will alter for the NCSL Pairs shown inTable 1, but as Unal and Mitchell found [7], it is still thecase that there is no orientation relationship betweenSi3N4 and 3C SiC which has extremely low misfits andlow values of61 and62.

Determining misfits between supercells ofSi3 N4 3C SiC lattices is of course only a first step inproviding a rationale for the observed orientation rela-tionships adopted between Si3N4 and 3C SiC. Althoughwe have shown that the dominant orientation relation-ships approximating to [110] 3C SiC‖ [001]β-Si3N4

and (001) 3C SiC‖ (100)β-Si3N4 have low misfits, wecannot infer on the basis of geometry alone that lowenergy interfaces between 3C SiC andβ-Si3N4 nec-essarily occur when these orientation relationships areadopted [19]. However, once suitable atomistic mod-elling algorithms are available, it would clearly beworthwhile to attempt to determine by atomistic simu-lation whether low energy Si3N4 3C SiC interfaces aregenerated when these orientation relationships arise,in comparison with other possible orientation relation-ships, such as ones describable using NCSL Pair No. 11in Table 1, as experimental evidence from a number ofsources would tend to suggest that this is likely to bethe case.

Finally in this section, it is worthwhile using theabove methodology to examine the proposition thatthe orientation relationship between theα-SiC and aβ-Si3N4 grain in Fig. 8 (§3.2) is not one where lowmisfits might be expected. A careful examination ofthe electron diffraction pattern in Fig. 8(b) shows thatthe4041 diffraction spot from theβ-Si3N4 grain over-laps with the 0,0,0,11 spot in the 000l systematic fromthe 6Hα-SiC polytype, giving the appearance of anelliptical diffraction spot (arrowed in Fig. 8(b)), andimplying that, to a good approximation, the (4041)β-Si3N4 plane is parallel to the basal plane of 6H SiC. A

further feature of the orientation relationship in Fig. 8 isthat since the electron beam is parallel to the [1120] 6HSiC and [1, 5,4, 12]β-Si3N4 directions, (i.e. [110] 6HSiC and [134]β-Si3N4 using the three-index notation),it follows that a variant of this orientation relationshipcan be defined in which in three indices (401)β-Si3N4

is parallel to (001) 6H SiC and [104]β-Si3N4 is parallelto [510] 6H SiC, because the angle between [134] and[104] in β-Si3N4 is 70.8◦ and the angle between [510]and [010] in 6H SiC is 70.9◦. It also follows that [010]β-Si3N4 must be within a few degrees of a〈210〉 6HSiC direction.

Results from the computation procedure of Bonnetand Cousineau for near-coincidence cells between 6H-SiC andβ-Si3N4 are presented in Table 2. For these,the lattice parameters of the 6H-SiC were taken to bea= 3.073 A andc= 15.08 A (JCPDS-ICDD No. 29-1131), keeping the lattice parameters ofβ-Si3N4 asbefore. To ensure that the search procedure was as thor-ough as possible, three strategies were employed: (i) ageneral search with61 max= 17, Smax= 0.25, i.e., forlow6 and a relatively lowSmax, (ii) forced parallelismof [200]β-Si3N4 and [630] 6H SiC in the computationprocedure of Bonnet and Cousineau with61 max= 25andSmax= 0.4, so that NCSLs with these two vectorsmatching exactly or approximately could be generated,and (iii) forced parallelism of [104]β-Si3N4 and [510]6H SiC with61 max= 25 andSmax= 0.35, for the samereason as in (ii).

It is apparent from Table 2 that although there aresome NCSLs with relatively low principal strains, suchas Pair No. 6, none of these 21 NCSLs can accountfor the orientation relationship seen in Fig. 8 in which(001) 6H SiC is parallel to (401)β-Si3N4. Moreover,the NCSLs in this table generated by forcing paral-lelism of vectors fromβ-Si3N4 and 6H SiC have un-realistically large principal strains, while in additionfailing to be even approximately a description of theorientation relationship in Fig. 8. Thus, we can inferfrom this analysis that the null hypothesis holds, i.e.,the interface in Fig. 8 in which an intergranular filmis seen is indeed one which cannot be understood interms of any ‘low misfit’ orientation betweenβ-Si3N4

and 6H SiC.

4.2. Equilibrium Film Thicknessat Interphase Boundaries

The experimental results in §3.1 show that amorphousfilms were present at Si3N4 3C SiC interfaces even

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292 Turan and Knowles

Table 2. Near-coincident cells forα-SiC (lattice 1) andβ-Si3N4 (lattice 2).

NCSLPair no. 61 62 M1 M2 ε1, ε2, ε3 N [U ]F1 (×N)

0 0 1 4 −1 −2 −0.085 0 0 41 5 4 5 0 −2 0 1 0 0.010 4 5 5 2

−2 1 1 0 0 1 0.145 −2 2 0

16 −9 −2 7 −4 −1 −0.060 16 1 22 9 7 −1 2 1 0 1 0 −0.002 7 −1 10 6

1 −1 0 0 0 1 0.161 1 −3 1

0 0 2 2 −1 0 −0.085 0 0 43 8 8 0 4 1 0 2 0 −0.067 4 0 8 2

−1 1 0 0 0 2 −0.008 −2 1 0

0 0 1 2 0 −1 −0.085 0 0 44 9 8 0 9 −4 0 4 −2 −0.008 4 0 9 2

−1 1 0 0 0 1 0.050 −2 1 0

20 −14 −17 8 −5 −7 −0.095 20 −12 45 9 8 1 −2 0 0 1 0 −0.005 8 1 −11 7

1 −1 −1 0 0 1 0.059 1 −3 −1

5 −5 1 4 −2 0 −0.008 5 −5 46 10 8 10 −10 0 0 2 0 0.010 4 10 −10 0

1 0 0 0 0 1 0.057 1 1 0

11 −3 −8 4 0 −3 −0.083 11 −6 17 10 8 7 −2 −6 0 2 0 0.004 4 7 −4 −3

0 1 0 0 0 1 0.150 0 2 0

25 −15 −22 9 −5 −8 −0.052 25 −10 28 11 9 15 −8 −14 0 1 0 0.000 9 15 3 −6

−1 1 1 0 0 1 0.092 −1 4 1

28 −18 −25 10 −6 −9 −0.090 28 −12 29 11 10 17 −10 −16 0 1 0 −0.004 10 17 2 −7

−1 1 1 0 0 1 0.029 −1 4 1

1 6 1 2 0 0 −0.081 3 6 610 15 12 2 11 0 0 6 0 0.056 6 6 11 0

−1 2 0 0 0 1 0.090 −3 2 0

33 −12 −30 12 −4 −11 −0.064 33 −12 311 15 12 18 −5 −17 0 1 0 −0.001 12 18 12 −6

−2 1 2 0 0 1 0.132 −2 4 2

16 −9 −13 6 −2 −5 −0.028 16 −11 212 15 12 8 −8 −7 0 2 0 −0.010 6 8 −16 −2

1 0 −1 0 0 1 0.100 1 1 −1

17 −14 −14 6 −4 −5 −0.021 17 −8 113 16 12 11 −9 −10 0 2 0 0.005 6 11 −5 −5

0 1 0 0 0 1 0.148 0 3 0

19 −10 −16 7 −3 −6 −0.102 38 −13 414 15 14 9 −1 −8 0 2 0 −0.001 14 18 20 −4

−1 1 1 0 0 1 0.012 −2 4 2

22 −9 −19 8 −2 −7 −0.185 22 −14 215 15 16 11 −8 −10 0 2 0 −0.027 8 11 −21 −3

1 0 −1 0 0 1 0.002 1 1 −1

22 −9 −19 8 −2 −7 −0.220 22 −14 216 15 16 10 −8 −9 0 2 0 0.000 8 10 −22 −2

1 0 −1 0 0 1 0.018 1 1 −1

0 0 1 4 0 −2 −0.085 0 0 417 17 16 −1 9 1 0 4 0 −0.058 4 −1 9 2

−2 1 1 0 0 1 0.043 −2 1 0

(Continued on next page.)

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Crystallography of Interphase Boundaries 293

Table 2. (Continued).

NCSLPair no. 61 62 M1 M2 ε1, ε2, ε3 N [U ]F1 (×N)

7 0 −2 4 0 −2 −0.079 7 0 318 17 16 −2 0 3 0 2 −1 −0.014 4 −2 0 4

1 −1 0 0 0 2 −0.008 1 −2 0

6 −3 0 2 0 0 0.029 6 −3 019 6 4 3 −1 −1 0 2 0 0.050 2 3 −1 −2

0 1 0 0 0 1 0.176 0 1 0

2 −1 3 3 0 0 −0.261 2 −1 320 22 27 −6 2 2 0 3 0 −0.070 3 −6 2 2

0 −1 0 0 0 3 0.003 0 −1 0

2 −1 3 3 0 0 −0.237 2 −1 321 22 27 −6 3 2 0 3 0 −0.080 3 −6 3 2

0 −1 0 0 0 3 −0.017 0 −1 0

For NCSL Pair Nos. 1–18 computations were performed for61 max= 17, 62 max= 17,1L = 0.5A,Smax= 0.25,1u= 0.4 and1θ = 0.003 rad. For NCSL Pair No. 19 computations were performedby matching the vector pairs [200]2 and [630]1 in the algorithm of Bonnet and Cousineau (1977)with61 max= 25, 62 max= 29,1L = 0.8A, Smax= 0.4,1u= 0.4 and1θ = 0.003 rad. For NCSL PairNos. 20 and 21 computations were performed by matching the vector pairs [104]2 and [510]1 with61 max= 25, 62 max= 28,1L = 0.5A, Smax= 0.35,1u= 0.4 and1θ = 0.003 rad.

when there was evidence for a preferred orientationrelationship between particles and surrounding matri-ces. One obvious reason for why this was so is thatthe process whereby Si3N4 particles are consumed by3C SiC grains at high temperature does not allow suf-ficient time for the expulsion of all the liquid initiallysurrounding a Si3N4 particle, so that even though apreferred orientation relationship can be established,with some Si3N4 3C SiC interfaces free of liquid, in-evitably some liquid remains trapped around the parti-cles. Such an explanation, although qualitative, wouldalso account for the observation by Pan et al. [8, 18] ofthin amorphous films at some parts of the SiCβ-Si3N4

interfaces for their ‘type A’ SiC particles.The occurrence of amorphous phases at general

Si3N4 3C SiC interfaces is consistent with Clarke’smodel of ceramic interfaces [26]. The significant newresult we have here which requires explanation isthe noticeable difference in film thicknesses betweenboundaries IB(b) and IB(c) in Fig. 9. Such a differencecould be explained in terms of highly non-equilibriumfilm thicknesses, different local film compositions (e.g.,[27]) or as an effect arising from the orientation rela-tionships between the Si3N4 grains and the common3C SiC grain. The recent analysis of the dependenceof equilibrium film thickness on grain orientation atinterphase boundaries in ceramic-ceramic compositesby Knowles and Turan [28] concluded that an orienta-

tion dependence will only arise if one or more phasesis highly anisotropic optically, as will be the case formaterials like graphite and hexagonal boron nitride.Silicon nitride is anisotropic, but while there is dataon optical properties of thin films available in the lit-erature (e.g. Taft [29] quoted by [26]), Xu and Ching[30] were unable to compare their calculations of therefractive indices parallel and perpendicular to [0001]with any single crystal data forα-Si3N4 andβ-Si3N4.Their calculations of the electronic part of the staticdielectric constant, the square root of which is a goodestimate of the refractive index, were 4.01‖ [0001]and 3.67⊥ [0001] forβ-Si3N4 and 4.45‖ [0001] and4.09⊥ [0001] forα-Si3N4. It is apparent from the re-cent analysis of Knowles and Turan that such relativelyweak anisotropy is not sufficient to account alone forthe marked differences seen in the interfaces in Fig. 9either side of the same triple junction, even if one in-terface were to have been oriented parallel to (0001)β-Si3N4 and the other were to have contained the vec-tor [0001]β-Si3N4.

Thus, other than suggesting that Fig. 9 actually rep-resents a highly non-equilibrium situation, in whichamorphous material has simply been trapped at inter-face IB(b), we are left with an interesting explanation,albeit one which we admit is speculative, given the highdiffusion rates which will be present at 2373 K: sinceduring sintering the rate of reprecipitation ofβ-Si3N4

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294 Turan and Knowles

from the liquid is highly anisotropic, with growth paral-lel to [0001] faster than growth in the (0001) plane, it ispossible that growth was slower at interface IB(b), thusleaving behind a more nitrogen-saturated amorphoussilica phase. This would have the effect of increasingthe refractive index of the glass locally, leading to asmaller Hamaker constant at this interface and conse-quently a higher equilibrium film thickness [26, 28].

5. Conclusions

Interphase boundaries between 3C SiC andβ-Si3N4

have been characterised by bright field TEM, dark fieldTEM, electron diffraction and HRTEM. The crystal-lography ofβ-Si3N4 particles embedded in 3C SiCgrains is shown to be similar to that reported in previousstudies of Si3N4 3C SiC interphase boundaries wherespecific orientation relationships were reported. A sur-vey using the near-coincidence site lattice approach hassuccessfully identified orientations at which relativelylow misfits between Si3N4 and 3C SiC supercells canarise at Si3N4 3C SiC interphase boundaries devoid ofamorphous intergranular film. Interestingly, the dom-inant orientation relationships at clean, or relativelyclean, Si3N4 3C SiC interphase boundaries approx-imating to [110] 3C SiC‖ [0001] β-Si3N4 and (001)3C SiC‖ (1010)β-Si3N4 were found to have low mis-fits relative to other possible orientation relationships.Interphase boundaries between largeβ-Si3N4 grainsand 3C SiC grains of a similar size contain amorphousfilms and appear not to exhibit characteristic orienta-tion relationships. Local differences in amorphous filmthicknesses are explicable either in terms of a highlynon-equilibrium situation or local changes in refractiveindex arising from variations in chemical compositionof the amorphous phase.

Acknowledgments

We would like to thank Dr. S.M. Winder of The Car-borundum Company, Niagara Falls, U.S.A. for the pro-vision of the samples. We would also like to thankProfs. C.J. Humphreys and A.H. Windle, F.R.S., forthe provision of laboratory facilities during the courseof this work.

Notes

1. α-Si3N4 has a trigonal structure witha= 7.7541 A andc= 5.6217A (JCPDS-ICDD No. 41-0360), whereasβ-Si3N4

has an hexagonal structure witha= 7.6044A andc= 2.9075A(JCPDS-ICDD No. 33-1160).

2. α-SiC refers to a mixture of hexagonal (e.g., 6H) and rhombohe-dral (e.g., 15R) polytypes, whereasβ-SiC refers to the only cubicpolytype, also known as 3C, which has the sphalerite structure.In this number and letter notation [31], the number refers to thenumber of Si C double layers in the unit cell and the letter refersto the crystal symmetry.

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