Electronic Structure and Bonding of b-SiAlON

Electronic Structure and Bonding of b-SiAlON

Wai-Yim Ching,* Ming-Zhu Huang, and Shang-Di Mo

Department of Physics, University of Missouri-Kansas City, Kansas City, Missouri 64110

The a- and b-SiAlONs are ceramic solid solutions withcharge-neutral substitutions in a- and b-Si3N4. They havehigh potential for applications as structural materials. Wehave calculated the electronic structure and bonding ofb-Si6–zAlzOzN8–z for z 5 0, 1, 2, 3, 4 using a first-principlesmethod. Total energy calculations show that the bulk modulusof b-Si6–zAl z

OzN8–z decreases asz increases, in general agree-ment with experimental trends. Simultaneous substitution ofthe (Si,N) pair by (Al,O) results in impurity-like states in theupper portion of the bandgap of b-Si3N4. As z increases, moreand more states are introduced into the gap, forming a newconduction band (CB) edge for SiAlON. At z 5 4, thecalculated bandgap is;1.3 eV. Density of states (DOS) calcu-lations show the top of the valence band remains steep for allz, and the bottom of the CB is formed predominately by Si–Oantibonding states. Orbitally resolved partial DOS calculationsin the CB region are used to predict the trends of theelectron-energy-loss near-edge spectra (ELNES) of Si-L2,3,Al-L2,3, Si-K, Al-K, O-K, and N-K edges in b-SiAlON. Theimpurity-like states near the CB edge result in pre-edgestructures in all ELNES spectra. Effective charge and bondorder calculations show that the overall bond strength inb-SiAlON decreases only slightly asz increases. Although thestronger Si–N bonds are replaced by weaker Al–O bonds, theremaining Si–N and Al–O bonds actually strengthen aszincreases because of the effective charge redistribution aftersubstitution. This is a very interesting finding that may partlyexplain the superior mechanical properties of the SiAlONsystem that render them suitable for structural applications.

I. Introduction

NITROGEN ceramics, especially Si3N4 and SiAlONs, are impor-tant structural ceramic materials used in a variety of engineer-

ing and microelectronic applications.1–4 This is because of theirmany outstanding properties, such as high strength, wear resis-tance, and chemical inertness. For structural applications, the mechan-ical properties and microstructure of the bulk material are central to itssuccess. Although Si3N4 has been studied for a long time,5,6 SiAlONceramics have been developed mostly within the past 15 years.7,8

SiAlON materials are easier to densify and more ductile at hightemperatures than Si3N4.

8,9 Over the years, many researchers havefound that the intergranular glassy phase, mostly of oxides betweenb-Si3N4 grains or at triple junctions, substantially controls themechanical properties and the fracture behavior of sintered materialsat elevated temperature.10–14It has also been found that the thickness(usually of the order of 1 nm), the properties of the intergranularphases, and the aspect ratio of the Si3N4 grains can be altered bydifferent sintering aids, mostly rare-earth elements.12,15–17The pres-ence of aluminum and oxygen in the intergranular films affects the

growth of elongated grains and the strength of the crystalline/glassinterface.18–20 It has been suggested that the increased high-temperature ductility of SiAlON may be related to enhanced self-diffusivity in the presence of the ionic Al–O pairs.9

The precise control and nature of atomistic bonding at thecrystalline/glass boundary is one of the biggest problems facingthe materials community. Microscopic understanding of the ce-ramic material when it is macroscopically deformed is the key toits improvement. Needless to say, this problem has attracted manyresearchers using different techniques to elucidate the structure,composition, and behavior of the intergranular phases in Si3N4.

21–26

Despite these endeavors, no clear understanding has emerged. Exper-imental development is usually conducted by a trial-and-error ap-proach. Because of the structural complexity at interphase boundaries,theoretical investigations of such systems are almost nonexistent orare done in an oversimplified manner. Tanaka and co-workers9,27areperhaps the only group who have attempted electronic structurecalculations using the molecular orbital method to explain the me-chanical properties and solution effects in the SiAlON system.Recently, Dudse´k and Benco28 have studied simple models ofSi3N4(110) surfaces and interfaces and interpreted their results interms of the electron density of states (DOS). They show that aSiAlON-like boundary phase should have a stable electronic config-uration with all states in the valence band (VB) occupied.

There are two major SiAlON systems,a- and b-SiAlON,derived froma- and b-Si3N4 by substitution of (Si,N) pairs by(Al,O) pairs, respectively. Similar pair substitutions in Si2N2Oresult in the so-called O9-SiAlON series, which also has gainedrecent attention.8,29 Epitaxial growth of SiAlON on b-Si3N4

particles has been observed. Sunet al.15 found that an increase of(Al,O) content appears to strengthen the interfacial toughness ofthe SiAlON epitaxial layer at the interface. It is also possible tohave mixed phases that can improve mechanical properties.25

Recently, it was reported that dilute SiAlON ceramics consistingof a mixture ofb-SiAlON and O9-SiAlON can reduce or eliminateresidual glassy films and increase hardness.17 Transformationproperties betweena- andb-SiAlONs also have been a subject ofactive pursuit.30,31 There are SiAlON polytype phases that areordered based on the wurtzite structure of AlN.32 It is conceivablethat many glassy phases in the intergranular thin films can havecompositions and local bonding similar to SiAlON solid solutions.

Here, we report a systematic investigation of the electronicstructure and bonding inb-Si6–zAlzOzN8–z, providing insight intothe nature of intergranular phases. Our goal is to understand thestructure and properties of intergranular thin films, their interfaceswith Si3N4 crystallites, and their dependence on dopants in theglassy phase. The atomic-scale structure of such systems is toocomplicated for an exact calculation. In theb-Si6–zAlzOzN8–z

series, the geometric structure of the system is known unambigu-ously. Specifically, we performab initio band structure calcula-tions for theb-Si6–zAlzOzN8–z solid solutions forz ranging from 0to 4. Here,z represents the number of (Al,O) pairs substituting for(Si,N) pairs inb-Si3N4. The complex interplay between the morecovalent Si–N and Al–N bonding and the more ionic Al–O andSi–O bonding, as a function ofz, sheds light on the overall bondingand debonding mechanisms in the SiAlON system.

The primary results of our study are the density of states (DOS),atomic and orbitally resolved partial DOS (PDOS), the bulkmodulus, and its variation withz. Effective charges and the overlap

R. H. French—contributing editor

Manuscript No. 189633. Received January 12, 1999; approved August 12, 1999.Supported by U.S. Department of Energy under Grant No. DE-FG02–84ER45170.*Member, American Ceramic Society.

J. Am. Ceram. Soc.,83 [4] 780–86 (2000)

780

journal

population (also called bond order) calculation, together with thecharge density map, enable us to reveal the details of bonding inb-SiAlON. We pay particular attention to the orbitally resolvedPDOS in the empty conduction band (CB), which can be used tointerpret Si-L2,3, Al-L2,3, O-K, and N-K edges from electron-energy-loss near-edge spectroscopy (ELNES).33 Electron-energy-loss spectroscopy (EELS) has been widely used for quantitativechemical analysis of materials with high spatial resolution. Inparticular, ELNES, which probes the inner shell excitation of acore electron to the unoccupied CB states, can provide usefulinformation on the local chemical and structural environment ofthe excited atom.33 Such studies are most effective when themeasured data are interpreted together with parallel theoreticalcalculations, as was recently demonstrated for the Y–Al–O com-pounds34 and in the grain boundaries of SrTiO3.

35 Careful andsystematic calculations of the ELNES spectra in the SiAlONsystem can facilitate interpretation of the data on phase boundariesbetweenb-Si3N4 and the intergranular glassy films.21,22

II. Method of Calculation

The electronic structure ofb-Si6–zAlzOzN8–z is calculated usingthe ab initio orthogonalized linear combination of atomic orbitals(OLCAO) method36 with local approximation to the densityfunctional theory (LDA).37 The method of calculation has beenapplied to many complex crystals and has been well-documented.36 The calculations are similar to the ones fora-Si3N4, b-Si3N4, and Si2N2O bulk crystals.38 Recently, Zhao andBachlechner39 applied the same method to study the electronicstructure of the Si(111)/Si3N4(001) interface. In the present calcu-lation, the lattice constants forb-Si6–zAlzOzN8–z solid solutions aregiven bya 5 7.6031 0.02967z Å and c 5 2.9071 0.02554z Åbased on X-ray powder diffraction data.8 For eachz, appropriatesubstitutions of (Si,N) pairs by (Al,O) pairs are identified firstamong the 14 atoms in the unit cell ofb-Si3N4 with the latticeconstants scaled according toz. Lattice relaxation as a result ofsubstitution is ignored. Its effect on the electronic structure of thesolid solution is expected to be small. The crystal structure forz 50 is that of Borgen and Seip40 used in our earlier studies.38

Although a controversy continues as to whether the structure ofb-Si3N4 should have a space group ofP63/mor P63 without mirrorsymmetry, as suggested by Gru¨n,41 we believe the differencebetween the two has little effect on the electronic structure of theSiAlON solid solutions. ForzÞ 0, several sites for substitution arepossible. We have investigated this effect on a few representativecases for eachzand again found the electronic structure is not verysensitive to the specific sites of substitution. Ideally, it is desirableto use a supercell ofb-Si3N4 with a large number of atoms andinclude all possible substitutions to represent the structure ofb-Si6–zAlzOzN8–z. However, in the absence of any reliable elec-tronic structure results, the present calculation based on the unitcell of b-Si3N4 is a realistic first attempt at such studies.

The DOS and PDOS are calculated using the wave functionsobtained at the 30k points in the Brillouin zone (BZ) of the unitcell and the Mulliken analysis scheme42 as described before.43,44

The effective charges on each atom and the bond order betweenpairs of atoms are obtained by separate minimal basis calculations.One of the special advantages of the OLCAO method is the easewith which the effective charge and the bond order can beobtained, because the basis functions are expanded in terms ofatomic orbitals. This facilitates the interpretation of the electronicstructure and bonding in complex solid solutions.

For each value ofz, the total energy (TE) of the solid solutionis calculated according to the usual expression from the LDA theory.

ET 5 On,k

occ

En~k ! 1 Er~r !S εxc 2 Vxc 2Ve2e

2 D dr

1Og,d

zgzd

Rg 2 Rd

(1)

In Eq. (1), the summation overEn(k) is for the occupied bandsand over the entire BZ using specialk point sampling.Vxc andVe-e

are the exchange-correlation and electron-electron parts of thepotential, andεxc the exchange-correlation energy functionalrepresented by the Wigner interpolation formula.36 The last termrepresents the interaction between the nuclei of the ions.

III. Results of Calculation

(1) Bulk PropertiesThe TE calculation for the solid solution is repeated for

different crystal volumes. The calculated TE data are fitted to theMurnaghan equations of states (EOS)45 and also to the Birch–Murnaghan EOS46 to obtain the bulk modulusB and the pressurecoefficientB9 for each crystal. The results from the two differentequations of states are quite similar, and those obtained by theMurnagahan EOS are summarized in Table I. The results forb-Si3N4 (z 5 0) are slightly different from the previous studies44

because of slightly improved basis functions used in the presentcase. Figure 1 shows that the calculated bulk modulusB decreasessmoothly asz increases. Also displayed are the experimental data9

for thez dependence of the Young’s modulusY. Both B andY arerelated to the elastic properties of the materials, and Fig. 1 showsthat the trends in thez dependence are similar.

(2) DOS and PDOSFigure 2 shows the total DOS ofb-Si6–zAlzOzN8–z for different

values ofz. The zero of energy is set at the top of the VB. Forb-Si3N4, the VB DOS consists of two segments, mainly originat-ing from N-2s (from –14.3 to –18.9 eV) and N-2p (from 0 to –11.0eV) states. The sharp peak centered at –1.5 eV is the signature ofthe nitrogen nonbonding orbital. The DOS in the CB consists ofmultiple peaks. The calculated bandgap is;4.2 eV compared withthe reported experimental values ranging from 4.0 to 5.5 eV.47 Thediscrepancy in the experimental values of the gap is probably dueto variation among samples prepared at different temperatures andunder different conditions, because single crystalb-Si3N4 is notavailable. Both the CB and the VB edges in the DOS are verysharp, as is typical for large-gap insulators.

When a pair of (Al,O) atoms is substituted for a pair of (Si,N)atoms, the DOS becomes much more complex (Fig. 2(b)) becauseof the introduction of Al–N, Al–O, and Si–O bonds. In the VB,multiple peaks of O-2s origin appear in the –22 to –23 eV region.Additional states appear below the N-2p band edge of –11 eV andabove the N-2s band edge of –14.3 eV. These states are related tothe O-2p bonding orbitals with silicon and aluminum. The top ofthe VB has a single sharp peak attributed to the Al–N interaction.Most conspicuous is the presence of peaks at 1.5, 2.6, and 3.4 eVin the gap ofb-Si3N4. These can be interpreted as impurity-likestates resulting from the substitution. Asz increases from 1 to 4(see Figs. 2 (b)–(e)), these additional features grow with aconcomitant reduction in the N-2s and N-2p states. Forz 5 4, theVB can be divided into regions of O-2s (–18.3 to –22 eV), N-2s(–12.2 to –16.5 eV), and a mixture of N-2p and O-2p from 0 to–11.2 eV. As more impurity-like bands fill into the upper portionof the gap, a new CB edge is formed, and a reduced bandgap of;1.3 eV is obtained.

Table I. Calculated EquilibriumVolume, Bulk Modulus B (GPa),and Pressure CoefficientB* in

b-Si6–zAlzOzN8–z

z V/V0 B B9

0 0.99 343 4.321 0.99 311 4.362 0.99 286 4.183 0.995 250 4.274 0.995 237 4.38

April 2000 Electronic Structure and Bonding ofb-SiAlON 781

To identify specific bonding inb-SiAlON, we consider thePDOS ofb-Si5AlON7 (z 5 1) in more detail. It was reported bySuzuki et al.23 that the most desirable mechanical and thermalproperties ofb-SiAlON, which is prepared by slip casting, areobtained for small values ofz ranging from 0.5 to 1.0.25 We indexthe 14 atoms in the unit cell forz 5 1 as follows: Si(1) to Si(5),Al(6), N(7) to N(11), O(12), N(13), and N(14). Positions 1 to 6 areSi (6h) sites, 7 to 12 are N (6h) sites, and the last two are N (2c)sites, with reference to theb-Si3N4 crystal.40 The structure can beviewed as two staggered (Si3N4)n layers perpendicular to thec-axis. Thez5 1 configuration considered here is the one in whichAl(6) replaces Si(6) and O(12) replaces N(12) at the 6h sites, sothat (Al,O) pairs are nearest neighbors (NN) in the same layer.

The PDOS of these 14 atoms are shown in Fig. 3. The left(right) panel is for atoms in the top (lower) layer. The lower layercontains the (Al,O) pair (also see Fig. 4(a)). In the first-orderapproximation, these 14 PDOS can be grouped into six types: (1)silicon with four nitrogen atoms as NN (Si(3), Si(4), Si(5)); (2)silicon with three nitrogen atoms and one oxygen atom as NN(Si(1), Si(2)); (3) nitrogen with three silicon atoms as NN (N(8),N(10), N(11), N(13)); (4) nitrogen with two silicon atoms and onealuminum atom as NN (N(7), N(9), N(14)); (5) the substitutedAl(6) that bonds to three nitrogen atoms and one oxygen atom; and(6) the substituted O(12) that bonds to two silicon atoms and onealuminum atom. The PDOS of the atoms within the same group arealmost the same. The minor differences reflect the second NNeffects. In the case of the nitrogen sites, it also depends on whetherthe sites are 6h or 2c, because of their different bond lengths.Figure 3 shows that the impurity-like gap states near the CB edgeoriginate from antibonding states between Si(2) and O(12). Theextra-sharp peak at the top of the VB is due to the interaction ofAl(6) with N(7) and N(14). The shift of the centroid of the DOS inthe upper VB region asz increases (Fig. 2) can be understood bycomparing the PDOS of nitrogen and oxygen (Fig. 3) in the sameenergy region. The sharp peak at –13.5 eV in Fig. 2(b) is the resultof bonding between Al(6) and N(7).

(3) Charge DistributionThe valence charge density distribution ofb-Si5AlON7z (z 5 1)

on a (001) plane containing the substituted aluminum and oxygenatoms is shown in Fig. 4. This is the same configuration whosePDOS is shown in Fig. 3. At first glance, one cannot distinguish

Fig. 1. (F) Calculated bulk modulus ofb-Si6–zAlzOzN8–z. (E) Experi-mental data for Young’s modulus from Ref. 9.

Fig. 2. Calculated total DOS inb-Si6–zAlzOzN8–z for (a) z 5 0, (b) z 51, (c) z 5 2, (d) z 5 3, and (e)z 5 4.

Fig. 3. Calculated atom-resolved PDOS inb-Si5Al1O1N7. The 14 atomsin the unit cell are as indicated (see text for detail). Left panel is for theupper-layer, right panel for the lower-layer atoms. Atom No. 6 and No. 12in the right panel are substituted aluminum and oxygen atoms, respectively.N(13) and N(14) are nitrogen at (2c) sites. Other atoms are at (6c) sites.

782 Journal of the American Ceramic Society—Ching et al. Vol. 83, No. 4

between silicon and aluminum or between oxygen and nitrogen.This indicates that the substitution of the (Al,O) pair for the (Si,N)pair has little effect as far as charge density is concerned. This maybe the reason why, experimentally, it is difficult to identify thesubstituted sites in the dissolved solid solution. This also justifiesour assumption that there should be little or no lattice relaxation asa result of substitution. The silicon and aluminum atoms loseelectrons, while nitrogen and oxygen gain them, with the differ-ence between the substituted pairs fairly balanced even though O(Al) is more electronegative (electropositive) than N (Si). Ourabinitio calculation in Fig. 4(a) shows strong bonding between Si(Al) and the next neighbor N (O). Figure 4(b) shows the differencebetween the charges in the solid solution and the superposition offree atoms in the same plane as in Fig. 4(a). Again, the presence ofthe Al–O pair is barely noticeable, indicating very efficient chargeredistribution in theb-SiAlON system.

(4) Effective Charge and Bond OrderThe calculated effective charges,Q* per atom (averaged over

all sites), in b-Si6–zAlzOzN8–z are calculated from the minimalbasis wave functions using the Mulliken scheme and are listed inTable II. For b-Si3N4, the QSi

* and QN* are 2.45 and 6.17,

respectively (or equivalently,12.44 and –1.83, respectively, inionic notation). This is very close to the earlier values of12.50and –1.87 using a real-space integration scheme.38 Both indicate asubstantial covalent-bonding character in Si3N4. For b-SiAlONsolid solutions with a much more complex bonding structureamong the four elements, the minimal basis Mulliken scheme is a

very effective way to study the trends of charge transfer aszvaries.Table II shows thatQSi

* and QAl* fluctuate betweenz 5 0 and 4,

while QN* and QO

* increase steadily asz increases. The overallpicture from the effective charge calculation is that of an increasein the ionic character asz increases. This is expected, becauseAl2O3 is much more ionic than Si3N4.

The results of bond order calculations are shown in Fig. 5 andreveal several interesting facts: (1) The Si–N and Al–N bonds aremuch stronger than the Si–O and Al–O bonds; (2) Asz increases,the average Si–N and Al–O bond orders actually increase, and theaverage Al–N and Si–O bond orders remain roughly constant; (3)The bond order of Al–O atz 5 4 is almost double that ofz 5 1,indicating that an isolated Al–O bond in Si3N4 is a very weakbond; and (4) The total bond strength inb-Si6–zAlzOzN8–z isobtained by averaging all pairs of bond orders in the solid solution.Bond strength decreases only slightly asz increases and is mainlydue to the replacement of the stronger Si–N bonds with weakerAl–O bonds. This result is consistent with the variation of the bulkmodulus of the solid solution discussed in Section III(1). SiAlON9sslow decrease in overall bond strength with substantial substitution

Fig. 4. (a) Calculated valence charge density ofb-Si5Al1O1N7 in the extended zone for the lower plane' c-axis. Dashed parallelogram indicates the unitcell boundary. Silicon and aluminum atoms are as indicated. Atoms numbered 10, 11, 14 are nitrogen atoms and atom 12 is an oxygen atom. Contour linesare from 0.01 to 0.25 by 0.005 in unit of electrons/(a.u.)3. (b) Difference contour between crystalline and atomic valence charges in the same plane as (a).Dashed lines are for negative values of charge density.

Table II. Calculated Average Effective Charge per Atom inb-Si6–zAlzOzN8–z

Average effectivecharge

z

0 1 2 3 4

Q*Si 2.445 2.459 2.454 2.502 2.434Q*Al 1.600 1.617 1.560 1.582Q*N 6.166 6.169 6.174 6.182 6.233Q*O 6.921 6.952 6.968 6.969 Fig. 5. (F) Overall bond strength inb-Si6–zAlzOzN8–z as function ofz.

(M) Si–N, (X) Al–N, (1) Si–O, and (E) Al–O.


of (Si,N) pairs by (Al,O) pairs is the main reason it can be as tougha ceramic asb-Si3N4 for structural applications. The microscopicexplanation of this is the effective charge redistribution in theSiAlON system. Although the stronger Si–N bonds are replaced byweaker Al–O bonds, the remaining Si–N bonds and increasedAl–O bonds actually become stronger asz increases.

(5) ELNES SpectraThe orbitally resolved PDOS of each atom in the unoccupied

CB region can be used to interpret the ELNES spectra.33 TheSi-L2,3 and Al-L2,3 edges involve transitions from the 2p corelevels of silicon and aluminum and should be roughly representedby the (s1d) components of the PDOS of the respective atoms inthe CB. Likewise, Si-K, Al-K, O-K, and N-K edges are related totransitions from the 1s core states, so thep component of thePDOS in the CB should mimic theK edges of these atoms. ThePDOS interpretation of the ELNES spectra neglects the effect ofcore–hole interaction, which may be important for theL2,3

edges.48 Inclusion of core–hole effect is not attempted in thepresent study. Although no systematic measurements of theELNES on well-characterized SiAlON samples have been re-ported, it is our belief that such measurements will be availablesoon, and our calculation will be useful for their interpretation.Recently, there have been some reports of ELNES spectra onintergranular thin films of Si3N4 that consist of a silicate glassyphase.23

The calculated orbitally resolved PDOS (s 1 d and pcomponents) for silicon, aluminum, oxygen, and nitrogen inb-Si6–zAlzOzN8–z averaged over each type of atom are shown inFig. 6–8. A Gaussian broadening of 1 eV has been applied to eachPDOS curve, and the zero of energy is set at the top of the VB. Thetheoretical ELNES spectra represented by PDOS are very rich instructure because of the presence of multiple bonding and thecomplex local environments of each atom. It is premature to attachany significance to the specific structure in the PDOS, and it ismore important to observe the general trends of the spectra aszvaries. We focus our discussion onb-Si3N4 (z 5 0), b-Si5AlON7

(z 5 1) cases, whose atomic-scale structures are described inSection III(2), and also on the limiting case ofz 5 4, where thenumbers of nitrogen and oxygen atoms in the unit cell are equal.The most significant feature in all these spectra is the presence ofa pre-edge structure that grows asz increases. The pre-edgestructure is related to the impurity-like states in the gap ofb-Si3N4

and the formation of the new lower CB edge discussed earlier,which could be detected experimentally.

For the Si-L2,3 edges, the (s 1 d) PDOS (Fig. 6, left panel)consists of many multiple structures, even forz 5 0, where thereare only two atomic species—silicon and nitrogen. This is relatedto the complexity of the crystal structure ofb-Si3N4 itself. Thesestructures can be grouped into three regions, R1, R2, and R3,separated by two deep minima at 8.3 and 20.9 eV. The major peaksin these three regions are A at 5.9 eV; B1, B2, and B3 at 10, 12,and 16 eV, respectively; C at 25.8 eV; and additional minor peaks.The relative positions and strengths of the peaks change aszincreases. Atz5 4, the main peaks A1, A2, B1, B2, B3, and C areat 5.3, 7.6, 10.2, 12.0, 16.0, and 22.1 eV, respectively, in additionto the pre-edge structure in the 2.0 eV range. For the Al-L2,3 edge(Fig. 6, right panel) in thez 5 1 case, there is only one aluminumatom. The spectra show a deep minimum at 19.5 eV and a majorpeak at 12.0 eV. There are many other structures that evolve aszincreases, reflecting a steady increase of the Al–O bonds relativeto the Si–N bonds. A remarkable feature is that the main edge at;5.5 eV is relatively independent ofz, even with the presence ofthe pre-edge structure discussed earlier.

The PDOS (p component) for the Si-K and Al-K edges areshown in Fig. 7. Experimentally, the Si-K and Al-K edges have amuch lower energy resolution because of the higher transitionenergies for the 1score electron. There are many structures in bothspectra, and the amplitudes decrease as energy increases. Atz5 4,Si-K has two well-defined peaks at 5.2 and 8.0 eV. The presence

of the pre-edge structure is again obvious. The centroid of theoverall spectra is at a lower energy in Si-K than in Al-K.

The PDOS for the N-K and the O-K edges are shown in Fig. 8.For N-K, we can separate the spectra into two regions above andbelow the minimum at 20 eV. We may consider the structuresbelow 20 eV as a single broad peak that centers at;10 eV inb-Si3N4. As z increases, the peak position shifts slightly upward,and the width of the peak increases. For the O-K edge, we canagain divide the spectra into two regions—above and below 15 eV.For z 5 1, where there is only a single oxygen in the unit cell, themain peak in the lower region centers at 6.5 eV. This peakstructure again evolves asz increases, and, atz5 4, the peak looksmore like a plateau with rather sharp edges on either side. Thereare multiple structures in the region above 15 eV in both cases thatare difficult to interpret in a simple way.

IV. Conclusions

Based on detailedab initio calculations of the electronicstructure and bonding inb-Si6–zAlzOzN8–z for z ranges of 0 to 4,the main conclusions are as follows:

(1) The bulk modulus and bonding strength in the SiAlONsolid solution decrease only slightly withz.

(2) At z 5 1, impurity-like states are introduced near the CBedge, and, at a higherz, the crystal is a semiconductor with a gapof the order of 1.3 eV.

(3) The charge density plot shows very little disturbance as aresult of pair substitution. Effective charge calculation shows only

Fig. 6. (s 1 d) components of orbitally resolved PDOS of silicon (leftpanel) and aluminum (right panel) ofb-Si6–zAlzOzN8–z in the CB region.These spectra should mimic Si-L2,3 and Al-L2,3 edges. Curves are broad-ened by a Gaussian of 1 eV.


a slight decrease in the covalent character of the solid solution asz increases.

(4) Substitution of the (Si,N) pair with (Al,O) actuallystrengthens the remaining bonds because of the efficient redistri-bution of charge. This is one of the reasons SiAlON can be aneffective structural ceramic with superior mechanical properties.

(5) Orbitally resolved DOS and PDOS calculations reveal theintricate interplay of the Si–N, Si–O, Al–N, and Al–O bonds in thesolid solution. The orbitally resolved PDOS in the CB are used topredict thez dependence of the ELNES spectra, which has yet tobe measured experimentally.

These results also affect the electronic structure of the inter-granular thin films, consisting mainly of doped silicates, betweenSi3N4 particles. Detailedab initio results can be used to constructeffective pair potentials for large-scale simulations whereab initiocalculations become prohibitive. Recently, such effective pairpotentials for a- and b-Si3N4 have been obtained with verysatisfactory results.44 For intergranular phases, good pair poten-tials are more difficult to obtain because of the multiple atomicspecies present and the need to account for the environmentaldependence of the potentials. Electronic structure calculationsshould be extended toa-SiAlON and the O9-SiAlON series to seeif changes in local bonding can affect the ELNES spectra and bedetected experimentally. Calculations should also be conducted onmore-complicated solid solutions, such as in the Y-SiAlON series.This will enable us to ascertain the solution effect of the rare-earthelements. The room-temperature toughness ofb-SiAlON can besignificantly improved by a small addition of Y2O3.

20 The fact that

an increase in the Y:Al and O:N ratio promotes interface debond-ing demonstrates the importance of interfacial chemistry andcomposition in determining the mechanical properties. It is alsodesirable to model the structures at the interface between Si3N4

crystal and the glassy phases and then conduct direct electronicstructure calculations of these models. Together with increasedexperimental effort, greater understanding can be obtained of thestructure and bonding of the intergranular phases and the deter-mining role they play in a material’s mechanical properties, whichare crucial for its application as a structural ceramic.

References

1D. W. Richerson and P. M. Stephan, “Evolution of Applications of Si3N4-BasedMaterials,”Mater. Sci. Forum, 47, 282–307 (1989).

2Silicon Nitride Ceramics, Materials Research Society Symposium Proceedings,Vol. 287. Edited by I-W. Chen, P. F. Becher, M. Mitomo, G. Petzow, and T.-S. Yen.Materials Research Society, Pittsburgh, PA, 1993.

3 M. J. Hoffmann, P. F. Becher, and G. Petzow (Eds.),Silicon Nitrides 93,TransTech Publications, Aedermannsdorf, Switzerland, 1994.

4R. Raj, “Fundamental Research in Structural Ceramics for Service near 2000 C,”J. Am. Ceram. Soc., 76, 2147–74 (1993).

5S. Wild, P. Grieveson, and K. H. Jack,Special Ceramics, Vol. 5; p. 385. Editedby P. Popper. British Ceramic Research Association, Stoke-on-Trent, U.K., 1972.

6J. Weiss, “Silicon Nitride Ceramics: Composition, Fabrication Parameters, andProperties,”Annu. Rev. Mater. Sci., 11, 381–99 (1981).

7(a)K. H. Jack and W. I. Wilson, “Ceramics Based on the Si-Al-O-N and RelatedSystems,”Nature (London), Phys. Sci.,238, 28–29 (1972). (b)K.H. Jack, “TheSiAlONs,” Mater. Res. Bull.,13, 1327–33 (1978).

8T. Ekstrom and M. Nygren, “SiAlON Ceramics,”J. Am. Ceram. Soc., 75 [2]259–76 (1992).

9I. Tanaka, S. Nasu, H. Adachi, Y. Miyamoto, and K. Niihara, “ElectronicStructure behind the Mechanical Properties ofb-SiAlONS,” Acta Metall. Mater., 40[8] 1995–2001 (1992).

Fig. 7. Same as Fig. 6 for thep-component of PDOS, which shouldrepresent Si-K and Al-K edges.

Fig. 8. p-component of orbitally resolved PDOS of nitrogen (left panel)and oxygen (right panel) ofb-Si6–zAlzOzN8–z mimics O-K and N-K edges,respectively. All spectra are broadened by a Gaussian of 1 eV.


10D. R. Clarke, “On the Equilibrium Thickness of Intergranular Glass Phases inCeramic Materials,”J. Am. Ceram. Soc., 70, 15–22 (1987).

11D. R. Clarke, “High-Temperature Microstructure of a Hot-Pressed SiliconNitride,” J. Am. Ceram. Soc., 72, 1604–609 (1989).

12M. J. Hoffmann, “Analysis of Microstructural Development and MechanicalProperties of Si3N4 Ceramics”; pp. 59–72 inTailoring the Mechanical Properties ofSi3N4 Ceramics. Edited by M. J. Hoffmann and G. Petzow. Kluwer, Dordrecht, TheNetherlands, 1994.

137. X. Pan, H. Gu, R. v. Weeren, S. C. Danforth, R. W. Cannon, and M. Ru¨hle,“Grain-Boundary Microstructure and Chemistry of a Hot Isostatically Pressed HighPurity Silicon Nitride,”J. Am. Ceram. Soc., 79 [9] 2313–20 (1996).

14H.-J. Kleebe, M. K. Cinibulk, I. Tanaka, J. Bruley, J. S. Vetrano, and M. Ru¨hle,“High Resolution Electron Microscopy Studies on Silicon Nitride Ceramics”; pp259–274 inTailoring of High Temperature Properties of Si3N4 Ceramics. Edited byM. J. Hoffmann and G. Petrow. Kluwer, Dordrecht, The Netherlands,1994.

15H.-J. Kleebe, M. K. Cinibulk, R. M. Cannon, and M. Ru¨hle, “Statistical Analysisof the Intergranular Film Thickness in Silicon Nitride Ceramics,”J. Am. Ceram. Soc.,76 [8] 1969–77 (1993).

16E. Y. Sun, P. F. Becher, S. B. Waters, C. H. Hsueh, K. P. Plucknett, and M. J.Hoffmann, “Control of Interface Fracture in Silicon Nitride Ceramics: Influence ofDifferent Rare Earth Elements”; inCeramic Microstructures ’96. Edited by A. P.Tomsia and A. Glaser. Plenum, New York, 1998.

17G. Pezzotti, K. Ota, and H.-J. Kleebe, “Grain-Boundary Relaxation in High-Purity Silicon Nitride,”J. Am. Ceram. Soc., 79 [9] 2237–46 (1996).

18T. Ekstrom, P. O. Kall, M. Nygren, and P.O. Olsson, “Dense Single-PhaseSiAlON Ceramics by Glass-Encapsulated Hot Isostatic Pressing,”J. Mater. Sci., 24,1853–61 (1989).

19G. Pezzotti, H.-J. Kleebe, K. Ota, and K. Yabuta, “Supression of ViscousGrain-Boundary Sliding in a Dilute SiAlON Ceramic,”J. Am. Ceram. Soc., 72,1604–609 (1989).

20P. F. Becher, E. Y. Sun, C. H. Hsueh, K. B. Alexander, S. L. Hwang, S. B.Waters, and C. G. Westmoreland, “Debonding of Interfaces betweenb-SiliconNitride Whiskers and Si-Al-Y Oxynitride Glasses,”Acta Mater., 44 [10] 3881–93(1996).

21H. Gu, R. M. Cannon, and M. Ru¨hle., “Composition and Chemical Width ofUltrathin Amorphous Films at Grain Boundaries in Silicon Nitride,”J. Mater. Res.,13 [2] 376–87 (1998).

22R. H. French, H. Mu¨llejans, D. J. Jones, G. Duscher, R. M. Cannon, M. Ru¨hle,“Dispersion Forces and Hamaker Constants for Intergranular Films in Silicon Nitridefrom Spatially Resolved Valence Electron Energy Loss Spectrum Imaging,”ActaMater., 46, 2271–87 (1998).

23S. Suzuki, N. Takakuni, S. Hayama, and M. Ozawa, “Mechanical and ThermalProperties ofb-Sialon Prepared by Slip Casting Method,”J. Am. Ceram. Soc., 79 [6]1685–88 (1996).

24L. L. K. Falk, Z.-J. Shen, and T, Ekstro¨m, “Microstructural Stability of Duplexa–b-Sialon Ceramics,”J. Eur. Ceram. Soc., 17, 1099–112 (1997).

25X. Jiang, Y.-K. Baek, S.-M. Lee, and S.-J. L. Kang, “Formation of ana-SiAlONLayer onb-SiAlON and its Effect on Mechanical Properties,”J. Am. Ceram. Soc., 81[7] 1907–12 (1998).

26A. J. Pyzik and D. R. Beaman, “Microstructure and Properties of Self-ReinforcedSilicon Nitride,” J. Am. Ceram. Soc., 76 [1] 3–28 (1993).

27(a)T. Nakayasu, T. Yamada, I. Tanaka, H. Adachi, and S. Goto, “ElectronicStructure of Ln31 a-SiAlONs, with Correlation to Solubility and Solution Effect,”J. Am. Ceram. Soc.,79 [10] 2527–32 (1996). (b)“Calculation of Grain-BoundaryBonding in Rare Earth-Dopedb-Si3N4,” ibid., 81 [3] 565–70 (1998).

28P. Dudse´k and L. Benco, “Cation-Aided Joining of Surfaces ofb-Silicon Nitride:Structural and Electronic Aspects,”J. Am. Ceram. Soc., 80 [5] 1248–54 (1998).

29M. E. Bowden, G. C. Barris, and I. W. M. Brown, “A New, Low-TemperaturePolymorph of O9-SiAlON,” J. Am. Ceram. Soc., 81 [8] 2188–90 (1998).

30H. Mandal, D. P. Thompson, and T. Ekstro¨m, “Reversible a7b SialonTransformation in Heat-Treated Sialon Ceramics,”J. Eur. Ceram. Soc.,12, 421–29(1993).

31M. Camuscu, D. P. Thompson, and H. Mandal, “Effect of Starting Composition,Type of Rare Earth Sintering Additive, and Amount of Liquid Phase ona7b SialonTransformation,”J. Eur. Ceram. Soc.,17, 599–613 (1997).

32D. P. Thompson, P. Korgul, and A. Hendry, “The Structural Characterization ofSialon Polytypoids”; pp. 61–74 inProgress in Nitrogen Ceramics.Edited by F. L.Riley. Martinus Nijhoff, The Hague, The Netherlands (1983).

33R. F. Egerton,Electron Energy Loss Spectroscopy in the Electron Microscope.Plenum, New York, 1993.

34M. Gulgun, Y.-N. Xu, W. Y. Ching, and M. Ru¨hle, “Electron States of YAGProbed by Energy-Loss Near-Edge Spectrometry andab initio Calculations,”Philos.Mag., B, 79 [6] 921 (1999).

35S.-D. Mo, W. Y. Ching, M. F. Chisholm, and G. Duscher, “Structure andBonding of a Grain Boundary Model in SrTiO3,” Phys. Rev. B: Condens. Matter,60[4] 2416–24 (1999).

36W. Y. Ching, “Theoretical Studies of the Electronic Properties of CeramicMaterials,”J. Am. Ceram. Soc., 73, 3135–60 (1990).

37(a)P. Hohenberg and W. Kohn, “Inhomogeneous Electron Gas,”Phys. Rev.[Sect.] B, 136, B864–B871 (1964). (b)W. Kohn and L. J. Sham, “Self-ConsistentEquations Including Exchange and Correlation Effects,”Phys. Rev.[Sect.[ A , 140,A1131–A1138 (1965). (c)L. J. Sham and W. Kohn, “One-Particle Properties of anInhomogeneous Interacting Electron Gas,”Phys. Rev.145,561–67 (1966).

38Y.-N. Xu and W. Y. Ching, “Electronic Structure ofa- andb- Phases of SiliconNitride, Silicon Oxynitride, and with Comparison to Silicon Dioxide,”Phys. Rev. B:Condens. Matter,51, 17379–89 (1991).

39G. L. Zhao and M. E. Bachlechner, “Electronic Structure and Charge Transfer ina-and b-Si3N4 and the Si(111)/Si3N4(001) Interface,”Phys. Rev. B, 58, 1887–95(1998).

40O. Borgen and H. M. Seip, “The Crystal Structure ofb-Si3N4,” Acta Chem.Scand., 15, 1789–89 (1961).

41R. Grun, “The Crystal Structure ofb-Si3N4: Structural and Stability Consider-ations betweena- andb-Si3N4,” Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst.Chem.,35, 800–804 (1979).

42(a)R. S. Mulliken, “Electron Population Analysis on LCAO-MO Molecular WaveFunctions, I,” J. Am. Chem. Soc., 23, 1833–40(1955). (b)“Electron PopulationAnalysis on LCAO-MO Molecular Wave Functions, II,” ibid., 23, 1841–46 (1955).

43W. Y. Ching, Y.-N. Xu, and M. Ru¨hle, “Ab initio Calculation of Y-SubstitutionalImpurity in a-Al2O3,” J. Am. Ceram. Soc., 80 [12] 3199–204 (1997).

44W. Y. Ching, Y.-N. Xu, J. D. Gale, and M. Ru¨hle, “Ab initio Total EnergyCalculation ofa- and b-Phases of Silicon Nitride and the Derivation of EffectiveInter-Atomic Pair Potentials with Application to Lattice Dynamics,”J. Am. Ceram.Soc., 81 [12] 3189–96 (1998).

45F. D. Murnagahn, “The Compressibility of Media under Extreme Pressures,”Proc. Natl. Acad. Sci., U. S. A, 30, 244–47 (1944).

46F. Birch, “Finite Strain Isotherm and Velocities for Single Crystal and Polycrys-talline NaCl at High Pressure and 300 K,”J. Geophy. Res., D: Atmos., 83, 1257–68(1978).

47J. T. Milek, Handbook of Electronic Materials, Vol. 3. IFI/Plenum, New York,1971.

48J. Zaanen, “Theory of Correlated Holes (and Electrons): from Satellites toLuttinger Liquids”; pp. 89–137 inUnoccupied Electronic States—Fundamentals forXANES, EELS, IPS and BIS,Topics in Applied Physics, Vol. 69. Edited by J. C.Fuggle and J. E. Inglesfield. Springer–Verlag, New York, 1992. M


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Electronic Structure and Bonding of b-SiAlON