Ceramics Science and Technology, Volume 4: Applications

Although ceramics have been known to mankind literally for millennia, research has never ceased. Apart from the classic uses as a bulk
material in pottery, construction, and decoration, the latter half of the twentieth century saw an explosive growth of application fields, such as
electrical and thermal insulators, wear-resistant bearings, surface coatings, lightweight armour, and aerospace materials. In addition to plain,
hard solids, modern ceramics come in many new guises such as fabrics, ultrathin films, microstructures and hybrid composites.

Built on the solid foundations laid down by the 20-volume series Materials Science and Technology, Ceramics Science and Technology picks
out this exciting material class and illuminates it from all sides. Materials scientists, engineers, chemists, biochemists, physicists and
medical researchers alike will fi nd this work a treasure trove for a wide range of ceramics knowledge from theory and fundamentals to practical approaches and problem solutions.

• Language: English
• Publisher: Wiley
• Release date: Aug 5, 2013
• ISBN: 9783527676736

Book preview

Preface

Along with metals and polymers, advanced ceramics are one of the most promising classes of materials for the key technologies of the 21st century. Recent developments in the field has resulted in a number of new synthesis, processing and sintering techniques for the production of novel structural and functional ceramics and ceramic composites. Significant progress has also been made in the past two decades in the production of novel multifunctional ceramics with a tailor made micro- and/or nanoscale structure to respond to the increasing technological demand for advanced ceramic materials.

The four-volume series of Ceramics Science & Technology covers various aspects of modern trends in advanced ceramics reflecting the status quo of the latest achievements in ceramics science and development. The contributions highlight the increasing technological significance of advanced ceramic materials and present concepts for their production and application. Volume 1 deals with structural properties of ceramics by considering a broad spectrum of length scale, starting from the atomic level by discussing amorphous and crystalline solid state structural features, and continuing with the microstructural level by commenting on microstructural design, mesoscopic and nano structures, glass ceramics, cellular structures, thin films and multiphase (composite) structures. Volume 2 focuses on i) various distinct classes of ceramic materials, namely oxides, carbides and nitrides, and ii) physical and mechanical properties of advanced ceramics. The series is continued with Volume 3 with chapters related to advanced synthesis and processing techniques used for the production of engineering ceramics and is here completed by Volume 4 which is devoted to applications of engineering and functional ceramics.

Quo vadis ceramics? The four-volume series intends to provide comprehensive information relevant to the future direction of ceramics. In this respect, Volume 4 describes commercial applications of several advanced, engineering ceramics to offer evidence for their technological importance and to point to trends for the further development of this fascinating class of materials. Latest examples of commercial ceramics are found in transportation industry: PZT (Pb(Zr,Ti)O3)-based piezoelectric actuators and Si3N4-based ball bearings and glow plugs are used in diesel engines, carbon fiber reinforced silicon carbide (C/SiC) is used for brakes, and oxide ceramics-based thermal barrier coatings are used in jet engines; in lighting industry: sialon-derivative-based luminescent ceramics for LED applications, and GaN-based ceramics for optoelectronics; and in many others.

As novel ceramics are called for and expected to establish a commercial status in the future in a number of emerging application fields, there is the need for a long-term alignment with the emerging fields and for continued fundamental research in ceramics science and technology. Along this line, Volume 4 highlights potential applications of advanced ceramics in applications such as fuel cells, membranes, gas sensors, and energy storage. In addition, specific functions uniquely delivered by ceramic materials are described: nanostructured ceramics for superhard applications, ceramics for ultrahigh temperature and corrosive environment applications, and ceramics for magnetic and microwave applications. Finally, novel compositions based on polymer-derived ceramics and nitridosilicates are discussed as promising future materials with properties unmatched by any material known today and ones that can only be realized by designing the material structure at the nanoscale. In this way, we hope this final volume and the four-volume series will celebrate and contribute to the exciting development of ceramics and technology by providing the latest scientific knowledge to ceramic students and ceramic research community.

We wish to thank all the contributing authors for their great enthusiasm in compiling excellent manuscripts in their respective area of expertise. We also acknowledge the support of the Wiley-VCH editors, Bernadette Gmeiner and Martin Preuß, for their continuous encouragement to work on this project.

Darmstadt and Philadelphia

May 2013

Ralf Riedel

I-Wei Chen

List of Contributors

Jörg Adler

Fraunhofer Institute for Ceramic Technologies and Systems

Winterbergstrasse 28

01277 Dresden

Germany

Lambert Alff

Technische Universität Darmstadt

Institute of Materials Science

Petersenstr. 23

65287 Darmstadt

Germany

Natalia N. Bramnik

Karlsruher Institut für Technologie (KIT)

Institut für Angewandte Materialien- Energiespeichersysteme (IAM-ESS) & Institut für Anorganische Chemie

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

Paolo Colombo

University of Padova

Dipartimento di Ingegneria Meccanica

Settore Materiali

35131 Padova

Italy

and

The Pennsylvania State University

Department of Materials Science and Engineering

University Park, PA 16802

USA

Helmut Ehrenberg

Karlsruher Institut für Technologie (KIT)

Institut für Angewandte Materialien- Energiespeichersysteme (IAM-ESS) & Institut für Anorganische Chemie

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

Aleksander Gurlo

Technische Universität Darmstadt

Fachbereich Material- und Geowissenschaften

Petersenstr. 32

64287 Darmstadt

Germany

Naoto Hirosaki

National Institute for Materials Science (NIMS)

Namiki 1-1, Tsukuba

Ibaraki 305-0044

Japan

Peter Holtappels

Technical University of Denmark

Department of Energy Conversion and Storage

Frederiksborgvej 399,

4000 Roskilde

Denmark

Pavel Holubá

SHM s.r.o.

Pr myslová 3

787 01 Šumperk

Czech Republic

Nathan S. Jacobson

NASA Glenn Research Center

MS 106-1, 21000 Brookpark Road

Cleveland, OH 44135

USA

Bo tjan Jan ar

Jožef Stefan Institute

Advanced Materials Department

Jamova 39

1000 Ljubljana

Slovenia

Allan P. Katz

Air Force Research Laboratory

Materials and Manufacturing Directorate, AFRL/RXCC

Wright-Patterson AFB, OH 45433-7817

USA

Ronald J. Kerans

Air Force Research Laboratory

Materials and Manufacturing Directorate, AFRL/RXCC(Emeritus)

Wright-Patterson AFB, OH 45433-7817

USA

Ralf Kriegel

Fraunhofer Institute for Ceramic Technologies and Systems

Michael-Faraday-Str. 1

07629 Hermsdorf

Germany

Gabriela Mera

Technische Universität Darmstadt

Institute for Materials Science

64287 Darmstadt

Germany

Mamoru Mitomo

National Institute for Materials Science (NIMS)

Namiki 1-1, Tsukuba

Ibaraki 305-0044

Japan

Takeshi Mitsuoka

NGK Spark Plug Co., Ltd

Material Research Dept R&D Center

2808 Iwasaki Komaki-shi

Aichi 485–8510

Japan

Sandro Pagano

Ludwig-Maximilians-University Munich

Department of Chemistry

Butenandtstrasse 5–13

81377 Munich

Germany

Elizabeth J. Opila

University of Virginia

Department of Materials Science and Engineering

395 McCormick Rd.

Charlottesville, VA 22904

USA

Ralf Riedel

Technische Universität Darmstadt

Institute for Materials Science

64287 Darmstadt

Germany

Wolfgang Schnick

Ludwig-Maximilians-University Munich

Department of Chemistry

Butenandtstrasse 5–13

81377 Munich

Germany

Gian Domenico Sorarù

University of Trento

Materials Science and Technology

38122 Trento

Italy

Bhaskar Reddy Sudireddy

Technical University of Denmark

Department of Energy Conversion and Storage

Frederiksborgvej 399,

4000 Roskilde

Denmark

Danilo Suvorov

Jožef Stefan Institute

Advanced Materials Department

Jamova 39

1000 Ljubljana

Slovenia

Robert Vaßen

Forschungszentrum Jülich

Institut für Energieforschung

Wilhelm-Johnen-Straße

52425 Jülich

Germany

Stan Vep ek

Technical University Munich

Department of Chemistry

Lichtenbergstr. 4

85747 Garching

Germany

Maritza G.J. Vep ek-Heijman

Technical University Munich

Department of Chemistry

Lichtenbergstr. 4

85747 Garching

Germany

Ingolf Voigt

Fraunhofer Institute for Ceramic Technologies and Systems

Michael-Faraday-Str. 1

07629 Hermsdorf

Germany

Marcus Weyd

Fraunhofer Institute for Ceramic Technologies and Systems

Michael-Faraday-Str. 1

07629 Hermsdorf

Germany

Rong-Jun Xie

National Institute for Materials Science (NIMS)

Namiki 1-1, Tsukuba

Ibaraki 305-0044

Japan

Martin Zeuner

Ludwig-Maximilians-University Munich

Department of Chemistry

Butenandtstrasse 5–13

81377 Munich

Germany

Part One

Structural Applications

1

Oxidation and Corrosion of Ceramics

Elizabeth J. Opila and Nathan S. Jacobson

1.1 Introduction

Ceramics are compounds with strong covalent or ionic bonds, typically rendering them very stable with high melting points. While oxides in oxidizing environments are quite stable at high temperatures, carbides, nitrides, and borides are all less thermodynamically stable than their corresponding oxides. For this reason, the reaction of non-oxide ceramics to form oxides is a very important problem in many high-temperature environments. These types of reactions are important for structural ceramics used in a wide variety of applications including furnaces, engines, land-based turbines for power generation, heat-exchangers, hot-gas filters, chemical process containers, and re-entry shields. In addition, non-oxide ceramic materials are often used as substrates in high-temperature functional devices such as sensors, actuators, and fuel cells wherein environments can also be oxidizing.

The oxidation and corrosion of many technologically important ceramics are detailed in this chapter, with emphasis placed on the reactions of non-oxide ceramics. Classes of ceramics with the same cation are considered together. Silica formers, alumina formers, and then hafnia and zirconia formers are discussed explicitly. The effects of carbon, nitrogen and boron on the formation of the more stable condensed phase oxides are also discussed. Within each section, the ideal oxidation reaction is discussed first, after which complications due to complex materials and complex environments are considered. Finally, a short discussion of oxide degradation is provided.

Emphasis is placed on the thermodynamics and kinetics of the oxidation and corrosion reactions with the aim of describing the current capability to predict the rate of material degradation. Areas requiring additional elucidation are noted. Generally, at moderate temperatures the rate of material degradation is limited by the surface reaction of the material with its environment; the reactions are thus sensitive to the processing, crystal structure and orientation of the ceramic. At higher temperatures, however, the degradation rate is typically diffusion-controlled, and under these conditions the reaction rate is controlled by reactant or product transport through the growing oxide, or vapor transport through a gaseous boundary layer. These reaction mechanisms are shown schematically in Figure 1.1.

Figure 1.1 Rate-limiting material degradation mechanisms. Reaction-limited oxidation; (b) Solid-phase diffusion-limited oxidation; (c) Gas-phase diffusion-limited volatilization.

1.2 Silica-Forming Ceramics

Silicon carbide (SiC) and silicon nitride (Si3N4) are two ceramic materials that show promise for long-term, high-temperature applications due to the formation of a slow-growing protective silica film that forms in oxidizing environments. Extensive studies have been made of the oxidation and corrosion of SiC and Si3N4, as reviewed previously [1,2]. Consequently, much of this chapter will cover these materials, with ideal behavior being discussed first in this section. Complications for real materials in real environments are then presented.

1.2.1 Ideal Oxidation Behavior of Silica-Forming Ceramics

1.2.1.1 Structure of Silica and Transport of Oxygen in Silica

In order to understand the oxidation of silica-formers, the structure of silica must first be discussed (the reader is referred to an in-depth review by Lamkin, Riley, and Fordham [3] for a more detailed discussion of this topic). Silica exists in several polymorphs, the amorphous phase, and the crystalline phases. The crystalline phases are – from the low-temperature polymorphs to the high-temperature polymorphs – quartz, tridymite, and cristobalite, respectively. Amorphous silica is composed of an irregular network of SiO4 tetrahedra. A two-dimensional (2-D) representation of amorphous silica is shown in Figure 1.2a, with rings of varying numbers of Si–O bonds. Figure 1.2b shows a 2-D representation of crystalline silica in which the structure is ordered into six-member rings of Si–O bonds. The density of cristobalite (2.32 g cm−3) is closest to amorphous silica (2.20 g cm−3). Both, the amorphous phase and cristobalite have a relatively open structure that allows the permeation of molecular oxygen through the interstices of the structure. Figure 1.2c shows the case where the silica network has been modified by cations incorporated in the interstices of the glass structure. These modifying cations, which typically are the alkali metals and alkaline earths, are charge-compensated by the formation of non-bridging oxygen. The glass network is thus disrupted by the incorporation of these cations, which then affects transport of oxidant through the silica.

Figure 1.2 Schematic structure of silica. (a) Amorphous silica; (b) Cristobalite; (c) Alkali-modified silica. Silicon atoms are represented by small dark circles, oxygen atoms by open circles, and alkali impurities as large cross-hatched circles.Reproduced with permission from Ref. [3]; © 1992, Journal of the European Ceramic Society.

The transport of oxygen through silica can occur by several mechanisms: (i) by molecular permeation through the interstices of the structure; and (ii) by the exchange of oxygen ions with the network oxygen. The permeability of oxygen in silica has been measured by Norton [4], and shown to be a product of the diffusivity and the solubility of oxygen in silica. Norton showed that the rate of permeation was proportional to the first power of the pressure, thus indicating that molecular oxygen was the diffusing species. Several ¹⁸O tracer diffusion studies of oxygen transport in silica have also been conducted, but only some of the more recent are detailed here [5,6]. In these studies, the exchange of oxygen with the silica network – which is slower than that of oxygen permeation – is measured. Thus, the oxidation of silica-formers is expected to be dominated by rates of permeation of molecular oxygen through the silica interstices. This transport mechanism will be discussed in the following sections.

1.2.1.2 Oxidation of Silicon in Dry Oxygen

A discussion of the oxidation of silicon is included here for two reasons. First, oxidation occurs by a simple reaction without the formation of any products except silica:

(1) equation

Second, this reaction has been studied extensively due to its application for semiconducting microelectronics.

The classic study for the oxidation of silicon is that of Deal and Grove [7], which makes several important points. First, the overall oxidation reaction kinetics for silicon can be described by the relationship:

(2) equation

where x o is the oxide thickness, t is time, τ is a shift in time that corrects for the presence of any native oxide layer, and A and B are constants. At short times, or for thin oxide scales, the relationship reduces to a linear rate law:

(3) equation

where B/A is the linear rate constant. Here, the oxidation rate is controlled by the reaction of the oxidant with the substrate at the oxide/substrate interface. At long times, and for thick oxide scales, Eq. (2) reduces to

(4) equation

where B is the parabolic rate constant. (Note: While Deal and Grove use the symbol B, the oxidation community generally uses the symbol k p to represent the parabolic rate constant.) In the case of parabolic oxidation, oxidation is limited by transport of the oxidant through the silica scale, and the oxidation rate slows parabolically with time as the scale thickens. Linear kinetics are observed at low temperatures and short times, whereas parabolic kinetics are observed at long times and high temperatures. Under intermediate conditions the complete expression (Eq. (2)) must be used. The complete expression and the transition between the two limiting cases (Eqs (3) and (4)) are shown in Figure 1.3. These oxidation kinetics can be determined by either measuring weight gain due to silica formation or by measuring the oxide thickness.

Figure 1.3 General linear-parabolic oxidation kinetics showing the limiting linear kinetics at short times/thin oxide scales and limiting parabolic kinetics at long times/thick oxide scales.Reproduced with permission from Ref. [7]; © 1965, The American Institute of Physics.

Another important result of the Deal and Grove [7] study was that the activation energy (E a) for the oxidation of silicon (119 kJ mol−1) was in agreement with the E a for the molecular permeation of oxygen through silica of 113 kJ mol−1, as measured by Norton [4]; this indicated that the mechanism of oxygen transport was the same. In addition, Deal and Grove found that the parabolic oxidation rate constant was proportional to the first power of the oxygen pressure, indicating that molecular oxygen is the diffusing species.

1.2.1.3 Oxidation of Silicon Carbide in Dry Oxygen

The oxidation of SiC is expected to be similar to that of silicon, since the only solid oxidation product is silica. However, in this case, the carbon is also oxidized to form gaseous carbon monoxide:

(5) equation

Results for the oxidation of chemical vapor deposited (CVD) SiC show many similarities to silicon oxidation. First, at lower temperatures, linear kinetics are important [8], while at higher temperatures (≥1200 °C) parabolic kinetics are adequate to describe oxidation under most conditions [9]. Second, the E a for parabolic oxidation [9] (118 kJ mol−1) agrees with that of Norton [4] and Deal and Grove [7], as shown in Figure 1.4. This suggests that molecular oxygen permeation through the growing silica scale limits the oxidation rate.

Figure 1.4 Parabolic oxidation rates of pure silicon, SiC and Si3N4 in dry oxygen.Reproduced with permission from Ref. [10]; © 2000, Wiley-VCH Verlag GmbH & Co. KGaA.

There are a number of differences for the oxidation of SiC compared to that of silicon that should be mentioned. First, the linear rate constants for SiC are in general lower than those of silicon [8]. The reaction of oxygen at the substrate surface will be different due to the presence of C. Second, the parabolic rate constant is expected to be 1.5- to 2-fold lower for SiC than for Si, since additional oxygen is used to form CO(g) or CO2(g) [11]. A factor of 2.5 reduction in oxidation rate for polycrystalline β-SiC compared to Si was observed by Ogbuji and Opila [9]. Additionally, Ramberg [8] and others have shown that parabolic oxidation rates of SiC vary with crystallographic orientation. While polycrystalline SiC oxidation rates differ only slightly from silicon oxidation rates, the oxidation rates of single crystals are much slower on the silicon-terminated faces than the carbon-terminated faces of SiC. The faster oxidation rates for the carbon-terminated faces are similar to those of silicon. Because the oxidation rates on the silicon-terminated faces are also parabolic, it is postulated that an inner oxide layer of composition different from silica is formed. This is consistent with the observation that silicon oxycarbide phases form in the initial oxidation stages of silicon-terminated faces of SiC [12,13].

1.2.1.4 Oxidation of Silicon Nitride in Dry Oxygen

Unlike SiC, the oxidation rates of Si3N4 are different from the oxidation rates of silicon. This is unexpected, as the overall oxidation reaction is similar to that of SiC in that a solid oxidation product – silica – and a gaseous product – nitrogen – are formed:

(6) equation

The parabolic oxidation rate of Si3N4 has been observed to be lower than that of SiC, and it has a much larger E a than was observed for the permeation of silica and the oxidation of silicon and SiC [9]. The Ea for the oxidation of Si3N4 has been reported as 363 kJ mol−1 [9], with the parabolic oxidation rate of Si3N4 converging with the other silica-forming materials around 1500 °C, as shown in Figure 1.4. The difference in Ea for Si3N4 oxidation has been attributed to the rate-limiting step of oxygen transport through an inner scale of silicon oxynitride. A simple formation reaction for the oxynitride is [14]:

(7) equation

with subsequent oxidation of the oxynitride to form silica:

(8) equation

The silicon oxynitride has been observed using both scanning electron and transmission electron microscopies [14], as shown in Figure 1.5. The inner oxynitride layer was found to be amorphous, even when the outer layer of silica was crystalline, thus explaining the contrast in Figure 1.5. More detailed examinations of the silicon oxynitride layer using X-ray photoelectron spectroscopy (XPS) [16], Auger electron spectroscopy (AES) and Rutherford backscattering (RBS) [17] showed the oxynitride to be continuously varying in composition, from nitrogen-rich at the nitride interface to oxygen-rich at the oxynitride–oxide interface [18]. Thus, the experimental observations and differences between SiC and Si3N4 oxidation are explained by a unique mechanism in which nitrogen is substituted for oxygen in the oxynitride, given by [19]:

(9)

equation

and shown schematically in Figure 1.6. Several other important experimental observations that support the proposed mechanism are that the oxynitride layer grows parabolically with time [20], and that the oxidation rate of silicon nitride depends on the oxygen partial pressure but not on the nitrogen partial pressure [21]. Thus, the parabolic rate can be limited by growth of the oxynitride layer and must be attributed to oxygen transport rather than to nitrogen transport.

Figure 1.5 Cross-section of CVD Si3N4 oxidized for 48 h at 1400 °C, showing the amorphous silicon oxynitride layer.Reproduced with permission from Ref. [15]; © 1994, Springer Science and Business Media.

Figure 1.6 Schematic diagram of SiN2−x O2+x resulting from Si3N4 oxidation in which continuously varying oxygen and nitrogen content is proposed.Reproduced with permission from Ref. [16]; © 1993, The Electrochemical Society.

At temperatures above approximately 1500 °C, the oxidation rate of silicon nitride is no longer limited by transport through the oxynitride layer. Transport of molecular oxygen through silica would again be the rate-limiting process [9].

1.2.2 SiC Oxidation: Deviations from Norton Permeation

At temperatures of around 1400 °C, an upturn in the Ea for oxidation of SiC has been observed by some investigators. This has variously been attributed to crystallization of the silica scale [22] or a change from molecular permeation to a transport mechanism dominated by exchange with the silica network [23–28]. However, evidence that suggests an alternative mechanism may also explain these results [9,28], as impurities from either the environment or the material under study may alter the silica structure and change the temperature dependence for oxygen transport. Each of these possibilities is considered in the following sections.

1.2.2.1 Crystallization of the Silica Scale: Effect on SiC Oxidation

At temperatures of 1300 °C and higher, the amorphous silica scale transforms to cristobalite [9] with a spherulitic structure, as shown in Figure 1.7. As mentioned above, cristobalite has almost the same density as amorphous silica, but the structure is more ordered and the larger interstices (shown schematically in Figure 1.2a) are lacking. Nevertheless, the molecular transport of oxygen through the interstices is still possible. Helium-permeation studies with β-cristobalite (the high-temperature form present during oxidation) and amorphous silica have shown similar permeation rates [29]. Although conclusive oxygen-permeation studies through cristobalite have not yet been performed, the larger size of the oxygen molecule (relative to that of helium) suggests that oxygen permeation in cristobalite may be slower than in amorphous silica. Subsequently, Ogbuji performed some experiments to test this hypothesis [30], whereby SiC was oxidized at 1300 °C – a temperature where devitrification of the silica scale to cristobalite is known to occur. While still in the oxidation furnace, the gas environment was changed to argon; this prevented further oxidation but allowed annealing of the thermally grown silica to permit a complete transformation to cristobalite. After some time, the argon was replaced by oxygen, which allowed oxidation to continue. The oxidation rates were found to decrease by a factor of 30 for the fully crystalline scales, indicating that the permeation of oxygen through cristobalite is 30-fold slower than through amorphous silica. However, a major conclusion of these studies was that, for actual oxidation processes, this effect would not be observed. Full crystallization of the silica scale would not occur as the oxide formed at the SiC silica interface would be amorphous and transform to cristobalite slowly over time. In addition, the spherulitic structure has many grain and subgrain boundaries which provide paths for faster oxygen transport. Thus, even at the high temperatures where cristobalite is formed, the oxidation rate is controlled by oxygen permeation through the amorphous portion of the silica scale, at least for the oxidation times typically studied in laboratory experiments (on the order of 100 h).

Figure 1.7 Spherulitic structure of cristobalite formed on SiC oxidized for 24 h at 1400 °C.Reproduced with permission from Ref. [1]; © 1993, Blackwell Publishing.

It is generally agreed that silica crystallization would decrease the oxidation rate of silica-formers, and consequently an apparent downturn in the Ea would be observed at the temperature where crystallization begins. However, this suggestion conflicts with experimental observations that showed an increase in Ea [22–27], and indicating that silica crystallization is not the phenomenon responsible for the change.

1.2.2.2 Ionic Exchange with the Silica Network: Effect on SiC Oxidation

It has been shown in various studies [5,25] that ¹⁸O exchange with vitreous silica and thermally grown silica does increase as the temperature increases. Cawley and Boyce [31] have modeled this process and shown that, as the temperature is increased, the amount of exchange with the network oxygen also increases, while molecular oxygen permeates through this network to oxidize the underlying SiC. Whereas network exchange has been clearly demonstrated, the Ea results obtained for the oxidation of pure CVD SiC [9,28] have shown for pure materials that molecular permeation remains the dominant oxidation mechanism. Thus, an alternative mechanism must be responsible for the upturn in Ea observed in the above-cited studies.

1.2.2.3 Effects of Low-Level Impurities on SiC Oxidation

The results of Ogbuji and Opila [9], and also of Ramberg [28], have shown that in clean conditions for pure materials, an upturn in Ea for the oxidation of SiC is not observed. Thus, it is postulated that impurities in the oxidation environment were responsible for these results. It has been observed that low-level impurities from alumina furnace tubes result in higher rates of oxidation [9,32,33]. The structure of silica and transport of oxygen through silica are both very sensitive to impurities (as will be discussed below). The transport rates of impurities to the growing silica would be expected to increase with temperature, and result in an increasing impurity of the silica scale and correspondingly higher oxidation rates as the temperature was increased. This mechanism would result in an apparent increase in the Ea for oxidation. Ramberg [28] has also shown that this increase in oxidation rate is not observed for very pure SiC in clean environments, but it is observed for less-pure starting materials (such as siliconized SiC) in the same environment. Consequently, based on the difference between very clean oxidation environments and those containing low-level impurities, it can be concluded that the upturn in Ea observed at temperatures of about 1400 °C is the result of low-level impurities, and not crystallization of the silica scale or ionic-dominated diffusion.

1.2.3 Oxidation of Silica-Formers in the Presence of Low-Level Impurities

1.2.3.1 Effect of Alkali-Metal Impurities on the Oxidation of Silica-Formers

As noted in Section 1.2.1.1 and Figure 1.2c, alkali metals are silica network modifiers that cause the formation of non-bridging oxygen in the silica and alter the permeability of silica to oxidants. At low levels of sodium and potassium in the oxidation environment, a parabolic oxidation of both silicon carbide and silicon nitride in oxygen is observed, but at rates more rapid than in the pure condition [34–36]. These low levels of impurities tend to promote crystallization of the silica scale [33] (see Figure 1.8). At higher impurity levels, the oxidation rates become linear, the silica scale is no longer protective, and the reaction rates limit the oxidation rather than transport through the silica scale [36–38]. Under these conditions, the scale is an amorphous alkali-silicate [36–39].

Figure 1.8 Macrographs of CVD SiC coupons oxidized for 100 h at 1300 °C in dry flowing oxygen. The sample on the left was oxidized in an alumina furnace tube and has a crystalline oxide scale. The sample on the right was oxidized in a fused quartz furnace tube and has an amorphous oxide scale.Reproduced with permission from Ref. [33]; © 1995, Blackwell Publishing.

Impurities affect the oxidation rate of silicon nitride more dramatically than silicon carbide [34,35]. Zheng et al. [34,35] have proposed that Na can also disrupt the silicon oxynitride layer that forms between silicon nitride and silica. Fox showed that CVD silicon nitride oxidizes at essentially the same rate as SiC when in the presence of low levels of impurities from alumina furnace tubes [40], which suggests that the silicon oxynitride layer is no longer limiting the oxidation rate. Backhaus-Ricoult and Gogotsi failed to show any evidence of oxynitride formation for hot isostatically pressed silicon nitride [41]. Nonetheless, it is possible that either the impurities from this material or the oxidation environment may be responsible for the lack of observed silicon oxynitride formation. Notably, the oxidation rates in the latter study were significantly higher than those of CVD silicon nitride [9], indicating a possible impurity-dominated oxidation.

At low levels, impurities also affect the structure of silica. Indeed, it was observed that impurities from an alumina furnace tube cause crystallization of the silica scale formed on SiC [33]. Tridymite, which is thought to be stabilized by the presence of impurities [42], was also observed in addition to cristobalite. Under clean conditions crystallization was observed, though at higher temperatures (≥1300 °C) than were found in environments with low levels of impurities. Under clean conditions only cristobalite – not tridymite – was observed.

1.2.3.2 Effect of Aluminum Impurities on Silica-Formers

While the alkali metal and alkaline earths act as silica network modifiers, aluminum ions act as intermediate cations and can serve either as network modifiers or network formers. As a network former, aluminum replaces the silicon ion in the network. The 3+ charge of the aluminum ion on the Si⁴+ site requires charge compensation by an additional lower-valence cation to preserve charge neutrality. As a result, aluminum impurities tie up the alkali metals in the silica structure and prevent disruption of the silica network. This effect has been demonstrated experimentally, whereby Si3N4 has been ion-implanted with Al, and then exposed to oxidizing environments containing sodium [43–45]. Increasing amounts of Al implantation under otherwise very clean conditions resulted in lower oxidation rates. These results contrasted with those of experiments in which aluminum and sodium contamination of the silica from alumina furnace tubes resulted in increased oxidation rates for SiC [33]. Clearly, the impurity levels must be carefully controlled and aluminum must act as a network former in order for it to counteract the effects of sodium impurities.

1.2.4 Additive Effects on the Oxidation of Silica-Formers

Pure silicon nitride and silicon carbide are grown either by a CVD process, or by hot-pressing or sintering at very high temperatures. Second-phase additions are made to SiC and Si3N4 to enable the sintering or hot-pressing of these materials at lower temperatures than are possible for the pure carbides and nitrides. However, these sintering additives affect the oxidation resistance of the materials, as described below.

1.2.4.1 Al and B Additions to SiC: Effect on Oxidation Rates

Studies of commercially available SiC containing sintering aids of Al2O3 or B4C [46] have shown that the Al or B from the sintering additives migrate to the silica scale [47,48]. Oxidation rates are higher than expected for transport of molecular oxygen through a pure silica scale; furthermore, these oxidation rates are shown to increase as the amount of Al2O3 additive is increased [49]. As previously described for impurities in the sample or environment, when the sintering additives are incorporated into the silica scale and modify the silica network, the result is an increased oxidation rate of the SiC.

1.2.4.2 Effect of Sintering Additives on the Oxidation of Silicon Nitride

Typical additives to silicon nitride are MgO, Al2O3, Y2O3, La2O3, and other rare earth oxides. These oxides are often present between β-Si3N4 grains as silicate phases, and it had been observed that oxidation of the additive-containing Si3N4 was relatively insensitive to oxygen and nitrogen partial pressures [50,51]. A silica scale is formed that is enriched at the surface with acicular grains of MgSiO3 or M2Si2O7 (where M is any of the rare earth ions [52]), as shown in Figure 1.9. It has been established that cation diffusion of the additives through the silica scale controls the oxidation rate of these materials [53–55]. Experiments were conducted in which the oxide scale was removed and no subsequent increase in oxidation rate was observed upon reoxidation [53–55] (see Figure 1.10). These data confirmed that the oxidation rate was not controlled by the oxide thickness, but rather by the depletion of additive cations from the underlying material. The thermodynamic driving forces for this reaction have been established [56]: (i) the concentration gradient of the additive cation results in a diffusion of the cation to the surface of the silica; and (ii) the crystalline silicate forms at the silica surface due to a reduction in free energy by formation of the crystalline phase from the amorphous phase.

Figure 1.9 Surface SEM image of Y2O3-containing Si3N4 oxidized for 97 h at 1300 °C in dry oxygen, showing acicular grains of Y2Si2O7 formed by migration of yttria into the silica scale.Reproduced with permission from Ref. [1]; © 1993, Blackwell Publishing.

Figure 1.10 Oxidation and reoxidation of Si3N4 with MgO additives at 1371 °C.Reproduced with permission from Ref. [53]; © 1978, Blackwell Publishing.

The oxidation rates of the additive-containing materials are generally higher than those of the pure CVD Si3N4, for several reasons. First, the protective silicon oxynitride subscale does not develop in the additive-containing materials [41], although it has been observed to form a discontinuous secondary phase in the silicon nitride grain boundaries beneath the silica scale [57]. Second, the glassy secondary phases formed by the additives offer less resistance to oxygen permeation than pure silica. At higher temperatures (≥1300 °C), this glassy phase can melt and lower the oxidation resistance significantly [50,58]. The formation of high-temperature crystalline secondary phases, as observed for some rare earth additives, benefits the oxidation resistance of the overall material [59]. Finally, it should be pointed out that the penetration of oxygen through the secondary phases results in an internal oxidation of the Si3N4 during long-term, high-temperature exposures. This internal oxidation results in a degradation of the mechanical properties of the material [57].

1.2.5 Deposit-Induced Corrosion of Silicon-Based Ceramics

In many applications, such as heat engines and heat-exchangers, condensed phase deposits will form on hot parts. The most important type of deposit is sodium sulfate (Na2SO4), which is formed via the combination of sodium impurities in the air or fuel with sulfur impurities in the fuel [60]:

(10)

equation

This type of deposit-induced corrosion is termed hot corrosion, and extensive information is available on the hot corrosion of metals [61,62]. In addition to Na2SO4-induced hot corrosion, other deposits such as magnesium sulfate [63], oxide slags [64], and sodium vanadate [65,66] can induce corrosion. Here, attention will be focused on Na2SO4-induced corrosion, though the basic principles discussed apply equally to other systems.

Hot corrosion attack occurs in two steps: (i) deposition; and (ii) corrosive attack. Generally, Na2SO4 is most corrosive above its melting point (884 °C), but below its dew point, the latter being related to the sulfur and sodium content, together with the total pressure. Dew points can be calculated using a free-energy minimization code [67], and are shown in Figure 1.11 [1,68]. In general, the range of Na2SO4 attack is narrow (typically only 100 °C, with higher pressures increasing the dew point and hence temperature range), but it may be quite severe when it does occur.

Figure 1.11 Calculated dew points for Na2SO4 deposition as a function of sulfur content of fuel as well as Na content.Reproduced with permission from Ref. [1]; © 1993, Blackwell Publishing.

A laboratory simulation of deposition and corrosive attack is challenging, and various methods have been used. Important issues include deposition rates as well as temperature, pressure, and velocity effects. The closest simulation to a heat engine is a fuel burner seeded with salt to form Na2SO4 [69], although such tests are expensive and it is difficult to control all parameters. The most common laboratory test involves airbrushing an aqueous Na2SO4 solution onto the sample and allowing the water to evaporate, leaving a thin film of Na2SO4. The sample is then exposed in a furnace, ideally with a set pressure of SO3 (or SO2/O2) to establish a fixed activity of Na2O [70]. Although such a test is easily conducted and allows the parameters to be accurately controlled, a one-time deposition of Na2SO4 may not serve as an adequate simulation of an actual heat engine situation. Other laboratory tests involve a two-zone furnace where a container of salt is heated in one zone while the sample is placed in a downstream zone [71]. These tests are more complex, but they create a more realistic continuous deposition situation.

Hot corrosion is generally described by a sulfidation and/or an oxide fluxing mechanism [72]. As condensed-phase silicon sulfide is not a thermodynamically stable compound, the sulfidation mechanism is not applicable to silicon-based ceramics. However, the process is described very well by an oxide fluxing mechanism that is based on the concept of acidic and basic oxides, as developed by Lux [72] and Flood and Förland [73]. By analogy with aqueous solutions, oxide reactions can be written as:

(11a) equation

(11b) equation

SiO2 is known to be an acidic oxide, and Na2O is a basic oxide. The acidity of an aqueous solution is obtained by measuring the activity of the hydrogen cation:

(12) equation

By analogy, the basicity of a molten salt is obtained by measuring the activity of the oxide anion.

(13a) equation

(13b) equation

The example in Eq. (11b) is actually the key reaction in the Na2SO4-induced corrosion of ceramics. The reactive component of Na2SO4 is Na2O formed by:

(14) equation

The equilibrium constant, Kp, for Eq. (14) is given by:

(15)

equation

where ΔG is the free energy change of reaction (14), R is the gas constant, T is the absolute temperature, a is activity, and P is pressure. In this case, a low thermodynamic activity of Na2O [a (Na2O)] set by a high partial pressure of SO3 [P (SO3)], is termed an acidic molten salt. A high thermodynamic activity of Na2O, set by a low P (SO3), is termed a basic molten salt. The activity of Na2O determines the feasibility of Eq. (11b), and it is thus critical to measure this value. In the melt at high temperatures, Na2O fully dissociates to the sodium cation and oxygen anion, and the activity of Na2O is taken equal to the activity of O=.

Just as a pH meter is used to measure acidity/basicity in an aqueous solution, a high-temperature electrochemical cell is used to measure oxide ion activity. Although many reports have been made of studies of suitable cells [74], the following cell is generally agreed to give the most suitable results:

(16)

equation

According to standard electrochemical cell notation, the vertical lines represent phase boundaries. The cell consists of two sections: the left-hand side measures the activity of O=, with the oxygen reference, denoted by O2(r), as the partial pressure of oxygen. The right-hand side measures the Na+ activity, with a Na2SO4–10 m/o Ag2SO4 reference electrode. It should be noted that other forms of Na+ conductors, such as β-Al2O3 or SiO2 glasses [61], have been used in place of the mullite membrane. The overall reaction is:

(17)

equation

By using thermodynamic data for these compounds from the JANAF tables [75,76], the following expression relates the measured voltage, E, to the thermodynamic activity of Na2O, a(Na2O) at 900 °C:

(18) equation

Actual measurements taken with the cell [68] for Na2SO4/SO3 and Na2SO4/SO3 with carbon are shown in Figure 1.12. The a (Na2O) results for Na2SO4/SO3 are close to those predicted. However, it should be noted that the carbon additions drive the melt basic, until it is consumed. This is an important result for silicon-based ceramics which often contain combined or free carbon.

Figure 1.12 Measured Na2O activities in Na2SO4 melts. SO3 gas compositions are shown as percentage.Reproduced with permission from Ref. [68]; © 1989, Springer Science and Business Media.

Given a known activity of Na2O, the next step is to determine if the activity is sufficient for reaction with SiO2:

(19) equation

This is simply a form of Eq. (11b). In an acidic molten salt, the dissolution of silica is minimal [77]; this contrasts with other oxides, which exhibit dissolution in both basic and acidic melts [61]. Figure 1.13 is a phase diagram calculated for the Na2O-SiO2 system [78], using a commercial free energy minimization code and database [79]. The diagram indicates the various sodium silicates formed at a particular temperature and activity of Na2O. Consider the bold line between the silica-rich sodium silicates and silica. This boundary provides a convenient method to predict dissolution of silica. If the P (SO3) over the Na2SO4 deposit leads to a (Na2O) greater than that given by the boundary in the figure, then dissolution will occur. This method has been used in a model situation in a burner to predict the behavior of quartz and fuels with different sulfur levels. The higher sulfur fuel (i.e., diesel) led to a low a (Na2O) and hence limited attack, whereas the lower-sulfur fuel (i.e., Jet A) led to a higher a (Na2O) and hence dissolution [68]. While the use of higher-sulfur fuels is not a practical way to control corrosion, it does confirm and illustrate the mechanism described by Eq. (19).

Figure 1.13 Activity of Na2O versus temperature phase diagram showing dissolution limit.Reproduced with permission from Ref. [78]; © 2005, ASM International.

Equation (19) above indicates the conversion of a solid, protective SiO2 film to a liquid sodium silicate. Transport rates of oxygen through the liquid sodium silicate are much faster than transport of oxygen through solid SiO2, so the underlying SiC or Si3N4 oxidizes readily, creating more SiO2 for dissolution. Hot corrosion is best described by a coupling of SiO2 formation on SiC or Si3N4, followed by dissolution according to Eq. (19). With a one-time deposition of a basic Na2O-containing deposit, it has been shown that these reactions continue until enough silica is formed so that the liquidus boundary of Na2O·x (SiO2)(l)/SiO2(s) (Figure 1.14) [80] is reached [81,82]. After the corrosion products form a layer of SiO2 at this liquidus boundary, the reaction slows. Figure 1.15 shows a cross-section of a sample of sintered α-SiC corroded with a film of Na2CO3, which is a strongly basic salt; the resultant Na2O·x (SiO2)/SiO2/SiC structure is shown. However, in a continuous-deposition situation there is no limit on the coupled oxidation/dissolution reactions, and this leads to very thick scales and substantial consumption of the ceramic.

Figure 1.14 Temperature versus composition phase diagram for the Na2O–SiO2 psuedo-binary. Dissolution of SiO2 continues until the liquid/tridymite boundary is reached.Reproduced with permission from Ref. [80]; © 2001, The Electrochemical Society.

Figure 1.15 Cross-section of sintered α-SiC with excess carbon corroded with a film of Na2CO3 for 48 h at 1000 °C.Reproduced with permission from Ref. [82]; © 1986, Blackwell Publishing.

The kinetics of this process are rapid due to the presence of a liquid film. The thick film shown in Figure 1.15 suggests the existence of rates of consumption that are several orders of magnitude greater than pure oxidation. Indeed, when Sun et al. [71] performed controlled experiments on the corrosion of Si3N4, using NaNO3 as a source of Na2O, they found linear reaction rates which indicated that diffusion was so rapid that it was the interface oxidation reaction which controlled the rate.

One important aspect of Na2SO4-induced corrosion on SiC and Si3N4 is the morphology of attack. The silica and silicate products can be cleanly removed with HF, leaving behind the SiC or Si3N4 substrate. Extensive grain boundary etching and pitting attack is observed, particularly on SiC [83]. Although exact mechanism of pitting is unknown, it appears that the grain boundaries are attacked preferentially and that grains are pulled out. Larger pits are associated with gas evolution and bubble formation in the oxidation/dissolution reactions; an example is shown in Figure 1.16. It should be noted that the pits are best revealed by removing the oxide and silicate corrosion film with HF. Pitting in a monolithic ceramic is significant as it leads to substantial strength degradation [84–88]. Detailed fractography reveals that the fracture origin is often a corrosion pit [86].

Figure 1.16 Sequence showing sintered SiC with boron and carbon additives. (a) Before corrosion; (b) After corrosion with Na2SO4/(0.01 SO3 + O2) at 1273 K for 48 h showing glassy product layer; (c) With glassy product layer removed using HF, to reveal highly pitted SiC.Reproduced with permission from Ref. [1]; © 1993, Blackwell Publishing.

These principles of SiO2 dissolution by a basic molten salt also describe corrosion by other condensed-phase deposits. Slags are complex oxide mixtures that may be deposited during coal combustion or other industrial processes, and their acidity/basicity depends on the relative amounts of acidic and basic oxides present:

Acidic oxides: SiO2, Al2O3, TiO2

Basic oxides: Na2O, K2O, MgO, CaO, Fe2O3

Basic slags clearly corrode SiC more than acidic slags [64,89]. In regions of low oxygen potential, Fe and Ni silicides are formed.

Lower-purity fuels contain vanadates and, as these fuels are necessarily utilized to a greater extent, corrosion by V2O5 will be important. Although V2O5 is an acidic oxide and forms no pseudo-binary compounds with SiO2, experimental results have indicated that V2O5 leads to a corrosion of SiC [65,66,90]. The V2O5–SiO2 phase diagram indicates that V2O5 forms a low-melting liquid (melting point 667 °C) with a limited solubility for SiO2. Thus, V2O5 is in direct contact with the SiC or Si3N5 and serves as a rapid path for oxygen to attack the ceramic substrate. V2O5 may also react with Na2O and other basic oxides to form complex melts.

1.2.6 Temperature Cycling

So far in this chapter, only isothermal exposures of silica-forming materials in oxidizing environments have been considered, but in many oxidizing applications SiC or Si3N4 will also undergo temperature cycling. The theory describing stress generation and oxide spallation has been extensively developed and verified experimentally for the thermal cycling of metals [91,92]. A simple expression to describe the thermal stresses generated in the oxide, σox, is:

(20) equation

where Eox is Young's modulus of the oxide, ΔT is the temperature change, and Δα is the difference in thermal expansion coefficient between the oxide and the substrate. For most metals, the coefficient of thermal expansion (CTE) is higher for the metal than for the oxide so that, upon cooling, the oxide is placed in compression, wherein it buckles, and spalls. For most real long-term applications of SiC and Si3N4, the oxide scale will be cristobalite. It can be seen from Figure 1.17 that the thermal expansion of cristobalite is greater than that of SiC and Si3N4. Upon cooling, the oxide will be placed in tension and tensile cracks are likely to form. The long-term thermal cycling of SiC and Si3N4 shows that, despite these tensile cracks, the oxide does not spall and oxidation rates are relatively unaffected [94]. Figure 1.18 shows cyclic oxidation kinetic results for several silica-forming ceramics. In general, parabolic-like oxidation is still observed, with gains in weight and the overall oxidation rate slowing with time. These results imply that, upon reheating, the tensile cracks will heal sufficiently to allow a protective behavior of the silica scale. In contrast, for most metals an initial weight gain would be observed, followed by a linear weight loss as the oxide grows, spalls, and reforms [95]. Oxide spallation leads to higher consumption rates of the underlying material.

Figure 1.17 Coefficients of thermal expansion for cristobalite, α-SiC, α- Si3N4, and amorphous silica as a function of temperature.Reproduced with permission from Ref. [93]; © 2003, ASME Press.

Figure 1.18 Weight change for SiC and Si3N4 oxidized for 200 cycles each of 5 h at 1300 °C in air.Reproduced with permission from Ref. [10]; © 2000, Wiley-VCH Verlag GmbH & Co. KGaA.

During thermal cycling, the silica scale transforms from the high-temperature β- to the low-temperature α-cristobalite at temperatures between 200 and 270 °C [96]. This transformation is displacive and reversible, but is accompanied by a 2.8% decrease in volume [97] that may cause additional cracking of the silica scale as it cools. Despite both the stresses due to CTE mismatch and cristobalite transformation, the results in Figure 1.18 demonstrate that any effects of this transformation will have a minimal effect on the protective capability of the silica scale.

1.2.7 Oxidation of Silica-Formers in Other Oxidants

So far, all of the results described for the oxidation of silica-forming ceramics have been obtained in oxygen or air. Yet, combustion environments are more complex and contain H2O and CO2 in significant amounts; for example, if a combustion is fuel-rich, then CO and H2 will also be found. The effect of these additional gas-phase constituents on the oxidation of SiC and Si3N4 will now be described, beginning with water vapor.

1.2.7.1 Oxidation of Silica-Formers in Other Oxidants: H2O

Water vapor has three important effects on the oxidation of silica-forming materials:

It increases the transport of impurities to the growing silica, extrinsically increasing the oxidation rate of silica-formers.

It intrinsically increases the oxidation rate of silica-formers due to the high solubility of water vapor in silica.

It reacts with the growing silica to form volatile silicon hydroxide species.

Each of these effects increases the recession rate of the underlying material, and will be discussed in detail below. Thus, water vapor is detrimental to the use of SiC and Si3N4 for long-term applications in combustion environments.

Extrinsic Effects of Water Vapor on the Oxidation of Silica-Formers: Impurity Transport

Water vapor reacts with many metals or metal oxides to form very stable hydroxide vapor species by reactions of the type:

(21) equation

For example, an increased transport of sodium impurities from furnace tubes to SiC in wet oxidation experiments was attributed to NaOH(g) formation [98]. Pareek and Shores [36] intentionally added water vapor to their oxidizing stream to control the amount of potassium transport to SiC when studying potassium effects on oxidation. The activity of K-containing vapor species formed from K2CO3 was substantially increased by the addition of water vapor to the gas stream. Na and K cations are silica network modifiers, and transport of these hydroxides to the growing silica scale results in the formation of less-protective silica and extrinsically increased rates of oxidation [98]. These effects have already been introduced earlier in the chapter (see Sections 1.2.1.1 and 1.2.2.3).

Intrinsic Effects of Water Vapor on the Oxidation of Silica-Formers: Silicon

To date, many studies have been conducted on the oxidation of silicon in water vapor due to the importance of silicon oxidation in semiconductor device fabrication. The classic study of Deal and Grove [7] describes the important results for silicon oxidation. First, the parabolic rates of oxidation in wet oxygen are significantly higher than those observed in dry oxygen, as shown in Figure 1.19. The Ea for a parabolic oxidation of Si in water vapor is 68 kJ mol−1, which is in agreement with the results of Moulson and Roberts for the transport of water vapor through silica [99]. However, this Ea value is somewhat less than that for molecular oxygen transport through silica, a fact attributed to the relatively smaller size of the water molecule compared to the oxygen molecule [100]. The parabolic rate constant, B, is a product of the effective diffusivity of the oxidant in silica, Deff, and the solubility, C *, of that oxidant in silica:

(22) equation

where N is the number of oxidant molecules incorporated into a unit volume of oxide. Deal and Grove have shown that the temperature dependence of oxidation in oxygen and water vapor is in agreement with the diffusivity of these oxidants in silica, but that the increased oxidation rate of silicon in water vapor cannot be explained by a higher value of Deff for water vapor. In fact, the effective diffusivity of water vapor in silica is about an order of magnitude slower than that of oxygen, as shown in Figure 1.20. The increased oxidation rate of silicon in water vapor is therefore attributed to a much greater solubility of water vapor in silica than oxygen (it is almost three orders of magnitude higher). The solubilities of the oxidant in silica have been determined for oxygen and water vapor by Norton [4] and Moulson and Roberts [99], respectively. The magnitudes of the measured solubilities are in agreement with values reported by Deal and Grove [7]. Doremus [101] attributed the solubility of water in silica to the formation of SiOH groups by the following reaction:

(23) equation

The OH groups are relatively immobile and diffusion of molecular water is the mechanism by which water diffuses in silica. Another important result is that the solubilities of both oxygen and water vapor are nearly independent of temperature over the temperature range of interest. Any temperature dependence of the parabolic rate constant therefore arises from the temperature dependence of the effective diffusivity.

Figure 1.19 Parabolic oxidation rate constants for Si oxidation in dry O2 and wet O2.Reproduced with permission from Ref. [7]; © 1965, The American Institute of Physics.

Figure 1.20 Diffusivities of molecular O2 and H2O in amorphous silica.Reproduced with permission from Ref. [7]; © 1965, The American Institute of Physics.

Deal and Grove [7] have also measured the pressure dependence for the parabolic oxidation of silicon in water vapor, as shown in Figure 1.21. The parabolic rate constant was directly proportional to the water vapor partial pressure, thus confirming that transport of water through the growing silica scale occurs by the permeation of molecular water.

Figure 1.21 Parabolic rate constant, B, for silicon oxidation in O2 and H2O is shown to be proportional to the oxidant pressure.Reproduced with permission from Ref. [7]. © 1965, The American Institute of Physics.

Intrinsic Effects of Water Vapor on the Oxidation of Silica-Formers: Silicon Carbide and Silicon Nitride

The oxidation rate of SiC and Si3N4 is also expected to intrinsically increase in water vapor relative to oxygen, due to the increased solubility of water vapor in silica. Typically, the oxidation of SiC and Si3N4 is conducted at temperatures higher than those for silicon, so the effects of impurities and silica volatility (see Section 1.2.7.3) are also enhanced and more difficult to separate from intrinsic effects. Studies in which these effects are separated from intrinsic oxidation have shown that the parabolic oxidation rate is increased in water vapor for both SiC [95–102,103] and Si3N4 [58]. The variation in parabolic oxidation rate with water vapor partial pressure has been studied for SiC (see Figure 1.22) [102–105]. The oxidation rate is found to be proportional to P (H2O)n, with the power law exponent (n) approaching one. The results obtained at water vapor partial pressures less than 1 atm have not been corrected for contributions of oxygen present in the carrier gas, and the power law exponents are expected to be higher than shown. A power law exponent of one indicates that oxidation occurs by molecular transport of water vapor. These results are consistent with those of Deal and Grove [7] for the oxidation of silicon in water vapor and the transport of water vapor in silica [101]. The lower temperature dependence for the oxidation of SiC in water vapor relative to the values obtained in dry oxygen is also consistent with molecular water vapor permeation through silica [103].

Figure 1.22 Parabolic rate constant for SiC in H2O is shown to be proportional to the water vapor partial pressure with a power law exponent approaching one.Reproduced with permission from Ref. [105]; © 2002, Techna Group Srl.

Intrinsic Effects of Water Vapor on the Oxidation of Silica-Formers: Effects on the Properties of Silica

Water vapor is known to affect the properties of silica, which in turn will affect the transport of water vapor during the oxidation of silica-formers. Two major effects are noted here:

Water vapor is known to lower the viscosity of silica [106]. Water vapor lowers the activation energy for viscous flow.

Water vapor has been shown to increase the crystallization growth rate by about a factor of two, but was found to have little effect on the nucleation rate of cristobalite [102,107].

Since water vapor increases the transport of impurities through the vapor phase, and impurities cause the crystallization of silica (see Section 1.2.3.1), it is difficult to separate the intrinsic effects of water vapor on crystallization from extrinsic, impurity-related effects.

Intrinsic Effects of Water Vapor on the Oxidation of Silica-Formers: Porous Scale Formation

It has been observed in several studies that the oxidation of SiC and Si3N4 in high-pressure water vapor results in the