Promoting
α-Al
2O
3layer growth upon high
temperature oxidation of NiCoCrAlY alloys
Bevorderen van
α-Al
2O
3laaggroei tijdens hoge
Promoting
α-Al
2O
3layer growth upon high
temperature oxidation of NiCoCrAlY alloys
Bevorderen van α-Al
2O
3laaggroei tijdens hoge temperatuur oxidatie van
NiCoCrAlY legeringen
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op maandag 14 november 2005 om 15.30 uur
door
Thijs Joost NIJDAM
materiaalkundig ingenieur geboren te Kerkrade
Toegevoegd promotor: Dr. ir. W.G. Sloof
Samenstelling promotiecommissie: Rector Magnificus, voorzitter
Prof. dr. B.J. Thijsse, Technische Universiteit Delft, promotor
Dr. ir. W.G. Sloof, Technische Universiteit Delft, toegevoegd promotor Prof. dr. J.H.W. de Wit, Technische Universiteit Delft
Prof. dr. ir. S. van der Zwaag, Technische Universiteit Delft
Prof. dr.-Ing. M. Schütze, Rheinisch-Westfälische Technische Hochschule Aachen, Duitsland Prof. dr.-Ing. C. Leyens, Brandenburgische Technische Universität Cottbus, Duitsland
Dr. L.P.H. Jeurgens, Max Planck Institut für Metallforschung, Duitsland
The work described in this thesis was made possible by financial support from the Technology Foundation STW.
ISBN-10: 90-90199-10-1 ISBN-13: 978-90-90199-10-8 Copyright © by T.J. Nijdam
Chapter I General Introduction 1
Part A Modelling the high temperature oxidation of γ-NiCrAl alloys 9
Chapter II Modelling the thermal oxidation of ternary alloys – compositional changes in the alloy and the development of oxide phases
11 Chapter III Promoting exclusive α-Al2O3 growth upon high temperature
oxidation of NiCrAl alloys: experiment versus model predictions
35 Chapter IV Oxide phase development upon high temperature oxidation of
γ-NiCrAl alloys
57
Part B Microstructure refinement of γ+β NiCoCrAlY alloys 75
Chapter V Microstructure refinement of NiCoCrAlY alloys by laser surface melting
77 Chapter VI The effects of alloy microstructure refinement on the short-term
thermal oxidation of NiCoCrAlY alloys
99
Part C Pre-oxidation of NiCoCrAlY bond coatings 121
Chapter VII On the microstructure of the initial oxide grown by controlled annealing and oxidation on a NiCoCrAlY bond coating
123 Chapter VIII The role of transient oxides during deposition and thermal cycling of
thermal barrier coatings
147 Chapter IX Development of a pre-oxidation treatment to improve the adhesion
between thermal barrier coatings and NiCoCrAlY bond coatings
165
Summary 193
Samenvatting 197
Curriculum vitae 201
General Introduction
NiCoCrAlY alloys are used as a coating material for high temperature applications to protect an underlying load bearing substrate against high temperature oxidation and corrosion. Good protection against high temperature corrosion is offered when a continuous α-Al2O3 layer is formed exclusively on top of this alloy. In this thesis, the fundamental aspects and the processing windows for promoting the growth of an α-Al2O3 layer on NiCoCrAlY alloys by thermal oxidation are addressed.
Application
Gas turbine engines are capable of generating large amounts of useful power for a relatively small weight and size in a relatively short amount of time. These factors make this engine a good choice for the propulsion of aircrafts and marine vessels or for generating electricity [1]. A gas turbine engine has three basic parts (Fig. 1): (i) the compressor to draw in and compress gas (most usually air) from the surrounding, (ii) the combustor, where fuel is added to heat the compressed air, and (iii) the turbine to extract energy from the hot gas stream coming from the combustor.
Figure 1 Cross-section of a gas turbine engine for aircraft propulsion. The approximate locations of
Figure 2 Turbine blades coated with Thermal Barrier Coating (TBC).
Part of the output power of the turbine is used to drive the compressor. The remainder of the energy is either accelerated into the atmosphere through a nozzle (Fig. 1) to provide thrust or propulsion power, or used to turn an energy conversion device, such as an electrical generator or a ship’s propeller [1].
The demand for higher efficiency of energy conversion makes higher engine operating temperatures necessary. Higher engine efficiency is not only economically beneficial, but it is also advantageous for the environment. Saving fuel reduces the emissions of CO2 and other exhaust gasses that may lead to global warming [1-3]. A drawback of increasing the operating temperature is the enhanced emission of NOx [4]. However, this problem may be solved by
changing the engine design [4].
The use of higher operating temperatures in combination with an aggressive environment puts high demands on materials, in particular on the materials used in the first row of rotating blades (Fig. 2) and stationary vanes of the turbine, where the temperatures are highest. Materials with both excellent mechanical properties and oxidation resistance at high temperature are required. Currently, there is no single material available that can fulfil both these requirements satisfactory. Therefore, generally a combination of materials is used, consisting of a metallic substrate, a metallic Bond Coating (BC) and a ceramic Thermal Barrier Coating (TBC) on top [5-12]. This combination of materials is further referred to as High Temperature (HT) coating system (Fig. 3).
Figure 3 Schematic illustration of a high temperature coating system.
Anatomy of the High Temperature coating system
Substrate
Ni based superalloys, which are air cooled from the inside or through internal hollow channels, are used as the substrate material [9-13]. The superalloy is designed to provide the high temperature strength of the turbine blade. Over the years, the strength of the superalloys has evolved considerably due to advances in casting technology and alloy design [6-13]. This has allowed the superalloys to be used at ever-higher operating temperatures (Fig. 4 and Refs. [6,11]). State-of-the-art turbine blades with cooling holes are cast as single crystals or in textured polycrystalline forms and next to Ni contain many additional elements, such as Co, Cr, Al, Mo, W, Ta, Re, Ti, Y and/or Hf.
Bond Coating (BC) and Thermally Grown Oxide (TGO)
Unfortunately, the improvement of high temperature strength and creep resistance of the superalloys has been obtained at the expense of the resistance of the superalloy against high temperature oxidation [10,13]. On a superalloy surface, generally, large amounts of fast-growing oxide products develop, which ultimately results in loss of structural integrity [10,13-17]. Oxidation of the superalloy is inevitable, since the TBC is ‘oxygen-transparent’ (due to the porous structure of the TBC and the high ionic diffusivity of oxygen in ZrO2 [9]). Therefore, a Bond Coating (BC) is applied in between the TBC and the superalloy (Fig. 3).
Figure 4 Increase of the operating temperatures in gas turbine engines, made possible by
improvements in alloy design and casting technology, as well as by the application of Thermal Barrier Coatings (after Ref. [6]).
The protection offered by the BC against high temperature oxidation and corrosion relies on the formation of a stable, slow-growing, adherent, continuous oxide layer over its surface, the Thermally Grown Oxide (TGO). This TGO serves as a barrier between the remaining unoxidised alloy and the environment [10,13-17]. For applications where the operating temperature is above 1273 K, α-Al2O3 is the principal oxide required for protection. The rates of metal and oxygen diffusion in this oxide are very low [13,16] and α-Al2O3 has a large negative Gibbs free energy of formation, such that the Al in the BC is oxidised preferentially [14].
Over the years, two major classes of bond coatings have been developed to ensure the formation of a continuous α-Al2O3 layer on their surface: Pt modified nickel aluminide and
MCrAlX (where M = Ni and/or Co, and X is a small amount of one or more reactive elements,
e.g. Y, Zr, Hf [6-12]). In this thesis, only the MCrAlX bond coatings are considered. Typical
MCrAlX coatings have a dual phase microstructure, consisting of an Al rich β phase (NiAl) and an Al poor γ phase (Ni solid solution). The role of the reactive element(s) X is mainly to improve the adhesion between the TGO and the BC [9,10,17]. This is accomplished by scavenging of the impurities (S, C, etc.) in the BC, thereby preventing these impurities to segregate to and weaken the TGO/BC interface [9,17].
Thermal Barrier Coating (TBC)
The primary function of the TBC is to provide a low thermal conductivity barrier to heat transfer from the hot gasses in the engine to the surface of the superalloy [5-12]. In combination with internal component cooling, the TBC can establish a thermal gradient of 150 - 200 K across its thickness [5-12]. In engine design the properties of the TBC can be utilised in three different ways [6]:
• Reduce the surface temperature of the superalloy substrate for a given cooling air flow and gas temperature.
• Reduce the amount of cooling air for a given superalloy surface and gas temperature. • Allow for a higher gas and superalloy surface temperature for a given cooling air flow
(Fig. 4).
Reduced metal surface temperatures result in prolonged lifetimes of the turbine blades, since a lower superalloy surface temperature (i) retards the onset of thermal fatigue (ii) reduces the rate of BC oxidation (which is a thermally activated process [14]). Reduced flows of cooling airs or higher turbine inlet temperatures improve the efficiency of the gas turbine engine.
A modern TBC consists of Partially Yttria (6-8 wt%) Stabilised Zirconia (PYSZ). ZrO2 has a combination of advantageous properties, such as a relatively low thermal conductivity, a high thermal expansion coefficient as compared to other ceramics (11-13x10-6 C-1 [8]), and a low density (important for minimising weight in rotating components). The addition of 6 to 8 wt% Y2O3 to ZrO2 is necessary to stabilise the metastable tetragonal phase (t´) of ZrO2, which does not transform upon cooling [6,7,11]. If ZrO2 is not stabilised, it will transform to monoclinic and cubic ZrO2 upon cooling. Such a phase transformation is associated with a volume increase and thus generates high stresses in the TBC. Then cracking and spallation of the TBC will occur [12].
In practice, generally, two methods are used to deposit the TBCs, namely Air Plasma Spraying (APS) and Electron Beam - Physical Vapour Deposition (EB-PVD). Both deposition methods result in different TBC microstructures [6-12]. For the EB-PVD process, the deposition conditions are chosen such that a disconnected columnar grain structure
perpendicular to the TBC surface develops. Such a structure provides a low overall elastic
modulus and thus a high ‘strain tolerance’ upon thermal cycling (i.e. the disconnected columns can separate at high temperature). The disconnected microstructure also helps to reduce the thermal conductivity of the TBC (1.5-2.0 W/mK for an EB-PVD TBC, and 2.3 W/mK for fully dense ZrO2 at 1273 K, respectively [9]). The much cheaper APS process is
structure helps to reduce the thermal conductivity of the TBC even further (to 0.8-1.7 W/mK [9]), but the ‘strain tolerance’ of this microstructure is inferior to that of the EB-PVD coatings [6-12].
A shortcoming of PYSZ is its inability to retain its advantageous properties for longer times at high temperatures. Above 1473 K, the metastable tetragonal phase decomposes, and the columnar structure of the PYSZ densifies rapidly due to sintering [6,7,11]. Sintering increases the elastic modulus of the TBC and thereby decreases its ‘strain tolerance’ [5,6,11]. Therefore, a search has begun for alternative ceramics that have a lower thermal conductivity, improved structural stability and reduced sintering rates at high temperatures [5-12].
The role of oxidation in the failure of the HT coating system
Current state-of-the-art HT coating systems are mainly used to prolong the life span of turbine components [6,7,9]. The full potentials of TBCs for higher engine efficiency are often not realised due to failure of the HT coating system before the ultimate lifetime of the blade (superalloy substrate) is reached [6,7,9]. Many factors can contribute to the failure of the HT coating system, since at the high operating temperatures the four constituents of the coating system interact with each other (e.g. compositional and microstructural changes in the BC due to oxidation and BC/superalloy interdiffusion 12]). However, it is generally recognised [6-12] that the two most important factors that drive the failure of the HT coating system during service are (i) the growth of the TGO and (ii) the mismatch strain within this TGO, as generated upon cooling due to the different coefficients of thermal expansion between the TGO (8-9x10-6 C-1 [8]) and the underlying substrate (13-15x10-6 C-1 [8]).
To enhance the life span of turbine components during service it is crucial to control the chemical composition, structure, morphology, and phase constitution (i.e. microstructure) of the TGO. Control of the TGO microstructure is of particular importance during the early stages of the oxidation process (prior to the development of the continuous α-Al2O3 layer), since the eventual microstructure and growth kinetics of the TGO after prolonged exposure (i.e. during service of the gas turbine) are too a large extent dependent on how the TGO establishes itself during these early oxidation stages.
For the high temperature oxidation of MCrAlX alloys, the early oxidation stages are generally associated with the simultaneous formation of α-Al2O3 and one or more fast growing, less protective oxide phases (also referred to as transient oxides [18-23]), such as (i) the Ni, Cr and/or Co-rich oxides Cr2O3, NiO, NiCr2O4 and NiAl2O4 [19-21], (ii) the metastable alumina phases γ or θ-Al2O3 [21-23], and (iii) the reactive element oxides Y2O3, YAlO3 and Y3Al5O12 [24,25]. Which less protective oxide(s) develop and to what extent is
determined by a complex interplay between the composition, microstructure and surface condition of the BC, the heating rate and atmosphere prior to oxidation, and the oxidation conditions, i.e. oxidation time, temperature and partial oxygen pressure (pO2) [14,16]. The formation of the less protective oxides is considered undesired, because they may promote the failure of the HT coating system upon thermal cycling [5]. Thus, ideally the formation of an oxide layer solely constituted of α-Al2O3 is preferred on the BC surface. To realise the formation of this advantageous TGO during service of the HT coating system, it is proposed to apply a combined BC pre-annealing and pre-oxidation treatment prior to the deposition of the TBC.
Outline of the thesis
To control the exclusive formation of α-Al2O3 at the onset of oxidation requires comprehensive and fundamental knowledge on the relations between the oxidation mechanism(s) and the composition and phase constitution of the developing oxide and underlying bond coating. To this end, a general Coupled Thermodynamic - Kinetic (CTK) oxidation model is presented in part A of this thesis. The CTK oxidation model computes the concentration depth profiles of the alloy elements in the BC alloy, as well as the amount of each oxide phase formed as a function of oxidation time (including the formation of less protective oxides during the initial, fast oxidation stage, see Chapter II). To verify the model calculations, the CTK model is applied to the high temperature oxidation of a single phase γ-Ni-27Cr-9Al (at.%) alloy (Chapters III and IV).
The effect of alloy microstructure refinement on the early stages of high temperature oxidation of dual phase γ+β NiCoCrAlY alloys is the topic of Part B of this thesis. Microstructure refinement is achieved by Laser Surface Melting (LSM) and EB-PVD of an as cast NiCoCrAlY alloy. To predict the degree of microstructure refinement accomplished with LSM, the relationships between laser processing conditions and alloy microstructure are established for the LSM of an as cast γ+β Ni-20Co-19Cr-24Al-0.2Y (at.%) alloy (Chapter V). The role of alloy microstructure on the formation and growth of an exclusive α-Al2O3 layer during the initial fast oxidation stages is described in Chapter VI.
Controlled pre-annealing and pre-oxidation, as a method to promote the exclusive formation of α-Al2O3 on the BC surface during the production and service of an actual HT coating system (René N5 superalloy / NiCoCrAlY BC / PYSZ TBC), is explored in part C of this thesis. First, the effects of the pre-oxidation parameters on the microstructure of the developed oxide layer after pre-oxidation are investigated for a γ+β Ni-20Co-18Cr-22Al-0.2Y
TGO upon TBC deposition and thermal cycling of the entire HT coating system are discussed for the different pre-oxidation treatments (Chapter VIII). Finally, the effects of the different TGO microstructures after pre-oxidation on the failure mechanisms and life span of the entire HT coating system upon thermal cycling are considered (chapter IX).
References
[1] LS Langston, G Opdyke Jr, Introduction to Gas Turbines for Non-Engineers (1997). http:// www.asme.org/igti/resources/articles/intro2gta.html.
[2] GW Goward, Surf Coat Technol, 108-109 (1998) 73. [3] C Coddet, Mater Sci Forum, 461-464 (2004) 193.
[4] J.E. Penner, D.H. Lister, D.J. Griggs, D.J. Dokken, M. McFarland, Aviation and the Global Atmosphere, Cambridge University Press (1999). http://www.grida.no/climate/ipcc/aviation/index.htm.
[5] MJ Stiger, NM Yanar, MG Topping, FS Pettit, GH Meier, Z Metallkde, 90 (1999) 1069. [6] M Peters, C Leyens, U Schulz, WA Kaysser, Adv Eng Mater, 3 (2001) 193.
[7] C Leyens, U Schulz, K Fritscher, M Bartsch, M Peters, WA Kaysser, Z Metallkde, 92 (2001) 762. [8] AG Evans, DR Mumm, JW Hutchinson, GH Meier, FS Pettit, Prog Mater Sci, 46 (2001) 505. [9] NP Padture, M Gell, EH Jordan, Science, 296(5566) (2002) 280.
[10] JR Nicholls, MRS Bull, 28 (2003) 659.
[11] DR Clarke, CG Levi, Ann Rev Mater Res, 33 (2003) 383. [12] CG Levi, Curr Opin Solid State Mater Sci, 8 (2004) 77. [13] GR Wallwork, AZ Hed, Oxid Met, 3 (1971) 171.
[14] P Kofstad, High Temperature Corrosion, Elsevier Applied Science, London and New York (1988). [15] GC Wood, FH Stott, Mater Sci Technol, 3 (1987) 519.
[16] MP Brady, B Gleeson, IG Wright, JOM, 52 (2000) 16. [17] JL Smialek, Surf Interface Anal, 31 (2001) 582.
[18] CS Giggins, FS Pettit, J Electrochem Soc, 118 (1971) 1782.
[19] BH Kear, FS Pettit, DE Fornwalt, LP Lemaire, Oxid Met, 3 (1971) 557. [20] JL Smialek, R Gibala, Metall Trans, 14A (1983) 143.
[21] CG Levi, E Sommer, SG Terry, A Catanoiu, M Rühle, J Am Ceram Soc, 86 (2003) 676. [22] J Doychak, JL Smialek, TE Mitchell, Metall Trans, 20A (1989) 499.
[23] C Mennicke, DR Mumm, DR Clarke, Z Metallkde, 90 (1999) 1079. [24] HM Tawancy, NM Abbas, A Bennett, Surf Coat Technol, 68/69 (1994) 10. [25] DR Mumm, AG Evans, Acta Mater, 48 (2000) 1815.
Part A
Modelling the high temperature oxidation of
Modelling the thermal oxidation of ternary alloys
Compositional changes in the alloy and the development of oxide phases
T.J. Nijdam
1, L.P.H. Jeurgens
2and W.G. Sloof
11 Department of Materials Science and Engineering, Delft University of Technology,
Rotterdamseweg 137, 2628 AL Delft, The Netherlands
2 Present address: Max Planck Institute for Metals Research, Heisenbergstrasse 3, D-70569, Stuttgart, Germany
Abstract
A coupled thermodynamic-kinetic oxidation model is presented that describes the thermal oxidation of a single phase ternary alloy. For given oxide layer growth kinetics, the model computes composition depth profiles in the alloy, as well as the amount of each oxide phase developed as a function of oxidation time, including the formation of multiple oxide phases during the initial stages of fast oxidation. Application of the model to the thermal oxidation of a γ-Ni-27Cr-9Al (at.%) alloy at 1373 K and a partial oxygen pressure (pO2) of 20 kPa
showed that the phase constitution of the developing oxide layer is predominantly governed by the growth rate and duration of the initial oxidation stage, whereas the eventual, steady-state interface composition of the alloy is mainly determined by the parabolic oxide layer growth rate.
1 Introduction
The protection offered by alloys against oxidation and corrosion at elevated temperatures relies on the ability of the alloy to produce and maintain a stable, adherent, slow growing oxide layer on its surface. In order to design alloys that are able to withstand high temperature degradation in aggressive environments, fundamental and comprehensive knowledge is required on the relations between the oxidation mechanism(s) and the resulting composition and microstructure of the developing oxide and alloy substrate. For the thermal oxidation of binary alloys, both analytical and numerical models have been developed to calculate compositional changes in single phase [1-5] and dual phase [6,7] binary alloys upon their oxidation. Also, criteria have been formulated for the possible oxidation modes for the thermal oxidation of binary alloys. For example, a criterion has been formulated to predict the minimum concentration of the alloy constituent required to form an external, single phase layer of the most stable oxide [1-3,7,8].
For practical applications, however, the presence of three or more alloy constituents is often required to offer adequate protection against corrosion at high temperatures without loss of good mechanical properties [9]. Despite the practical importance of such alloys, only few mathematical models have been developed for the thermal oxidation of ternary alloys [10-12]. Furthermore, in all of the oxidation models [1-8,10-12], it is assumed that oxidation is governed by parabolic oxide layer growth kinetics, and/or oxide layer growth occurs by the selective oxidation of the alloy constituent forming the most stable oxide phase. Then, the oxide layer growth rate is limited by solid-state diffusion of the reactants through the developing oxide layer under influence of the (electro)chemical potential gradient [13], and/or a single phase oxide layer develops on the alloy. Moreover, parabolic growth kinetics imply that the alloy composition at the oxide/metal (O/M) interface is constant with oxidation time [1,2]. However, in practice, pure parabolic growth kinetics are rarely observed for the initial stages of oxidation of ternary alloys at high temperature [9,14-16]. Usually, the relatively slow parabolic growth stage is preceded by an initial very fast oxidation regime for which the oxide layer growth rate is (also) determined by the solid-state diffusion of the reacting constituent(s) within the alloy [13]. Then, the alloy composition at the O/M interface may vary with oxidation time, resulting in the subsequent or simultaneous growth of different oxide phases. This may lead to the formation of complex oxide scales composed of multiple oxide phases [9,14-16].
In this work, a general Coupled Thermodynamic-Kinetic (CTK) oxidation model is presented that describes the thermal oxidation of a single phase ternary alloy exhibiting initial,
very fast oxide layer growth kinetics, followed by slow parabolic oxide layer growth kinetics. The model computes concentration depth profiles of the alloy constituents in the alloy, as well as the amount of each oxide phase developed as a function of oxidation time (including the formation of multiple oxide phases during the initial, fast oxidation stage).
The model was applied to the oxidation of a γ-Ni-27Cr-9Al (at.%) alloy at 1373 K and a partial oxygen pressure (pO2) of 20 kPa. Since accurate kinetic [17] and thermodynamic [18,19] assessments are available for the γ (fcc) phase of the NiCrAl system, the NiCrAl alloys are considered very suitable for modelling purposes (e.g. calculation of diffusional processes in single and multiphase diffusion couples [20-22]). Moreover, due to the application of NiCrAl alloys as bond coatings in modern high temperature coating systems, their oxidation behaviour has received considerable attention [9,14-16]. The protection offered by these alloys against high temperature oxidation and corrosion relies on the formation of a continuous α-Al2O3 layer. The formation of such an α-Al2O3 layer is generally preceded by an initial, very fast oxidation stage, associated with severe Al and Cr depletion in the alloy and the formation of the ‘non protective’ oxide phases Cr2O3 and NiO. The duration of this initial stage corresponds with the time required to form a continuous α-Al2O3 layer, which depends on the composition, microstructure and surface condition of the alloy, as well as on oxidation temperature and pressure [13,16].
In order to verify the model predictions, as obtained for the alloy after different oxidation times, calculated concentration depth profiles of Al and Cr in the alloy were compared to experimental concentration depth profiles, as determined using scanning Auger Electron Spectroscopy (AES). Furthermore, the effect of the oxide layer growth kinetics on the evolution of the interface composition in the alloy and the amount of α-Al2O3, Cr2O3 and NiO formed as function of oxidation time was investigated with the model.
2 Theory
Consider a single phase alloy M M M reacting with oxygen at temperature T and I II III
pressure p to form the pure oxide phase(s) IO
x y M , IIO x y M , and/or IIIO x y M , i.e. 2 2 2 (s) O (g) O (s) ( I, II, III) J J x y x M M J y + = y = (1) with 0I x y M O G Δ < 0II x y M O G Δ < 0III x y M O G Δ , where 0 J x y M O G
Δ denotes the standard Gibbs free energy of formation of oxide JO
x y
equilibrium partial oxygen pressure JO x y
M
Π for which oxide JO
x y
M is in local equilibrium with the alloy at the O/M interface is given by
2 0 O O 2 O exp ( ) J J x y x y J x y y M M J x M y j a G j M RT a ⎛Δ ⎞ ⎜ ⎟ Π = = ⎜ ⎟ ⎝ ⎠ (2) where a and j JO x y M
a are the thermodynamic activities of the alloy constituent M and the J
oxide JO
x y
M at the O/M interface, respectively. The thermodynamic activity a can be j
directly related to its respective concentration i
j
C or mole fraction i
j
N at the O/M interface by adopting a suitable treatment for the interaction between the alloy constituents within the alloy (see Sec. 4). The thermodynamic activities of the concerned oxide phases were taken equal to one, i.e. the solubilities of the oxide phases into one another were assumed to be negligible. Further, the formation of any mixed oxide phases (e.g. III I
2O4
M M or III II 2O4
M M ) due to the reaction between pure oxide phases within the developing oxide layer was not addressed.
Figure 1 Schematic two-dimensional representation of the quaternary thermodynamic phase diagram
Assuming local thermodynamic equilibrium at the O/M interface during oxidation at temperature T and pressure p, it follows from comparison of the concerned equilibrium partial
oxygen pressures for a given alloy composition at the O/M interface at time t, which oxide
phase(s) will be formed. This is illustrated by the two-dimensional representation of the quaternary isothermal phase diagram of the M M M alloy with oxygen (see Fig. 1). In this I II III
diagram, the concentrations for which the alloy is in equilibrium with the concerned oxide phases are projected on the base triangle of the M M M system [12]. I II III
For example, within the IO
x y
M field, it holds that IO IIO IIIO x y x y x y
M M M
Π < Π ≤ Π . Then, the alloy is in equilibrium with IO
x y
M at the O/M interface and the preferential oxidation of M I
from the alloy occurs. Along the composition line a-e it holds that IO IIO IIIO x y x y x y
M M M
Π = Π < Π .
Then, the alloy is in local equilibrium with IO
x y
M and IIO
x y
M at the O/M interface, resulting in the simultaneous formation of IO
x y
M and IIO
x y
M . The interface concentrations associated with the equilibrium IO IIO IIIO
x y x y x y
M M M
Π = Π < Π will be denoted further as i ,eq1
j
C . Likewise, for the unique interface composition I
i ,eq2 M C , II i ,eq2 M C , III i ,eq2 M
C (point e in Fig. 1), it holds that
IO IIO IIIO x y x y x y
M M M
Π = Π = Π and the simultaneous formation of IO
x y M , IIO x y M and IIIO x y M occurs.
The total oxide layer thickness dox at time t is related to the amounts JO x y
M
ϕ of the
oxide phases JO
x y
M (volumes per unit interface area) formed after time t by
III ox O I J x y M J d ϕ = =
∑
(3)Because each oxide phase contributes to the metal consumption from the alloy by the growing oxide layer [4], the resulting displacement of the O/M interface ξ at time t (with respect to its original position at t=0) can be expressed as
III O I O ( ) J x y J x y j j J M J M x V j M V ξ ϕ = =
∑
= (4) where J x y M OV is the molar volume of the oxide phase JO
x y
M , Vj is the partial molar volume of
component J
M in the alloy at the O/M interface, and x is the number of moles of j J M per
mole JO
x y
M .
Solid-state volume diffusion within the I II III
M M M alloy during oxidation at
temperature T can be described by the ternary equivalents of Fick´s second law. With
III
I II ( , , ) j n j n k jj jk C C C D D j k M M t z z z z ∂ = ∂ ⎛ ∂ ⎞+ ∂ ⎛ ∂ ⎞ = ⎜ ⎟ ⎜ ⎟ ∂ ∂ ⎝ ∂ ⎠ ∂ ⎝ ∂ ⎠ (5)
where Cj is the concentration of the alloy constituent M at depth z below the original J
position of the O/M interface at t = 0 (Fig. 2); n jj
D and n jk
D are the main and cross-term interdiffusion coefficients, respectively. At t = 0, uniform concentration profiles in the alloy
were considered, i.e.
0 ( 0) j j C t= =C (6) where 0 j
C is the concentration of constituent M in the bulk alloy. At depth z = L in the J
interior of the alloy (Fig. 2), a zero-flux plane boundary condition was employed, i.e.
0 j z L C z = ∂ ⎛ ⎞ = ⎜ ∂ ⎟ ⎝ ⎠ (7)
The total amount of alloy constituent M received by the oxide layer after time t must equal J
the total amount of M released by the alloy after time t. Hence, the mass balance for alloy J
constituent M at the O/M interface at time t can be written as J
0 O 0 O ( , I,II) J x y J x y L L j J j j M M x C dz C dz j M J V ϕ =
∫
−∫
ξ = = (8)Figure 2 Schematic concentration depth profile for alloy constituent MJ in the ternary alloy
I II III
Provided that the oxide layer growth kinetics of the alloy are given, the composition depth profiles in the alloy, as well as the amount of each oxide phase developed, can be solved numerically as a function of oxidation time using Eqs. (2) - (8). For this purpose, a numerical model was developed, using the finite difference method [24], as discussed in the next section.
3 Numerical procedure
At the start of the numerical calculations, a grid of equispaced nodes l with grid
spacing Δz and uniform concentration profiles were established across the ternary alloy of initial thickness L. Consider that at t = 0, it holds that IO IIO IIIO
x y x y x y
M M M
Π < Π < Π . For time step Δt, the initial value of the grid spacing Δz was taken equal to the average depth over which the alloy constituent M (forming the most stable oxide phase at the O/M interface at t = 0) can I
diffuse from the bulk of the alloy towards the O/M interface during Δt. A good approximate for this average depth is the root mean squared diffusion distance < Δ > of constituent z 2
I
M after time step Δt, i.e. 2
max
2
z D t
< Δ > = Δ , where Dmax is the corresponding (main or cross-term) interdiffusion coefficient of M with the highest value at t = 0 [23]. I
In order to calculate both the composition depth profiles in the alloy, and the corresponding amount of each oxide phase developed with increasing oxidation time, the following sequence of calculations was performed for each time step Δt: (i) evaluation of the total oxide layer thickness at time t + Δt, (ii) calculation of the concentrations in the alloy at nodes 2 to l at time t + Δt, (iii) simultaneous determination of the interface concentrations (i.e. at node 1 in the alloy), the displacement of the O/M interface and the amount of each oxide phase formed at time t + Δt, and (iv) adjustment of the grid to maintain an equidistant grid spacing.
Note that, the evaluation of the mass balance equations (cf. Eq. (8)) with respect to the initial concentration depth profiles prevented the accumulation of mass balance errors. The integrals, representing the areas beneath the concentration depth profiles in the alloy, were computed using the trapezoidal rule.
3.1 Oxide layer thickness
Evaluation of the total oxide layer thickness at time t + Δt requires a description of the oxide layer growth kinetics during the initial, fast and the second, slow oxidation stage. For the initial oxidation stage, a combination of a linear and cubic growth law was used, i.e.
ox( )c lin d t t≤ =k t (9a) 1/ ox(c p) 0 cub( 0) m d t ≤ ≤t t =d +k t t− (9b)
For the second oxidation stage, a parabolic law was used, i.e. [25]
ox( p) 1 x( 1)
d t t≥ =d + k t t− (9c)
Here, (tc, dc) and (tp, dp) are the time and thickness at the onset of the cubic and parabolic oxidation stage, respectively (Fig. 3). klin is the linear growth constant, kx is the parabolic growth constant (in terms of oxide layer thickness) and m and kcub are cubic growth constants. The constants (t0, d0) were used for a flexible description of the initial growth stage. The constants (t1, d1) were required to obtain the correct value for the parabolic growth constant kx [25]. Under the constraint that the growth curve is continuously differentiable at (tc, dc) and (tp, dp), it follows that the values of six arbitrary constants (out of the total of twelve) were required to fully describe the oxide layer growth kinetics.
Figure 3 Schematic oxide layer growth curve for the oxidation of an alloy, comprising an initial stage
of linear and cubic growth kinetics, followed by a second stage of parabolic growth kinetics. The inset shows an enlargement of the initial stage of oxidation (i.e. rectangular box). See Sec. 3.1 for details.
3.2 Concentrations at nodes 2 to l
The concentrations in the alloy at nodes 2 to l at time t + Δt were calculated utilising an explicit finite difference scheme [24] for Eqs. (5) and (7). Explicit finite difference equations were used to account for the concentration dependence of the ternary diffusion coefficients in the alloy. The partial derivatives for concentration with respect to depth (cf. the right hand side of Eq. (5)) were expressed in terms of first order, central differences. The
partial derivatives for concentration with respect to time (cf. the left hand side of Eq. (5)) were expressed in terms of first order, forward differences. For the explicit finite difference
method the value of Δt is limited by a stability criterion, which was met automatically by taking the initial value of the grid spacing Δz equal to the root mean squared diffusion distance < Δ > [24], see Sec. 3. z 2
3.3 Interface composition and oxide phases
In order to determine the concentrations at the O/M interface at t + Δt, as well as the amount of each oxide phase developed during the time step Δt, a sequence of calculations was performed.
First, the equilibrium concentration I
i, ,eq1
t t M
C +Δ was determined for which the oxide phases IO
x y
M and IIO
x y
M are both in local equilibrium with the alloy at the O/M interface at time t +
Δt (i.e. IO IIO x y x y
M M
Π = Π , see Sec. 2).1 Defining the accessible amount I
t M
Γ of alloy constituent
I
M at time t (Fig. 4) as the maximum amount of M (moles per unit interface area) that can I
be received by the growing phase IO
x y
M during time step Δt (i.e. until IO IIO x y x y M M Π = Π ), then I I I I I I I I * I * * i, i, * ,eq1 ( , ) t t t M L L t t t t t t t t t t M C dzM CM dz CM CM M VM M ξ ξ ξ ξ Δ +Δ +Δ +Δ Δ +Δ Γ =
∫
−∫
= Δ = Γ (10a) where I * t t M C+Δ and I * t M ξΔΔ are the hypothetical concentrations and displacement of the O/M interface associated with the release of t I
M
Γ during Δt (Fig. 4). If the total accessible
amount I
t M
Γ is received by the growing oxide layer, then the corresponding hypothetical
amount I * O x y M ϕ Δ of oxide phase IO x y
M formed during Δt equals
1 The equilibrium concentration
I
i, ,eq1
t t M
C +Δ at time t + Δt was calculated using Eq. (2), and adopting the relation
between the mole fractions of MI and MII at the O/M interface at time t and their corresponding equilibrium mole fractions after release of the accessible amount of MI by the alloy, i.e.
I I I I O * O x y x y t M M M M V x ϕ Γ Δ = (10b)
Figure 4 Representation of the accessible amount I
t M
Γ of alloy constituent MIat time t in the alloy (grey area). Note that the initial accessible amount I
0
M
Γ of alloy constituent MI at time t = 0 is approximately equal to I I I I 0 1 * 0 i, 2( )( ,eq1) t t M M M M z C z ξΔ C C Δ
Δ ⋅ − Δ − Δ + . Therefore, realistic values for Γ0MI
can only be obtained if the initial value of the grid spacing Δz is taken equal to the root mean squared diffusion distance < Δ >z 2 of MI at t = Δt (see beginning of Sec. 3).
In order to determine whether only IO
x y
M was formed during time step Δt, or whether the simultaneous growth of IO
x y
M with the less stable oxide IIO
x y
M (and possibly also IIIO
x y
M ) occurred, the value of I
* O
x y
M ϕ
Δ was compared to the actual increase in oxide layer thickness
ox
d
Δ during time step Δt, i.e. Δdox =doxt+Δt −doxt .
If I * ox O x y M d ϕ Δ ≥ Δ only IO x y
M was formed during time step Δt. Then, the total amount of IO
x y
M in the oxide layer at t + Δt equalled IO IO ox x y x y
t t t
M M d
ϕ+Δ =ϕ + Δ , and the total displacement
of the O/M interface ξt+Δt was calculated from Eq. (4). The new interface concentrations
I i,t t M C +Δ and II i,t t M
C +Δ were solved by iteration using Eq. (8).
On the other hand, if I
* ox O x y M d ϕ
Δ < Δ , the simultaneous growth of IO
x y
M together with the less stable oxide phase IIO
x y
M (and possibly also IIIO
x y
M ) occurred during time step Δt. For the simultaneous formation of IO
x y
M and IIO
x y
M , thermodynamic equilibrium exists between the oxide phases of IO
x y
M and IIO
x y
M at the O/M interface (i.e. IO IIO x y x y
M M
Π = Π ),
I I i, i, ,eq1 t t t t M M C +Δ =C +Δ and II II i, i, ,eq1 t t t t M M
C +Δ =C +Δ (see Sec. 2). Likewise, for the simultaneous formation of IO x y M , IIO x y M and IIIO x y
M , it holds that IO IIO IIIO
x y x y x y
M M M
Π = Π = Π , which implies that
I I i, i, ,eq2 t t t t M M C +Δ =C +Δ and II II i, i, ,eq2 t t t t M M
C +Δ =C +Δ (see Sec. 2). To determine whether the simultaneous
formation of IO x y M with only IIO x y M , or with both IIO x y M and IIIO x y
M , occurred (during time step Δt), first the accessible amount II
t M
Γ of alloy constituent M at time t had to be II
determined. Defining II
t M
Γ as the maximum amount of M (moles per unit interface area) II
that can be received by the growing phase IIO
x y
M during time step Δt (i.e. until
IO IIO IIIO x y x y x y M M M Π = Π = Π ), then I I I I I * I II * * i, i, ,eq2 ( ) t t t M M L L t t t t t t t t M C dzM CM dz CM CM ξ ξ ξΔ +Δ +Δ +Δ +Δ Γ =
∫
−∫
= (10c) II II II II II * I II * * i, i, ,eq2 ( ) t t t M M L L t t t t t t t t M C dzM CM dz CM CM ξ ξ ξΔ +Δ +Δ +Δ +Δ Γ =∫
−∫
= (10d) where II * t t MC+Δ are the hypothetical concentrations in the alloy associated with the release of
II
t M
Γ during Δt. The hypothetical displacement I II
* t M M ξΔ
Δ of the O/M interface associated with the release of both I
t M
Γ and II
t M
Γ , as well as the corresponding amounts I
* O x y M ϕ Δ and II * O x y M ϕ
Δ of the respective oxide phases developed, were solved by iteration using Eq. (3), (4), (8), (10c) and (10d) with the constraints that I I
i, i, ,eq2 t t t t M M C +Δ =C +Δ and II II i, i, ,eq2 t t t t M M C +Δ =C +Δ (see above). Thus, if II I * * ox O O ( ) x y x y M M d ϕ ϕ Δ + Δ ≥ Δ , besides IO x y M only IIO x y
M was formed during time step Δt (i.e. IO IIO
x y x y
M M
Π = Π , see Sec. 2). Then, the total amounts I
t+ t O x y M ϕ Δ and II t+ t O x y M ϕ Δ of the
respective oxide phases in the oxide layer and the total displacement of the O/M interface
t t
ξ +Δ were solved by iteration using Eqs. (3), (4) and (8). The equilibrium interface
concentrations I i, ,eq1 t t M C +Δ and II i, ,eq1 t t M
C +Δ were solved using Eq. (8) and the known relationship
between II i, ,eq1 t t M C +Δ and I i, ,eq1 t t M
C +Δ (i.e. line a-e in Fig. 1).
Finally, if II I * * ox O O ( ) x y x y M M d ϕ ϕ
Δ + Δ < Δ , the simultaneous formation of IO
x y M , IIO x y M and IIIO x y
M occurred during Δt (i.e. IO IIO IIIO x y x y x y
M M M
Π = Π = Π ). Then, the total amounts I
t+ t O x y M ϕ Δ , II t+ t O x y M ϕ Δ and III t+ t O x y M
ϕ Δ of the respective oxide phases in the oxide layer and the total displacement
of the O/M interface ξt+Δt were solved by iteration using Eqs. (3), (4) and (8) using
I I i, i, ,eq2 t t t t M M C +Δ =C +Δ and II II i, i, ,eq2 t t t t M M
C +Δ =C +Δ (i.e. point e in Fig. 1).
3.4 Grid adjustment
After performing the sequence of calculations for t + Δt as described above, the positions of the nodes were adjusted to maintain an equidistant grid spacing. The new grid
spacing zΔ at time t + Δt equalled (L−ξt+Δt) /(l− . The concentrations at the adjusted node 1) positions were determined by interpolation using a Piecewise Cubic Hermite Polynomial (PCHP) [26]. This approach was essential to obtain accurate results during the initial oxidation stage, where very steep concentration depth profiles occur in the alloy. Usually, linear interpolation between neighbouring nodes is applied [27]. However, this so-called Murray-Landis transformation results in zigzag concentration profiles and severe mass balance errors [28], which was avoided with the PCHP interpolation method, as is illustrated in Fig. 5.
Figure 5 Determination of the concentrations at the adjusted node positions in the alloy using linear
interpolation and a PCHP interpolation method. Linear interpolation results in zigzag concentration profiles and severe mass balance errors, which is avoided with the PCHP interpolation method. See Sec. 3.4 for details.
4 Application to the oxidation of
γ-NiCrAl
The CTK oxidation model was applied to the oxidation of a γ-Ni-27Cr-9Al (at.%) alloy at 1373 K and a pO2 of 20 kPa. To compute the Al and Cr concentration depth profiles in the alloy as well as the amounts of α-Al2O3, Cr2O3 and NiO formed as function of oxidation time, the following data were required.
The standard Gibbs free energies of formation of α-Al2O3, Cr2O3 and NiO per mole O2 at 1373 K and 20 kPa were calculated using data from Ref. [29]. The molar volumes of
α-Al2O3, Cr2O3 and NiO were taken equal to VAl O2 3 = 25.6 cm3/mol, VCr O2 3 = 29 cm3/mol and
NiO
V = 10.9 cm3/mol [30].
The oxide layer growth kinetics of γ-Ni-27Cr-9Al, thermally oxidised at 1373 K and 20 kPa, were established from experimental values of the oxide layer thickness as function of oxidation time [16] (see Fig. 6). The values of tp and dp, corresponding with the time and thickness for which a continuous α-Al2O3 layer developed on the alloy upon its oxidation, were selected as tp = 57600 s (i.e. 16 h) and dp = 6.75 μm, respectively [16]. The resulting coefficients for the growth curve, as obtained from a linear least squared fit of the experimental data to Eq. (9), were: kx = 1.25x10-5 μm2/s, (tp – t1) = 13320 s, tc = 510 s and klin = 3.8x10-3 μm/s.
Figure 6 Experimental and fitted oxide layer thickness as function of oxidation time for the thermal
oxidation of a γ-Ni-27Cr-9Al alloy at 1373 K and pO2 = 20 kPa.
The relationship between the activities of the alloy constituents and the alloy composition at 1373 K and 20 kPa was calculated with ThermoCalc [31], using a thermodynamic database for Ni-base superalloys [19]. The composition-dependent ternary interdiffusion coefficients Ni AlAl D , Ni AlCr D , Ni CrAl D and Ni CrCr
D at 1373 K were obtained as the product of a thermodynamic factor and a kinetic factor [32,33]. The thermodynamic factor
/
j Nk μ
∂ ∂ (i.e. the chemical potential gradient of alloy constituent MJ with respect to the
Ni-base superalloys. The kinetic parameters ΔG* that were used to evaluate the kinetic factor
[32,33] are listed in Table 1. The values of the partial molar volumes of Al, Cr and Ni were determined from the change in lattice parameter of the γ phase with alloy composition, as measured with X-Ray Diffractometry (XRD). Finally, the alloy thickness was always taken larger than the distance over which diffusion occurred (i.e. semi-infinite).
Table 1 Kinetic parameters ΔG* (in J/mol) used to obtain the composition-dependent ternary
diffusion coefficients DAlAlNi , DAlCrNi , DCrAlNi and DCrCrNi for γ-NiCrAl at 1373 K. Unless stated otherwise, all data were taken from Ref. [33].
* G Δ (J/mol) j = Al j = Cr j = Ni *Al j G Δ -241019 -266795 -234129 *Cr j G Δ -347586 -347586 -347586 *Ni j G Δ -366142 -375421 -382835 *Al,Ni j G Δ -166518 -118000 -23069 *Cr,Ni j G Δ -130000# -68000 -81000 *Cr,Al j G Δ 335000 17000# -1500000#
# Data assessed from own experiment.
4.1 Model versus experiment
Experimental Al and Cr concentration depth profiles of γ-Ni-27Cr-9Al after oxidation for 1 h, 4 h, 16 h and 64 h at 1373 K and pO2 = 20 kPa, were determined using scanning AES [34]. The thus obtained concentration depth profiles were in good agreement with the corresponding concentration depth profiles calculated with the CTK oxidation model (Fig. 7).
For the alloy considered, it held that at t = 0, ΠAl O2 3 < ΠCr O2 3 < ΠNiO. Hence, the onset of oxidation started with the preferential oxidation of Al from the alloy. However, due to the very fast oxide layer growth rate, the Al interfacial mole fraction instantaneously (within the first time step for Δt = 25 s) dropped towards its equilibrium value i
Al,eq1
N for which α-Al2O3 and Cr2O3 were in equilibrium with the alloy at the O/M interface, i.e. ΠAl O2 3 = ΠCr O2 3 (Fig. 8a
and 8b). Thermodynamic calculations using Eq. (2) showed that i Al,eq1
N was about 10 ppm Al at 1373 K for 27 at.% Cr at the O/M interface. Then, the early stage of oxidation proceeded with the simultaneous formation and growth of Cr2O3 and α-Al2O3 (Fig. 8c and 8d).
Figure 7 Calculated and experimental Al and Cr concentration depth profiles for the thermal oxidation
of a γ-Ni-27Cr-9Al alloy at 1373 K and pO2 = 20 kPa. Al profiles after (a) 1 h, (b) 4 h, (c) 16 h and (d)
Figure 8 Calculated Al and Cr interfacial mole fraction as a function of oxidation time for (a) the first 12
minutes of oxidation and (b) for 64 hours of oxidation, as well as the calculated amounts of α-Al2O3,
Cr2O3 and NiO formed as function of oxidation time for (c) the first 12 minutes of oxidation and (d) for
64 hours of oxidation for the thermal oxidation of a γ-Ni-27Cr-9Al alloy at 1373 K and pO2 = 20 kPa.
The simultaneous growth of α-Al2O3 and Cr2O3 caused a subsequent drop of the Cr interfacial mole fraction (Fig. 8a and 8b) towards the value i
Cr,eq2
N , for which α-Al2O3 and Cr2O3 and NiO were in equilibrium with the alloy at the O/M interface, i.e. ΠAl O2 3 = ΠCr O2 3 = ΠNiO. Again, thermodynamic calculations showed that i
Cr,eq2
N was about 1 ppm Cr at 1373 K for 1 ppm Al at the O/M interface. From this point on (within several time steps), besides α-Al2O3 and Cr2O3, also NiO was formed (Fig. 8c and 8d). These oxide phases indeed developed within the first ten minutes of oxidation of the alloy, as was shown in Refs. [16,34].
The total amount of NiO formed was relatively small, because the initial, very fast oxide layer growth rate levelled off rapidly with increasing oxidation time. Consequently, a fast increase in the Cr interface concentration occurred (Fig. 8b), because the amount of Cr received by the oxide layer was smaller than the amount of Cr that piled up at the O/M interface due to the oxide-layer-growth-induced interface recession. After about 2 h of oxidation, the oxide layer growth rate had decreased to such an extent that the growth of
Cr2O3 stopped and α-Al2O3 was formed exclusively (Fig. 8d). Then, both the Al and Cr interface concentrations increased, and the Cr concentration became enriched at the O/M interface with respect to its original bulk concentration. After 16 h of oxidation, the alloy composition at the O/M interface gradually attained a constant value, as imposed by the parabolic oxide layer growth kinetics [1,2]. At his point, a continuous α-Al2O3 layer had developed on the alloy [16,34].
It is noted that, although the model computes composition depth profiles within the alloy, as well as the amount of each oxide phase developed as function of oxidation time, it does not address the morphology and distribution of the evolved oxide phases within the developing oxide layer. For example, for γ-NiCrAl alloys with Al concentrations lower than about 5-8 at.% (the exact amount depends on Cr content, alloy microstructure, oxidation temperature and pressure [13]), a continuous α-Al2O3 layer (with Cr2O3, NiO and/or spinel oxides on top) will not develop. Instead, either, the formation and continuous growth of α-Al2O3 and Cr2O3 as internal oxide crystallites below a continuous NiO layer, or the formation and continuous growth of α-Al2O3 as internal oxide crystallites below a continuous Cr2O3 layer occurs [13-15]. Then, the oxide layer growth kinetics may be governed not only by the solid-state diffusion of the reactants through the developing oxide layer (Sec. 1), but also by the inward diffusion of oxygen into the alloy [35].
4.2 Effect of oxide layer growth kinetics
It is generally recognised that the oxide layer growth kinetics, and thus the resulting compositional changes in the alloy and the oxide phase constitution of the developing oxide layer, are strongly dependent on the oxidation conditions (e.g. T and pO2) and the composition, microstructure (e.g. grain size) and surface condition of the alloy [9,13]. For example, for the oxidation of γ-Ni-27Cr-9Al at 1373 K it was found that the growth rate and duration of the initial, fast oxidation stage was suppressed for lower pO2. Due to the lower activity of oxygen at the O/M interface during the initial, fast oxidation stage, the formation of a continuous α-Al2O3 layer was promoted. Consequently, the formation of the ‘non-protective’ oxide phases Cr2O3 and NiO, as well as the extent of Al and Cr depletion in the alloy, were strongly suppressed [16].
The CTK oxidation model was applied to investigate the effect of the oxide layer growth kinetics on the compositional changes within the alloy and the oxide phase constitution of the developing oxide layer, for the oxidation of a γ-Ni-27Cr-9Al alloy at 1373 K. The effect of the initial growth rate (i.e. the value of the growth constant klin) on the
resulting steady-state Al and Cr interface concentrations after 64 h of oxidation is shown in Fig. 9a. The relative amounts of the ‘non-protective’ oxide phases Cr2O3 and NiO (i.e.
ox O /
J x y
M d
ϕ ) formed after 64 h of oxidation as a function of klin are shown in Fig. 9b.
Figure 9 Effect of the initial growth rate (i.e. the value of klin) on (a) the steady-state Al and Cr interface
concentrations reached, and (b) the relative amounts of Cr2O3 and NiO formed, after 64 h of oxidation
of a γ-Ni-27Cr-9Al alloy at 1373 K. The dotted line represents the model solution for the experimental growth curve at pO2 = 20 kPa (see Figs. 6 - 8).
A higher initial growth rate enhanced the formation of ‘non-protective’ oxides during the initial stage of oxidation. Below a certain critical value of the initial growth rate, NiO was not formed, because the Cr concentration in the alloy at the O/M interface did not drop below its equilibrium value for the simultaneous formation of α-Al2O3, Cr2O3 and NiO (see Sec. 2). Above this critical growth rate value, both Cr2O3 and NiO were formed. With increasing initial growth rate, the relative amount of Cr2O3 formed was suppressed, whereas the relative
amount of NiO formed was enhanced. As a result, more Cr was piled up in the alloy contiguous to the O/M interface, leading to an increase of the Cr interface concentration in the alloy. The small increase in the steady-state Al interface concentration was a consequence of the fact that the oxide layer thickness reached at the onset of the parabolic oxidation stage (i.e. the value of dp) was kept constant.
Figure 10 Effect of the duration of the initial, fast oxidation stage (i.e. the value of tp for constant ratio
tp / dp) on (a) the steady-state Al and Cr interface concentrations reached, and (b) the relative amounts
of Cr2O3 and NiO formed, after 64 h of oxidation of a γ-Ni-27Cr-9Al alloy at 1373 K. The dotted line
In practice, the enhanced formation of a continuous α-Al2O3 layer (corresponding to a reduction of the value of tp), leads to a smaller thickness at the onset of the slow, parabolic oxidation stage (i.e. a lower value of dp) [16]. Therefore, the effect of the duration of the initial oxidation stage on the alloy interface composition and oxide phase constitution was investigated by varying tp while keeping the ratio tp/dp constant (see Fig. 10). The postponed formation of a continuous α-Al2O3 layer resulted in an increase of the amount of ‘non-protective’ oxides formed during the initial, fast oxidation stage and a decrease of the eventual, steady-state Al and Cr interface concentrations in the alloy, in agreement with the experimental findings in Refs. [16,34].
Figure 11 Effect of the growth rate during the parabolic oxidation stage (i.e. the value of kx) on (a) the
steady-state Al and Cr interface concentrations reached, and (b) the relative amounts of Cr2O3 and
NiO formed, after 64 h of oxidation of a γ-Ni-27Cr-9Al alloy at 1373 K. The dotted line represents the model solution for the experimental growth curve at pO2 = 20 kPa (see Figs. 6 - 8).
The effect of the growth rate during the parabolic oxidation stage (i.e. the value of the growth constant kx) on the eventual (i.e. after 64 h) alloy interface composition and oxide phase constitution is shown in Figs. 11(a) and (b), respectively. A higher growth rate during the parabolic oxidation stage imposed a larger supply of Al from the alloy, resulting in a
lower steady-state Al interface concentration. On the other hand, the accompanying increase of the O/M interface recession enhanced the Cr pile up near the O/M interface, leading to a
higher steady-state Cr interface concentration. Evidently, the relative amount of ‘non-protective’ oxides formed decreased with increasing parabolic growth rate, whereas the
absolute amount of ‘non-protective’ oxide phases developed during the initial, fast oxidation stage was insensitive to changes in the parabolic growth rate.
5 Conclusions
• A coupled thermodynamic-kinetic oxidation model was presented that describes the thermal oxidation of a single phase ternary alloy. For given oxide layer growth kinetics, the model computed composition depth profiles in the alloy, as well as the amount of each oxide phase developed as a function of oxidation time, including the formation of multiple oxide phases during the initial stage of fast oxidation.
• Application of the model to the oxidation of a γ-Ni-27Cr-9Al (at.%) alloy at 1373 K and a partial oxygen pressure of 20 kPa showed an almost instantaneous drop of the Al concentration at the oxide/metal (O/M) interface towards its equilibrium value for the simultaneous formation of α-Al2O3 of Cr2O3. Then, the Cr concentration at the O/M interface rapidly decreased towards its equilibrium value for the simultaneous formation of α-Al2O3, Cr2O3 and NiO. With increasing oxidation time, both the Al and Cr interface concentrations increased, and α-Al2O3 was formed exclusively. During the parabolic oxidation stage, the Al and Cr interface concentrations gradually attained a constant value. • The phase constitution of the developing oxide layer was predominantly governed by the
initial growth rate and the duration of the initial, fast oxidation stage, whereas the eventual, steady-state interface composition of the alloy was mainly determined by the parabolic oxide layer growth rate.
• To obtain realistic model predictions for the thermal oxidation of alloys at elevated temperatures, the inevitable initial stage of very fast oxide layer growth kinetics cannot be neglected, and a thermodynamic criterion that allows the subsequent or simultaneous
Acknowledgement
Financial support by the Technology Foundation STW is gratefully acknowledged.
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