James L. Smialek and Nathan S. Jacobson

Glenn Research Center, Cleveland, Ohio

Brian Gleeson

University of Pittsburgh, Pittsburgh, Pennsylvania

David B. Hovis and Arthur H. Heuer

Case Western Reserve University, Cleveland, Ohio

Oxygen Permeability and Grain-Boundary Diffusion 

Applied to Alumina Scales

NASA/TM—2013-217855

August 2013
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James L. Smialek and Nathan S. Jacobson

Glenn Research Center, Cleveland, Ohio

Brian Gleeson

University of Pittsburgh, Pittsburgh, Pennsylvania

David B. Hovis and Arthur H. Heuer

Case Western Reserve University, Cleveland, Ohio

Oxygen Permeability and Grain-Boundary Diffusion 

Applied to Alumina Scales

NASA/TM—2013-217855

August 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The following are acknowledged for their helpful discussions in the preparation of this manuscript: Dr. J.A. Nesbitt,

Dr. T. Nakagawa, Dr. S. Kitaoka, and Dr. D. Naumenko. This work was supported by the NASA Fundamental Aeronautics Program 

and by the Offi ce of Naval Research, Dr. David Shifl er, Program Manager.

Available from

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Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2013-217855 1 

Oxygen Permeability and Grain-Boundary Diffusion 

Applied to Alumina Scales 

James L. Smialek and Nathan S. Jacobson 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Brian Gleeson 

University of Pittsburgh 

Pittsburgh, Pennsylvania 15260 

David B. Hovis and Arthur H. Heuer 

Case Western Reserve University 

Cleveland, Ohio 44106 

Summary 

High-temperature oxygen permeability measurements had determined grain-boundary diffusivities 

(Dgb) in bulk polycrystalline alumina in a recent study by Wada, Matsudaira, and Kitaoka. They predict 

that oxygen Dgb,O varies with oxygen pressure as 6

1

O2



P and dominates at low O2 P whereas aluminum 

Dgb,Al varies with 16

3

O2



P and dominates at high O2 P . In the present study, these relations enable detailed 

evaluations of alumina scale growth in terms of diffusivity and grain size. It is deduced that coupling 

these relations with a modified Wagner treatment for dominant inward oxygen growth produces the 

concise solution: i = kp,iGi = 12 Dgb,O,int, where i is a constant and kp,i and Gi refer to instantaneous 

values of the scale parabolic growth constant and grain size, respectively. To support this analysis, a 

commercial FeCrAl(Zr) alloy was oxidized at 1100 to 1400 °C to determine kp,i, interfacial grain size, , 

and thus Dgb,O,int. The Dgb,O,int values predicted from oxidation were 10 to 40 times less than those 

obtained by the above solution, but closer than extrapolations from typical high-temperature bulk 

measurements. Furthermore, the activation energy predicted from permeability relations for Dgb,O,int

(298 kJ/mole) is shown here to be significantly lower than that predicted for bulk alumina (467 kJ/mole) 

under no O2 P gradient. In comparison, the activation energy determined from oxidation was 375 

kJ/mole. The experimental oxidation results here agree with similar alumina scale studies, especially 

where both kp,i and Gi were characterized. Temperature-sensitive grain enlargement, equilibrium interface 

O2 P variation, and grain-boundary diffusivities all affect the Arrhenius behavior of scale growth kinetics. 

1.0 Introduction: Alumina Scale Growth 

Many high-temperature Ni-, Co-, or Fe-based structural alloys and coatings depend on slow-growing 

alumina scales for oxidation resistance. Consequently, alumina scale growth has been the subject of 

intense study over many decades, and many excellent reviews are available that provide both a historical 

perspective of advances and summarize classic key features (Refs. 1 to 4). Briefly, alumina scales are 

shown to grow primarily by oxygen inward grain-boundary diffusion, with some contributions from 

outward aluminum grain-boundary diffusion. The presence of one or more reactive element dopants can 

affect diffusion, most commonly the reduction of outward aluminum diffusion, although no simple 

relationships between diffusivity and dopants have yet emerged. In any event, scale grain size is shown to 

be a critical factor, with most models assuming an inverse dependency between effective diffusion and 
NASA/TM—2013-217855 2 

average grain diameter. Efforts to elucidate diffusional behavior often include 16O/18O two-stage or 

double oxidation tracer studies with nuclear reaction analysis (NRA) or secondary ion mass spectroscopy 

(SIMS) reconstruction of diffusion profiles. Others utilize growth rate or electrical conductivity variations 

with O2 P , then model the ionic transport contributions as a function of the O2 P gradient (Refs. 5 to 11). 

This latter group provided the relations necessary for describing scale growth according to the Wagner 

relation in which diffusivity is characterized as a function of the chemical potential gradient across the scale. 

Others address the O2 P gradient in the integration limits for the modified Wagner equation in which ln

O2 P becomes the salient factor (Refs. 2 and 12 to 15), and many of these will be highlighted later. 

The present study is not a critical review or synthesis of the various kinetic studies. Rather, it applies 

grain-boundary diffusivity relations recently obtained via permeability measurements to the case of scale 

growth. In those studies diffusion in bulk alumina samples had been elegantly determined through oxygen 

permeability measurements as a function of O2 P gradients (Refs. 16 to 19). An oxygen flux had been 

produced across a thin polycrystal of alumina by establishing a O2 P gradient using gas tight seals and 

controlled 0.01 to 10 vol% O2/Ar or 0.01 to 1.0 vol% H2/Ar atmospheres. Typically, a high- O2 P regime 

was studied by keeping one side of the membrane at 1 Pa O2 and varying the other to 105

 Pa. 

Alternatively, a low- O2 P regime was explored by keeping one side of the membrane at 1 Pa O2 and 

varying the other down to 10–9 Pa. In some cases the entire pressure regime was studied as a closer 

simulation to a growing scale. Experiments were performed over the 1500 to 1700 °C temperature range, 

and O2 pressure was monitored via zirconia electrochemical cells. Oxygen permeability was determined 

from the change in steady-state O2 P on one side as the O2 P was changed on the other. The measured 

permeability and flux were converted to oxygen and aluminum diffusivities at the low- and high- O2 P

regimes, respectively, as they followed the expected 6

1

O2



P and 16

3

O2



P dependencies for n-type oxygen 

vacancy VO and p-type aluminum vacancy VAl defect equilibria. 

Experimentally, the present study draws from early grain size measurements made for alumina scales 

formed on a commercial FeCrAl(Zr) alloy, Hoskins 875 (Hoskins Manufacturing Co.), originally 

intended to verify grain size effects on oxidation rates in early transmission electron microscopy (TEM) 

studies of NiCrAl scales (Refs. 20 and 21). However, the primary purpose at present is to reconcile 

alumina growth kinetics and grain-boundary diffusivity obtained by combining the permeability equations 

with the Wagner model. To accomplish this, a number of relations must be derived. In Section 2.0 we 

present the basic grain-boundary diffusion equations resulting from the permeability studies. Their 

incorporation into the Wagner integral, using the concept of effective diffusivity Deff and grain size, yields 

the general interrelation of the parabolic growth rate constant kp and oxygen grain-boundary diffusivity at 

the interface Dgb,O,int. In Section 3.0, the experimental data set of kp and grain size are compared with 

values predicted from Dgb,O,int. Since the latter is dependent on the O2 P at the metal-scale interface, the 

thermodynamic calculation of O ,eq 2 P is first presented. The concept of a constant oxidation product, , is 

then introduced and used to extract Dgb,O,int from experimental values of kp and grain size. Comparable 

values and activation energies from the literature are noted throughout. Finally, grain-boundary 

diffusivities obtained from permeability, oxidation, and 18O tracer studies of scales and bulk alumina are 

compared and discussed. 

A list of symbols used in this report is given in Appendix A to aid the reader. 
NASA/TM—2013-217855 3 

2.0 Development of Diffusivity and Oxidation Equations 

This section addresses new relations for Al and O grain boundary diffusivity as obtained from oxygen 

permeability studies. These are then combined with the standard Wagner analyses that relates scale 

growth rates to diffusivities. 

2.1 Permeability and Grain-Boundary Diffusivity 

The assumption of the primary ionic species is essential to the treatment of diffusion across a O2 P

gradient in alumina. For the sake of brevity, we consider charged O and Al vacancies (   VO and VAl  , 

respectively) as likely candidates to be formed at interfaces and incorporated as charged polarons 

diffusing within grain boundaries (Ref. 22). The standard relations connecting defect concentrations with 

O2 P are developed in Appendix B. These relate the reaction of Al and O to form Al2O3 and the formation 

of charged    VO and   VAl  in accordance with equilibrium thermodynamics using Kröger-Vink notation 

(Ref. 23). Then, electroneutrality is defined for the primary charged ionic vacancies and electron or hole 

charge carriers. By combining the latter with the equilibrium constants and solving for defect 

concentrations, one obtains    VO proportional to 6

1

O2



P at the low- O2 P surface (n-type) and   VAl 

proportional to 16

3

O2



P at the high- O2 P surface (p-type). Indeed, the grain-boundary diffusivities calculated 

from permeability studies accordingly yield expected 6

1

O2



P (Eq. (1)) and 16

3

O2



P (Eq. (2)) dependencies at 

low (1 Pa) and high (1 Pa) O2 P , for oxygen and aluminum vacancies, respectively (Ref. 24). Fe, Ni, Y, 

Hf, and Zr dopant effects as well as Schottky and Frenkel defect equilibria are significant considerations 

and have been considered in numerous permeability, conductivity, and oxidation studies. However, the 

present discussion will refer to the simple 6

1

O2



P and 16

3

O2



P relations in Appendix B, since they agree with 

the permeablility results for grain-boundary diffusion in pure alumina. Resulting from this are highly 

useful relations for both O and Al grain-boundary diffusion (Eqs. (1) and (2), respectively) as a function 

of temperature and oxygen pressure. From Reference 24, 

6

1

6

1

2 s Pa

m 467 kJ 2.207 10 exp

3

O ,I

9

gb,O 

 

 



 



     P

RT

D (1) 

16

3

16

3

2 s Pa

m 604 kJ 2.475 10 exp

3

O ,II

5

gb,Al 

 

 



 



     P

RT

D (2) 

where R is the ideal gas constant, T is temperature, I refers to the low- O2 P surface, and II refers to the 

high- O2 P surface. These relations therefore define Dgb,O and Dgb,Al as a function of temperature and 

oxygen pressure, allowing full predictions of transport across a O2 P gradient, such as in a growing 

alumina scale. These authors (Ref. 24) applied such equations to FeCrAl oxidation literature values and 

provided a basis for the extended comparisons developed in this paper. Combined with the appropriate 

chemical potential gradients, these diffusivities present a strong case in support of primary inward oxygen 

flux and secondary aluminum outward flux for alumina scale growth (Ref. 24). 

As the following sections rely on a number of derivations from various kinetic relations, it may be 

useful to refer to the flow diagram in Figure 1 for an overall perspective of corresponding sections. 
NASA/TM—2013-217855 4 

2.2 Oxidation Models 

Oxidation processes are generally described by the Wagner relation for the counterdiffusion of ionic 

species across the chemical potential gradient in the scale, with za and zc ionic charge and Da and Dc

diffusivity of each anion (a) or cation (c) species (Ref. 23). With the parabolic rate constant kp defined as 

given below in (Eq. (3)), the appropriate form of the Wagner relation follows as (Eq. (4)). (Note: A factor of 

1/2 is often employed before the integral, but corresponds to the less frequently used differential form of kp

= 1xdx/dt, rather than the kp = 2xdx/dt definition used here; note t is time. Also, for the purpose of direct 

comparisons to diffusivities, the thickness form of scaling constants, in m2

/s, was ultimately adopted.) 

t

x

x k t k x p p i d

d

; 2 , 2   (3) 

2

O ,gas

O ,int

d ln

2

2

O

P

P

c a

a

c p D D P

z

z k  











   (4) 

where z is the valence of anions and cations in the compound. Now, turning to fine grain alumina scales, 

the importance of grain-boundary diffusion is well recognized and illustrated by the Hart/Smeltzer 

equations for alumina in Equations (5) and (6) (Refs. 25 to 27). Here the effective diffusion coefficient 

Deff is a function of the area fraction of short-circuit grain-boundary paths f, often simplified as 2/G, where 

 is the grain-boundary width and G is the grain size (diameter). In the case of alumina, it is generally 

observed that Dgb  DL (lattice diffusivity), leading to the following simplification in Equation (6): 

  eff 1 gb D   f DL  fD (5) 
NASA/TM—2013-217855 5 

G

D

D fD gb    2

eff gb (6) 

Most transport marker and tracer studies have indicated that the primary growth of alumina scales 

takes place by oxygen inward diffusion, although some outward growth of alumina scales has been 

clearly documented (Refs. 28 to 31). For the purpose of illustration, it is assumed here that Dgb,O  Dgb,Al; 

thus the latter will be omitted from the Wagner integral at present. However, it is also well established 

that grain “growth” can occur, increasing with scale thickness and temperature. Thus the scale growth rate 

becomes grain-size dependent and is best treated as an instantaneous value (subscript “i”). The resulting 

expression for kp,i is obtained by substitutions in Equations (3) to (6) to yield 

   

O ,gas

O ,int

2

2

2

O

gb,O

, d ln

2

d

d 2

P

P i

p i P

G

D

t

x k x (7) 

If the diffusion product Dgb,O and grain size are arbitrarily assumed to be invariant across the O2 P

gradient, the following oft-used integration for kp,i results: 

ln [LNP]

2

2

gb,O

, O

i

p i P

G

D

k 

 



 (8) 

Here  Dgb,O is designated as an approximate or average value and is referred to as the “LNP” solution. 

However, with the complete O2 P dependence provided by the permeability studies of Wada, Matsudaira, 

and Kitaoka (Ref. 24), the more precise relations for kp,i are obtained by integrating below, where A is the 

pre-exponential constant in Equation (10): 

  2 2

O ,gas

O ,int

d

2 exp 7 / 6 ,

2

2

O O

P

P i

p i P P

G

RT

Q A

k 

 



 





 (9) 

    [W-W- S]

12

6

467 kJ 2 2.207 10 exp gb,O,int

9

, 6

1

2 i

O

i

p i G

D

P

G

RT k



     

 (10) 

Finally, since 6

1

2

6

1

2 O O ,int

  P  P , it is seen by inspection that the Wagner integral of the Wada, 

Matsudaira, and Kitaoka diffusivity kp,i is reduced to a quite simple relation in Dgb,O, abbreviated here as 

the Wagner-Wada-Smialek (W-W-S) solution (Eq. (1)). Furthermore, the deviation in Dgb,O calculated 

from the W-W-S solution can be shown as an offset from the constant  Dgb,O (LNP solution, Eq. (8)) by 

the factor ln 6 O2  P in the final relation: 

i

O

i

p i G

D P

G

D

k 2 12 2 gb,O ln gb,O

,

 



 



 (11) 
NASA/TM—2013-217855 6 

[LNP] 6

ln

[W-W- S] gb,O

O

gb,O 2  



  D

P

D (12) 

3.0 Experimental and Predicted kp and Dgb,O 

Given these derivations and expressions, predictions for kp (W-W-S) from the Wagner integral will be 

compared, using these permeability expressions for grain-boundary diffusivity, with those determined 

experimentally. The results for the reverse calculation, showing what values of Dgb,O are obtained from 

applying the experimental oxidation results to the W-W-S solution, are then compared to those defined by 

the permeability expression, Equation (1). Results will also be presented for  Dgb,O , reflecting the 

departure that occurs if one assumes diffusivity is a constant or average across the O2 P gradient in the 

scale. This begins with the necessary thermodynamic treatment to obtain O ,int 2 P for the given alloy 

versus temperature, allowing the calculation of Dgb,O from the permeability expressions. This is followed 

by a summary of the experimental oxidation results needed to make these comparisons. The kp and Dgb,O

determined from experimental oxidation and diffusion models can then be compared to those predicted by 

the permeability relations. 

3.1 O2 P Calculations Versus Temperature 

The Wagner integration is performed over the O2 P limits for the scale, from the equilibrium 

dissociation pressure at the oxide-metal interface to that of the external gas. The former is obtained from 

the equilibrium constant of the oxidation reaction and the activity of aluminum in the alloy. The approach 

follows previous studies that predict O ,int,eq 2 P from thermodynamic databases and estimate diffusivity 

from scale growth kinetics (Refs. 10, 12, 14, 15, and 32). For the present example, using a typical 

Hoskins 875 heater alloy, approximately Fe-22.5Cr-5.5Al-0.5Si-0.2Zr by weight, Al activities were 

calculated by using the Pandat thermodynamic software package (CompuTherm LLC, Ref. 33) in 

conjunction with the Paniron database and equilibrium constants obtained from the FactSage 

thermodynamic database for chemical reactions (Center for Research in Computational Thermochemistry, 

Ref. 34). The pertinent relations are given below as Equations (13) and (14). The obtained activities aAl, 

equilibrium constants Keq, and O ,eq 2 P are given as a function of temperature in Table I and Figure 2. 

Given the high degree of linearity, a relation for the equilibrium pressure is also presented (Eq. (15)), 

obtained by regression of the data with a correlation coefficient of 1.000. This enabled the corresponding 

6

1

O2

 P and O2 ln P to be evaluated, as listed in the table. (These essentially converge to 6

1

2 O ,int

  P and 

–ln O ,int 2 P , respectively, because of the extremely low values of O ,int 2 P compared to O ,gas 2 P .) 

Al O2 Al2O3 2 2  3  (13) 

2

3

O2

2

Al

eq

1

a P

K  (14) 

 Pa 1012 kJ 6.117 10 exp 15

O2 , eq 



 



   

RT

P (15) 

   
NASA/TM—2013-217855 7 

TABLE I.—TEMPERATURE EFFECTS ON THERMODYNAMIC FACTORS FOR ALUMINA SCALES IN 

EQUILIBRIUM WITH FeCrAl(Zr)a,b

[Oxygen pressure at gas surface 4 PO2 ,gas  2.027 10 Pa.] 

Temperature, 

T, 

°C 

Aluminum 

activity, 

aAl

Equilibrium 

constant,a

Keq

Oxygen pressure at 

metal interface, 

O ,int 2 P , 

Pa 

6

1

O2

 P , 

6

1

Pa 

O2 ln P , 

Pa 

1000 9.76010–04 1.4001052 1.77810–26 19573.36 69.21 

1100 1.74710–03 1.2451047 1.90610–23 6118.07 62.23 

1200 2.89610–03 5.4091042 7.86110–21 2242.40 56.21 

1300 4.50910–03 8.4901038 1.49710–18 934.75 50.96 

1400 6.66510–03 3.8221035 1.51410–16 432.97 46.34 

  2

3

O2

2 eq Al a K  1 a P for 2Al 2O2 Al2O3  3  . 

b

Wagner integral limits on PO2 ,eq fixed by corresponding interfacial aluminum activity and equilibrium constant.

At this point, the relationships between kp, Dgb,O and O ,eq 2 P can now be employed to evaluate 

experimental data for scale growth and grain size as a function of time and temperature. However, it is 

instructive to first illustrate some broad implications for Dgb,O and Dgb,Al at both sides of the scale and 

for bulk alumina as well. The gas surface values are obtained from Equations (1) and (2), using O ,gas 2 P = 

2.027104

 Pa (0.2 atm). However, the interfacial equilibrium O ,int 2 P (i.e., referring to the metal-oxide 

interface) is given by Equation (15). Both result in a modified Ai

 exp  Qi RT form, where i designates 

an O or Al ion. Ai,gas  is given by n AiPO ,gas 2 and Qi

 = Qi from Equations (1) and (2). Ai,int  is given by 

n AiAPO ,gas 2 and O2 Qi,int  Qi  niQP  , as summarized in Table II (and compared further in Section 5.0). 
NASA/TM—2013-217855 8 

TABLE II.—GRAIN-BOUNDARY DIFFUSION COEFFICIENTS Dgb,X PREDICTED FROM 

PERMEABILITY RELATIONSa 

Temperature, 

T, 

°C 

Grain-boundary diffusivity, 

m3

/s 

Oxygen Aluminum 

Gas surface 

(bulk), 

Dgb,gas,O 

Metal 

interface, 

Dgb,int,O 

Gas surface 

(bulk), 

Dgb,gas,Al 

Metal 

interface, 

Dgb,int,Al 

1000 2.91210–29 2.97610–24 2.61810–29 6.05710–35

1100 7.24110–28 2.31310–23 1.67110–27 1.43110–32

1200 1.16410–26 1.36310–22 6.06610–26 1.60610–30

1300 1.31410–25 6.41610–22 1.39510–24 9.88310–29

1400 1.11110–24 2.51210–21 2.20510–23 3.71210–27

Pressure exponent, n –1/6 –1/6 +3/16 +3/16 

Pre-exponential factor, Aʹ, m3/s 4.2310–10 5.1610–12 1.5910–04 2.2610–02

Activation energy,a Qʹ, kJ/mole 467 298 604 794 a

Pre-exponential factors  i A and activation energies  i Q are adjusted by pressure, exponents, and energy associated with 

 PO2 ,eq in the general Arrhenius form of Dgb,i  Ai

exp  Qi RT .

The limiting relations for Dgb at each reaction surface for each ion are plotted in Figure 3. The 

highest Dgb is predicted for oxygen at the scale-metal interface, consistent with primary inward growth 

of alumina scales, as confirmed by virtually every diffusion study for -Al2O3 scales. Oxygen diffusivity 

at the interface is about 4 to 5 orders of magnitude higher than at the gas surface. Conversely, the highest 

Dgb for Al occurs at the outer gas surface. It is 3 to 5 orders of magnitude higher than at the scale-metal 

interface and similar to or slightly above the corresponding Dgb,O,gas. 
NASA/TM—2013-217855 9 

The broad arrows in Figure 3 indicate the changes in diffusivity obtained as the scale is traversed 

inward. The transition between predominantly Al outward to predominantly O inward has been predicted 

by Wada, Matsudaira, and Kitaoka (Ref. 24) and Matsudaira et al. (Ref. 18) to be extremely close to the 

gas surface, at just 0.01 percent of the thickness, consistent with the frequent observation of some slight 

outward growth of alumina scales. Thus they project that double oxidation experiment utilizing 16O/18O 

diffusion profiles actually ”probe” levels deeper than this transition and reflect transport still dominated 

by Dgb,O. 

Finally, it should be pointed out that Dgb,O measured on bulk alumina with no O2 P gradient (i.e., 

self-diffusion) should follow the relations for Dgb,O,gas, as appropriate to the external pressure. This is 

suggested as “bulk” behavior in Figure 3 and would be quite lower than (chemical) diffusivity throughout 

the scale (arrows). 

3.2 Oxidation Procedures 

To provide comparisons between permeability predictions for scales and actual data, we draw from an 

older dataset, originally intended to augment some early scale diffusivity discussions for NiCrAl 

(Refs. 20 and 21). For this purpose, a commercial ferritic FeCrAl(Zr) heater alloy, Hoskins 875, was 

utilized. The composition is listed in Table III. The alloy was obtained as rolled strip ~1 mm (~40 mil) 

thick and sectioned into 1.25- by 2.54-cm (0.5- by 1-in.) coupons. These were metallographically 

polished on emery paper down to a 600-grit finish, washed in detergent, and rinsed ultrasonically in 

ethanol. Samples were oxidized in high purity alumina boats at 1100, 1200, 1300, and 1400 C in static 

ambient air. Weight change was measured for samples pulled at various times up to 1000 h (at 1100 and 

1200 °C), 500 h (at 1300 °C), and 100 h (at 1400 °C). (Longer tests at the higher temperatures resulted in 

chemical failure of the scale at temperature.) Thus, each weight for each time and temperature exposure 

corresponds to a specific sample. As a consequence, these results may be subject to sample-to-sample 

variations, especially regarding dx/dt. In a few cases minor spalling was measured in the small crucibles 

containing the samples and was incorporated into the total mass gain, but it made little difference. 

Samples were pulled for grain-size measurements after oxidation for 0.1, 1, 10, 50, 100, 200, 500, and 

1000 h, where applicable. Grain size was measured at the oxide-metal interface by detaching the scale. To 

accomplish this, aluminum stubs were attached to the scale with epoxy, then detached by pulling in a 

tensile adhesion test jig. Numerous representative micrographs of the underside of the alumina grains 

were obtained by SEM. Also, the corresponding grain imprints in the exposed metal side of the coupon 

were measured. The recorded grain size was the largest diameter of a grain, averaged over ~100 grains 

measured for a given test condition. 

The underside of representative scale samples are presented in Figure 4. Figure 4(a) shows the 

noticeable temperature effect on the enlargement of grains formed after 100 h, and Figure 4(b) shows the 

time effect for grains formed at 1400 °C. At higher temperatures, a tendency for dimpled grains was 

noticed. These were matched and in contact with intergranular protrusions on the metal side and so were 

not voids. These features may indicate an increasing inward oxygen flux in the vicinity of the grainboundary relative to that along the lateral interface at higher temperatures. 

TABLE III.—COMPOSITION (wt.%) OF FeCrAl(X) ALLOYS WHERE OXYGEN GRAIN-BOUNDARY 

DIFFUSIVITY Dgb,O IS PREDICTED FROM OXIDATION KINETICS AND GRAIN SIZE 

Study Alloy Alloy composition, 

wt% 

Fe Cr Al Si Zr Y Other 

Smialek (current study) Hoskins 875 Bal. 22.5 5.5 0.5 0.2 ---- ---- 

Naumenko (Ref. 35) FeCrAlY Bal. 19.9 5.00 0 ---- 0.051 ---- 

Messaoudi (Ref. 36) Imphy Bal. 22.6 4.36 0.85 0.13 ---- 0.38 Mn, 0.35 Ni 

Ramanarayanan (Ref. 10) MA956 Bal. 20.0 4.5 ---- ---- ---- 0.5 Ti, 0.5 Y2O3
NASA/TM—2013-217855 10 

3.3 Experimental Weight Gain and Grain Size Data 

The weight gain and interfacial grain size data are given in Table IV. Although the details of the 

kinetic behavior are the subject of another study, it is noted that the weight gain was subparabolic, 

yielding a time exponent of t

0.37, while grain size followed a ~t0.26 dependence, on average. This is quite 

consistent with Deff being inversely related to grain size, where a t

0.375 oxidation law was predicted for the 

t

0.25 grain “growth.” (Oxidation time exponents (1/n) and grain growth time exponents (1/m) are related 

by n = 2m/(m–1), Refs. 21, 37, and 38). The t

0.37 rate is similar to the cubic FeCrAl(Y) oxidation law 

presented by Quadakkers et al. (Refs. 38 and 39). 

Similary, the grain expansion can be assessed in relation to the findings of Naumenko et al. for the 

case of FeCrAlY oxidized at 1200 and 1250 °C (Ref. 35). Here grain size G, elegantly measured by 

EBSD (electron backscatter diffraction) of FIB (focused ion beam) cross sections, was found to be a 

temperature-invariant function of scale thickness x in the form G = 0.27 + 0.13x (both in m). Using 

weight gain obtained in the present study of FeCrAl(Zr) (converted to 5.34 m thickness for each mg/cm2

of oxygen gained) from Table IV, interfacial grain size versus scale thickness was plotted in Figure 5. It is 

seen that the thinner scales cluster along the single curve of the Naumenko relation; however, positive 

deviation appears significant at the higher 1300 and 1400 °C temperatures. In any event, the importance 

of increasing grain size for thicker scales is clearly demonstrated. This treatment simply employs the 

instantaneous grain size (Table IV). 
NASA/TM—2013-217855 11 

TABLE IV.—PERTINENT SCALE GROWTH AND GRAIN SIZE DATA 

USED TO ESTIMATE i AND Dgb,O FOR HOSKINS 875a

(a) 1100 °C 

Time, 

h 

Scale weigh gain, 

x, 

mg/cm2

Scale growth rate, 

dx/dt

mg/cm2

h 

Grain size, 

G, 

m 

Oxidation product,a 

, 

m3

/h 

0.1 ----- ----- ----- ----- 

1 0.027 ----- 0.56 ----- 

10 0.192 1.0210–02 0.42 4.6910–02

50 0.438 4.2510–03 0.59 6.2810–02

100 0.591 2.2410–03 0.70 5.2810–02

200 0.752 1.3610–03 0.62 3.6110–02

500 1.010 3.9210–04 1.01 2.2810–02

1000 1.077 4.8010–05 1.18 3.4810–03

 

(b) 1200 °C 

0.1 ----- ----- ----- ----- 

1 0.152 ----- ----- ----- 

10 0.453 1.6610–02 0.53 2.2710–01

50 0.731 6.6710–03 0.80 2.2210–01

100 1.153 3.9410–03 1.05 2.7210–01

200 1.38 2.100–03 1.07 1.7710–01

500 1.725 8.0010–04 2.18 1.7210–01

1000 1.979 4.1910–04 1.66 7.8510–02

 

(c) 1300 °C 

0.1 0.125 9.5010–01 0.45 3.05 

1 0.492 1.8710–01 0.75 3.93 

10 0.910 3.6210–02 1.25 2.35 

50 ----- ----- ----- ----- 

100 2.147 8.5010–03 2.22 2.31 

200 2.801 5.1710–03 3.67 3.03 

500 3.713 1.2010–03 4.09 1.04 

1000 ----- ----- ----- ----- 

(d) 1400 °C 

0.1 0.246 1.7010+00 0.58 1.3810+01

1 0.764 3.4310–01 1.27 1.9010+01

10 1.731 7.1210–02 2.31 1.6210+01

50 ----- ----- ----- ----- 

100 4.063 1.1310–02 5.51 1.4410+01

200 ----- ----- ----- ----- 

500 ----- ----- ----- ----- 

1000 ----- ----- ----- ----- 

a

I is oxidation product i (= kp,i·Gi, where kp,i is the instantaneous value of the 

 parabolic growth constant and G, the instantaneous grain size) at the 

 low-oxygen-pressure surface. Dgb,O is the oxygen grain-boundary diffusion product. 
NASA/TM—2013-217855 12 

The corresponding specific, individually measured, instantaneous kp,i were determined from 

Equation (3), obtaining dx/dt graphically from the slope of x versus t plots. The variation with grain size is 

given in Figure 6. The initial values of kp,i decrease at the predicted rate according to G–1. These portions 

are thus consistent with the treatment of kp,i as a function of Deff = 2Dgb.O/Gi (Eq. (10)), with Dgb.O
NASA/TM—2013-217855 13 

assumed to be constant with time. They are therefore considered suitable for assessing grain-boundary 

diffusion as an invariant parameter in the scaling process. The minor fluctuations in each curve are 

believed to arise from graphically determining 2xdx/dt from a single oxidation curve generated by 

multiple samples, with perhaps some sample-to-sample variation, rather than using one continuous curve 

for one sample. Additionally, the variation in grain size could be substantial within any given sample, but 

the average values of many measurements should provide valid trends. 

3.4 Arrhenius Behavior of kp,i 

For purposes of consistent comparisons and subsequent calculation of a deconvoluted activation 

energy, the instantaneous kp,i were determined at the same grain size (0.5 m) for each temperature. Other 

grain sizes would also be appropriate for this analysis, up to about 1 m, according to Figure 6. An 

Arrhenius plot of the aforementioned kp,i,0.5, is presented in Figure 7. The fitted relation for kp,i,0.5, 

(r

2

 correlation coefficient of 0.98) is given by Equation (16) and shows an activation energy of 

375 kJ/mole. 

 m /s 375 kJ 4.29 10 exp 3 2 , ,exptl 



 



    

RT

k p i (16) 

This curve is now compared with data from the literature, where grain size was provided in addition 

to kinetics. Both parameters are available unequivocally from the study of Naumenko et al. (Ref. 35). 

Here, well-defined data were examined to determine the equivalent thickness for a 0.5-m grain size for 

scales grown on FeCrAlY (Table III) at 1200 °C. Their equation for grain size yields a scale thickness of 

1.77 m for an interface grain size of 0.5 m. This was then used in their cubic polynomial describing 

scale growth, 0.13x

3

/3 + 0.27x

2

/2 = Ct, where C can be shown to be 0.2273 m3/h. Differentiating and 

solving for 2x dx/dt yields 2C/G. At G = 0.5 m, 2C/G yields 0.909 m2

/h or 2.52510–16 m2/s for kp,i. 

The latter value, plotted as the square symbol in Figure 7, is seen to fall directly on the 0.5-m regression 

curve for the present FeCrAl(Zr) alloy. This agreement provides some degree of confidence with the 

present technique in which separate samples were used to determine kp,i and Gi. 
NASA/TM—2013-217855 14 

Similarly, the oxidation behavior of an Imphy FeCrAl(Zr,Si) alloy (Imphy Alloys, Inc.) 

(see Table III) by Messaoudi, Huntz, and Lesage (Ref. 36) is presented as open diamonds. Here the 48-h 

average parabolic growth rate kp,avg was reported, but it corresponds to similar but slightly varying G48h = 

0.3, 0.6, and 0.8 m at 1000, 1100, and 1200 °C, respectively. Again, the data are seen to fall near the 

present data or regression line. Finally, the average 100-h data of Ramanarayanan et al. (Ram) from 

Reference 10 for MA956 (an FeCrAl-Y2O3 alloy, Special Metals Corp.), Table III, oxidized at 900 to 

1200 °C, are presented according their Arrhenius relation, converted to kilojoules and meters squared per 

second:

 m /s 388 kJ [Ram] 1.20 10 exp 2 2 , ,100 



 



    

RT

k p i (17) 

Here it should be noted that a relatively constant grain size of 0.5 m was reported for the 100-h TGA 

(thermogravimetric analysis) test (increasing to only 0.75 and 1.25 m for 300- and 1000-h exposures, 

respectively). This effectively allows direct comparison with the present kp,i data and is seen to lie 

essentially on the same line. 

3.5 kp,i Predicted From W-W-S Permeability Relations 

Having established a valid Arrhenius plot of kp,i (i.e., without grain growth), it is now possible to 

compare predicted kp from the permeability studies and the W-W-S solution (Eq. (10)) developed above, 

all for a grain size of 0.5 m. Using the permeability equation reported for Dgb,O and the values for 

6

1

O2

 P from Table I, the values shown as “” in Figure 7 are produced. These are higher than those 

determined from oxidation experiments and result in an activation energy of 298 kJ/mole, somewhat 

below the 375 kJ/mole determined from oxidation. The Arrhenius dependency obtained with r

2

 = 1.000, 

when combining equations for Dgb,O and O ,int 2 P in the W-W-S solution (Eqs. (1), (10), and (15)), is 

given by 

 m /s 298 kJ [W-W-S] 1.24 10 exp 4 2 , 



 



   

RT

k p i (18) 

As will be discussed later, the discrepancy between the refined oxidation data (Eq. (16)) and the derived 

W-W-S solution (Eq. (18)) may be due in large part to the fact that the former pertains to doped alumina 

scales while the latter pertains to pure alumina. 

3.6 kp,i Prediction Assuming O2 P -Independent Diffusivity (LNP Integral) 

As will be discussed below, analyses of alumina scale growth frequently assume a constant diffusivity 

across the scale. The permeability studies of Matsudaira (Ref. 18) suggest that this is somewhat true for 

much of the thickness for the proposed oxidation case modeled for FeCrAlY (Y2O3) alloys at 1100 °C and 

an interfacial O2 P of ~10–23 Pa. Their model predicts Dgb across the much of scale is close to that given 

by the O2 P at the interface (10–23 Pa). A simple comparison of the LNP solution to the W-W-S solution 

was given as Equation (12) and can be shown to be approximately a factor of 8 to 11 higher: 

10

6

ln

6

ln

[W-W-S]

[LNP] O O ,int 2 2     P P

k

k

p

p (12b) 
NASA/TM—2013-217855 15 

This is presented as the topmost LNP curve in Figure 7 and is seen to have a slightly lower activation 

energy and to deviate further from the experimental data. Alternatively, experimental values of kp,i can be 

used to predict the grain-boundary diffusion product Dgb,O,int by both the W-W-S or LNP approaches, 

then compared to those predicted by permeability studies from Equation (1) as well as values obtained 

from tracer studies on bulk alumina. These results are presented in the following section. 

4.0 Dgb,O Predicted From Permeability Relations and Oxidation Data 

The permeability studies have offered relations allowing for the prediction of Dgb,O once the O ,int 2 P

has been determined. This enabled the prediction of oxidation rates for given scale grain sizes using both the 

LNP and W-W-S solutions to the Wagner equation (Eqs. (8) and (10)) and comparison to those actually 

measured. In the following the reverse occurs; namely, estimates of Dgb,O are obtained from the oxidation 

data and then compared to those predicted by the permeability and 18O tracer studies of bulk alumina. 

4.1 Time-Invariant Oxidation Product, 

In order to properly assess the calculation of Dgb,O,int from oxidation data, it is first useful to 

introduce the concept of a time-invariant constant scaling product, i = kp,iGi. This follows from 

Equation (10) when the inputs to the Wagner integral, the diffusion product Dgb and O2 P at the interface 

(fixed by interface composition), do not change with time. Accordingly, the experimental values of i are 

presented as a function of time for the four temperatures of this study in Figure 8. (The use of t

1/2 as the 

x-axis is of no mechanistic significance; it was adopted merely to provide a reasonable comparison of the 

data without going to the extreme of a log scale). The plot does suggest invariance of i, at least for most 

of the initial portion of the oxidation curves. The dashed lines indicate average values for the invariant 

regions (first three or four data points to about 200 h). An appreciable drop in i is noted at long 500- to 

1000-h exposures and suggests a reduction in Dgb or an increase in O ,int 2 P , perhaps due to aluminum 

depletion. 
NASA/TM—2013-217855 16 

Finally the rigorously measured 1200 °C FeCrAlY data of Naumenko et al. (Ref. 35) are presented 

here as open symbols for kp,iGi. Here grain size data (G) and scale thickness (x) (from Figs. 6 and 10 in 

Ref. 35) were used for samples oxidized for 24, 93, 500, and 2000 h. The quantity dx/dt was estimated 

graphically (from curves in Fig. 10 of Ref. 35). Thus kp,i = 2x dx/dt and i = kp,iGi were evaluated from 

the raw experimental data (symbols). It is also noted that i may be obtained more analytically from their 

relations for x(t) and G(t) determined from the continuous 100-h isothermal oxidation TGA data. It can be 

shown that 2C = kp,iGi = i, a constant equal to 0.4546 m3

/h (1.26310–4m3/s) (dashed line) and 

implies Dgb for the more general case. 

4.2 FeCrAl(Zr) Oxidation Results (This Study) 

With well-behaved kinetic behavior established under defined microstructural conditions, 

experimental kp,i and Gi can now be used to predict Dgb derived from scale growth data. Again the 

W-W-S solution (Eq. (10)) is employed, but in reverse. The resulting behavior is given in the Arrhenius 

plot of Figure 9. The same activation energy and correlation coefficient of r

2

 = 0.98 are obtained, and the 

full relation given as– 

 m /s [W- W -S] 375 kJ (oxidation) 1.79 10 exp 10 3

gb,O 



 



     

RT

D (19) 
NASA/TM—2013-217855 17 

The same offset is seen from the values predicted from permeability relations here as found for kp,i in 

Figure 7. Values of Dgb.O,int. determined from the Wada, Matsudaira, and Kitaoka (Ref. 24) relations in 

Equation (1) using the interface values of O ,eq 2 P in Table I yield 

 m /s [Wada, ] 298 kJ (permeability) 5.16 10 exp gb

12 3

gb,O D

RT

D   

 



      (20) 

Also,  Dgb,O treated as an average or constant value across the O2 P gradient (outside the Wagner 

integral) yields the LNP solution (Eqs. (8) and (11)): 

 m /s [LNP] 394 kJ (oxidation) 8.12 10 exp 11 3

gb,O 



 



      

RT

D (21) 

This is seen in Figure 9 (filled triangles) to be below that produced by using the experimental data in 

the W-W-S solution, again by the factor ln 6 O2  P as expected from Equation (12). The differences 

reflect the 6

1

O2



P versus O2 ln P integration limits for the two expressions in the Wagner integral. 

Also shown are literature values obtained as in Figure 7, when the grain size was known well enough 

to estimate the oxidation product . They are seen to essentially lie on the same curve as the present data. 

4.3 Comparisons to Oxidative Literature Values for  Dgb,O

Now Figure 10 compares the  Dgb,O results for the LNP solution with similar values obtained from 

the oxidation literature. Data from Young et al. (Ref. 12), obtained from the same FeCrAlY alloy as 

Naumenko et al. (Ref. 35), are included as the cross-square symbols (Eq. (16) in Ref. 12). They are seen 

to fall close to values predicted for the present data using this LNP formula (i.e., assuming that Dgb,O is 

independent of ) O2 P . Also included are data similarly obtained for Y2O3-dispersion-strengthened 

FeCrAl, MA956 (Refs. 13 and 14), with a reported activation energy of 294 kJ/mole, as compared to the 

394 kJ/mole determined from the LNP analyses of the present FeCrAl(Zr) data. The same alloy had been 

characterized earlier by Ramanarayanan et al. (Ref. 10). Using their reported average kp and grain size, 

the LNP results are again seen to fall exactly on the line representing the present study, with an activation 

energy of 388 kJ/mole, and remarkably close to those reported by Clemens et al. for this alloy (Ref. 14). 

However, Ramanarayanan et al. (Ref. 10) also performed their own Dgb,O analyses but arrived at a 

different expression: 

 m /s 560 kJ (oxidation) 4.92 10 exp 8 3

gb,O 



 



      

RT

D (22) 

This was seen to diverge to substantially higher values of Dgb,O and is not shown here. It is also said 

to be adjusted by 6

1

O2

 P , presumably for the environmental test atmosphere, the gas surface. 

Furthermore, an analogous LNP analysis was performed on the MAX compound, Ti3AlC2 (Ref. 32), 

shown as the crossed diamonds in Figure 10. Except for short times, especially at lower temperatures, the 

scales were primarily -Al2O3. Their results are very close to that presented for the four FeCrAl alloys in 

Figure 10, and linear regression produced 375 kJ/mole. In total, the plot in Figure 10 shows reasonable 

agreement from seven separate studies. Although this agreement in experimental data is encouraging, it does 

not necessarily indicate that the LNP solution is the preferred method of calculating Dgb,O. It just means 

that there are many studies with an available  Dgb,O determined this way. Had all the studies provided kp,i

and corresponding Gi data one could evaluate the same studies via the W-W-S solution as well. 
NASA/TM—2013-217855 18 
NASA/TM—2013-217855 19 

Regarding the two W-W-S and LNP techniques used to calculate kp,i from Dgb,O, it is again useful to 

recall the standard factor relating these terms as stated in Equations (8) and (10). Here it was shown that 

the factor relating kp,i (LNP), as a constant or average  Dgb,O , to the kp,i (W-W-S) was ln 6 O2  P

(Eqs. (11) and (12)). This offset was indicated in Figure 7. Conversely, any Dgb,O determined from the 

same experimental kp,i using a constant  Dgb,O outside the Wagner integral will be the inverse factor of 

O2 6 ln P times Dgb,O,int determined from the W-W-S relation. This factor is so indicated in Figures 9 

and 10. It is thus seen that the LNP analyses predicted kp further from the experimental kp (Fig. 7) or 

Dgb,O,int further from the permeability derived relations than did the W-W-S analyses (Fig. 9). 

4.4 Comparison With Dgb,O Measured by 18O Tracer Studies 

Finally, as with most discussions of diffusion in alumina scales, a more global perspective is provided 

by comparing these predictions with summary plots of diffusion in alumina, such as those recently 

discussed by Heuer et al. (Refs. 22 and 40) in Figure 11. Here Dgb,O data measured from 18O tracer 

experiments for both bulk alumina (under no O2 P gradient) and alumina scales (growing in a large 

gradient) are compared. The top curve (i) is that obtained by applying the Wada, Matsudaira, and Kitaoka 

(Ref. 24) relation for diffusivity to the low O2 P interface on a growing scale (Eqs. (1) and (20), Table II). 

The middle curve (ii) is that predicted from the present data for alumina scales formed on Hoskins 875 

FeCrAl(Zr) (Eqs. (10) and (18)). Here oxidation kinetic and grain size data use the W-W-S solution, 

predicting diffusivity from i (kp,i and Gi). The next curve (iii) is that obtained from the same oxidation 

data, but now using the O2 ln P solution (LNP, assuming a constant average  Dgb,O , Eqs. (8), (11), and 

(21)). The individual data points for curves 1 to 3 had been shown in Figures 9 and 10. The lowest curve 

(iv) was obtained from the permeability-derived equation for Dgb,O,gas for the case of exposure to 1 atm 

air, with no O2 P gradient (Eq. (1), Table II, Fig. 3). 

The 18O tracer studies for bulk alumina refer to pure or Mg-doped Al2O3 for Reddy and pure or Y-doped 

Al2O3 from Prot et al. (Refs. 41 to 43). Only curve 4, appropriate for bulk alumina without a O2 P gradient, 

appears to approach magnitudes of the undoped or Mg-doped Al2O3, but the data are quite high compared to 

that extrapolated from Y-doped Al2O3.Curve 4 does not have an activation energy similar to any of these, 

but at least is much closer than any predictions for Dgb,O appropriate for oxidation (curves 1 to 3). 

The 18O tracer studies for double oxidation of FeCrAl alloys refer to those of Messaoudi et al. 

(circles, squares, and diamonds) (Ref. 36) and Chevalier et al. (triangles) (Ref. 44). The 1100 °C point for 

MA956 (Refs. 14 and 45) is also included (dotted hexagon) as it corresponds to fitting an 18O SIMS 

profile. All the alloys of Messaoudi are in the vicinity of curve (iv) for bulk alumina, whereas the 

undoped alloy of Chevalier (open triangles) is grouped near curve (ii) predicted for growing scales. The 

Y-doped alloy (filled triangle), however, is near the Messaoudi data and curve (iv). The Clemens/ 

Bongartz point falls directly on the permeability LNP solution, as in Figure 10. Thus only some 18O tracer 

data seems comparable to the appropriate permeability predictions. These inconsistencies are difficult to 

resolve and underscore the challenges encountered with measuring or predicting diffusivity in alumina 

scales and comparing the same to that measured for bulk alumina. (It should be noted that more 

measurements for bulk alumina from Reference 44 (not shown) fall between the oxidation values, far 

from other bulk data, and are not reconciled here). Overall it is seen, as in Figure 3, that the O2 P gradient 

in a scale can result in diffusivities expected to be 3 to 5 orders of magnitude greater than for bulk 

alumina in no O2 P gradient. It also appears that some double oxidation experiments may reflect this in 

varying degrees. 
NASA/TM—2013-217855 20 
NASA/TM—2013-217855 21 

Finally, comparison is now made to more recent data for individual grain boundaries in bulk alumina 

(Fig. 12). The lower band (oriented) refers to bicrystal studies with varying habit planes and coincident 

site lattice  values (Ref. 46). The values for two 7 and 31 boundaries are quite close to those projected 

from the permeability relations for bulk alumina at atmospheric conditions, whereas the remaining curves 

are well below these. The upper cluster of points (random), recently obtained for individual grain 

boundaries in bulk polycrystalline (Ref. 47, personal communication), appears in a band with values near 

the projection of the W-W-S curve for scales. Since these represent boundaries where substantial tracer 

concentrations were observed, they may represent an upper band of diffusivities. In all, a variability of up 

to 8 orders of magnitude may be concluded from the bulk alumina data. Clearly, the nature of each grain 

boundary is of great importance and will enter into any discussion of alumina scale growth. At present, 

we can only assume that scale growth is controlled by some distribution of countless grain-boundary 

orientations, perhaps affected by growth textures in special cases. 
NASA/TM—2013-217855 22 

5.0 Activation Energies 

A catalogue of activation energies obtained is presented in Table V. The top entry indicates the 

thermodynamic parameter resulting from an Arrhenius relation of the equilibrium O2 P for the oxidation 

reaction (Fig. 2). The temperature dependence of the free energy of Al2O3 formation provides the 

dominant effect here. The next two values are those determined by Wada, Matsudaira, and Kitaoka 

(Ref. 24) for oxygen and aluminum boundary diffusion under atmospheric conditions, with O2 P

~0.2 atm, independent of temperature (Fig. 2). The following two apply to the scale-metal interface 

(Table II and Fig. 2). It is seen that Qint = Qperm+ nQeq, where Qint is the activation energy resulting for 

diffusivity at the O2 P calculated for the scale-metal interface, Qperm is that provided from the 

permeability-derived diffusion relations (Eq. (1)), n is the exponent of the n PO2 term in the latter, and Qeq

is that produced by the temperature dependence of O ,eq 2 P . Thus, the activation energies for oxygen and 

aluminum diffusivity at the interface are reduced by 1/6  (1012 kJ/mole) and increased by 3/16 

(1012 kJ/mole), respectively. 

TABLE V.—ACTIVATION ENERGIES REPORTED FOR Dgb,O AND Dgb,Al 

[Calculated from permeability equations and estimated Dgb,O for FeCrAl(X) alloys using 

Wagner-Wada-Smialek (W-W-S) and O2 ln P solutions.] 

Source Application Valuea Activation energy, 

Q, 

kJ/mole 

Reference 

Thermodynamic Al2O3 - FeCrAl PO2 ,eq 1012 Jacobson (current study) 

Wada Bulk, scale (gas) Dgb,O 467 Wada (Ref. 24) 

Wada Bulk, scale (gas) Dgb,Al 604 Wada (Ref. 24) 

Wagner-Wada Scale, interface Dgb,O 298 Current study 

Wagner-Wada Scale, interface Dgb,Al 794 Current study 

FeCrAl(Zr) Scale (measured) kp,i 375 Current study 

FeCrAl(Zr) Scale (W-W-S) Dgb,O 375 Current study 

FeCrAl(Zr) Scale (LNP) Dgb,O 394 Current study 

FeCrAl-Y2O3 Scale (W-W-S) Dgb,O 388 Ramanarayanan (Ref. 10) 

FeCrAl-Y2O3 Scale (LNP) Dgb,O 294 Clemens (Refs. 13 and 14) 

FeCrAlY Scale (LNP) Dgb,O 321 Young (Ref. 12) 

Ti3AlC2 Scale (LNP) Dgb,O 375 Wang (Ref. 32) 

NiAl(Zr) Scale (creep) Dgb 434 Veal (Ref. 48) 

a PO2 ,eq is equilibrium oxygen pressure, Dgb is grain-boundary diffusion product (for oxygen, O, and 

aluminum, Al), and Dgb is grain-boundary diffusivity.

The kp,i experimental data of the present study are given next and yield 375 kJ/mole. This is 

maintained in the Wagner-Wada-Smialek derivation of Dgb,O, but changes to 394 kJ/mole in the O2 ln P

analysis, similar to 388 kJ/mole determined from the Ramanarayanan data. The last three list O2 ln P

results, giving 294, 321, and 375 kJ/mole for Dgb,O from oxidation of MA956, FeCrAlY, and Ti3AlC2, 

respectively. The first value (Ref. 14) may have been influenced by the high value at 900 °C; the next 

series (Ref. 12) was obtained from a narrow 100 °C temperature range, and the last (Ref. 32) is in closer 

agreement with the present study. All of these are substantially lower than the bulk alumina studies shown 

in Figure 11. 
NASA/TM—2013-217855 23 

6.0 Additional Transport Issues 

Up to this point the coupling of the permeability relations with oxidation kinetics has concentrated on 

oxygen grain-boundary diffusion in pure alumina. To some extent, this is all that is practical given that it 

is difficult to reliably separate any Al outward growth from primarily inward O growth. Furthermore, the 

study of dopant effects on diffusivity in bulk alumina is ongoing, with perhaps a tenuous connection to 

thermally grown scales with various grain-boundary dopant distributions. 

6.1 Aluminum Diffusion 

The importance of aluminum outward diffusion is often discussed in the literature, but it is not 

considered here given the detail required to cover just oxygen diffusion. For the sake of completeness, the 

same Wagner-type integrations were performed for the Wada relation for Dgb,Al (Eq.(2)) and are listed in 

Appendix C. It is noteworthy that similar reduced terms result, allowing the Al diffusional component of 

kp to be given as a simple function of Dgb,Al,gas (Eq. (C4)), such that 

i

p i G

D

k

W-W-S

gb,Al,gas

, ,Al

16   (C4) 

and the W-W-S expression is related to the LNP solution or average diffusivity by the factor 3/16 

ln . O2  P The difficulty, as with any system exhibiting mixed transport, is experimentally differentiating 

the minor Al contribution from that of oxygen to kp,i (Refs. 29 to 31). 

We expect that the majority of transport is by oxygen diffusion, as controlled by the interface , O2 P

such that oxygen diffusivity at the interface is 2 to 5 orders of magnitude greater than aluminum at the gas 

surface, the largest differential being at lower temperature. Furthermore in the modeled case of oxidation 

at 1100 °C, Al diffusivity is seen to be negligible except at the outermost near surface of the scale (Fig. 10 

in Ref. 18). Thus the focus on oxygen diffusivity in the present study is consistent with the permeability 

projections. 

6.2 Dopant Effects 

It must be acknowledged that Al transport is a key factor in explaining growth stress and the 

formation of oxide within the scale or at outer grain-boundary ridges. The effects of impurities or 

intentional dopants often enter this conversation, as in producing charge compensating defects that may 

affect Al diffusion. Although, again, not the focus of the present study, the permeability experiments 

performed on Lu-, Y-, and Hf-doped alumina addressed these issues, reaching O2 P down to 10–8 Pa 

(Refs. 17, 18, and 49). It was found in general that Lu and Y dopants (on the order of 0.4 at.% Lu2O3) 

reduced oxygen grain-boundary diffusivity by about 3 times, with no change in aluminum diffusivity, 

whereas Hf dopants (0.2% HfO2) reduced Al diffusivity by about 2 times, with no change in oxygen 

diffusivity. This is supported by an order of magnitude reduction in oxygen diffusivity for an Y-doped 

bicrystal found in tracer studies (Ref. 50). Surprisingly, co-doping with equal amounts of Lu and Y 

produced about a 1.5-times increase in both Al and O diffusivity in the permeability studies (Ref. 18). 

These results support the often-observed beneficial effect of Hf dopants on alumina scale growth, but do 

not completely resolve effects typically reported for optimum Y-doping or co-doping where Al diffusivity 

and outward growth appear to be reduced. In the present study, it may be expected that some of the 10 to 

40 times lower offset of oxidation-derived values in comparison to permeability predictions (Figs. 7, 9, 

and 10) are due to dopant effects. In this work and the Messaoudi data (Ref. 36), the dopant was Zr and 

may be expected to exhibit effects similar to those of Hf. However, examination of these figures shows 

that the data for Zr, Y, Ti, and Y2O3 dopants all agree with nearly a single Arrhenius relationship. Thus 
NASA/TM—2013-217855 24 

clear discrimination of oxidation kinetics by dopant type, to the extent suggested by the permeability 

studies, has not emerged. 

There has been much discussion of various effects of Y-doping (or other reactive elements). Initially 

reduced Al transport, growth stress, and buckling occur as Y levels increase and then give way to 

increased weight gains and disruptions from oxidation of Y-rich precipitates (e.g., YAG, yttrium 

aluminum garnet) and oxide intrusions. Finally, Hf dopants are recognized as perhaps the most effective 

in reducing kp, by about an order of magnitude, and receive a great deal of attention in protective 

commercial Hf-modified MCrAlY overlay or NiAl diffusion coatings (Ref. 4). There does not yet seem to 

be an exact correlation between dopant effects on oxidation with those predicted by the permeability 

studies. 

It is acknowledged that 10 to 100 ppm of common Ni, Co, Fe, Cr, and Si base metal impurities may 

be present in alumina scales grown on typical alloys. A comparison of reactive element dopant effects in 

bulk aluminas containing these metals may thus provide further insight if data from a “pure” alumina 

scale were analyzed, such as that formed on Pt-Al alloys. 

6.3  Decay for FeCrAl(Zr) 

According to Equation (10) the oxidation product  = kp,iGi should be a constant and equal to 12 

Dgb,O. This was indeed the case for the 1200 °C FeCrAlY data in Figure 8 (Ref. 35), even out to 2000 h. 

However, the present study suggests an accelerating decrease in this term after about 200 h. One potential 

cause might be reduced grain-boundary diffusion according to Equation (10). Although there is no 

evidence either way, significant Al depletion would reduce the interfacial Al activity and increase O ,eq 2 P

according to Equation (14). Then an increase in O2 P would result in a decrease in Dgb,O according to 

Equation (1). Since the Al content and thickness of the Naumenko samples were less than the present 

FeCrAl(Zr) alloy, it cannot be argued that greater Al depletion from a reduced Al reservoir resulted in the 

present study. Nor was greater spallation observed. At present there is no compelling explanation for the 

long-term decay in the oxidation product, . 

7.0 Summary and Concluding Remarks 

The temperature and pressure dependence of oxygen and aluminum grain-boundary diffusivity were 

determined by permeability studies of pure bulk alumina wafers by Wada, Matsudaira, and Kitaoka in 

2011. Their work is extended in the present study to further elucidate the growth kinetics of hightemperature alumina scales as a function of grain-boundary diffusivity, Dgb. First, equilibrium 

thermodynamics was applied to the case of a commercial FeCrAl alloy to determine the equilibrium 

oxygen pressure at the metal interface O ,int,eq 2 P . These values and the permeability relations were 

applied to a modified Wagner equation for ionic scales. For growth primarily by oxygen grain-boundary 

diffusion, the following relation was developed (Eq. (18)) for the instantaneous parabolic rate constant 

(at a grain size of 0.5 m): 

 m /s 298 kJ [W- W-S] 1.24 10 exp 4 2 , 



 



    

RT

k p i

This is compared to a relation determined experimentally (exptl) for the same scales (Eq. (16)), with a 

moderately higher activation energy: 

 m /s 375 kJ 4.29 10 exp 3 2 , ,exptl 



 



    

RT

k p i
NASA/TM—2013-217855 25 

It is also found that a grain-size invariant oxidation rate product,  = kp,i·Gi is a simple function of 

oxygen grain-boundary diffusivity from a Wagner-Wada-Smialek (W-W-S) derivation. Thus, from 

Equation (10), 

, gb,O,int i  k p iGi  12D

here Dgb is a strong function of O2 P and varies across the scale. This provides a surprisingly convenient 

means of drawing comparisons: it allows either prediction of oxidation rates from independently measured 

diffusivity or prediction of grain-boundary diffusivity from instantaneous oxidation rate and grain size. As 

simple as this relation appears, the real complexity of transport issues are embedded in the starting 

permeability relations, the Wagner integral, and the Hart/Smeltzer diffusivity equations. 

Comparisons to similar oxidation studies yielded relative overall agreement, confirming some level of 

confidence in the experimental data and the concept of an invariant oxidation constant, . The predicted 

oxidation kinetics trended from ~10 to 40 times greater than the experimental values as temperature was 

reduced. Although this is not exact agreement, it is enormously closer than extrapolations of bulk alumina 

diffusivity studies obtained with no O2 P gradient. Moreover, the discrepancy may be partially ascribed to 

the experimental data pertaining to doped alumina scales, whereas the predicted data are for pure alumina. 

For the sake of completeness, comparisons were made to predictions where constant (average) 

diffusivity was assumed across the scale. Here a standard correction factor,  ln  6 O2  P could be 

applied to obtain kp,i from the comparable W-W-S expression or the inverse factor for obtaining 

diffusivity from the experimental kp,i. Also, the extremes of aluminum and oxygen diffusivity were 

explored at each interface, and Dgb,Al was found to be negligible compared to Dgb,O, except at the gas 

surface. Though not utilized here, an analogous method resulted in a simplified W-W-S relation for 

Dgb,Al, which can just be added to the oxygen contribution for a full solution to the Wagner integral 

(Eq. (B4)): 

W-W-S , ,Al gb,Al,gas k p i Gi 16D

In all, the permeability studies, by quantifying O2 P effects on grain-boundary diffusivity, have allowed 

for improved insights and closer connections between predicted diffusivity and alumina scale growth 

kinetics. 

NASA/TM—2013-217855 27 

Appendix A.—Symbols 

Symbols: 

A pre-exponential exponent from Equation (9) 

a activity 

D diffusivity 

f area fraction of short-circuit grain-boundary paths 

G grain size (diameter) 

k oxidation rate constant 

K equilibrium constant 

P pressure 

Q activation energy 

R ideal gas constant 

r

2

 correlation coefficient 

T temperature 

t time 

x scale weight gain, or equivalent thickness 

z ionic charge 

 grain-boundary width 

 oxidation product 

Subscripts: 

0.5 0.5-m grain size 

I low- O2 P surface 

II high- O2 P surface 

a anion 

Al aluminum 

c cation 

eff effective 

eq equilibrium 

exptl experimental 

gas gas 

gb grain boundary 

i instantaneous 

int interface 

L lattice 

m grain growth time exponent 

n oxidation time exponent 

O oxygen 

O2 oxygen gas 

p parabolic 

perm permeability 

NASA/TM—2013-217855 29 

Appendix B.—Defect Equilibria, Electroneutrality, and O2 P

The oxidation reaction and basic defect equilibria for undoped alumina can be described by Equations 

(B1) to (B5) using Kröger-Vink notation (Ref. 23). Equations (B2) and (B4) apply to the oxygen vacancy 

concentration    VO at the low- O2 P surface (n-type), and Equations (B3) and (B5) apply to the aluminum 

vacancy concentration   VAl  at the high- O2 P surface (p-type). The equilibrium constants are then written 

as Equations (B6) to (B8), corresponding to Equations (B1) to (B3). Solving the electroneutrality 

relations Equations (B4) and (B5) for [Vi] and substituting into the corresponding equilibrium relations 

Equations (B7) and (B8) produce Equations (B9) and (B11), respectively. Finally, combining Equation 

(B1) with (B9) produces Equation (B10). Thus, at the low- O2 P surface    VO is proportional to 6

1

O2



P , and 

at the high O2 P surface   VO

 is proportional to 16

3

O2 P . 

Al O2 Al2O3 2 2  3  (B1) 

2Al  2AlAl  3VO  6e(n - type)   (B2) 

O 3OO 2 Al 6 (p - type) 2 2 3     V  h (B3) 

V    e  2 O (B4) 

     3VAl   h (B5) 

2

3

O2

2

Al

1

1

a P

K  (B6) 

   

2

Al

6 3

O

2

2

1

a

V e K  



 (B7) 

    2

3

O2

6 2

Al

3

3

1

P

V h K

   (B8) 

 

2

Al

9

O

6

2

2

a

V K



 (B9) 

  6

1

2

3

2

O

1 9

1

2

O 2   















  P

K

K V (B10) 

  3 16

O

1 8

3 ''' 3 4

Al 2 3  V  K P (B11) 

   

NASA/TM—2013-217855 31 

Appendix C.—Relations Derived for Aluminum 

Grain-Boundary Diffusivity, Dgb,Al

The complete Wagner expression for alumina growth by aluminum and oxygen diffusion is obtained 

from Equation (4) as 

     

O2 ,gas

O2 ,int

O O2 , eff,Al eff, d ln 2

3

d

d 2

P

P

p i D D P

t

x k x (C1) 

Dealing again only with one component, the aluminum contribution, obtained from Equation (2) 

(repeated here): 

16

3

2 O ,II

5

gb,Al

604 kJ 2.475 10 exp   



 



     P

RT

D

produces the following form, Equation (C2), integrated to Equation (C3) (Wagner-Wada-Smialek, 

W-W-S) and simplified to Equation (C4) (and (C5) if a constant  Dgb,Al is assumed). Finally, the 

relationship between the W-W-S and LNP solutions for Dgb,Al are given by Equation (C6): 

  

O2 ,gas

O2 ,int

d ln

2

2

3 gb,Al

, ,Al

P

P i

p i P

G

D

k (C2) 

16

3

O2

2 2

, ,Al 16

exp  





 





 P

G

RT

Q A

k

i

p i (C3) 

i

p i G

D

k

W-W-S

gb,Al,gas

, ,Al

16  (C4) 

O2

gb,Al

, ,Al ln

3

P

G

D

k

i

p i 

 



 (C5) 

 



  gb,Al

W-W-S O

gb,Al,gas 16

3 ln 2 D

P

D (C6) 

   
NASA/TM—2013-217855 32 

References 

1. Hindam, H.; and Whittle, D.P.: Microstructure, Adhesion and Growth Kinetics of Protective Scales 

on Metals and Alloys. Oxid. Met., vol. 18, nos. 5‒6, 1982, pp. 245‒284. 

2. Hou, Peggy Y.: Impurity Effects on Alumina Scale Growth. J. Am. Ceram. Soc., vol. 86, no. 4, 

2003, pp. 660‒668. 

3. Stott, F. Howard: The Oxidation of Alumina-Forming Alloys. High Temperature Corrosion and 

Protection of Materials 4, vols. 1 and 2, 1997, pp. 19‒32. 

4. Pint, B.A.: High Temperature Corrosion of Alumina-Forming Iron, Nickel and Cobalt-Base Alloys. 

Schreir’s Corrosion, Fourth ed., vol. 1, 2010, pp. 606‒645. 

5. Huntz, A.M., et al.: Diffusion Studies in Oxides Scales Grown on Alumina- and Chromia-Forming 

Alloys. Scr. Mater., vol. 37, no. 5, 1997, pp. 651‒660. 

6. Balmain, J.; Loudjani, M.K.; and Huntz, A.M.: Influence of Yttrium on Transport Properties of α

Alumina Scales Developed on Yttrium Implanted β NiAl. Radiat. Eff. Defects Solids, vol. 137, 

nos. 1‒4, 1995, pp. 291‒294. 

7. Balmain, J.; and Huntz, A.M.: Improvement of the Application of an Electrochemical Method for 

the Determination of Transport Properties of an Alumina Scale. Part I: Alumina Scale on a β-NiAl 

Alloy. Oxid. Met., vol. 45 nos. 1‒2, 1996, pp. 183‒196. 

8. Balmain, J.; and Huntz, A.M.: Improvement of the Application of an Electrochemical Method for 

the Determination of Transport Properties of an Alpha-Alumina Scale. Part II: Influence of Yttrium 

and Palladium on Alumina Scales Developed on a β-NiAl Alloy. Oxid. Met., vol. 46, nos. 3‒4, 

1996, pp. 213‒234. 

9. Balmain, J.; Huntz, A.M.; and Philibert, J.: Atomic Transport Properties in Alumina Scales and 

Calculation of the Oxidation Parabolic Rate Constant. Defect and Diffusion Forum, vol. 143, no. 2, 

1997, pp. 1189‒1194. 

10. Ramanarayanan, T.A.; Raghavan, M.; and Petkovic-Luton, R.: The Characteristics of Alumina 

Scales Formed on Fe‐Based Yttria‐Dispersed Alloys. J. Electrochem. Soc., vol. 131, no. 4, 1984, 

pp. 923‒931. 

11. Balmain, J.; Loudjani, M.K.; and Huntz, A.M.: Microstructural and Diffusional Aspects of the 

Growth of Alumina Scales on β-NiAl. Mater. Sci. Eng., A, vol. 224, nos. 1‒2, 1997, pp. 87‒100. 

12. Young, D.J., et al.: Oxidation Kinetics of Y-Doped FeCrAl-Alloys in Low and High pO2 Gases. 

Mater. Corros., vol. 61, no. 10, 2010, pp. 838‒844. 

13. Clemens, D., et al.: Analysis and Modelling of Transport Processes in Alumina Scales on HighTemperature Alloys. Fresen. J. Anal. Chem., vol. 346, nos. 1‒3, 1993, pp. 318‒322. 

14. Clemens, D., et al.: Determination of Lattice and Grain-Boundary Diffusion Coefficients in 

Protective Alumina Scales on High Temperature Alloys Using SEM, TEM and SIMS. Fresen. 

J. Anal. Chem., vol. 353, nos. 3‒4, 1995, pp. 267‒270. 

15. Chatterjee, A., et al.: Kinetic Modeling of High Temperature Oxidation of Ni-Base Alloys. Comput. 

Mater. Sci., vol. 50 no. 3, 2011, pp. 811‒819. 

16. Kitaoka, Satoshi; Matsudaira, Tsuneaki; and Wada, Masashi: Mass-Transfer Mechanism of Alumina 

Ceramics Under Oxygen Potential Gradients at High Temperatures. Mater. Trans., JIM, vol. 50, 

no. 5, 2009, pp. 1023‒1031. 

17. Matsudaira, Tsuneaki, et al.: The Effect of Lutetium Dopant on Oxygen Permeability of Alumina 

Polycrystals Under Oxygen Potential Gradients at Ultra-High Temperatures. Acta Mater., vol. 58, 

no. 5, 2010, pp. 1544‒1553. 

18. Matsudaira, Tsuneaki, et al.: Oxygen Permeability in Cation-Doped Polycrystalline Alumina Under 

Oxygen Potential Gradients at High Temperatures. Acta Mater., vol. 59, no. 14, 2011, 

pp. 5440‒5450. 

19. Matsudaira, Tsuneaki, et al.: Mass Transfer Through a Single Grain-Boundary in Alumina Bicrystals 

Under Oxygen Potential Gradients. J. Mater. Sci., vol. 46, 2011, pp. 4407‒4412. 
NASA/TM—2013-217855 33 

20. Smialek, J.L.: Microstructure of Al2O3 Scales Formed on NiCrAl Alloys; Ph.D. Thesis; Case 

Western Reserve Univ., NASA TM‒81676, 1981. 

21. Smialek, J.L.; and Gibala, R.: Diffusion Processes in Al2O3 Scales—Void Growth, Grain Growth, 

and Scale Growth. High Temperature Corrosion. Proceedings of the International Conference, San 

Diego, CA, 1983, pp. 274‒283. 

22. Heuer, Arthur H., et al.: Alumina Scale Formation: A New Perspective. J. Am. Ceram. Soc., vol. 94, 

no. S1, 2011, pp. S146‒S153. 

23. Kofstad, Per: High Temperature Corrosion. Elsevier, London, 1988. 

24. Wada, Masashi; Matsudaira, Tsuneaki; and Kitaoka, Satoshi: Mutual Grain-Boundary Transport of 

Aluminum and Oxygen in Polycrystalline Al2O3 Under Oxygen Potential Gradients at High 

Temperatures. J. Ceram. Soc. Jpn., vol. 119, no. 11, 2011, pp. 832‒839. 

25. Hindam, H.M.; and Smeltzer, W.W.: Growth and Microstructure of α-Al2O3 on β-NiAl Alloys. 

J. Electrochem. Soc., vol. 127, no. 7, 1980, pp. 1630‒1635. 

26. Hart, E.W.: On the Role of Dislocations in Bulk Diffusion. Acta Metall., vol. 5, 1957, p. 597. 

27. Smeltzer, W.W.; Haering, R.R.; and Kirkaldy, J.S.: Oxidation of Metals By Short Circuit and Lattice 

Diffusion of Oxygen. Acta Metall., vol. 9, 1961, p. 880. 

28. Doychak, J.; Smialek, J.L.; and Mitchell, T.E.: Transient Oxidation of Single-Crystal β-NiAl. 

Metall. Trans. A, vol. 20, no. 3, 1989, pp. 499‒518. 

29. Nychka, J.A.; and Clarke, D.R.: Quantification of Aluminum Outward Diffusion During Oxidation 

of FeCrAl Alloys. Oxid. Met., vol. 63, nos. 5‒6, 2005, pp. 325‒352. 

30. Prescott, R., et al.: Oxidation Mechanisms of β-NiAl+Zr Determined by SIMS. Corros. Sci., vol. 37, 

no. 9, 1995, pp. 1341‒1364. 

31. Tolpygo, V.K.; and Clarke, D.R.: Microstructural Evidence for Counter-Diffusion of Aluminum 

and Oxygen During the Growth of Alumina Scales. Mater. High Temp., vol. 20, no. 3, 2003, 

pp. 261‒271. 

32. Wang, X.H., et al.: Insights Into High Temperature Oxidation of Al2O3-Forming Ti3AlC2. Corros. 

Sci., vol. 58, 2012, pp. 95‒103. 

33. CompuTherm LLC: PandatTM. 2008. 

http://www.computherm.com/index.php?route=product/category&path=71 Accessed April 19, 2013. 

34. ThermFact Inc. and GTT-Technologies: FactSage 6.3. 

http://www.factsage.com/ Accessed April 19, 2013. 

35. Naumenko, D., et al.: Correlation Between the Microstructure, Growth Mechanism, and Growth 

Kinetics of Alumina Scales on a FeCrAlY Alloy. Metall. Mater. Trans. A, vol. 38A, no. 12, 2007, 

pp. 2974‒2983. 

36. Messaoudi, K.; Huntz, A.M.; and Lesage, B.: Diffusion and Growth Mechanism of Al2O3 Scales on 

Ferritic Fe-Cr-Al Alloys. Mater. Sci. Eng., A, vol. A247, 1998, pp. 248‒262. 

37. Tolpygo, V.: Grain Growth Effects on Alumina Scale Kinetics. Presented at the High Temperature 

Corrosion and Protection of Materials Conference, P. Steinmetz et al., eds., les Embiez, France, 

2008. 

38. Quadakkers, W.J.: Growth Mechanisms of Oxide Scales on ODS Alloys in the Temperature Range 

1000‒1100 C. Mater. Corros., vol. 41, no. 12, 1990, pp. 659‒668. 

39. Quadakkers, W.J., et al.: Growth Rates of Alumina Scales on Fe-Cr-Al Alloys. Oxid. Met., vol. 61, 

nos. 1‒2, 2004, pp. 17‒37. 

40. Heuer, A.H.: Oxygen and Aluminum Diffusion in α-Al2O3: How Much Do We Really Understand? 

J. Eur. Ceram. Soc., vol. 28, no. 7, 2008, pp. 1495‒1507. 

41. Reddy, K. Pattabhi Rami: Oxygen Diffusion in Close Packed Oxides. Ph.D. Thesis, Case Western 

Reserve Univ., 1979. 

42. Prot, D., et al.: Self-Diffusion in α-Al2O3. IV. Oxygen Grain-Boundary Self-Diffusion in Undoped 

and Yttria-Doped Alumina Polycrystals. Philos. Mag. A, vol. 73, no. 4, 1996, pp. 935‒949. 

43. Le Gall, M., et al.: Oxygen Self-Diffusion in Y2O3 Doped α Alumina. Mater. Sci. Forum, 

vols. 126‒128, 1993, pp. 411‒414. 
NASA/TM—2013-217855 34 

44. Chevalier, S., et al.: Oxygen Diffusion in Alumina. Application to Synthetic and Thermally Grown 

Al2O3. Defect and Diffusion Forum, vols. 237‒240, 2005, pp. 899‒910. 

45. Bongartz, K., et al.: Mathematical Modeling of Oxide Growth Mechanisms Measured by 18O Tracer 

Experiments. Surf. Sci., vol. 292, nos. 1‒2, 1993, pp. 196‒208. 

46. Nakagawa, Tsubasa, et al.: Grain Boundary Character Dependence of Oxygen Grain-Boundary 

Diffusion in α-Al2O3 Bicrystals. Scr. Mater., vol. 65, no. 6, 2011, pp. 544‒547. 

47. Nakagawa, T.; and Heuer, A.H.: Case Western Reserve University, Cleveland, OH, personal 

communication, 2012. 

48. Veal, B.W.; and Paulikas, A.P.: Growth Strains and Creep in Thermally Grown Alumina: Oxide 

Growth Mechanisms. J. Appl. Phys., vol. 104, no. 9, 2008. 

49. Kitaoka, Satoshi; Matsudaira, Tsuneaki; and Wada, Masashi: Effect of Dopants on Interdiffusion of 

Aluminum and Oxygen Through Grain-Boundaries in Polycrystalline Alumina. International 

Symposium on Defects, Transport and Related Phenomena, Pittsburgh, PA, 2012. 

50. Nakagawa, T., et al.: Oxygen Diffusion Blocking of Single Grain-Boundary in Yttria-Doped 

Zirconia Bicrystals. J. Mater. Sci., vol. 40, no. 12, 2005, pp. 3185‒3190. 

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4. TITLE AND SUBTITLE

Oxygen Permeability and Grain-Boundary Diffusion Applied to Alumina Scales 

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6. AUTHOR(S)

Smialek, James, L.; Jacobson, Nathan, S.; Gleeson, Brian; Hovis, David, B.; Heuer, Arthur, 

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14. ABSTRACT

High-temperature oxygen permeability measurements had determined grain-boundary diffusivities (δDgb) in bulk polycrystalline alumina 

(Wada, Matsudaira, and Kitaoka). They predict that oxygen δDgb,O varies with oxygen pressure as P(O2)

-1/6 at low pressure whereas 

aluminum δDgb,Al varies with P(O2)

+3/16 at high pressure. These relations were used to evaluate alumina scale growth in terms of diffusivity 

and grain size. A modified Wagner treatment for dominant inward oxygen growth produces the concise solution: Пi

 = kp,i×Gi = 12 δDgb,O,int, 

where Пi

 is a constant and kp,i and Gi refer to instantaneous values of the scale parabolic growth constant and grain size, respectively. A 

commercial FeCrAl(Zr) alloy was oxidized at 1100 to 1400 °C to determine kp,i, interfacial grain size, П, and thus δDgb,O,int. The δDgb,O,int

values predicted from oxidation at (375 kJ/mole) were about 20 times less than those obtained above (at 298 kJ/mole), but closer than 

extrapolations from high-temperature bulk measurements. The experimental oxidation results agree with similar FeCrAl(X) studies, 

especially where both kp,i and Gi

 were characterized. This complete approach accounts for temperature-sensitive oxidation effects of grain 

enlargement, equilibrium interface pressure variation, and grain-boundary diffusivity.

15. SUBJECT TERMS

High-temperature alloys; Oxide scales; Diffusion 

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