James L. Smialek

Glenn Research Center, Cleveland, Ohio

Diffusivity in Alumina Scales 

Grown on Al-MAX Phases 

NASA/TM—2014-218344

August 2014
	
	
	








	



	

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NASA/TM—2014-218344 1 

Diffusivity in Alumina Scales Grown on Al-MAX Phases 

James L. Smialek 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

Ti3AlC2, Ti2AlC, and Cr2AlC are oxidation resistant MAX phase compounds distinguished by the 

formation of protective Al2O3 scales with well controlled kinetics. A modified Wagner treatment was 

used to obtain interfacial grain boundary diffusivity, Dgb,O,int., from scale growth rates and corresponding 

grain size. It is based on the p(O2)

–1/6 dependency of [VO

] and oxygen diffusivity, coupled with the 

effective diffusion constant for short circuit grain boundary paths. Data from the literature for MAX 

phases was analyzed accordingly, and Dgb,O,int. was found to nearly coincide with the Arrhenius line 

developed for Zr-doped FeCrAl, where: 

m s

375 kJ 1.8 10 exp 10 3 , , 



 



	 
   


RT

Dgb O int.

Furthermore, this oxidation relation suggests the more general format applicable to bulk samples under 

ambient conditions: 

1 6

3 1 6

O

8 ,O

s Pa

544 kJ m 7.567 10 exp 2 



 



 



 



	 
   p RT

Dgb

Data from many other FeCrAl(X) studies were similarly assessed to show general agreement with the 

relation for Dgb,O,int.. This analysis reinforces the view that protective alumina scales grow by similar 

mechanisms for these Al-MAX phases and oxidation resistant FeCrAl alloys. 

Introduction 

MAX phase compounds represent a unique class of ceramic materials with exceptional strain and 

damage tolerance, thermal shock resistance, and machinability (Barsoum and El-raghy, 2001). While over 

60 compounds have been reported, a much smaller subset claims optimum oxidation resistance at 

temperatures greater than 1000 °C. These include Ti3AlC2, Ti2AlC, and Cr2AlC, which are the primary 

compounds reported to develop protective alumina scales (Wang and Zhou, 2003a) (Wang and Zhou, 

2003b) (Lee and Park, 2007). These properties and attractive thermal expansion matches with alumina, 

YSZ, or Ni alloys make alumina-forming MAX phase compounds an interesting option for hybrid high 

temperature systems (Smialek and Garg, 2014). 

As with metallic substrates, alumina scale growth on MAX phases has been identified to be 

controlled by short circuit grain boundary diffusion, primarily oxygen, whereby scale grain growth can 

reduce the number of short circuit through-paths and directly slow the rate of scale thickening (X.H. 

Wang, Li, Chen, and Zhou, 2012) (Tallman, Anasori, and Barsoum, 2013) (Song et al., 2012). Here 

precise analyses of scale microstructure proved that grain growth leads to subparabolic (cubic or quartic) 

oxidation kinetics, analogous to prior treatments of alumina scales on metallic substrates, such as 

FeCrAl(X)-type alloys. Furthermore, estimates of oxygen grain boundary diffusion were obtained from 

modified Wagner models of scale growth. Here excellent agreement was obtained for Ti3AlC2 and 

FeCrAl-Y2O3 (Wang et al., 2012) (Clemens et al., 1995), suggesting a commonality of the basic transport, 

rate-controlling mechanism. 
NASA/TM—2014-218344 2 

In that regard, another solution to the Wagner integral has been recently proposed (Smialek, et al., 2013) 

(Smialek, et al., 2014). It takes into account the variation of grain boundary diffusivity across the scale, 

according to p(O2)

–1/6, as shown from bulk permeability studies of polycrystalline alumina which yielded 

(Wada, Matsudaira, and Kitaoka, 2011): 

1 6

3

1 6

O

9

,O

s Pa

467 kJ m 2.207 10 exp 2 



 



 



 



	 
   p RT

Dgb (1)

The conventional form of the Wagner equation (where instantaneous kp,i is given by 2x dx/dt and x is scale 

thickness) is then coupled with standard relations for Deff. Although grain growth results in subparabolic 

overall scale growth rates, the Wagner treatment can still be applied to an instantaneous or differential kp. 

Assuming negligible contributions from Al outward diffusion, the following Wagner integral was obtained: 

  

,gas

,

O

,O

,

O2

O2

2 ln

2

2

p

p int. i

gb

p i d p G

D

dt

dx k x (2) 

Here is the grain boundary width (~ 1 nm), and Dgb,O,int. is oxygen diffusivity at the scale-substrate 

interface. Integration is performed over the p(O2) gradient across the scale, where p(O2)int. refers to the 

equilibrium oxygen pressure at the scale-metal interface, and p(O2)gas refers to the external oxygen partial 

pressure. By substitution of Equation (1), It was further shown that the oxygen grain boundary diffusion 

product can be given by /12, where i is the oxidation product of the instantaneous parabolic rate 

constant (kp,i) and the corresponding grain diameter at that time (Gi): 

i  k p,iGi 12Dgb,O,int. (3) 

(This approach essentially parallels that set forth by Pint, albeit with minor alterations (Pint, 1992) (Pint 

and Deacon, 2005). By applying this to a large data set (for x and G versus T, t) in the oxidation of 

FeCrAl(Zr), it was then found that (Smialek et al., 2013): 

m s

375 kJ 1.8 10 exp 10 3 ,O, 



 



	 
   


RT

Dgb int. (4) 

or about a factor of 10 to 40x lower than those predicted by Equation (1) for undoped bulk alumina. Note 

that this value applies to diffusivity at the low p(O2) interface, which had been shown to be operative over 

99% of the scale thickness and well above the diffusivity corresponding to atmospheric conditions (Wada 

et al., 2011). 

This was a reasonable baseline for other FeCrAl alloys as well, to be shown in detail later as a wellcharacterized alumina-forming system. The purpose of the present work is to assess diffusional control of 

alumina scale growth on MAX phase compounds using the same treatment. The analysis enabled by 

Equation (3), resulting from the p(O2)

–1/6 dependency of diffusion, leads to more appropriate values of 

Dgb,O. Data sets where the time dependence of both scale thickness and grain diameter are given lead to 

the most accurate results, though estimates of Dgb,O were included where only average growth rate and 

grain diameters were reported. 

Results and Discussion 

Diffusivity analyses of Ti3AlC2 oxidation was performed by Wang et al. (Wang et al., 2012). Both 

instantaneous kp (figure 6 in Wang) and grain size were measured for 0 to 20 h oxidation at 1000, 1150, 

and 1250 °C. Since grain size was given only for 1250 °C (figure 9 in Wang), the initial calculation of 

Dgb,O,int. from Equation (4) was limited to that temperature in Figure 1. The results are seen to be quite 
NASA/TM—2014-218344 3 

close to the fitted line for FeCrAl(Zr). More commonly, D

gb,O,int. had been assumed to be constant () 

across alumina scales (Clemens et al., 1995) (Young et al., 2010) (Wang et al., 2012), yielding: 

ln (O )

2

2

,O

p G

D

k gb

p 





 (5) 

This solution of Equation (2) leads to values that are 1/6 ln[p(O2)] lower than those calculated from 

Equation (3), (Smialek et al., 2013). Also, p(O2)eq had been calculated at 1000 to 1400 °C from 

computational thermodynamic codes by Jacobson and Zhang, 2012, (FactSage (Bale et al., 2009) and 

Pandat (Chen et al., 2002), , yielding this fitted approximation: 

 Pa 1012 kJ 6.117 10 exp 15

O2 ,eq 



 



	 
  

RT

P (6) 

Thus the D

gb,O values reported in (Wang et al., 2012) were multiplied by 1/6 ln[p(O2)] (a factor 

ranging from 11.5 at 1000 °C to 7.8 at 1400 °C) to yield the open ‘X’ symbols in Figure 1. Good 

agreement is shown with the prior calculation from Equation (3) at 1250 °C as well as with the 

FeCrAl(Zr) baseline. (Note that this treatment for Ti3AlC2 assumes a similar and small role of Al activity 

in the calculation of p(O2)eq from Keq for Ti3AlC2 and FeCrAl.) 

Next, data for Ti2AlC is considered. The interfacial grain size and continuous weight gain were 

obtained at 1200 °C for 80 h. From the instantaneous power law exponent, ni, (Song et al., 2012): 

x kt n  (7) 

and Equation (2), it can be shown that: 

i i

i

p i

n t

x k

2

,

2  (8) 

This allows Dgb,O,int. to be determined by combining Equations (3) and (8), shown in Figure 1 as the 

upper ‘plus’ + symbol. Again there is good agreement with the fitted FeCrAl(Zr) line. 

Figure 1.—Arrhenius plot of oxygen grain boundary diffusivity estimated for alumina scales 

grown on Ti3AlC2, Ti2AlC, and Cr2AlC MAX phase compounds. Results agree with 

Hoskins 875 FeCrAl(Zr) oxidation behavior within experimental scatter. 
NASA/TM—2014-218344 4 

Oxidation kinetics and interfacial scale grain size were also measured for Ti2AlC at 1200 °C for up to 

2800 h (Tallman et al., 2013). Relations for subparabolic scale kinetics: 

x(m) = 1.2(t/t0)

0.36 (h) (9) 

and grain growth kinetics: 

G
!IJFt

0.31 (h) (10) 

were reported. Equation (9) was used to derive kp,i, then combined with Equation (10) to determine 

Dgb,O,int. from Equation (3): 

Dgb,O (m3

/s) = 0.0.254t

0.03(h) (11) 

This indicates a very slight time dependence, with Dgb,O,int. increasing from 710–24 to just 910–24 m3

/s from 

t=1 to 2800 h. The mid-value of 8.110–24 m3

/s corresponding to ~100 h is plotted in Figure 1. Again the 

diffusion product is seen to agree quite well with the FeCrAl(Zr) baseline. TiO2 is often observed to some 

small degree in Ti-Al-C MAX phase oxidation and may account for the slight offset compared to FeCrAl(Zr). 

Finally, the oxidation of Cr2AlC is addressed. Data for both kinetics and corresponding scale 

microstructure is sparse. An average parabolic rate constant was reported as 7.510–11 kg2

/m4s at 1100 °C 

(50 h). The same authors later present an interfacial microstructure after 480 h oxidation at 1100 °C 

(Lee 2012). The scale grain size was measured from imprints in the adjacent Cr7C3 sublayer as 1.28 

0.47 m. This allows estimates of  and Dgb,O,int., namely 0.10 m3

/h and 2.2810–24 m3/s. The latter, 

shown in Figure 1, is seen to be slightly above the fitted line for FeCrAl(Zr) and within a scatter band 

typical of the other MAX phase results with similar offsets. Another study examined scales formed on 

sputter coatings of Cr2AlC during oxidation at 1230 to 1410 °C for various times (Hajas, et al., 2011). 

TGA revealed near-parabolic kinetics, and grain structure was revealed by means of FIB-XTEM. Here 

larger grains are seen to be at the gas-scale interface (scales formed at 1320 °C up to 5 h), at odds with 

most studies of alumina scales. Nevertheless the rates are reported to be near those obtained for NiAl and 

bulk Cr2AlC. A summary of estimated of grain size, , and Dgb,O,int. is presented in Table 1. Using the 

longest time and thickest scale as most representative of the average kp, the obtained diffusion product is 

seen to agree with the previous data, Figure 1. However, this agreement is subject to questions raised by 

an uncertain growth direction and by using an average kp. 

TABLE 1.—OXIDATION PRODUCT () AND DIFFUSION PRODUCT (DGB,O) FOR Cr2AlC SPUTTERED FILM. 

DETERMINED FOR 1320 C FROM XTEM GRAIN SIZE AND TGA kP = 3.1610-9 kg2

/m4s (HAJAS, ET AL., 2011)

Time, 

h 

G (fine), 

m 

G (coarse), 

m 

, 

m3/h 

Dgb, 

m3/sec 

Log Dgb

0.065 ? 0.13 0.422 9.76510–24 –23.010 

0.65 0.56 0.71 2.30 5.33310–23 –22.273 

4.7 0.96 1.71 5.55 1.28510–22 –21.891 

Other FeCrAl(X) data. Published FeCrAl(X) oxidation data is often quoted in comparisons of scale 

grain boundary diffusivity. These are presented in Figure 2 to provide a more global perspective, now all 

obtained by using Equation (3) in the same framework as above. A few comments are offered below. 

A comprehensive study of FeCrAlY oxidation at 1200 °C was presented with detailed microstructural 

characterizations (Naumenko, Gleeson, Wessel, Singheiser, and Quadakkers, 2007). The precise 

determination of scale grain size as a function of thickness, coupled with an exact polynomial fit of 

thickness vs oxidation time, allowed the determination of the unique value for  = 0.4546 μm3

/h, 

equivalent to Dgb,O,int. = 1.05210–23 m3

/s (Smialek et al., 2013). Because of many overlapping points at 

1200 °C, the plot is expanded by alloy group in Figure 3 for clarity. This FeCrAlY datum is quite close to 

the fitted (dashed) line for FeCrAl(Zr). Grain diameters were not available for the same alloy oxidized in 
NASA/TM—2014-218344 5 

Figure 2.—Oxygen grain boundary diffusivity from Figure 1 compared to other FeCrAl(X) alloy behavior. 

Calculated from oxidation data for undoped and Y, Zr, Y2O3, and ZrO2 doped FeCrAl. 

Figure 3.—Expanded 1200 C diffusivity data from Figure 2 showing overlap and range of 

variations for specific material classes. 
NASA/TM—2014-218344 6 

another study using Ar-20% O2 (Young et al., 2010). However D

gb,O data was presented for the Wagner 

solution assuming constant D

gb,O across the interface. As with the Ti3AlC2 data, these values were 

multiplied by the 1/6 ln[p(O2)] correction factor to yield the upper crossed square symbol. The lower 

symbol corresponds to a similarly corrected value that integrated both variable Dgb,O and grain size 

across the scale thickness (Young et al., 2010). Finally, data for G=0.5 μm scales grown on FeCrAl and 

FeCrAlY after 100 h at 1200 °C (B. Pint, 1992) are shown as the upper and lower triangles, respectively. 

They indicate a reduced diffusivity of ~3x due to Y-doping. Values for these FeCrAlY alloys are close 

and ~2x below the fitted FeCrAl(Zr) line.

Hoskins 875 FeCrAl(Zr) (circles) were used to define our Arrhenius line in Figures 1 and 2. 

However, the 1200 °C value is shown to be about 40% below the fitted line (Figure 3) for unknown 

reasons (Smialek et al., 2013). This applies to measurements made on numerous separate samples over a 

10, 20, 50, 100, and 200 h time period. By comparison, Dgb,O,int. calculated from a single 48 h grain size 

and fitted kp for an Imphy FeCrAl(Zr) alloy, similarly doped with 0.2 wt.% Zr, follows the same 

temperature dependence in Figure 2, as does their Y-implanted FeCrAl(Zr), but with more scatter 

(Messaoudi, Huntz, and Lesage, 1998). 

Next we consider a number of studies of the Y2O3 oxide-dispersed MA 956 alloy. In one of the 

earliest modified Wagner treatments of alumina scales, parabolic kinetics were found from 900 to 

1200 °C in 25 to 100 h tests (Ramanarayanan, Raghavan, and Petkovic-Luton, 1984). While some scatter 

existed, he described the average behavior by one Arrhenius relation: 

kp = 1.210–2exp(–388 kJ/RT) m2

/s (12) 

A slowly changing, temperature independent interfacial grain size of 0.5 μm was reported, with little 

elaboration. This allows Dgb,O, int. to be roughly approximated according to Equation (3) and are shown as 

the crossed circles quite near the FeCrAl(Zr) baseline in Figures 2 and 3. In a subsequent study, grain 

boundary diffusivity was determined for MA 956 over the same temperature range assuming a constant 

D

gb,O across the scale (Clemens et al., 1995). Grain size was again reported to be relatively temperature 

independent, but ranged from 0.2 to 1 μm across the thickness, again with insufficient detail to use 

Equation (3) directly. The reported D

gb,O values were therefore multiplied by 1/6 lnp(O2) as discussed 

for Ti3AlC2. Shown as the red stars in Figures 1 and 2, reasonably good agreement with the FeCrAl(Zr) 

baseline is observed, except perhaps at 900 °C. The 48 h MA 956 data from (Messaoudi et al., 1998) 

(small red circles) yields perhaps the most divergence from the Arrhenius baseline, with no apparent 

explanation at present. 

Precise relations for scale thickness and interfacial grain size were reported for MA 956 and Kanthal 

APM (ZrO2-oxide dispersed FeCrAl) oxidized at 1200 °C for up to 300 h (Tolpygo, 2008) (Tolpygo, 

private communication). In that study, the scale thickness (x) and grain size (G) were described by the 

power law relations below. A, B are scale growth constants, m is the grain growth exponent, and k is a 

grain growth constant, as listed in Table 2: 

( 1)

2





  

Gk m

G G

x At B m

o m

 (13) 

m m G Go kt 1/  (  ) (14) 

It then follows that: 

 = AGi +B/m (15) 

The corresponding Dgb,O,int. , given as hexagons in Figures 2 and 3, are seen to be slightly above the 

FeCrAl(Zr) reference line in juxtaposition to some of the previous values below the line. Overall, 

reasonable consistency is seen for Dgb,O,int. determined for the various FeCrAl(X) alloys and in the same 

range as the MAX phase alloys. 
NASA/TM—2014-218344 7 

TABLE 2.—TOLPYGO’S OXIDATION AND GRAIN GROWTH 

CONSTANTS FOR KINETIC EQUATIONS (13) TO (15) (TOLPYGO, 2008) 

 

A, 

μm2

/h 

B G0 

μm

k m 

MA956 0.0455 2.5513 0.1755 0.0146 4.4693 

APM –0.0228 1.8455 0.3615 0.0161 3.4700 

While a single value of  is sufficient to warrant inclusion in the previous plots, a number of these 

studies followed kinetics and grain size over a substantial time interval. This allows the determination of 

multiple values of  versus time at one temperature, which lead to highly validated average values of 

Dgb,O,int.. Examples of the studies that provided detailed kinetic fits at 1200 °C, and thus  versus t, are 

provided in Figure 4 (Tallman et al., 2013) (Tolpygo, 2008) (Naumenko et al., 2007)(Smialek et al., 

2013). The FeCrAl(Zr) behavior had been presented for 1100 to 1400 °C in a more compressed plot 

(Smialek et al., 2013). Much of the data indicated periods of nearly constant values, as expected for scale 

growth controlled by a constant value of Dgb,O,int. for a given temperature. This is especially born out for 

the 2000 h FeCrAlY and 2800 h Ti2AlC results (Naumenko et al., 2007) (Tallman et al., 2013). 

It is significant that this treatment produced a self-consistent assessment of data from 12 studies on 15 

materials. There is no consistent or dramatic difference between scales doped with Ti, Zr, or Y, with 

perhaps the largest reduction (3x) shown by Y-doping (B. Pint, 1992). Given that all the validated data 

falls within tight bands shown in Figure 2, it can be expected that variation limits for the activation energy 

may be so defined. It is found that these bands define a slope, with Q  375  25 kJ/mole, which can be 

taken as a working value for the nearly invariant primary rate controlling factor for oxidation, i.e., inward 

oxygen grain boundary diffusion. It is subject to assumptions of minimal contributions from Al diffusion. 

Slight variability may also be expected from different oxidation environments, such as dry or humid ArO2, N2-O2, or pure O2, which are not differentiated or addressed here. It is nevertheless more fundamental 

than activation energies obtained from the oxidation constant alone, now widely accepted to be affected 

by an indeterminate grain growth process and its temperature dependence. Alternatively, more attention 

can be focused on the oxidation product, , as proposed for FeCrAl(Zr), as a more invariant constant 

(i.e., equivalent to ‘2C’ in (Naumenko et al., 2007). 

Figure 4.—Time invariant oxidation product, , at 1200 C for Ti2AlC 

MAX phase and four FeCrAl(X) alloys.
NASA/TM—2014-218344 8 

These Dgb,O,int. and activation energy enable more direct comparisons to diffusivity measured for bulk 

alumina. The oxidation analysis produced diffusivities 10 to 40x lower than those predicted from bulk 

alumina permeability studies, with an activation energy of 375 kJ/mole compared to 300 kJ/mole (Wada 

et al., 2011) (Smialek et al., 2013), and already discussed at length without a totally satisfactory 

resolution. Dopant effects and atomistic models of transport explain some of the discrepancy and provide 

deeper insight into mechanisms (Matsudaira, Wada, Saitoh, and Kitaoka, 2010) (Matsudaira, Wada, 

Saitoh, and Kitaoka, 2011) (Matsudaira, Wada, and Kitaoka, 2013) (Heuer, Hovis, Smialek, and Gleeson, 

2011) (Heuer et al., 2013). Some aluminum outward diffusion is well-documented, but is considered to be 

less important since oxygen inward diffusion predominates through the majority of the scale (Wada et al., 

2011). These topics warrant further discussion, but at present cannot resolve all discrepancies and are 

considered beyond the scope of this paper. 

It should be pointed out that the /12 solution was enabled by assuming the p(O2)

–1/6 dependency of 

oxygen diffusion as verified by (Wada et al., 2011) and Equation (1). However its possible role, 

associated with VO

 creation predicted from classic Kroger-Vink equilibrium and charge neutrality 

conditions, has indeed been raised a number of times, for example by (Ramanarayanan et al., 1984) (Pint, 

1992) (Pint and Deacon, 2005) (Messaoudi et al., 1998). The solution from Pint et al. also highlighted the 

dominant p(O2)int. aspect of controlling inward oxygen diffusion as compared to the external pressure, 

leading to a concise working relation such as Equation (3). This can be further addressed by the 

appropriate p(O2)eq correction (Eq. (6)) to give a more general relation for other p(O2) along the format of 

Pint and Equation (1): 

6

1

3

6

1

O

8 ,O

s Pa

544kJ m 7.567 10 exp 2 



 









 



	 
   p RT

Dgb (16) 

This equation is useful for comparisons to tracer studies in bulk alumina under atmospheric conditions, 

which indicate reductions of 102

 to 105 when compared to alumina scale transport. 

Summary 

Published oxidation data for Ti3AlC2 ,Ti2AlC, and Cr2AlC have been analyzed by a recent 

modification of the Wagner solution by which the oxidation product  = 12Dgb,O,int.. The values so 

determined were found to be in the same population as numerous similar studies of FeCrAl(X) oxidation. 

Neither group showed any large or consistent trend with either Cr, Ti, Zr, Y, ZrO2, or Y2O3 doping. Thus 

most behaviors are adequately generally described by the relation developed for FeCrAl(Zr): 

m s

375 kJ 1.8 10 exp 10 3 ,O,int 



 



	 
   


RT

Dgb (4) 

Oxidation results were shown for just one value for  as well as multiple detailed measurements, 

sometimes spanning thousands of hours at a given temperature. Studies assuming a constant diffusion 

product, D

gb,O, were adjusted by the factor 1/6 ln[p(O2)]. This produced values consistent with the 

present Wagner solution where Dgb,O was assumed to vary as p(O2)

–1/6. In summation, a large population 

of alumina scale kinetic data, normalized by grain size and spanning 900 to 1400 °C, cluster about a 

single relation based on oxygen grain boundary diffusion control. 

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