Volume 6 Preprint 66
Internal-Corrosion Processes in Ni-Base Alloys
U. Krupp, S.-Y. Chang, H.-J. Christ
Keywords: Internal Corrosion, Internal Nitridation, Internal Oxidation, Nitrogen Diffusion, Ni-Base Alloys, Finite-Difference Method
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Volume 6 Paper H008
Internal-Corrosion Processes in Ni-Base Alloys
U. Krupp, S.-Y. Chang, H.-J. Christ
Institut für Werkstofftechnik, Universität Siegen, 57068 Siegen,
Wagner's theory of internal oxidation provides a fundamental and
simple description for several internal-corrosion phenomena. The
present paper shows that also internal nitridation of Ni-base alloys
follows generally a parabolic rate law as it was proposed by Wagner.
On the other hand, internal corrosion under near-service conditions
depends on a great variety of factors, e.g., the local chemical
composition and the oxide scale integrity. Therefore, a numerical
computer model has been developed that combines a finite-difference
diffusion calculation with a powerful thermodynamic software
ChemApp. The technical value and required extensions of the model
are discussed by means of applying it to experiments that simulate
internal corrosion as a consequence of oxide scale failure.
Keywords: Internal Corrosion, Internal Nitridation, Internal Oxidation,
Nitrogen Diffusion, Ni-Base Alloys, Finite-Difference Method.
Alumina-forming Ni-base superalloys, which are frequently used for
cast gas-turbine blades, may suffer a strong attack by internal
oxidation and nitridation when the near-surface concentration of
aluminium drops locally below a critical value that is required to form
a superficial Al2O3 scale. This can happen as a consequence of
repeated scale spalling or cracking and re-healing at mechanically or
thermally high-loaded locations, e.g., leading edges and cooling holes
of turbine blades. The transition from external to internal oxidation of
Al allows nitrogen to penetrate the underlying alloy and to form Al, Ti,
and Cr nitrides [#ref1]. Due to the high diffusivity of N as compared to
O in Ni-base alloys [#ref2], the high specific volume of the nitride
precipitates and the dissolution of the γ´phase, internal nitridation
causes a deep deterioration of the mechanical properties of Ni-base
The occasional occurrence of internal Ti nitrides during hightemperature oxidation of Ni-base superalloys is reported in several
papers, e.g., [#ref3][#ref4], as well as internal nitridation processes in
ammonia-containing atmospheres, e.g., [#ref5] [#ref6], but only a few
studies are focussed on a quantitative description of internal
nitridation in nitrogen-based atmospheres, e.g., [#ref7] [#ref8].
The following chapters give an introduction in Wagner's classical
theory and an alternative numerical approach to treat internalcorrosion processes. These concepts are discussed by examples for
internal nitridation, without oxidation in pure nitrogen as well as a
consequence of oxide scale failure.
The Classical Theory of Internal Oxidation
According to the classical concept, which was originally proposed by
Wagner [#ref9], internal oxidation is driven by the diffusion of a
gaseous species, e.g., oxygen, nitrogen or carbon, into an at least
binary alloy (AB) and the chemical reaction with the less-noble solute
(B) leading to the precipitation of a thermodynamically-stable
compound (BOν). With the simplifying assumptions that (i) the progress
of the internal precipitation front ξ is a parabolic function of the
exposure time t, (ii) the thermodynamic stability of the precipitating
compound is very high, i.e., the concentration of the reacting species
drops to zero at the reaction front ξ, (iii) the surface concentration
cOs of the penetrating species is constant, i.e., there is no interaction
with a growing scale, and (iv) the diffusion of the alloying element B
(DB) is slow compared to the diffusion of the penetrating species O
<< 0 << 1 ,
coupling of the diffusion fluxes at ξ in combination with mathematical
rearrangements and simplifications (for details see [#ref9]) yields the
Wagner approach for the internal precipitation depth ξ as a function of
the permeability of the penetrating element DO cO , the stoichiometric
coefficient ν of the precipitate ΒΟν and the initial concentration cB of
the less-noble alloying element B:
Fig. 1 shows schematically the concentration profiles of the reacting
species during internal oxidation.
Fig. 1: Schematic representation of the concentration profiles of
oxygen and the oxide-forming alloying element B during internal
Note that the concentrations of the diffusing species are close to zero
at the reaction front. While the negligibility of the solubility product is
a useful assumption for stable compounds like Al2O3 or TiN, many
high-temperature corrosion processes involve the formation of
compounds of moderate stability. Additionally, boundary conditions
may not be constant, i.e., the formation of a superficial oxide scale
changes the concentration of oxygen and nitrogen at the metal surface
and the chemical alloy composition in the near-surface area as a
function of time. Due to oxide spalling or cracking events the
concentration gradients can be inhomogeneous along the specimen
Even though Wagner's theory has been tried to modify and to adapt to
more complex situations, e.g., in [#ref10], a numerical model taking
local thermodynamic equilibrium into consideration seems to be the
most-flexible approach to simulate internal corrosion processes under
Treating Internal Corrosion Processes by Computer Simulation
The most common approach to solve the diffusion differential
equation (Fick’s 2nd law)
= −D 2
is the finite-difference method, which is described in detail in [#ref11].
Here, the partial derivatives in equ. 3, usually normalized according to
X =x d
T= D t d2 ,
C = c c0
where d denotes a characteristic length, e.g., the specimen thickness,
and c0 the initial concentration of the diffusing species (with diffusivity
D), are expressed by differential quotients
∂ C Ci j +1 − Ci j
∂ 2C Ci+j 1 − 2Ci j + Ci−j 1
Inserting equ. 5 in equ. 4 yields the normalized concentration Ci j +1 for
the time step j+1 from three concentrations at the location steps i-1,
i, and i+1 for the preceding time step j (explicit method).
C i j +1 = C i j +
C i j+1 − 2C i j + C i j−1
A higher precision and stability is obtained when applying the implicit
method (Crank-Nicholson method, see [#ref11]) where the partial
derivation ∂ C ∂X is substituted by the mean of the finite difference
expressions for the time steps j and j+1, respectively:
∂ 2C 1 Ci+j +11 − 2Ci j +1 + Ci−j +11 Ci+j 1 − 2Ci j + Ci−j 1
∂X 2 2
Then the corresponding finite-difference equation becomes:
C i j +1 = C i j +
C i +j 1+1 + 2C i +j 1 − 2 C i j +1 + 2C i j + C i −j1+1 + 2C i −j 1 ,
which requires an implicit algorithm to obtain the concentrations
Ci =j +11...n at the time step j+1 from the preceding time step j.
Since internal corrosion is a diffusion-controlled process accompanied
by chemical reaction and precipitation, the concentrations calculated
for each time step have to be corrected according to thermodynamic
equilibrium. This was realized by integrating the commercial
thermodynamic program library ChemApp into the finite-difference
model, which is based on the Gibb’s energy minimization method
making use of problem-specific data sets.
To optimise this procedure with respect to the processing time the
originally-developed model was recently replaced by a parallel
computation unit, which enables to allow multiple starts of the
thermodynamic subroutine at the same time [#ref13].
Figure 2 shows a schematic representation of the finite-difference
mesh for a one-dimensional treatment of multi-component internal
corrosion phenomena. Examples for the application of the model are
given in the following chapters (see Fig. 7 and Fig. 9).
Internal Nitridation of Ni-Cr-Al-Ti Alloys
For many high-temperature processes nitrogen is considered as a
non-corrosive inert gas. Especially Ni alloys seem not to have any
susceptibility to nitridation since the nitrogen solubility is extremely
low (cN≈0.005At.%, T=1000°C at p(N2)=1bar [#ref14]).
Fig. 2: Schematic representation of the simulation procedure for
internal corrosion combining the finite-difference algorithm (compare
equ. 8) with the thermodynamic program library ChemApp
Therefore, exposure of a Ni-6Ti model alloy to nitrogen atmosphere
(50 Vol.% N2, 45 Vol.% He, 5 Vol. % H2 supplemented by a small
amount of Ti sponge to minimize the content of residual oxygen and
to suppress oxidation) does not result in internal nitridation – but as a
consequence of the high affinity of Ti to nitrogen a superficial TiN
scale is formed (Fig. 3a). Only when the solute concentration (cTi) falls
below a critical value (cTi<6 wt%) nitridation attack changes from
external scale formation to internal precipitation. Exemplary, this is
shown in Fig. 3b for internal nitridation of a Ni-2Ti model alloy during
exposure to nitrogen atmosphere.
Fig. 3: (a) External TiN scale formation on Ni-6Ti and (b) internal
nitridation by TiN precipitates in Ni-2Ti (80h, 900°C, nitrogen)
The necessity to treat internal corrosion phenomena by a sound
thermodynamic equilibrium calculation becomes obvious when
chromium is added to Ni-2Ti. Depending on the temperature Cr does
not form nitrides itself as long as its concentration is held below a
≈ 20 wt% at T=1000°C) but the exposure of Ni-xCrcritical value ( cCr
2Ti model alloys to nitrogen atmosphere yields an increasing depth of
TiN precipitation with increasing initial Cr concentration (compare Fig.
4a and b).
The internal nitridation kinetics as a function of the Cr concentration
are summarized in Fig. 4d, where the nitridation constant kN refers to
the parabolic equation for the TiN penetration depth ξ
ξ 2 = 2k N t .
On the other hand, when keeping the Cr concentration constant at
cCr=20wt% and increasing the Ti concentration from cTi=2wt% to
cTi=6wt%, then the internal TiN precipitation depth decreases while the
TiN volume fraction becomes higher (compare Fig. 4b (Ni-20Cr-2Ti)
with Fig. 4c (Ni-20Cr-6Ti) both represent the same experimental
conditions). This result is in agreement with the prediction of the
Wagner approach (equ. 2) , where the solute concentration (here cTi) is
part of the denominator of the constant (kN, corresponds to kO in equ.
Cr promotes the susceptibility of Ni-base alloys to internal nitridation
by boosting their solubility for atomic nitrogen, probably as a
consequence of an increase in the lattice spacing (see [#ref153]).
Fig. 4: Internal Nitridation by TiN in Ni-Cr-Ti alloys (100h, 1100°C,
nitrogen) (a) cCr=5%, cTi=2% (b) cCr=20%, cTi=2% (c) cCr=20%, cTi=6%
and (d) corresponding nitridation constants kN
Figure 5 shows the dependence of the maximum soluble nitrogen
concentration in Ni-Cr alloys as a function of the Cr concentration at
different temperatures, calculated by ChemApp in combination with a
special data set for the system Ni-Cr-Al-Ti-N [#ref12]. The slope of
the curves becomes zero at Cr concentrations above that Cr nitrides
(CrN, Cr2N, and the ternary π phase [#ref16]) are stable.
Fig. 5: Nitrogen solubility in Ni-Cr alloys as a function of the Cr
concentration for T=800°C, 900°C, and 1000°C at p(N2)=0,5 bar
Using the data given by Fig. 5 to estimate the surface concentration of
nitrogen c N (corresponding to cO in equ. 2) during exposure in N2
atmosphere and applying equ. 2 to the internal nitridation (TiN) data in
Fig. 4d the effective diffusion coefficient DN for nitrogen in Ni-Cr
alloys can be obtained, e.g., for nitrogen diffusion through a TiN
precipitation zone in the model alloy Ni-20Cr DN becomes:
= 4.7 ⋅10
DN in Ni-20Cr
The results revealed that it is probably not only the solubility of
nitrogen in Ni-base alloys, that is affected by the initial Cr content, but
also the nitrogen diffusion that is accelerated when a higher Cr
concentration is present.
When more than one solute can form stable internal corrosion
products, then the application of the Wagner approach is not useful
any more. E.g., to treat the simultaneous internal precipitation of TiN
and AlN during exposure of the model alloy Ni-20Cr-2Al-2Ti to
nitrogen atmosphere (Fig. 6a) the estimated diffusion coefficient DN in
equ. 10 (literature data for the Al and Ti diffusivity) and the
thermodynamic data set for the system Ni-Cr-Al-Ti-N [#ref12] in
combination with the finite-difference simulation (see previous
chapter) were used. Figure 6b represents the concentration profiles
and the predicted internal precipitation depths calculated by this
approach, which are in reasonable agreement with the experimental
Internal Corrosion of Ni-Base Superalloys as a Consequence of
Oxide Scale Failure
Since Ni-base superalloys contain Cr concentrations between
cCr=10wt% and cCr=20wt% they are basically prone to internal
nitridation. Usually a dense Al2O3 scale protects the alloys against
nitrogen penetration, but when the scale is repeatedly damaged by
cracking and spalling at high-loaded locations, e.g., sharp corners,
this protection can get lost and the alloy suffers massive attack by
internal oxidation and nitridation. Such a situation is shown in Fig 7
schematically (a) and for a specimen edge of the single-crystalline Nibase superalloy CMSX-6 after isothermal exposure to air (b).
Fig. 5: Simultaneous internal nitridation by TiN and AlN in
Ni-20Cr-2Al-2Ti (100h, 1000°C, nitrogen) (a) experimental result and
(b) corresponding calculated concentration profiles
Fig. 7: (a) Schematic representation of the mechanism of internal
corrosion caused by cracks in the oxide scale and (b) internal
oxidation and nitridation at a specimen edge of the superalloy CMSX-6
after 1000h exposure to nitrogen atmosphere at T=1000°C
Oxide-scale cracking occurs also as a consequence of thermal cycling
due to the difference in the coefficient of thermal expansion between
the oxide and the underlying alloy. Figure 8 compares the oxidation
and nitridation behavior within the Ni-base alloy Ni-20Cr-2Ti-2Al
during isothermal exposure (a) and under thermal-cycling conditions
(b), where the specimen was cooled down periodically for 15 minutes
after 5h intervals. While an intact Cr2O3 scale reduces the nitrogen
activity aN at the metal interface to a value that is not sufficient for
strong internal nitridation attack, cracks in the oxide scale shifts the
atmospheric nitrogen activity aN toward the metal interface resulting in
a deep zone of internal TiN precipitation. It should be emphasized that
internal oxidation of Al is present in both cases. This is because the
oxygen activity below the Cr2O3 scale is still high enough to form
Al2O3, which is of high thermodynamic stability.
Fig. 8: Oxidation/nitridation behavior of the Ni-base alloy Ni-20Cr2Al-2Ti (a) after isothermal exposure for 100h at T=1000°C to air and
(b) after thermal-cycling (100h, 5h intervals at T=1000°C, air)
To simulate such complex situations leading to internal corrosion the
finite-difference computer model was extended by a start condition,
which takes oxide growth and thermally-induced cracking into
account. Once a crack has been established, inward diffusion starts
from the root of the crack acting as a source into a two-dimensional
finite-difference mesh [#ref18] while internal corrosion is considered
by the integrated thermodynamic module ChemApp. Fig. 9a shows an
example of a calculated two-dimensional internal TiN zone emanating
from a crack in the oxide scale. The predicted lateral dimension of the
internal nitridation front agrees with the one obtained in a nitridation
experiment where a crack in a thermally-grown Cr2O3 scale on Ni-
20Cr-2Ti was generated artificially by a small diamond saw cut before
exposing the specimen to nitrogen atmosphere [#ref18].
Fig. 9: Internal nitridation by TiN in Ni-20Cr-2Ti as a consequence of a
crack in the Cr2O3 scale (a) calculated lateral TiN concentration profile
and (b) TiN-precipitation zone (100h, T=1000°C, nitrogen, after preoxidation and crack generation)
Under simplified conditions internal nitridation of Ni-base alloys can
be treated by Wagner’s classical theory of internal oxidation. However,
since this analytical approach is restricted to only one precipitated
compound of high thermodynamic stability and constant boundary
conditions, a numerical simulation was applied to predict internal
corrosion phenomena under more complex near-service conditions.
This simulation integrates the thermodynamic module ChemApp into a
finite-difference diffusion calculation. By applying the program in
combination with a special data set to internal nitridation of Ni-Cr-AlTi alloys, the experimental results could be reproduced, e.g., (i) that Cr
promotes the internal corrosion attack by TiN in Ni-xCr-2Ti alloys and
(ii) that internal TiN formation is accompanied by simultaneous AlN
formation in Ni-20Cr-2Al-Ti. The model has been extended to
describe internal corrosion as a consequence of oxide-scale failure
and it is intended to comprise also oxide growth and breakdown
kinetics, corrosion-induced phase transformations in the alloy and
interactions between internal corrosion and mechanical loading.
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Temperature Exposure of Nickel-Base Superalloys’, U. Krupp, H.-J.
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!ref16 ‘Precipitation of the ternary π phase during Nitriding of Ni-Cr
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Processes, Frankfurt, Germany, 2001