A theory of pack aluminization has been formulated by combining gaseous and solid-state diffusion rates. This theory relates the surface composition of the coating and therefore, in principle, the phase morphology and the growth rate of the coating, to pack operating parameters such as pack aluminum  density, type of activator, temperature and others. Experimental data on the aluminization of unalloyed nickel in pure aluminum packs obtained to date are in good agreement with the predictions of the theory

Gupta, B. K.

Sarkhel, A. K.

Seigle, L. L.

English

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,a NO- 3 3— N5 —160
ON THE KINETICS OF PACK ALUMINIZATION
B.K. Gupta, A.K. Sarkhel, and L.L. Seigle
Department of Materials Science, S.U.N.Y., Stony Brook, N.Y. 11194
ABSTRACT
A theory of pack aluminization ha; been formulated by combining
gaseous and solid-state diffusion rates. This theory relates the
surface composition of the coating and therefore, in principle, the
phase morphology and the growth rate of the coating, to pack operating
parameters such as pack Al density, type of activator, temperature and
ot:ers. Experimental data on the aluminization of unalloyed Ni ins
pure Al packs obtained by us to date are in good agreement with the
predictions of the theory.
( NA SA-CF-147232) ON 2HE KINETICS OF FACK
ALUMINIZATICN (State Univ. of NPw York)	 N76-239117 p HC $3.5C
	 CSCI 11F
Unclas
G3/26 26920
OR- 33-615-I66 ,
1	 ^
ON THE KINETICS OF PACK ALUMINIZATION
B.K. Gupta, A.K. Sarkhel, and L.L. Seigle
Department of Materials Science, S.U.N.Y., Stony Brook, N.Y. 11794
ABSTRACT
A theory of pack aluminization ha: been formulated by combining
gaseous and solid-state diffusion rates. This theory relates the
surface composition of the coating and therefore, in principle, the
phase morphology and the growth rate of the coating, to pack operating
-;arameters such as pack Al density, type of activator, temperature and
ot:-ers. Experimental data on the aluminization of unalloyed Ni n
pure .Al packs obtained by us to date are in good agreement with the
predictions of the theory.
(NASA-C- 167232)	 ON ZHF KINETI^_S of FACK
AIUMI"IZATICN
17 p
	
(Sty±F Cniv. of Vew Yolk)
$3HC	 . _`^ (.SCL 11F
1:75	 ?u13
Unclas
6
	 63/22 6 25920
ON THE KINETICS OF PACK ALUMINIZATION
Introduction
The pack aluminization process is extensively used to form pro-
tective coatings on superalloy components of aircraft gas turbines.
In this process the metal to be coated is placed in a powder mixture
consisting essentially of Al, a halide activator such as NaF, and an
inert filler material such as Al 203' Other metals such as Ni, Cr,
Si, Ti are sometimes added (1, 2) to control the Al activity or other-
wise influence the properties of the coating. During aluminization,
Al is transferred from the pack to the specimen surface in the form of
aluminum halides. These compounds decompose at the surface to release
Al which diffuses into the metal, creating the Al-rich coating. The
aluminization process thus involves three steps: 1) gaseous diffusion,
2) surface reaction and 3) solid diffusion. Of these three it is
assumed that the surface reaction step is rapid and the kinetics of the
process is governed by a combination of gaseous diffusion in the pack
and solid state diffusion in the coating. The gaseous diffusion step
was recently analyzed by Levine and Caves (3). In the following a quant-
itative description of the kinetics of aluminization is given which takes
diffusion in the solid as well as the gas phase into account.
Kinetics of Pack Aluminization
A. Gaseous Diffusion: Levine and Caves' (3) model which applies to
packs containing unalloyed Al, assumes that aluminum is transferred from
the pack to the coating surface by the diffusion of aluminum halides
through an Al-free zone in the pack adjacent to the specimen surface.
In the body of the pack, the halide vapor pressures are taken as those
in equilibrium with the bulk pack composition. The halide vapor pressures
at the specimen surface, which is assumed to be at a constant Al activity,
are determined by mass-balance and thermodynamic equilibrium conditions
at this surface. Chemical reactions are assumed to occur rapidly enough
at the pack-coating interface to allow the establishment of a local
equilibrium.
As Al is transformed from the pack to the specimen surface it is
assumed that the width of the depleted zone and consequently the dif-
fusion distance for the halide vapor increases. This leads to a para-
bolic relationship between the weight of Al transferred W g , in gms./cm2
and time, t, in seconds,
W2 = ZoeM NAld t
	
K t	 (1)
9 Z	 V_	 9
in which E and t are correction factors for pack porosity and pore length,
M is the atomic weight of Al, p is the pack Al concentration in gms/cm3,
d is the diffusion distance in cm, A is the total area in cm 2 , and NA1
is the overall rate of diffusion of Al through the gas phase in moles/sec.
The instantaneous flow of Al through the gas phase is given by
	
NAl d = 1 z Di
 ( P i - P i)	 (2)
_T_ TR7 —i
where Di is the diffusivity, P i and Pi are the partial pressures of the
i th Al-bearing species in the pack and at the coating surface, respectively,
T is the temperature and R the gas constant. Hence the parabolic rate
constant, Kg , is given by
Kg 
= , 
EM 
E Di ( P i -Pi )	 (3)
1
JApplication of the above equations involves calculation of the
equilibrium pressures P i and Pi. The method of calculation depends
upon pack operating conditions and type of activator used.
The pack aluminization process is generally carried out at atmo-
spheric pressure by placing a semi-open retort with the pack and the
parts to be coated in a flowing H 2 or inert atmosphere. The activators
in common use can be divided into two classes. The sodium halides
i.e.,Na(F, Cl, Br, I) as well as AlF 3 remain in the pack as condensed
phases at the usual activator ratios (1-10w/o) and pack cementation
temperatures (800-11000C). If NH4F or NH4F.HF are used as activators,
crystalline A1F 3 forms in the pack by reaction with aluminum. With
the highly volatile activators Al (Cl, Br, I) 3 and NH4(C1. Br,I), no
condensed phase is formed in the pack. The composition of the gas-
mixture that forms in the pack will be unstable because of continuous
losses. While the function of both kinds of activators is qualitatively
identical, only the former class can be quantitatively analyzed. The
composition of the gas phase can be calculated given the temperature,
aluminum activity and the total pressure. For NaX, the partial pressure
(pi) of the significant species in the bulk pack will be given by the
equilibrium constants of the following chemical reactions, subject to
the last two conditions:
NaX (t) + Al - A1X(g) + Na( g )	 (4)
2 NaX (L) + Al - AlX2 (g) + 2Na(g) (5)
3 NaX (¢) + Al - A1X3 (g) + 3Na(g) (6)
NaX (t) - NaX (g)	 (7)
NaX(Z) + h H2 ( g ) - HX ( g ) + Na( g )	 (8)
2 AIX3 (g) - Al 2X6(g)	 (g)
PNa(g)= 3 
PAIX3(g)+ 
6 PAl2X&(9)+ 2 PA1X2(9)
	
+ PA1X(g) + PHX( g )
	
(10)
E P i = 1 atm.	 (11)
For A1F3
 or ammonium fluoride activators, the partial pressure of A1F3(g)
equals the vapor pressure of A1F 3 (g) and is independent of the aluminum
activity. The other partial pressures can be calculated from:
A1F3 (g) + 2 Al
	 3 A1F(g)	 (12)
2A1F3 (g) + Al
	 3 A1F2 (g)	 (13)
AlF3(g) + ?2 ( g ) = 3 HF( g ) + Al	 (14)
PA1F3 (g) + PA1F2 ( g ) + PHF( g ) + PH2(g) = 1 atm.
	 (15)
Similar calculations for Pi at the specimen surface must take into
account certain kinetic considerations. The pack gases not only trans-
port Al, but also halogen, hydrogen and sodium gas. For the NaX activators,
Na(g) and halogen must be transported in equimolar proportions, so that
they react and condense back into NaX(i) near the specimen surface.
Therefore, eq. (10) is modified to:
DNa ( PNa - PA 	 3 
03 (PAIX	 - PA1X ) + 2D2 (PAIX - PAiX ) + D1 (PAlX PA1X)3	 3	 2	 2
+ DHX (PHX	 PHX ) + 6 D6 (PAl 2X6
 - 7Al2X6)
	
(16)
For A1F3 , since its vapor pressure must be constant throughout the pack,
a part of the Al that is carried by A1F and A1F 2
 to the specimen surface
is lost due to formation of A1F 3 (s), for example: 3AlF(g) - A1F 3 (s) + 2 Al.
This implies that the actual Al transfer equation should be:
Wg2 = 2^ ((2/3) ' D 1 •(PA1F -
 PA1F ) + (1/3).D2' (PA1F2- PA1F2)].t
(11)
Iz
In principle, a N Z balance equation should be incorporated, but has
been found to be practically unimportant. The Al deposition rate con-
stant, Kg , has been computed at 8000C and 10930C for NaCl, NaF, NaI
and A1F3 as a function of specimen surface composition. The Al activity
as a function of composition in the Ni -A1 system (4) and thermochemical
data (5) are available in the literature. The gas diffusivities and
the value of i - 4 were taken from Levine and Caves' paper (3). The
pack compositions we selected corresponded to p - 0.04 gm/cm 3 and
porosity, e = 0.70.
B. Solid Diffusion: If the surface of the specimen remains at constant
composition, assuming that diffusion takes place into an infinitely ex-
tended medium, the rate of diffusion in the solid will also obey a par-
abolic law expressed by the equation
WS = Ks t	 (18)
where Ks , the parabolic rate constant for diffusion in the solid, will
depend upon the value of the surface composition. It is evident that in
order for the composition at the surface of the coating to be time in-
variant, the K values must be identical, i.e., the surface composition
must assume that value for which K s = Kg . This unknown value of surface
composition can be predicted if K s , as well as Kg , can be calculated.
For complex superalloys, the necessary diffusivity and thermodynamic
data are not yet available to carry out the calculation of K s . Sufficient
data are available for the binary Ni-A1 system, however, to permit calcu-
lation of the Ks values for the aluminization of unalloyed Ni.
RFFRODUICT. T ,ITY OF THE
4MT
The altmdnide coating on nickel will consist of single-phase
intermetallic layers of progressively decreasing Al content, such as
Ni2A13 , NiAl, Ni3A1 and the Ni(A1) terminal phase. The identity of
the first layer is determined by the surface composition. The position
of the interface between any two layers i and j is given by:
xij = pij
 r (19)
The free surface of the coating also moves outward parabolically with
time, because Al is gained but Ni not lost in pack aluminization (6).
The thickness of the layer j is:
t  = (pij - pjk) r s
 qj/t—	 (20)
The growth rates of the various layers, as well as of the coating as a
whole are known if the constants p ij can be calculated. These depend
on the interdiffusion coefficients and the composition parameters of
the various phases.
The first step in calculating p ij is to set up material balance equations
at the interfaces. Thus, the rate of movement of the ij interface is
given by:
(C ij- cji) (dxij/dt) _ -Di(aci/ax)ij + Dj(acj/ax)ij 	 (21a)
cij and cji are the equilibrium compositions, in atom fraction, of the
phases i and j, respectively, at the interface ij. For a surface composition
cs , the material balance equation for the free coating surface i.e., the
vapor-solid interface, s, is:
(1 - cs) (dxs/dt) = Dj (acj /ax) s	 (21b)
If the interdiffusion coefficients D i do not vary with composition, then
analytical solutions are known (7,8) for the composition profile in each
phase, for instance the solution for the phase j is:
erf (x/2VT—t) - erf (pi . /2^
c.(x,t) = C.
	 (c.. -c. ^.	 _
3 i	 32 3k	 j	 j	 !ij	 j	 (22)
With the help of these and eq. (19), all the derivatives in eq. (21a,b) can
be replaced, and a system of n equations in n unknowns, pij , where n is
the total number of phases in the coating, can be generated and solved.
This analytical scheme suffices in many practical cases of binary dif-
fusion. In the Ni-A1 system, however, it has been found that while
Ni 2A13 , Ni3Al and the Ni(Al) terminal solution have diffusivities
practically invariant with composition, the interdiffusion coefficient
in NiAl varies strongly with composition (9). It has a minimum at
around the equiatcmic composition, and on either side of this composition,
D varies exponentially:
DNiAl = Do ExP (sc)
	
(23)
For such a case, an analytical solution is not known. Therefore, the
composition profile in NiAl has to be computed numerically. This is
done by first transforming the diffusion equation in NiAl:
(ac/at) = Ox [D (ac/ax)]	 (24)
to an ordinary differential equation:
y(d2y/dz 2) * (P12/ 2 Do) z (dy/dz) = 0	 (25)
by substitution of the new variables:
y = exp (sc) and z = (x/pl23t^  [P12= rate const. for theNiAl/Ni 3Al interfacd
The transformed eq. (25) can be solved by a numerical procedure described
in detail in Ref (8). In Fig. 2, we show a number of concentration pro-
files across NiAl-Ni-Al-Ni(A1) terminal solution type of coatings, num-
s--
	 erically computed for 20 hours of pack cementation at 1100°C. The
_	 numerical method becomes important only when NiAl is the surface layer
a
of the coating. If the surface composition is such that Ni 2A1 3 is the
first layer, then we have found that all the other layers develop relatively
small thicknesses. In these cases, a constant value of the interdiffusion
coefficient for NiAI, obtained by averaging the D over its homogeneity
range, can be used in the analytical scheme to give accurate enough
results for Ni 2A1 3-NiAl- Ni 3A1-Ni(A1) type of coatings.
Thus, by the appropriate application of the analytical or numerical
method the growth-rate constants 
pij or qj , and the composition profile
across the coating ci.n be calculated, for any surface composition. The
Al intake of the nickel specimen, W s , and the rate constant Ks are then
obtained by integrating the profile.
In Fig. 1 (a) and (b) the K s versus surface composition curves at
10930C and 8000C have been superimposed on the Kg curves to locate their
intersections.
Comparison with Ex periment
Data have been obtained for the aluminization of unalloyed Ni in
packs activated with A1F3 , NaF,	 NaCl and NaI. The packs contained
4 w/o Al. 4 w/o activator, balance Al 2 03 , and were contained in alumina-
lined iron retorts with a slide-fitting cover. The retorts were heated
in an atmosphere of H2 . After removal, the coated specimens were cleaned
by brushing and in an ultrasonic bath. Surface compositions were determined
by microprobe analysis of the as-coated surfaces.
The square of the weight gain and surface composition vs. time curves
for a number of specimens are shown in Fig. 3. It was observed that
surface melting had occurred on specimens aluminized at 1093 O in packs
N
RM
activated with A1F3 and NaF, and curves for these specimens are not
given. Also low and erratic weight gains were obtained with Nal ac-
tivated packs, and these results are not shown. For the eemainder of
the activators and temperatures studied it was observed that the surface
compositions of the coated specimens were relatively independent of time.
Furthermore the square of weight gain vs. time curves were nearly
straight line obeying parabolic relationship. These results indicate
that within a short period the system reaches steady-state at the pack
cicating interface. The surface compositions obtained under various
criditions are compared with those predicted theoretically in Table 1.
It will be noted.the activators ar- properly ordered by the theory.
Furthermore, there is good correspondence between the predicted and
observed values of surface composition. This is felt to be a strong
confirmation of the basic validity of the proposed model.
Summary and Conclusions
By combining the gaseous diffusion model of Levine and Caves with
a calculation of diffusion rates in the solid a theory of pack alumini-
zation has been formulated. This theory relates the surface composition
of the coating (and therefore, in principle, the coating formation rate)
to pack operating parameters such as pack Al density, type of activator,
temperature and others. Experimental data on the aluminization of un-
alloyed Ni in pure Al packs obtained by us to date are in good agreement
with the predictions of the theory.
Acknowledgement: This work was supported in part by the NASA Lewis'
Research Lab under Grant No. NGR 33-015-160.
Table 1. Conwarison of theoreticall y Predicted and observed results
Pack Conditions Phaset Surface composition (a/o Al)
Activator Coating Temperature Observed Predicted
A1F3 10930C Liquid, >62.5 Liquid, >62.5
A1F3 8000C Ni2A139 59.0 Ni2A1311 59.10
NeF 1000 o Ni2A13 Ni2Al3
NaCl 10930C NiA1, 53.2 NiAl, 54.0
References
1. P. N. Walsh, "Chemical Vapor Deposition; Fourth International
Conference, G. F. Wakefield and J. M. Blocher, Jr., Ed., The
Electrochemical Soc., Inc., Princeton, N.J. (1963).
2. M. A. Levinstein, "Enriched Aluminide Coatings for Dispersion
Strengthened Nickel Materials", G. E. Aircraft Engine Group,
Cincinnati, Ohio (1973).
3. S. R. Levine and R. M. Caves, J. Electrochem. Soc. 121, 1051 (1974).
4. A. Steiner and K. L. Komarek, Trans. TMS-AIME 230, 786 (1964).
S.	 JANAF Thermochemical Tables, Dow Chemical Co., Midland, Mich. (1972).
6. R. Sivakumar, N. B. Menon and L. L. Seigle, Met. Trans. 4, 396 (1973).
7. A. J. Hickl and R. W. Heckel, Met. Trans. 6A, 431 (1975).
8. A. K. Sarkhel and L. L. Seigle, Met. Trans. (accepted for publication).
9. B. Gupta, A. Sarkhel, S. Shankar and L. Seigle, Fourth Semiannual
Report, 6/1/14 - 11/30/74, Sixth Semiannual Report, 6/1/75 - 11/30/75,
NASA Research Grant NGR-33-015-160, NASA Scientific and Technical
Information Facility, P.O. Box 33, College Park, Maryland.
4List of Figures
Fig.	 I	 (a) Gaseous and solid diffusion rate constants (K and Ks)
as a function of surface composition at 1093°C (calculated).
Fig.
	
I	 (b) Gaseous and solid diffusion rate constants (K
9
and KS)
as a function of surface composition at 800 °C (calculated).
Fig. 2 Typical composition profiles in the diffusion zone,
competed for pack aluminization at 1100°C for 20 hours.
Fig.	 3 Variation of square e l weight gain and surface composition
with time in pure Al packs.
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On the kinetics of pack aluminization

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