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Interdiffusion and coating design
Surface and Coatings Technology, 43/44 (1990) 371—380
371
INTERDIFFUSION AND COATING DESIGN J. E. MORRAL Department of Metallurgy and Institute of Materials Science, University of Connecticut, Room 111, U-136, 97 North Eagleville Road, Storrs, CT 06269-3136 (U.S.A.) M. S. THOMPSON United Technologies Research Center, MIS 24, East Hartford, CT 06108 (U.S.A.)
Abstract Interdiffusion between a coating and its underlying substrate can change the oxidation properties of the coating and the mechanical properties of the coated material. An approach is given here for analyzing electron probe microanalyzer (EPMA) data in order to measure the amount of interdiffusion and to predict how interdiffusion can be reduced by changing the coating chemistry. The approach makes use of “zero flux planes” and “composition vectors”. It is shown how to eliminate or reduce Kirkendall porosity in a systematic manner. Experimental results obtained on nickel base alloys are used for illustration.
1. Introduction When nickel base superalloys are coated with aluminide or MCrA1Y coatings and are heated above 1000 °C,the coating will interdiffuse with the substrate alloy causing undesirable changes [1]. One change is that aluminum leaves the coating, thereby reducing its useful life. Another change is that a reaction zone forms which degrades the mechanical properties of the substrate and can lead to premature coating failure. Interdiffusion is a general problem which is also expected in other types of high temperature coating, but this work focuses on superalloys as an example system. Two questions are addressed in this work with regard to complex commercial coatings: first, how can interdiffusion be measured with the electron probe microanalyzer (EPMA), and second, how can the data be used to predict a coating chemistry which minimizes interdiffusion? These questions can be answered quantitatively for multicomponent coatings and substrates that have the same crystal structure. Recent experiments [2—4] and theory [5—10]on such systems have demonstrated that interdiffusion can be measured and accurately predicted using fundamental equations as a basis. With this approach, single-phase systems containing ten or more components can be treated with the same ease and insight as binary 0257.8972/90/$3.50
©
Elsevier Sequoia/Printed in The Netherlands
372
or ternary alloys. This approach is given below, followed by a similar, but empirical, approach for multiphase systems (e.g. coated superalloys).
2. Interdiffusion measurements A “reaction zone” surrounds the initial coating—substrate interface and is the region where interdiffusion occurs. As shown schematically in Fig. 1, the microstructure of this zone can be complex, containing dendritic, cellular or other structures formed by diffusion and phase transformation. In multiphase systems it is common to measure reaction zone or individual layer size [11]. These can be normalized to account for coating thickness [12] and plotted vs. the square root of time to predict long-term behavior. However, size measurements have inherent limitations. For example, two coatings with slightly different chemistry may contain different phases, preventing direct comparisons [13] and the reaction zone may appear large when the amount of interdiffusion is relatively small. In addition, the effect of individual alloying elements on interdiffusion is obscured when analyzing size measurements alone. However, the automated EPMA can obtain detailed chemical information about the reaction zone. The composition of individual phases can be measured and used to construct ternary [14] and higher order phase diagrams [15], and average concentrations can be used to construct “composition paths” [16]. This work is concerned with how average concentration data can be applied to coating design. Figure 2 shows how the average concentration C~is measured by the EPMA in a multiphase reaction zone. A sufficient amount of each phase must be included in the measurement in order to obtain a representative average.
SUBSTRATE ALLOY
COATING
~1rr ::Ji
Fig. 1. The coating substrate interface before and after interdifflision.
373
Fig. 2. Average concentration measurements by the EPMA. Top, reaction zone microstructure with the masked area being measured for average concentration. Bottom, average concentration C~of element i plotted vs. distance perpendicular to the reaction zone.
3. Analysis of data Once average concentration profiles have been measured for each element in the system, the Matano interface position is determined [17]. The Matano interface, given as x = 0, is obtained from the construction shown in Fig. 3, where the shaded areas on either side of x = 0 are equal. The shaded area on the right side of Fig. 3 is termed S, and is the amount of solute i which has left the coating and entered the substrate. The units of S~depend on the units of concentration obtained from the EPMA (e.g. if S, has units of grams per square meter, then the average concentration C has units of grams per cubic meter). In the initial stages of interdiffusion S~vs. the square root of time is linear for single-phase systems as shown in Fig. 4. The same behavior is expected for multiphase systems which are diffusion controlled. By convention [6], elements that are leaving the coating have negative values of S, as shown in the figure and those that enter the coating have positive values. It is possible for S~to be zero vs. the square root of time as shown for element 3 in the figure. In this case there is a “zero flux plane” (ZFP) for element 3 at the Matano interface. A ZFP is defined as a position in the reaction zone where the flux of an element is zero [18]. These positions move
374
Fig. 3. The amount of element i that has crossed the Matano interface is given by the area S~to the right of x = 0.
0
Fig. 4. The amount of each alloying element crossing x = 0 vs. the square root of time. Negative values of S, indicate that element i is leaving the coating, and positive values indicate that it is entering the coating.
with time except when they are at the Matano interface. When the ZFP for an element is at the coating—substrate interface, there will be no net change in the amount of the element in the coating in the early stages of interdiffusion. However, the element will redistribute in the coating with time, as required by the diffusion equation.
375
Figure 4 gives the kinetic behavior expected for the initial stages of interdiffusion. If there is a change in the interdiffusion zone due to the nucleation of additional phases, the S, vs. the square root of time plots will change slope to reflect the new reaction zone microstructure. In addition, changes will always occur once the reaction zone has covered the entire coating [19].
4. Minimizing interdiffusion by varying one concentration Experimental studies on nickel alloys [2, 3] have shown that in singlephase systems containing small concentration differences (e.g. less than 10 at.%), the amount of solute that crosses the Matano interface is a linear function of the original concentration, regardless of the number of alloying elements present. Theory predicts this relationship when the diffusivity is constant [5, 6, 10] via the equation
S~= —(t/x)”2(r~1AC?+ r12AC°2+.
—
.
.
r,
,,
—
1AC°~_ ~)
(1)
in which t is time and AC~is the initial concentration difference of element i between the coating and the substrate
AC~= C~coating
C~substrate
(2)
The ~ coefficients are matrix elements of the “square root diffusivity” [5—7], a property matrix Er] that is related to the “diffusivity” [D] by
[D] = [r][r]
(3) 112 is plotted vs. any of the concentration differences Therefore if S~/(t/ir) ACJ° as illustrated in Fig. 5, a straight line is obtained with slope ~ In addition, the concentration that yields a ZFP for element j is given by where the straight line crosses the ACJ°axes. From eqn. (1), a ZFP for element i occurs when —
A_/
~~—kr~l
Ar’O
Af’O
AflO
~ 1+r~2
~
Therefore there is a range of coating compositions which will have a ZFP for element i. Because of this flexibility, coatings can be designed that have ZFPs for more than one element. The coating compositions can be calculated by solving eqn. (4) for more than one element simultaneously. It is possible to obtain simultaneous ZFPs for up to (n 2) alloying elements. In the limiting case of (n 2) ZFPs, one element will diffuse to the right through x = 0 and another element will diffuse to the left to replace it, while all other elements will not cross the interface. As shown in Fig. 5, data for multiphase systems can be plotted in the same way as for single-phase systems. However, the data may have curvature as well as discontinuities in both slope and value. The discontinuities reflect abrupt changes in microstructure with composition. Therefore data must be extrapolated with caution. Nevertheless, these plots show both trends and —
—
376
(b)
(a)
Fig. 5. InterdifTusion of element i vs. the concentration of another alloying element j. The relationship is a straight line for single-phase systems (a), but it can be a curved line with changes in slope and value for a multiphase system (b).
I
ZFP-~r
/~ S2
Fig. 6. Variation in the “total interdiffusion” ST with concentration of element 2. A minimum in ST coincides with a ZFP for element 1.
377
compositions where ZFPs occur. In addition, the ZFP compositions for multiphase systems may follow a nearly linear relationship with composition and can be modeled by eqn. (4). However, the coefficients will be empirical instead of square root diffusivities and the relationship will probably fail if there is a change in microstructure with composition. ZFPs are important because they correspond to zero interdiffusion for certain elements and also because they are associated with minima in the “total interdiffusion” ST defined by the expression
ST=>ISjI
(5)
Half of this sum is equal to the amount of solute which has left the coating and the other half is equal to the amount of solute which has entered the coating. Figure 6 illustrates how the sum is related to individual S~values and their variation with concentration. It is shown that local minima may occur in ST at a ZFP concentration. Deeper minima can be found by inspecting compositions where simultaneous ZFPs are found.
5. Minimizing interdiffusion by varying the “composition vector” A global view of interdiffusion is obtained by considering variables associated with the “composition vector”, defined by AC°=[AC1,AC2,...AC~.1]
(6)
When plotted on concentration coordinates, it is the vector between the initial composition of the coating and the substrate alloys. In single-phase systems the amount of interdiffusion (e.g. either S~or ST) is related to the length of the vector AC°I and the vector orientation which can be seen by writing eqn. (1) in vector notation as a dot product 12(r~ AC°) (7) S, = (t /it) ‘ or in trigonometric form as .
—
S,
=
—(t/it)”2Ir
1IIAC°~cos 0
(8)
in which r~is a vector defined by the ith row of the square root diffusivity matrix. When r~and AC°are parallel (cos 0 = 1), there is maximum interdiffusion of element i for a given length of AC°.When r~and AC°are perpendicular (cos 0 = 0), S~is zero, regardless of the length of AC°. Figure 7 gives r, vectors that were measured for an Ni—7.5at.%Al— 9.Oat.%Cr alloy at 1100 “C [2]. Both r~ and rcr are rows of the measured [r], while r~,was obtained from [7] r1.~,= —(rAl +
rcr)
(9)
It can be seen in Fig. 7 how the orientation of AC°influences the interdiffusion of various elements. For example, when it aligns with r~ there is
378
rcr
at.Jc:
Ni
5
at.%AI
10
Fig. 7. r, vectors for each element in an Ni 7.5at.%Al-9.Oat.%Cr 0.The circle on the alloy tail at of the 1100vector C plotted is at the on substrate composition cencentration axes withand a “composition the circle on vector” the arrowhead L~iC is at the coating composition. When the composition vector is parallel to ZMM, no Kirkendall effect is expected.
maximum loss of aluminum from the coating for a given length of AC°, whereas when it is perpendicular to rA] there is no loss of aluminum, regardless of the length of AC°. Previous work has shown that Kirkendall marker movement is also a function of the composition vector orientation [4, 9]. When AC°is parallel to the broken line labeled ZMM (zero marker movement) there is no marker movement and no Kirkendall porosity is expected for these systems. Experimental evidence for this effect of orientation on porosity has been obtained by Nesbitt and Heckel [21]. Figure 8 illustrates composition vectors plotted on a phase diagram for two coating—substrate systems. One is a F + F’ superalloy coated with a (/3) aluminide coating and the other is a similar superalloy coated with a (fJ + F) MCrA1Y coating. It can be seen that the composition vector increases in length, changes orientation and crosses multiphase regions. If only one phase were involved it would be possible to predict from theory how varying the vector would affect interdiffusion. However, current theory does not apply to multiphase systems and an empirical approach is required in order to find zero flux planes or to reduce Kirkendall porosity. For example, experimental work suggests that rotating the composition vector from the MCrA1Y to the
379 y+a
30
20
at.%Cr
MCrAIY coating
10
.,. ,.,
11
Aluminide
Ni
I
10
I 20
tin9I
30 at.%AI
c~oa 40
I
50
Fig. 8. The Ni—Al—Cr phase diagram at 1100°C [141 and composition vectors for two coating— substrate systems. Rotating and extending the composition vector from the MCrA1Y coating to the aluminide coating, as shown by the broken arrow, reduces the interdiffusion of aluminum.
aluminide composition results in a reduction of the interdiffusion of aluminum [22]. 6. Conclusions The interdiffusion of coating—substrate systems that are either single phase or develop complex multiphase reaction zones can be studied by a similar approach. The approach is to measure average concentrations of each element present across the reaction zone. These give the amount of each element that has crossed the Matano interface. By investigating a series of coatings that have systematic changes either in individual concentrations or in the “composition vector”, it is possible to determine conditions for the formation of ZFPs, the minimization of interdiffusion and the elimination of Kirkendall porosity. Acknowledgments The authors are grateful to the National Science Foundation for financial support under grant DMR-8711899 and to Mr. Fred Massicotte for preparing the figures.
380
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
T. N. Rhys-Jones, Corros. Sci., 29(1989) 623. M. S. Thompson, Ph.D. Thesis, University of Connecticut, 1988. M. K. Stalker, MS. Thesis, University of Connecticut, 1989. Y.-H. Son and J. E. Morral, Metal!. Trans. A, 20 (1989) 2299. J. E. Morral, Scr. Metall., 18(1984)1251. M. S. Thompson and J. E. Morral, Acta Metall., 34 (1986) 339. M. S. Thompson and J. E. Morral, Acta Metall., 34 (1986) 2201. M. S. Thompson and J. E. Morral, Metall. Trans., 18 (1987) 1565. J. E. Morral, Y.-H. Son and M. S. Thompson, Acta Metall., 36(1988)1787. M. K. Stalker and J. E. Morral, Acta Metall., 38 (1990) 439. J. B. Clark and F. N. Rhines, Trans. Am. Soc. Met., 51 (1959) 199. J. E. Morral and R. H. Barkalow, Scr. Metal!., 16(1982) 593. S. Levine, Metall. Trans. A, 9(1978)1237. S. M. Merchant and M. R. Notis, Mater. Sci. Eng., 6(1984) 47. J. Zhoa, Z. P. Jin and P. Y. Huang, Scr. Metall., 22 (1988) 1825. M. R. Jackson and J. R. Rairden, General Electric Technical Rep. 77CRD029, 1977. F. J. A. den Broeder, Scr. Metal!., 3 (1969) 321. M. A. Dayananda and C. W. Kim, Metall. Trans. A, 10 (1979) 1333. M. S. Thompson and J. E. Morral, in M. K. Khobaib and R. C. Krutenat (eds.), High Temperature Coatings, The Minerals, Metals and Materials Society, Warrendale, PA, 1987, p. 55. 20 J. E. Morral, M. K. Stalker and M. S. Thompson, DIMETA-88, Vol. 66—69, Defect and Diffusion Forum, Trans. Tech., Brookfield, VT, 1989, p. 1275. 21 3. A. Nesbitt and R. W. Heckel, Metall. Trans. A, 18(1987) 2061. 22 P. J. Fink and R. W. Heckel, in M. K. Khobaib and R. C. Krutenat (eds.), High Temperature Coatings, TMS, Warrendale, PA, 1987, p. 21.
371
INTERDIFFUSION AND COATING DESIGN J. E. MORRAL Department of Metallurgy and Institute of Materials Science, University of Connecticut, Room 111, U-136, 97 North Eagleville Road, Storrs, CT 06269-3136 (U.S.A.) M. S. THOMPSON United Technologies Research Center, MIS 24, East Hartford, CT 06108 (U.S.A.)
Abstract Interdiffusion between a coating and its underlying substrate can change the oxidation properties of the coating and the mechanical properties of the coated material. An approach is given here for analyzing electron probe microanalyzer (EPMA) data in order to measure the amount of interdiffusion and to predict how interdiffusion can be reduced by changing the coating chemistry. The approach makes use of “zero flux planes” and “composition vectors”. It is shown how to eliminate or reduce Kirkendall porosity in a systematic manner. Experimental results obtained on nickel base alloys are used for illustration.
1. Introduction When nickel base superalloys are coated with aluminide or MCrA1Y coatings and are heated above 1000 °C,the coating will interdiffuse with the substrate alloy causing undesirable changes [1]. One change is that aluminum leaves the coating, thereby reducing its useful life. Another change is that a reaction zone forms which degrades the mechanical properties of the substrate and can lead to premature coating failure. Interdiffusion is a general problem which is also expected in other types of high temperature coating, but this work focuses on superalloys as an example system. Two questions are addressed in this work with regard to complex commercial coatings: first, how can interdiffusion be measured with the electron probe microanalyzer (EPMA), and second, how can the data be used to predict a coating chemistry which minimizes interdiffusion? These questions can be answered quantitatively for multicomponent coatings and substrates that have the same crystal structure. Recent experiments [2—4] and theory [5—10]on such systems have demonstrated that interdiffusion can be measured and accurately predicted using fundamental equations as a basis. With this approach, single-phase systems containing ten or more components can be treated with the same ease and insight as binary 0257.8972/90/$3.50
©
Elsevier Sequoia/Printed in The Netherlands
372
or ternary alloys. This approach is given below, followed by a similar, but empirical, approach for multiphase systems (e.g. coated superalloys).
2. Interdiffusion measurements A “reaction zone” surrounds the initial coating—substrate interface and is the region where interdiffusion occurs. As shown schematically in Fig. 1, the microstructure of this zone can be complex, containing dendritic, cellular or other structures formed by diffusion and phase transformation. In multiphase systems it is common to measure reaction zone or individual layer size [11]. These can be normalized to account for coating thickness [12] and plotted vs. the square root of time to predict long-term behavior. However, size measurements have inherent limitations. For example, two coatings with slightly different chemistry may contain different phases, preventing direct comparisons [13] and the reaction zone may appear large when the amount of interdiffusion is relatively small. In addition, the effect of individual alloying elements on interdiffusion is obscured when analyzing size measurements alone. However, the automated EPMA can obtain detailed chemical information about the reaction zone. The composition of individual phases can be measured and used to construct ternary [14] and higher order phase diagrams [15], and average concentrations can be used to construct “composition paths” [16]. This work is concerned with how average concentration data can be applied to coating design. Figure 2 shows how the average concentration C~is measured by the EPMA in a multiphase reaction zone. A sufficient amount of each phase must be included in the measurement in order to obtain a representative average.
SUBSTRATE ALLOY
COATING
~1rr ::Ji
Fig. 1. The coating substrate interface before and after interdifflision.
373
Fig. 2. Average concentration measurements by the EPMA. Top, reaction zone microstructure with the masked area being measured for average concentration. Bottom, average concentration C~of element i plotted vs. distance perpendicular to the reaction zone.
3. Analysis of data Once average concentration profiles have been measured for each element in the system, the Matano interface position is determined [17]. The Matano interface, given as x = 0, is obtained from the construction shown in Fig. 3, where the shaded areas on either side of x = 0 are equal. The shaded area on the right side of Fig. 3 is termed S, and is the amount of solute i which has left the coating and entered the substrate. The units of S~depend on the units of concentration obtained from the EPMA (e.g. if S, has units of grams per square meter, then the average concentration C has units of grams per cubic meter). In the initial stages of interdiffusion S~vs. the square root of time is linear for single-phase systems as shown in Fig. 4. The same behavior is expected for multiphase systems which are diffusion controlled. By convention [6], elements that are leaving the coating have negative values of S, as shown in the figure and those that enter the coating have positive values. It is possible for S~to be zero vs. the square root of time as shown for element 3 in the figure. In this case there is a “zero flux plane” (ZFP) for element 3 at the Matano interface. A ZFP is defined as a position in the reaction zone where the flux of an element is zero [18]. These positions move
374
Fig. 3. The amount of element i that has crossed the Matano interface is given by the area S~to the right of x = 0.
0
Fig. 4. The amount of each alloying element crossing x = 0 vs. the square root of time. Negative values of S, indicate that element i is leaving the coating, and positive values indicate that it is entering the coating.
with time except when they are at the Matano interface. When the ZFP for an element is at the coating—substrate interface, there will be no net change in the amount of the element in the coating in the early stages of interdiffusion. However, the element will redistribute in the coating with time, as required by the diffusion equation.
375
Figure 4 gives the kinetic behavior expected for the initial stages of interdiffusion. If there is a change in the interdiffusion zone due to the nucleation of additional phases, the S, vs. the square root of time plots will change slope to reflect the new reaction zone microstructure. In addition, changes will always occur once the reaction zone has covered the entire coating [19].
4. Minimizing interdiffusion by varying one concentration Experimental studies on nickel alloys [2, 3] have shown that in singlephase systems containing small concentration differences (e.g. less than 10 at.%), the amount of solute that crosses the Matano interface is a linear function of the original concentration, regardless of the number of alloying elements present. Theory predicts this relationship when the diffusivity is constant [5, 6, 10] via the equation
S~= —(t/x)”2(r~1AC?+ r12AC°2+.
—
.
.
r,
,,
—
1AC°~_ ~)
(1)
in which t is time and AC~is the initial concentration difference of element i between the coating and the substrate
AC~= C~coating
C~substrate
(2)
The ~ coefficients are matrix elements of the “square root diffusivity” [5—7], a property matrix Er] that is related to the “diffusivity” [D] by
[D] = [r][r]
(3) 112 is plotted vs. any of the concentration differences Therefore if S~/(t/ir) ACJ° as illustrated in Fig. 5, a straight line is obtained with slope ~ In addition, the concentration that yields a ZFP for element j is given by where the straight line crosses the ACJ°axes. From eqn. (1), a ZFP for element i occurs when —
A_/
~~—kr~l
Ar’O
Af’O
AflO
~ 1+r~2
~
Therefore there is a range of coating compositions which will have a ZFP for element i. Because of this flexibility, coatings can be designed that have ZFPs for more than one element. The coating compositions can be calculated by solving eqn. (4) for more than one element simultaneously. It is possible to obtain simultaneous ZFPs for up to (n 2) alloying elements. In the limiting case of (n 2) ZFPs, one element will diffuse to the right through x = 0 and another element will diffuse to the left to replace it, while all other elements will not cross the interface. As shown in Fig. 5, data for multiphase systems can be plotted in the same way as for single-phase systems. However, the data may have curvature as well as discontinuities in both slope and value. The discontinuities reflect abrupt changes in microstructure with composition. Therefore data must be extrapolated with caution. Nevertheless, these plots show both trends and —
—
376
(b)
(a)
Fig. 5. InterdifTusion of element i vs. the concentration of another alloying element j. The relationship is a straight line for single-phase systems (a), but it can be a curved line with changes in slope and value for a multiphase system (b).
I
ZFP-~r
/~ S2
Fig. 6. Variation in the “total interdiffusion” ST with concentration of element 2. A minimum in ST coincides with a ZFP for element 1.
377
compositions where ZFPs occur. In addition, the ZFP compositions for multiphase systems may follow a nearly linear relationship with composition and can be modeled by eqn. (4). However, the coefficients will be empirical instead of square root diffusivities and the relationship will probably fail if there is a change in microstructure with composition. ZFPs are important because they correspond to zero interdiffusion for certain elements and also because they are associated with minima in the “total interdiffusion” ST defined by the expression
ST=>ISjI
(5)
Half of this sum is equal to the amount of solute which has left the coating and the other half is equal to the amount of solute which has entered the coating. Figure 6 illustrates how the sum is related to individual S~values and their variation with concentration. It is shown that local minima may occur in ST at a ZFP concentration. Deeper minima can be found by inspecting compositions where simultaneous ZFPs are found.
5. Minimizing interdiffusion by varying the “composition vector” A global view of interdiffusion is obtained by considering variables associated with the “composition vector”, defined by AC°=[AC1,AC2,...AC~.1]
(6)
When plotted on concentration coordinates, it is the vector between the initial composition of the coating and the substrate alloys. In single-phase systems the amount of interdiffusion (e.g. either S~or ST) is related to the length of the vector AC°I and the vector orientation which can be seen by writing eqn. (1) in vector notation as a dot product 12(r~ AC°) (7) S, = (t /it) ‘ or in trigonometric form as .
—
S,
=
—(t/it)”2Ir
1IIAC°~cos 0
(8)
in which r~is a vector defined by the ith row of the square root diffusivity matrix. When r~and AC°are parallel (cos 0 = 1), there is maximum interdiffusion of element i for a given length of AC°.When r~and AC°are perpendicular (cos 0 = 0), S~is zero, regardless of the length of AC°. Figure 7 gives r, vectors that were measured for an Ni—7.5at.%Al— 9.Oat.%Cr alloy at 1100 “C [2]. Both r~ and rcr are rows of the measured [r], while r~,was obtained from [7] r1.~,= —(rAl +
rcr)
(9)
It can be seen in Fig. 7 how the orientation of AC°influences the interdiffusion of various elements. For example, when it aligns with r~ there is
378
rcr
at.Jc:
Ni
5
at.%AI
10
Fig. 7. r, vectors for each element in an Ni 7.5at.%Al-9.Oat.%Cr 0.The circle on the alloy tail at of the 1100vector C plotted is at the on substrate composition cencentration axes withand a “composition the circle on vector” the arrowhead L~iC is at the coating composition. When the composition vector is parallel to ZMM, no Kirkendall effect is expected.
maximum loss of aluminum from the coating for a given length of AC°, whereas when it is perpendicular to rA] there is no loss of aluminum, regardless of the length of AC°. Previous work has shown that Kirkendall marker movement is also a function of the composition vector orientation [4, 9]. When AC°is parallel to the broken line labeled ZMM (zero marker movement) there is no marker movement and no Kirkendall porosity is expected for these systems. Experimental evidence for this effect of orientation on porosity has been obtained by Nesbitt and Heckel [21]. Figure 8 illustrates composition vectors plotted on a phase diagram for two coating—substrate systems. One is a F + F’ superalloy coated with a (/3) aluminide coating and the other is a similar superalloy coated with a (fJ + F) MCrA1Y coating. It can be seen that the composition vector increases in length, changes orientation and crosses multiphase regions. If only one phase were involved it would be possible to predict from theory how varying the vector would affect interdiffusion. However, current theory does not apply to multiphase systems and an empirical approach is required in order to find zero flux planes or to reduce Kirkendall porosity. For example, experimental work suggests that rotating the composition vector from the MCrA1Y to the
379 y+a
30
20
at.%Cr
MCrAIY coating
10
.,. ,.,
11
Aluminide
Ni
I
10
I 20
tin9I
30 at.%AI
c~oa 40
I
50
Fig. 8. The Ni—Al—Cr phase diagram at 1100°C [141 and composition vectors for two coating— substrate systems. Rotating and extending the composition vector from the MCrA1Y coating to the aluminide coating, as shown by the broken arrow, reduces the interdiffusion of aluminum.
aluminide composition results in a reduction of the interdiffusion of aluminum [22]. 6. Conclusions The interdiffusion of coating—substrate systems that are either single phase or develop complex multiphase reaction zones can be studied by a similar approach. The approach is to measure average concentrations of each element present across the reaction zone. These give the amount of each element that has crossed the Matano interface. By investigating a series of coatings that have systematic changes either in individual concentrations or in the “composition vector”, it is possible to determine conditions for the formation of ZFPs, the minimization of interdiffusion and the elimination of Kirkendall porosity. Acknowledgments The authors are grateful to the National Science Foundation for financial support under grant DMR-8711899 and to Mr. Fred Massicotte for preparing the figures.
380
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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