Solidification of Nb-Bearing Superalloys: Part II. Pseudoternary Solidification Surfaces

Transcription

1 Solidification of Nb-Bearing Superalloys: Part II. Pseudoternary Solidification Surfaces J.N. DuPONT, C.V. ROBINO, A.R. MARDER, and M.R. NOTIS Equilibrium distribution coefficients and pseudoternary solidification surfaces for experimental superalloys containing systematic variations in Fe, Nb, Si, and C were determined using quenching experiments and microstructural characterization techniques. In agreement with previous results, the distribution coefficient, k, for Nb and Si was less than unity, while the solvent elements (Fe, Ni, and Cr) exhibited little tendency for segregation (k 1). The current data were combined with previous results to show that an interactive effect between k Nb and Fe content exists, where the value of k Nb decreases from 0.54 to as the Fe content is increased from 2 wt pct to 47 wt pct. This behavior is the major factor contributing to formation of relatively high amounts of eutectic-type constituents observed in Fe-rich alloys. Pseudoternary -Nb-C solidification surfaces, modeled after the liquidus projection in the Ni-Nb-C ternary system, were proposed. The Nb compositions, which partially define the diagrams, were verified by comparison of calculated amounts of eutectic-type constituents (via the Scheil equation) and those measured experimentally, and good agreement was found. The corresponding C contents needed to fully define the diagrams were estimated from knowledge of the primary solidification path and s for Nb and C. I. INTRODUCTION IN a previous article, [1] the solidification reaction sequences of experimental superalloys with systematic variations in Fe, Nb, Si, and C were established through differential thermal analysis (DTA) and microstructural characterization techniques. In that work, it was shown that the solidification reactions in the multicomponent alloys could be qualitatively understood based on knowledge of the pure ternary Ni-Nb-C liquidus surface. This analogy is quite useful as it forms the basis for developing a model for providing quantitative relations between alloy composition and microstructural development. Such a solidification model requires knowledge of the equilibrium distribution coefficients for the pertinent solutes (Nb and C), the liquidus surface, and solute redistribution equations to describe mass transport between the liquid and solid during solidification. In this article, the previous results [1] are extended in more quantitative fashion to determine equilibrium distribution coefficients and pseudoternary solidification diagrams. The so-called pseudoternary diagrams are analogous to a true liquidus surface, which represents composition regimes of primary solidification phases for a pure ternary system. This information is used for modeling solute redistribution and microstructural development in a separate article. [2] II. EXPERIMENTAL PROCEDURE Details of the experimental procedure, including alloy compositions, can be found in the previous article. [1] Microsegregation profiles across dendrites in autogenous gas J.N. DuPONT, Research Scientist and Associate Director, Energy Liaison Program, and A.R. MARDER and M.R. NOTIS, Professors, Materials Science and Engineering Department, are with Lehigh University, Bethlehem, PA C.V. ROBINO, Principal Member of the Technical Staff, is with Sandia National Laboratories, Albuquerque, NM Manuscript submitted January 29, tungsten arc (GTA) s, prepared under the conditions previously described, were measured by electron probe microanalysis. Additional s were prepared on alloys 8 and 16 using the same process and parameters. However, during these s, a high pressure water spray was directed at the to quench the dendrite tips growing into the liquid pool. Composition profiles of the quenched dendrites were then obtained by electron microprobe and compared to profiles obtained on s prepared with no forced cooling. Dendrite arm spacings of the autogenous GTA s (prepared with no forced cooling) were determined at the centerline using quantitative image analysis. III. A. Elemental Segregation RESULTS A DISCUSSION Figures 1(a) and (b) show the quenched front of dendrite tips in the of alloy 8, and the composition profile of the dendrite tip outlined in Figure 1(b) is presented in Figure 2. For comparison, the composition profile across several parallel dendrites in a normally cooled of alloy 8 is shown in Figure 3 (Figure 1(c) shows the region of this electron probe microanalysis (EPMA) scan). In each case, the dendrite cores are depleted in Nb and Si and slightly enriched in Fe, Ni, and Cr. Table I summarizes the dendrite core compositions of quenched and normally cooled s for several alloys. This information can be combined with analytical considerations to determine values of equilibrium distribution coefficients, k, and assess the extent of solute backdiffusion, which may occur during solidification. The solute redistribution model developed by Brody and Flemings [3] can be used to estimate the significance of solidstate diffusion during solidification, which, for a parabolic growth rate, is given by k 1 * 1 2 k s 0 s C kc [1 (1 2 k) f ] [1a] METALLURGICAL A MATERIALS TRANSACTIONS A VOLUME 29A, NOVEMBER

2 Fig. 1 (a) and (b) SEM photomicrographs of quenched metal microstructure in alloy 8. (c) LOM photomicrograph of region of EPMA analysis conducted on cellular dendrites in normally cooled of alloy k 1 Tm T k 1 s 1 2 k T T m l Dt sf L 2 f 1 [1b] [1c] Here, k is the equilibrium distribution coefficient, C 0 is the solute content, f s is the fraction solid, D s is the diffusivity of solute in the solid (assumed constant in the derivation of Eq. [1]), t f is the local solidification time, L is half the dendrite arm spacing, T m is the melting point of the pure solvent, and T l is the liquidus temperature of the alloy. The value of C s given by Eq. [1a] is the solid composition at the solid/liquid interface. The backdiffusion potential is dependent on the diffusion distance (L), the time available for diffusion (t f ), and the diffusivity of solute in the solid (D s ). Assuming a constant cooling rate during the short solidification time interval, the solidification time is given by the ratio of solidification temperature range ( T) to cooling rate, ε. If the diffusion distance of the solute is very short in relation to half the dendrite arm spacing ( 1), then solid-state diffusion is negligible and Eq. [1a] reduces to the well-known Scheil equation: * k 1 C s kc 0 [1 f s] [2] Available values for t f, D s, and L can be used to estimate the significance of backdiffusion. Such estimates are provided below for Nb and C, as these elements will be chosen as the solutes in the pseudoternary approach to be developed. The DTA data showed that the solidification temperature range of these alloys, T, is about 140 C. [1] The cooling rate in the s can be determined experimentally 2798 VOLUME 29A, NOVEMBER 1998 METALLURGICAL A MATERIALS TRANSACTIONS A

3 (a) (a) (b) Fig. 2 EPMA composition trace conducted across quenched dendrite tip shown in Fig. 1(b): (a) Fe, Ni, and Cr; and (b) Nb and Si. through measurements of the dendrite arm spacing, ( 2L), using the following semiempirical relation developed for type 310 stainless steel [4] (an alloy that also solidifies as primary austenite): ε [3] where is in microns and ε is the cooling rate in C/s. Type 310 stainless steel has a composition of Fe- 21Ni-25Cr, which is similar to the matrix composition of the Fe-base alloys used in this work (Fe-32Ni-19Cr). Thus, by measuring the dendrite arm spacing in the iron-base alloys, the cooling rate can be estimated via Eq. [3]. Values of were determined by making 20 measurements at the centerline of each iron-base alloy. The average of all the alloys was m, and the values exhibit a range of 8.4 to 10.4 m. Use of these values in Eq. [3] indicates that, under these processing conditions, the s cool at a rate of 460 C/s to 860 C/s (average 660 C/s). With a solidification temperature range of 140 C and a (b) Fig. 3 EPMA composition trace conducted across parallel cellular dendrites shown in Fig. 1(c): (a) Fe, Ni, and Cr; and (b) Nb and Si. cooling rate of 660 C/s, the local solidification time, t f,is 0.2 s. The value of D s chosen for estimating the significance of backdiffusion will obviously vary significantly with the temperature chosen. Calculations were made at temperatures near the liquidus ( 1400 C) and lowest terminal solidus ( 1200 C) in order to bound the possible range of. Values of D s for Nb in a Ni-base alloy were not available in the literature. As an estimate, D s values were determined from the diffusion data for Nb in Fe: [5] D m 2 /s and Q 264 kj/mol. The D s values for C were determined from the data by Bose and Grabke, [6] where D 0 values and activation energies were determined in Fe-Ni alloys with varying carbon contents (0.05 to 0.20 wt pct). The following values were used: D m 2 /s and Q 125 kj/mol. Use of these values along with L /2 4.6 m and t f 0.2 s yields values of for Nb of and at 1400 C and 1200 C, respectively. Since Nb METALLURGICAL A MATERIALS TRANSACTIONS A VOLUME 29A, NOVEMBER

4 Table I. Dendrite Core Compositions, Nominal Compositions, and Distribution Coefficients* Alloy/ Sample Alloy 4 Alloy 7 Compositions and k Values Iron Nickel Chromium Niobium Silicon dendrite core dendrite core dendrite core Alloy Alloy 8 dendrite core quenched Average value of k in nickel-base alloys Alloy 15 Alloy 16 Alloy 16 quenched dendrite core k-value dendrite core dendrite core Average value of k in iron-base alloys *All compositions are in weight percent , Nb diffusion in the solid can be neglected under these solidification conditions. The EPMA data summarized in Table I provide experimental verification of this. The dendrite core Nb concentrations in quenched and normally cooled s in alloys 8 and 16 are similar. If backdiffusion were significant under these ing conditions, then the Nb concentration at the cores of dendrites in normally cooled s would be higher than dendrite tip concentrations, which were frozen in from the water quench. In fact, the similarity in core and tip compositions of all elements listed in Table I indicates that all of these elements exhibit negligible diffusion in the solid during solidification. Since solid-state diffusion is insignificant for the elements listed in Table I, the EPMA data can be used to determine equilibrium distribution coefficients for these elements. At the onset of solidification, the following conditions apply to Eq. [2]: f s 0, C 1 C 0 and C s C core (dendrite core composition), and the value of k at the onset of solidification is given by k C core /C 0. The implicit assumption of this approach is that solute buildup at the dendrite tip is negligible. Any buildup of solute at the tip will cause the initial solid to form at a higher composition (compared to the case of no solute buildup) and, as a result, lead to a higher measured value of k. Thus, the approach used here provides an upper bound when k 1. The dendrite core and compositions and s for all the alloys analyzed by EPMA are summarized in Table I. Within a given alloy class (i.e., Ni-base or Fe-base alloy class), the data indicate that k for each element is independent of the alloy content. Thus, average values of k are presented in the table. Comparison of these values to commercial alloy systems is made in Section B. Repeating the calculations for C leads to values of 5.9 at 1400 C and 1.7 at 1200 C. These values are well in excess of unity and solid-state diffusion is therefore likely to be important. In fact, Clyne and Kurz have shown [7] that C can typically diffuse fast enough in austenite at solidification temperatures such that concentration gradients do not form in the solid and equilibrium is maintained. A simple calculation using the Clyne Kurz model [7] indicates such behavior is also expected under the current set of conditions and is presented subsequently. The Brody Flemings (B F) model, Eq. [1], is only valid provided solid-state diffusion is relatively slow. The model breaks down at values above approximately 0.1, since, in the presence of a fast diffusing element, solute is no longer conserved within the volume element considered in derivation of Eq. [1]. [7] This is readily apparent by noting that the B F model does not reduce to the equilibrium lever rule when. Clyne and Kurz have proposed a modification to the B F model by replacing the term with ', where ' 1 exp exp [4] 2 2 Use of this value correctly reduces the B F model to the Scheil equation when 0 and to the lever rule as. While it is generally recognized that more recent models for backdiffusion exist, [8,9] combined use of the B F model (Eq. [1]) and Clyne Kurz model (Eq. [4]) has been shown to be useful for showing the expected behavior of C solute redistribution during solidification of austenitic alloys. [7] Eqs. [1] and [4] were used to estimate the significance of C diffusion during solidification. The t f and L values noted previously were used (t f 0.2 s and L 4.6 m). For the case of a simple binary system, T m in Eq. [4] is the 2800 VOLUME 29A, NOVEMBER 1998 METALLURGICAL A MATERIALS TRANSACTIONS A

5 Fig. 4 Calculated variation in solid composition (wt pct C) with fraction solid for equilibrium lever law, Clyne Kurz model, and Scheil equation. Table II. Comparison of Distribution Coefficients Determined from Commercial Alloys and the Experimental Alloys in This Study Alloy Fe Ni Cr Nb Si C Reference Alloys 1 through 8 Alloys 9 through 16 IN 625 IN 625/C steel IN 718 IN 909 Thermospan 20 Cb-3 not determined. NP not present NP Table III. Summary of Nominal Composition, Dendrite Core Compositions, and k Values for 20Cb-3 20Cb-3 Fe Ni Cr Nb Si C 0, wt pct C core, wt pct k (0.8) (0.5) (0.3) (0.02) (0.01) 0.89 melting temperature of the pure solvent. Here, the Fe-Ni- Cr matrix is modeled as the pure solvent, which, according to the available Fe-Ni-Cr liquidus surface projection, [10] has a value of approximately 1410 C for the Ni-base alloys (alloys 1 through 8). The Ni-base alloys are used as an example here, as they solidify at temperatures lower than the Fe-base alloys and will thus reveal the influence of C at the low range of C diffusivity. Use of this model also requires a value of k for C. Using DTA techniques, Cieslak et al. [11] have measured a value of k for C in the Nb bearing commercial alloy IN625 at k c. Like the experimental alloys used in this work, this commercial alloy also solidifies as primary austenite. In addition, the for C in the binary Ni-C system is similar at 0.28, [12] indicating the presence of additional alloying elements has little effect on the segregation potential of C. Thus, the value of k for C in IN625 should be readily applicable to the alloys used in this work. The D s and the corresponding and ' values were calculated at each temperature step during solidification starting at the liquidus temperature. Once ' was established as a function of temperature, these values were used in Eq. [1b] to calculate f s as a function of temperature. The f s values were then used to generate the C s /f s curve via Eq. [1a]. Figure 4 shows the results of the calculations. The calculations are made for a C content of 0.15 wt pct and a liquidus temperature of 1400 C. Comparisons are made with the equilibrium lever law and the Scheil equation. These two conditions provide useful comparisons as they bound the possible extent of microsegregation during solidification. The significance of Figure 4 lies within the similarities between the equilibrium lever law and Clyne Kurz model when C diffusivity is considered. These results demonstrate that, even under these relatively high cooling rate conditions, the diffusivity of C in is high enough such that the equilibrium lever law can be used to describe the segregation behavior of C with introduction of little error. This behavior of C is certainly not surprising and has been suggested in other work as well. [7] Thus, based on these results, the equilibrium lever law is assumed to provide a good estimate for describing the solute partitioning behavior of C during solidification, while the Scheil equation provides an accurate description of Nb partitioning. B. Comparison to Commercial Alloy Systems Table II compares the range of s reported in the literature for commercial alloy systems and that determined from the alloys in this study. All the matrix elements (Fe, Ni, and Cr) exhibit similar behavior and show little tendency for segregation during solidification (i.e., their s are all close to unity). As previously discussed, the segregation potential of Nb and C plays a key role in microstructural development during solidification of these alloys. The low value of k determined for Nb in the Fe-base alloys is rather surprising, considering that k Nb values reported in the literature for commercial Ni-base superalloys range from 0.42 to [11,13 15] Such a low value of k implies that Nb segregates more strongly to the liquid in the Fe-base alloys than in the Ni-base alloys. This increased segregation tendency of Nb is expected to have significant effects in terms of secondary phase formation, since both of the secondary phases that form during solidification (NbC and Laves) are Nb rich. The main difference among commercial alloys used in previous studies and those used here is in Fe content, where alloys 9 through 16 exhibit Fe contents higher than most commercial superalloys. To serve as a check on the k Nb value determined here for the Fe-base alloys, an autogenous in a commercial Nb-bearing stainless steel, 20Cb-3, was prepared and analyzed by the same procedure used for the experimental alloys. This alloys has an intermediate Fe content of 40.2 wt pct. The summary of compositions (determined by wet chemical analysis), dendrite core compositions (determined by EPMA), and s is given in Table III. Note that the value of k for Nb in this Fe-base alloy is only Reference to the Ni-Nb phase diagram [10] indicates that the maximum solid solubility of Nb in -Ni is 18.2 wt pct METALLURGICAL A MATERIALS TRANSACTIONS A VOLUME 29A, NOVEMBER

6 comparison to the Ni-base alloys). This effect would induce concomitant decreases in the value of k Nb. Figure 5 plots k Nb against the Fe content of the alloys listed in Table II. The general trend between k Nb and iron content is readily apparent. This effect accounts for the relatively high amounts of eutectic-type constituents observed in the Fe-base alloys and can be understood by examination of the Scheil Eq. [2]. The counterpart to Eq. [2], which describes the relation between fraction liquid and liquid composition, is given by C Cf (k 1) l 0 l [5a] When the liquid composition, C l, reaches a line of twofold saturation on the liquidus surface (the eutectic composition, C e ), C l C e and the remaining liquid, f l, transforms to a eutectic-type constituent(s), f e. Inserting these conditions into Eq. [5a] and solving for f e yields Fig. 5 Variation in Nb distribution coefficient, k nb, with Fe content. f e 1 C e k 1 C 0 [5b] Thus, for a given value of C e and C 0, the value of f e will increase as k decreases. This trend is readily apparent in the quantitative image analysis results displayed in Figure 6 of the previous article, [1] where the total amount of eutectic-type constituent(s) is consistently higher in the Febase alloys with similar solute concentrations. Fig. 6 Schematic illustration of general solidification process for experimental alloys. Nb (at 1286 C). In contrast, -Fe can only dissolve a maximum of 1.5 wt pct Nb at a comparable temperature of 1210 C. [10] Thus, based on these significant differences, it might be expected that iron additions to these alloys would decrease the solubility of Nb in the -(Fe,Ni-Cr) matrix. As the Fe-rich dendrites begin to form, less Nb is taken into the solid and, as a result, more is rejected to the liquid (in C. Pseudoternary Solidification Surfaces As previously discussed, the ternary Ni-Nb-C liquidus projection provides a basis for developing a qualitative understanding of microstructural evolution during solidification. [1] In this section, ternary liquidus surfacelike diagrams, referred to as pseudoternary solidification surfaces, are estimated for the alloys of interest to this study. The distribution coefficients for the matrix elements (Fe, Ni, and Cr) in commercial systems and these experimental alloys are similar and take on a value close to unity, indicating they all behave in a comparable manner and exhibit little tendency for segregation. Thus, the elements in the matrix (Fe, Ni, and Cr) are all grouped together to form one component of the diagram. Based on the similarity between reaction sequences observed in these multicomponent alloys and those expected in the Ni-Nb-C system, Nb and C are chosen as the solute elements in this pseudoternary solidification model. (The relatively minor effect of Si is initially ignored, but qualitative remarks on its effect are provided in the separate article. [2] ) Last, the Ni 3 Nb phase is replaced by the Laves phase. The system can now be represented by a -Nb-C solidification diagram, which exhibits primary phase fields of, NbC, and Laves. The objective of this section is to estimate where the lines of twofold saturation separating the, NbC, and Laves phases are positioned in this -Nb-C solidification diagram. 1. Niobium compositions The general solidification process for alloys in this study that exhibit both the L ( NbC) and L ( Laves) eutectic-type reactions is shown schematically in Figure 6. The process is shown for a representative volume element, which starts at the dendrite core, where f s 0, and extends to the midpoint between two neighboring dendrites, where 2802 VOLUME 29A, NOVEMBER 1998 METALLURGICAL A MATERIALS TRANSACTIONS A

7 Table IV. Liquid Nb Concentrations at the Line of Twofold Saturation Separating and NbC Table V. Comparison of Calculated and Measured Total Volume Fractions of Eutectic-Type Constituents Alloy /NbC f /NbC Composition (Vol Pct) (Wt Pct Nb) /Laves f /Laves Composition (Vol Pct) (Wt Pct Nb) C e (Wt Pct Nb) Alloy C 0 Wt Pct Nb C e f e, Calculated Wt Pct Nb k Nb Vol Pct f e, Measured Vol Pct f s 1. The corresponding solidification path is depicted on the solidification surface in the top right of the figure. Solidification starts with formation of primary dendrites (step 1). The dendrites advance into the liquid and cause an enrichment of Nb and C as the path proceeds from step 1 to step 2. At step 2, the liquid composition reaches the line of twofold saturation separating and NbC. Thus, the Nb and C contents in the liquid at step 2 define one point on the /NbC line of twofold saturation. The exact liquid composition at step 2 depends on the solidification path during primary L solidification, which, in turn, depends on the Nb and C contents and values of k Nb and k C. After reaching the line of twofold saturation between and NbC, solidification continues from step 2 to step 3 as and NbC form simultaneously from the liquid. At step 3, the liquid composition reaches the class II reaction, at which point the L ( NbC) reaction is replaced by the L ( Laves) reaction, and the remaining liquid transforms to the /Laves eutectic-type constituent as solidification goes to completion (step 4). The volume fraction of each eutectic-type constituent is also noted in the figure. The Nb and C concentrations in the liquid at steps 2 and 3 must be known in order to estimate data points for the solidification surface. The liquid composition at step 2 is related to the volume fractions and compositions of the /NbC and /Laves eutectic-type constituents in the as-solidified microstructure (i.e., that shown in step 4) by f /NbC C /NbC f /Laves C /Laves Ce [6] f f /NbC /Laves where C e is the liquid composition at step 2 (i.e., the eutectic composition), f and f are the volume fractions / NbC / Laves of the /NbC and /Laves constituents after solidification is complete, and C and C are the average composi- / NbC / tions of the /NbC and /Laves constituents. In order to maintain consistency of units in Eq. [6], the amounts of /NbC and /Laves should strictly be expressed in weight fractions. However, it has been shown that the densities of the, NbC, and Laves phases are very similar. [15] Thus, the use of volume fractions in Eq. [6] can be used with introduction of little error. The liquid composition at step 3 is simply equivalent to the average composition of the /Laves constituent in the as-solidified microstructure. For Nb, it was possible to obtain all the quantities in Eq. [6] for alloys 6, 8, 14, and 16, and these data are summarized in Table IV. As previously discussed, there was a trace amount of Laves phase in alloy 6, which could not be accurately quantified; thus, f /Laves 0 for this alloy. Consid- ering that the Laves phase content in this alloy is very low, this approximation should not lead to significant error. The accuracy of these values can be checked by comparing the measured amounts of total eutectic-type constituent vs those predicted via the Scheil Eq. [5b]. The values of total eutectic constituent calculated via Eq. [5b] are compared to measured values in Table V. For the Ni-base alloys, k Nb, while, for the Fe-base alloys, k Nb. The agreement between experimentally measured and calculated values is very good, particularly when one considers that the comparison requires input data from four different sources: C 0 (wet chemical analysis), C e (EPMA and quantitative image analysis (QIA)), k Nb (EPMA), and f and f (QIA). / / NbC Laves The Nb composition of the /Laves constituent was obtained on a number of metals and DTA samples (Table 8 of Reference 1). Reference to this data indicates there is an apparent trend between the Fe, Nb, and Si contents of the /Laves constituent. In general, the Nb content tends to decrease as the Fe and Si contents increase. Thus, less Nb is apparently needed in the liquid at step 3 to start forming the /Laves constituent as the Fe and Si contents of the liquid increase. Considering that Fe and Si both promote the Laves phase, this trend is not surprising. However, there is insufficient data for any quantitative correlations. The only distinction made here is to separate the average Nb concentration of the /Laves constituent based on the matrix composition, where the Fe-base alloys exhibit a slightly lower Nb content (average of 20.4 wt pct Nb) than the Ni-base alloys (average of 23.1 wt pct Nb). Alloy Fe-1 was not included in the average Nb value reported for the Fe-base alloys, as it exhibited a high Fe and low Nb value compared to the other alloys. The Nb values listed in Table IV provide several data points for estimating the Nb content in the liquid at the twofold saturation line separating the and NbC phases (step 2), while the average Nb values from Table VIII in Reference 1 provide data for the point on the diagram where the L ( NbC) reaction is replaced by the L ( Laves) reaction (step 3). The corresponding values of C content in the liquid, which are needed to fully define the solidification diagram, are addressed below. 2. Carbon compositions Due to the limitations of the EPMA technique, the C contents of the /NbC and /Laves constituents cannot be accurately measured experimentally. However, if the solidification path (i.e., the relation between the Nb and C concentration in the liquid as solidification progresses) of the alloys during primary L solidification is known, then the corresponding C content in the liquid can be estimated. Mehrabian and Flemings [16] have shown that, when the diffusion of two solutes in a ternary system is negligible, the solidification path of the alloy is given by (using Nb and C as the solute elements ) METALLURGICAL A MATERIALS TRANSACTIONS A VOLUME 29A, NOVEMBER

8 while the f 1 -C 1 relation for Nb is given through the Scheil equation: (a) (b) Fig. 7 Primary solidification paths of (a) alloys 7 and 8 and (b) 15and 16. C l,c l,nb 0,Nb C 0,C knb 1 C C k C 1 [7] Equation [7] describes the relation between C 1,Nb and C 1,C during solidification of primary austenite. The same assumptions used in derivation of the Scheil equation also apply to Eq. [7]. As previously discussed, Nb diffusion is negligible under the current solidification conditions, while carbon diffuses rapidly enough to approach equilibrium. Equation [7] can be modified to reflect this behavior. Under this condition, the equilibrium lever law can be used to estimate the relation between f 1 and C 1 for carbon: C0,C kc C l,c fl (1 k C) Cl,C [8a] 1 C l,nb k Nb 1 l C 0,Nb f [8b] Proceeding in the same manner used by Mehrabian and Flemings to derive Eq. [7], Eqs. [8a] and [8b] are equated (since f 1 can only have one value) and solved for C 1Nb to obtain a new solidification path relation: C kc knb 1 0,C C l,c Cl,Nb C 0,Nb [9] (1 k ) C Equation [9] describes the solidification path of the liquid during primary solidification of assuming that Nb diffusion in the solid is negligible, while C diffuses fast enough to maintain equilibrium. Based on the discussion above, where diffusivity effects of Nb and C were considered, this relation should provide a reasonable description of the primary solidification paths in the alloys of interest to this study. Equation [9] is physically consistent at the limits of solidification. At the beginning of solidification, the liquid composition should equal the composition for both solutes. Insertion of C 1,C C 0,C into Eq. [9] yields C 1,Nb C 0,Nb. Under equilibrium conditions for carbon, the liquid will reach a maximum concentration of C 0,C /k C when solidification is complete, while the Nb concentration in the liquid should tend toward infinity, as predicted by the Scheil equation. Insertion of C 1 C 0,C /k C into Eq. [9] yields C 1,Nb. As an example, Figure 7 plots the primary solidification paths of several alloys according to Eq. [9]. The solidification path is terminated at the points where the L ( NbC) reaction initiates for alloys 8 and 16 and where the L ( Laves) reaction starts for alloys 7 and 15. Similar calculations made according to the original Mehrabian Flemings (M F) model, Eq. [7], are also shown. As expected, the C content in the liquid is higher when C is assumed to exhibit negligible diffusion in the solid. Although the difference between the two types of behavior is not large, particularly at low C contents, the modified form of the M F model should be better suited for describing solute partitioning of C. Equation [9] is useful here, as it permits calculation of the carbon content in the liquid (C 1,C ) when the corresponding Nb content (C 1,Nb ) is known along with the alloy content (C 0,Nb and C 0,C ) and distribution coefficients (k Nb and k C ). The C content in the liquid at which the L ( NbC) reaction starts is estimated by using Eq. [9] with the Nb compositions summarized in Table IV for alloys 6, 8, 14, and 16. The C content in the liquid at which point the L ( Laves) transformation begins (the class II reaction point) is estimated by using Eq. [9] on alloys 7, 13, and 15 with the average Nb content of the /Laves constituent previously described (23.1 wt pct Nb for the Ni-base alloys and 20.4 wt pct Nb for the Febase alloys). These three alloys exhibit trace amounts of the /NbC constituent and will thus provide a slight overestimation of the C content in the liquid at which point the L ( Laves) reaction is initiated. In other words, the primary solidification paths of these alloys intersect the line of twofold saturation between and NbC just slightly above the class II reaction point. However, the amount of C l,c 2804 VOLUME 29A, NOVEMBER 1998 METALLURGICAL A MATERIALS TRANSACTIONS A

9 Table VI. Summary of Data Used in Equation [9] to Determine Nb and C Contents, Which Define the Pseudoternary Solidification Surface Alloy C 0,Nb (Wt Pct) C 0,C (Wt Pct) k Nb k C Reaction L ( NbC) L ( Laves) L ( NbC) L ( Laves) L ( NbC) L ( Laves) L ( NbC) C l,nb (Wt Pct) C l,c (Wt Pct) at a temperature below the L ( NbC) reaction. The reasons for this will be discussed in more detail in the companion article. [2] Since the /NbC and /Laves constituents are not intermixed in the as-solidified microstructures, the direction of the solidification path along the /Laves boundary is directed toward the -Nb binary side of the diagram. In other words, solidification is not terminated by the ternary-type L ( NbC Laves) reaction, where all three phases would be intermixed in the as-solidified microstructure. Instead, solidification is terminated by the binary-type L ( Laves) reaction, in which the /Nbc and /Laves constituents are spatially separated. [19,20] (The position of the NbC/Laves boundary was not determined, as it is not needed here. The lines for this boundary are drawn only for clarity.) Fig. 8 Plot of pseudoternary -Nb-C solidification surfaces. /NbC in these alloys is very small and the amount of C in the liquid during the entire primary solidification stage is always very low. Thus, this estimation should not lead to significant error. Table VI summarizes the Nb and C contents used to define the pseudoternary solidification surfaces, and the data are plotted in Figure 8. As there is obviously not enough data to reveal any potential curvature in the boundaries, they are approximated as straight lines. Considering that the region of interest on the solidification surfaces exists over a narrow C concentration, this should provide a reasonable estimate. The positions of these boundaries were also compared with those calculated using the Thermo-Calc software program, and reasonable agreement was found. [17] In view of this, it is worth noting that significant progress has been made toward computerized calculations of phase diagrams using the CALPHAD phase diagram approach, which can avoid the need for adopting a pseudoternary approach to these multicomponent alloys. [18] Work is now in progress to couple this information to microsegregation calculations for understanding the solidification behavior of these experimental alloys. The direction of decreasing temperature along the L ( NbC) reaction is determined from the DTA data, [1] where the low C alloys exhibit a lower L ( NbC) reaction temperature than the high C alloys and the L ( Laves) reaction always occurs IV. CONCLUSIONS The solidification behavior of experimental superalloys with systematic variations in Fe, Nb, Si, and C was investigated by quenching experiments and microstructural characterization techniques. The following conclusions can be drawn from this work. 1. An interactive effect between the segregation potential of Nb and Fe content has been observed, where the value of k Nb decreases from 0.54 to as the Fe content is increased from 2 wt pct to 47 wt pct. This behavior is the major factor contributing to the formation of relatively high amounts of eutectic-type constituents in the Fe-base alloys. 2. An analytical solidification path expression, Eq. [9], has been proposed to describe the change in liquid composition during primary solidification in a ternary system in which one solute exhibits negligible diffusion while the other solute diffuses rapidly enough in the solid to maintain equilibrium. 3. Pseudoternary -Nb-C solidification surfaces have been proposed, which identify the locus of liquid compositions required to initiate the L ( NbC) and L ( Laves) eutectic-type reactions. The Nb compositions of the diagram were checked by comparison of calculated volume fractions of eutectic-type constituents (via the Scheil equation) and those measured experimentally, and good agreement was found. The C contents needed to fully define the diagram were calculated, as they could not be experimentally determined with the techniques used in this work. The solidification parameters, pseudoternary -Nb-C solid- METALLURGICAL A MATERIALS TRANSACTIONS A VOLUME 29A, NOVEMBER

10 ification surfaces, and established solute redistribution behavior of Nb and C will be combined in the companion article to model microstructural evolution in these experimental superalloys. [2] ACKNOWLEDGEMENTS One author (J) gratefully acknowledges financial support for this research from the American Welding Society Fellowship Award. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract No. DE-AC04-94AL C e C 1 C 0 C s C s * D s f e f 1 f s k L T T 1 T m t f LIST OF SYMBOLS eutectic composition liquid composition composition solid composition solid composition at solid/liquid interface diffusivity of solute in solid fraction of eutectic fraction of liquid fraction of solid equilibrium distribution coefficient one-half dendrite spacing solidification temperature liquidus temperature melting temperature of pure solvent local solidification time REFERENCES 1. J.N. DuPont, C.V. Robino, A.R. Marder, M.R. Notis, and J.R. Michael: Metall. Mater. Trans. A, 1998, vol. 29A, pp J.N. DuPont, C.V. Robino, and A.R. Marder: Acta Mater., 1998, vol. 46, pp H.D. Brody and M.C. Flemings: Trans. AIME, 1966, vol. 236, pp S. Katayama and A. Matsunawa: Proc. ICALEO, 1984, pp S. Kurokawa, J.E. Ruzzante, A.M. Hey, and F. Dyment: Met. Sci., 1983, vol. 17, pp S.K. Bose and H.J. Grabke: Z. Metallkd., 1978, vol. 69 (1), pp T.W. Clyne and W. Kurz: Metall. Trans. A, 1981, vol. 12A, pp I. Ohnaka: Trans. Iron Steel Inst., 1986, vol. 26 (12), pp C.Y. Wang and C. Beckermann: Metall. Trans. A, 1993, vol. 24A, pp Metals Handbook, 8th ed., ASM, Metals Park, OH, 1973, vol M.J. Cieslak, T.J. Headley, T. Kollie, and A.D. Roming, Jr.: Metall. Trans. A, 1988, vol. 19A, pp Constitution of Binary Alloys, 2nd ed., M. Hansen and K. Anderko, eds., McGraw-Hill Book Co., New York, NY, pp J.N. DuPont: Metall. Mater. Trans. A, 1996, vol. 27A, pp C.V. Robino, J.R. Michael, and M.J. Cieslak: Sci. Technol. Welding Joining, 1997, vol. 2, pp G.A. Knorovsky, M.J. Cieslak, T.J. Headley, A.D. Roming, Jr., and W.F. Hammetter: Metall. Trans. A, 1989, vol. 20A, pp R. Mehrabian and M.C. Flemings: Metall. Trans. A, 1970, vol. 1, pp J.N. DuPont: Ph.D. Dissertation, Lehigh University, Bethlehem, PA, B. Sundman, B. Jansson, and J.O. Andersson: CALPHAD, 1985, vol. 9, pp H.H. Stadelmaier and M.L. Fiedler: Z. Metallkd., 1975, vol. 66 (4), pp B. Radhakrishnan and R.G. Thompson: Metall. Trans. A, 1989, vol. 20A, pp VOLUME 29A, NOVEMBER 1998 METALLURGICAL A MATERIALS TRANSACTIONS A