Isothermal Section of Fe-Cr-Mo at 1200 °C
SEM backscattered electron (BSE) images of the Fe-Cr-Mo tri-junction in Sample #1 (1200 °C—500 h) are shown in Fig. 2. Literature results indicate that five phases are present in the 1200 °C isothermal section of Fe-Cr-Mo: the bcc phase (α), fcc phase (γ), sigma phase (σ), mu phase (μ), and R phase, respectively. The γ-Fe phase is of very high (>95 at.%) Fe concentration and it is far from the center of SEM images, and thus not seen in Fig. 2. Since the α/γ equilibrium is already well established, no effort was made in the present study to re-determine it.
Careful examination of the Fe-Cr-Mo tri-junction using both optical and electron microscopy allowed preliminary identification of all the three intermetallic phases (σ, μ and R) that are sandwiched between the Mo-rich part of the α phase (light area at the bottom) and the Cr and Fe rich part of the α phase (dark area at the top), Fig. 2(b). Due to similar chemical compositions, the contrast between the intermetallic phases is very subtle in Fig. 2(b). Thin layers of the μ phase and the R phases can be seen in Fig. 2(c) along the Fe/Mo interface. EPMA line scans were performed and most of them are marked in Fig. 2(b) with the scan numbers. Equilibrium tie-line information was obtained by plotting the EPMA scan profiles in both composition-distance plots as well as plotting scan-line compositions onto the compositional triangle. Detailed procedure of such analysis can be found in Ref 15.
The 1200 °C isothermal section of the Fe-Cr-Mo ternary system obtained from EPMA on Sample #1 is shown in Fig. 3. It contains a large number of tie-lines and single-phase data points obtained by EPMA, showing phase equilibria between/among the α, μ, R, and σ phases. The γ loop in Fe-rich corner of the isothermal sections was not experimentally measured (even though the information was available in the sample), and thus was only dashed in the phase diagram based on the information from the binaries. All the EPMA compositional data are presented as circles and the tie-lines are represented by dotted lines. The phase boundaries of single phase regions are extrapolated based on the consistency of tie-lines and available single-phase composition points for the intermetallics. Ternary phase regions are denoted as triangles. Part of the bcc α phase boundary is shown as a dashed line since the data trends seem to indicate the existence of a miscibility gap in Mo and Cr rich α phase, potentially creating an α-σ-α three-phase equilibrium which is tentative and thus represented as a dashed triangle. The information from the current study represents a well-defined isothermal section for the Fe-Cr-Mo system.
At 1200 °C, the μ and R phase regions in the ternary Fe-Cr-Mo isothermal section are extensions from their binary phases from Fe-Mo. The σ phase that is stable above 1236 °C in the binary Fe-Mo phase diagram and below ~840 °C in Fe-Cr is stabilized to 1200 °C with the addition of Cr. It is clear that Cr stabilizes all the binary intermetallic phases of this ternary system. The single phase region of the σ phase is shaped like a new moon with the tips pointing toward the binary Fe-Mo system. The Mo composition range of the R phase is very small for the binary Fe-Mo system, but it expands significantly in the ternary system with the addition of Cr.
Figure 4 compares the current results with prior experimental data as well as the computed 1200 °C isothermal section using Thermo-Calc™ and the TCFE5 thermodynamic database. It is clear that the new results agree reasonably well with those reported by Jin and Andersson and Lange except that the σ phase region is expanded to lower Cr concentrations in equilibrium with the R and μ phases. The results from this study and those of Jin and Andersson and Lange together clearly show that the existing thermodynamic assessment significantly underestimates the solubility of Fe and Mo in α (bcc) Cr and that the Cr-lean arm of the σ phase region is significantly off. In addition, the computed shapes of the single-phase regions of both the µ phase and the R phase from Thermo-Calc™ are quite different from those reported from the current experimental measurements, indicating a need for a re-assessment of the relevant thermodynamic parameters of these phases.
Isothermal Section of Fe-Cr-Mo at 900 °C
Figure 5 is an SEM BSE image montage of Sample #2 (1200 °C for 500 h and 900 °C for 500 h), showing that precipitates of various morphologies and phases were formed during annealing at 900 °C. Note that the 1200 °C for 500 h single-anneal diffusion multiple (Sample #1, Fig. 2) showed no precipitates, indicating that the water quench after the 1200 °C annealing was able to retain all the single phase compositions to ambient temperature. All the area to the top and right of Mo beyond the thin hockey-stick shaped intermetallic phases was originally single-phase α before the 900 °C annealing. The 900 °C solubility limit of α, which separates the precipitation regions from the precipitate-free region, is visible in Fig. 5 as the dashed line. Single-point EPMA measurements along this line provided the solubility information.
The blocky precipitates in the top region (Cr-rich) of Fig. 5 are the σ phase. Higher magnification images of areas marked as “a” and “b” in Fig. 5 are shown in Fig. 6(a) and (b). Figure 6(a) shows the blocky σ phase in the α matrix. Figure 6(b) shows the dark gray σ phase, the light gray χ phase in the dark α matrix; capturing the α-σ-χ three-phase equilibrium. The χ phase precipitates occupied a large near-top area in Fig. 5 and exhibited a predominately equiaxed morphology with widely varied precipitate sizes that will be the subject of a separate discussion in an upcoming article. Figure 6(c) is a high magnification image of area “c” in Fig. 5, showing the bright Mo-rich α phase on the left and the dark Fe-rich α phase matrix on the right. The large equiaxed precipitates are the χ phase and the small precipitates are the µ phase. It is emphasized that the thin layers of both µ and R formed at the 1200 °C-annealing (in comparison with Fig. 2(c)) are still present after being annealed at 900 °C for 500 h, Fig. 6(c). The µ is stable at 900 °C based on the Fe-Mo binary phase diagram and the existing information of the Fe-Cr-Mo ternary phase diagram, thus it should stay; but the R phase is unstable at 900 °C and thus it should decompose to reach equilibrium. The difficulty in decomposing a high-temperature formed intermetallic compound at lower temperatures is the culprit that led to the residual R phase in Sample #2. This important point has been discussed in detail separately and has important implications in interpreting equilibrium even for individually made alloys that usually go through a high-temperature homogenization annealing and a low-temperature equilibration annealing.
The bottom of Fig. 5, far away from the Cr piece (on the top-left corner), is essentially the Fe-Mo diffusion couple region without much Cr presence. The area “d”, with its high magnification image showing in Fig. 6(d), has an average composition of ~87.5 at.% Fe-12.5 at.% Mo. According to the binary Fe-Mo phase diagram, this composition should decompose to α and λ two phases. The λ (Laves) phase is a low temperature (stable up to 927 °C) intermetallic phase in the Fe-Mo binary system. As a matter of fact, all the compositions between area “d” to the solubility dashed line on the right at the bottom of Fig. 5 should decompose into α and λ two phases to reach equilibrium.
A high magnification image of the µ phase precipitates in area “e” of Fig. 5 is shown in Fig. 6(e). The dendritic nature of the precipitates is very apparent. It seems very likely that the µ phase appeared first in this region of the α phase matrix as a metastable precipitate phase, which is been consumed by the formation of the χ phase above (Cr-richer region) and the λ phase below (Cr-leaner region). If the diffusion multiple were annealed longer at 900 °C, the entire region of the µ phase precipitates were likely be consumed by the formation of equilibrium phases χ and λ.
The needle/thin-plate-like R-phase precipitates in area “f” of Fig. 5 are shown in Fig. 6(f), exhibiting a beautiful Widmanstätten pattern. The R-phase precipitates also appear as a metastable phase during the decomposition of the α phase at 900 °C and it appears that the R-phase needles are being consumed by the formation of other equilibrium phases, χ and λ.
EPMA across the interfaces between the precipitates and the adjacent matrix phases and single point EPMA analysis along the solubility boundaries such as the red dashed line in Fig. 5 afforded the data shown in Fig. 7, which is a partial 900 °C isothermal section of the Fe-Cr-Mo ternary system. Only large precipitates were used in the EPMA scans for tie-line evaluation. This is to avoid the compositional supersaturation associated with the Gibbs-Thomson effect on small particles and to allow reliable evaluation of the composition of the precipitate phase (the particle size needs to be greater than the interaction volume of the x-ray production under the SEM electron beam). Details of such EPMA evaluation of intermediate phase diagrams are explained before.
The results of EPMA single-point measurements of the Mo solubility in the Fe-rich α phase in the Fe-Cr-Mo system (e.g. along the dashed line in Fig. 5) agree well with the solubility line determined from tie-line analysis from EPMA scans across the precipitate/matrix interfaces, as shown in Fig. 7. The Mo-rich area of the isothermal section was left blank because the precipitates in this area of the compositions are too fine to allow reliable EPMA composition evaluation of the precipitates. Careful transmission electron microscopy (TEM) analysis or atom probe analysis will be necessary to obtain reliable compositional data to construct this part of the phase diagram. For the time being, the solubility of Mo in the Fe-rich α phase at 900 °C is well defined by the current experimental measurements. The single-phase composition region of the χ phase is also well defined. The phase equilibria around the χ phase should be very reliable since this phase precipitated out from the supersaturated solid solution without prior existence at 1200 °C and the precipitates are big enough to perform reliable EPMA analysis. The σ phase region with less than ~10 at.% Mo is defined/determined, but that at >10 at.% Mo is not, as shown by the dashed line surrounding the σ phase region. Our results clearly show that there is appreciable Cr solubility in the λ phase, not zero as previously assumed during experimental phase diagram assessments[2-4] as well as during thermodynamic modeling.[7,17] The finite Cr solubility leads to a α-λ-χ three-phase equilibrium, which is consistent with the observation of Liu et al. at 850 °C.
Figure 8 compares the current experimental data with results from thermodynamic calculations using Thermo-Calc™ and the TCFE5 database. The thermodynamic calculation does a good job in predicting the solubility of Mo in Fe-rich bcc (α) phase. The experimentally measured χ phase region is larger than the thermodynamic prediction, but the thermodynamic calculation is doing a reasonably good job in predicting the α/χ phase equilibrium. The thermodynamic calculations underestimated the stability of the λ (Laves) phase; and the thermodynamic parameters need to be adjusted to include the Cr solubility in the λ phase such that the α-λ-χ three-phase equilibrium comes to existence in thermodynamic calculations of Fe-Cr-Mo at 900 °C and lower temperatures.
There are no experimental data available for Fe-Cr-Mo at exactly 900 °C for comparison. The closest available data from the literature are at 950 °C which were reported by Andersson and Lange. Considering the temperature difference, the results are reasonably consistent with the current data, Fig. 9.
Isothermal Section of Fe-Cr-Mo at 800 °C
Sample #3 was first annealed at 1200 °C for 500 h and then at 800 °C for 1000 h. A montage of SEM BSE images of the Fe-Cr-Mo ternary area (Fig. 10) shows the morphology and relative locations of the various precipitates. The overall distribution of the different precipitate regions is very similar to that of Sample #2 (Fig. 5), but the precipitates are mostly at finer scales. The bottom location in Fig. 10 is far away from the Cr piece (on the top-left corner) and is essentially the Fe-Mo diffusion couple region without much Cr presence. The area “a”, with its high magnification image showing in Fig. 11(a), has an average composition of ~87.5 at.% Fe-12.5 at.% Mo. According to the binary Fe-Mo phase diagram, this composition should decompose to α and λ two phases. Figure 11(a) shows the bright blocky λ phase and finer µ phase in the dark α matrix. The λ phase grew at the expense of the metastable µ phase which precipitated out first. The equilibrium phases are λ and α, consistent with the binary Fe-Mo phase diagram.
Figure 11(b), taken from area “b” in Fig. 10, shows needle/thin-plate-like R-phase precipitates. The R phase is unstable at 800 °C and it precipitated as a metastable phase before the equilibrium phases. This area “b” in Fig. 10 is gradually being consumed by the equilibrium χ phase from the top and the equilibrium λ phase from the bottom. It is anticipated that at longer annealing time at 800 °C, the R phase would be completely replaced by the equilibrium phases. The wide compositions created by the high-temperature (1200 °C in this case) annealing of a DADM allow more systematic studies of the phase precipitations and better appreciation of the formation of metastable versus equilibrium phases. To better appreciate this point, one can think of making an alloy of the average composition of area “b”, performing an homogenization treatment at 1200 °C, and then performing an 1000-h heat treatment at 800 °C to try to reach equilibrium. These would be the steps one takes to make samples to determine phase diagrams using the so-called equilibrated alloy method. One would observe the same microstructure as that of Fig. 11(b): needle/thin-plate-like R-phase precipitates in the α phase matrix. The conclusion would be that the alloy consisted of two “equilibrium” phases of R and α because one would think 1000-h heat treatment should have been long enough to reach equilibrium. This conclusion would have been erroneous based on the analysis of DADM Sample #3.
Figure 11(c), taken from area “c” in Fig. 10, shows χ phase precipitates on the right. On the left-hand side, the R-phase layer formed during the 1200 °C annealing has not been decomposed even though R phase is unstable at 800 °C; again showing the difficulty of decomposing some intermetallics formed at a high-temperature. The DADM approach allows such information to be visible directly, thus helping interpret the equilibrium more systematically.
EPMA was performed to extract tie-line information from large enough precipitates and their adjacent matrix phases. In addition, solubility boundaries are obtained using EPMA point analysis as described before. All the tie-lines and solubility data are summarized in Fig. 12, showing only data that are available for the Fe-rich corner of the isothermal section. Precipitates in other composition regions of the phase diagram are too small to allow reliable composition evaluation using EPMA. TEM and atom probe methods need to be applied to extract the phase equilibrium information from small precipitates. Similar to the 900 °C results, there is significant solubility of Cr in the λ phase, creating an α-λ-χ three-phase equilibrium (Fig. 13), which is missing from the thermodynamic calculations, Fig. 14. It is necessary to incorporate Cr into the sublattice model of the λ phase in order to correctly compute the α-λ-χ three-phase equilibrium in the future. Thermo-Calc™ with the associated TCFE5 database does a decent job in predicting: (1) the solubility of Mo in the Fe-based α phase, (2) most of the α/χ equilibrium, and (3) most of the α/σ equilibrium. The experimentally determined phase diagram, however, shows that the χ composition extends as low as ~10 at.% Cr in contrast to the computed result of ~15 at.% Cr and the σ phase composition is as low at 30 at.% Cr in contrast to the computed result of ~35 at.% Cr.
The 700 °C Annealed Sample
Figures 14 and 15 show the morphologies and precipitates in Sample #4 that was annealed at 1200 °C for 500 h and then 700 °C for 1000 h. Except for the σ phase whose precipitate sizes are large enough for EPMA compositional analysis, all other precipitates are too small to be reliably analyzed using EPMA. This sample vividly illustrates the difficulty in experimentally determining the phase diagrams at intermediate temperatures, especially at the lower-intermediate temperatures where we are at the mercy of kinetics. TEM characterization or atom probe analysis will be required in the future to obtain reliable local equilibrium tie-line information to establish the phase diagram as demonstrated by Romig and Goldstein for the TEM case. The time and effort will be substantial to cut TEM foil samples or atom probe needles from the DADM in order to perform high-resolution EDS compositional analysis or atom probe tomography. Fortunately, localized extraction of TEM foils and atom probe needles using focused ion beam (FIB) is now a routine practice. Moreover, each DADM sample such as Sample #4 discussed here offers all the necessary composition variation to allow the establishment of a ternary phase diagram. It would take enormous effort to make many individual alloys, perform thousands of hours of heat treatment on each of them, and then extract TEM or atom probe samples for the compositional analysis of the phases. This is the reason that there is a worldwide shortage of intermediate and low temperature phase diagrams. The DADM approach can help accelerate the determination of such phase diagrams, but would require TEM or atom probe analysis for the lower-intermediate temperature range.
The DADMs were able to generate an amazing diversity of microstructures and precipitates in different regions/compositions of the diffusion multiples, which provide systematic information about the precipitation and phase equilibria. At the same time, the small precipitate sizes poise significant challenges to the extraction of phase equilibrium information for the phase diagram establishment. The small precipitate sizes demand careful TEM or atom probe characterization for phase identification as well as local equilibrium tie-line establishment.
The current study was able to establish a reliable 1200 °C isothermal section for the Fe-Cr-Mo ternary system. The sluggish kinetics of Mo makes the precipitation much harder. For this reason, the Mo-rich part of the isothermal sections of Fe-Cr-Mo at 900 and 800 °C were not determined at the present time without TEM characterization. This study have obtained reliable and systematic phase equilibrium data for the Fe-rich corner of the phase diagram for the Fe-Cr-Mo ternary system at both 900 and 800 °C. It is believed that the following data are reliable: (1) the Mo solubility in the Fe-rich and some Cr-rich bcc (α) phase; (2) the σ-α equilibrium at compositions with less than 10 at.% Mo, and (3) the χ-α equilibrium. Much more work needs to be performed to extract vast amount of information that exists in the DADMs.
Figure 16 compares the Mo solubility in the α phase (i.e., the α phase boundary) at different temperatures as a function of Cr concentration obtained from both local-equilibrium tie-line analysis and point probe EPMA measurements tracing the boundary between the precipitate regions and the precipitate-free region (such as the dashed line in Fig. 5). The excellent agreement validates the point-probe method in evaluating the phase boundaries.