Microstructural Impacts on the Oxidation of Multi-Principal Element Alloys

doi:10.21203/rs.3.rs-3150363/v1

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Microstructural Impacts on the Oxidation of Multi-Principal Element Alloys

https://doi.org/10.21203/rs.3.rs-3150363/v1

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published 16 Feb, 2024

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The impacts of thermal treatment on the precipitate morphology and oxidation behavior of a dual phase (FCC + L1₂) MPEA, Ni₄₅Co₁₇Cr₁₄Fe₁₂Al₇Ti₅, has been studied at 1000°C via nonisothermal-isothermal and cyclic testing. Thermogravimetric analysis and subsequent characterization revealed that smaller precipitates had an increased capacity to form protective sub-surface oxide layers which mitigated total mass gain. The smaller precipitate containing samples exhibited a decrease in thickness of primary Cr₂O₃ scale and parabolic growth rate. Mechanistically this behavior is believed to stem from the increased growth rate of initial Al₂O₃ nuclei and decreased inter-precipitate spacing which results in faster lateral diffusion and agglomeration.

High entropy alloys

Oxidation

Microstructure

Modelling

High entropy alloys (HEAs) and multi-principal element alloys (MPEAs), also called compositionally complex alloys (CCAs), are being intensely investigated in the materials community due to their often-unique microstructures and properties [1–3]. Unlike conventional engineering alloys, which are generally based on one or two principal elements, HEAs and MPEAs usually consist of five or more principal metallic elements without a clear base element [2]. Due to their complex chemical makeup, these alloys inherently exhibit high ideal configurational entropies of mixing (in excess of $1.5R$ where$R$ is the ideal gas constant) which is reported to favor the formation of solid solution phases with high symmetry face-centered cubic, body-centered cubic, or hexagonal close packed crystal structures as opposed to ordered intermetallic or topologically close packed phases [4, 5]. Though early research efforts focused on the development of single phase solid solution HEAs, much recent work has emphasized the formation of multiphase alloys, usually designated MPEAs or CCAs, where some or all of the constituent phases might themselves qualify as HEAs and is the subject of this research [1, 6].

Though the research of MPEAs for potential use in high temperature environments has led to investigations of a wide range of bulk compositions, little emphasis has been placed on understanding the impacts of microstructural variations on material properties other than strength. These structure-property relationships are well documented in commercial Ni-based superalloys, however, their relatively high concentrations of refractory elements such as tungsten, ruthenium, and rhenium drastically increase their density and cost [7–10]. The unique properties of MPEAs, particularly those based exclusively on transition metals, make them potentially attractive candidates for replacing certain superalloy components. As the field matures, more investigations are warranted on how traditional thermal and mechanical processing steps, which must take place from a manufacturing standpoint, will affect the microstructures and thus performance of the alloys from mechanical properties and oxidation resistance perspectives [11]. With regards to high temperature oxidation, most studies have either focused solely on the behavior of arc-melted microstructures that are known to have different bulk oxidation kinetics than homogenized and thermally processed materials [12] or have exclusively varied the bulk composition to achieve some microstructural changes [13–17]. In recent literature, there has been some focus on microstructural features in the more developed transition metal MPEAs [13, 18], including those only accessible through additive manufacturing pathways that may prove beneficial in the future [19].

Traditional alloying strategies to impart oxidation resistance have relied upon additions of elements such as aluminum, chromium, or silicon which preferentially oxidize to form slow growing, continuous, and adherent Al₂O₃, Cr₂O₃, or SiO₂ surface scales [20–22]. For high temperature applications above 1000°C, Al₂O₃ scales have generally been prioritized due to their higher thermodynamic stability. However, in the never-ending quest for higher temperature capabilities, it is clear the total concentration of aluminum needs to be minimized to preserve the elevated melting point of the alloy [9]. This poses a fundamental problem for oxidation mitigation as many Al containing alloys rely heavily on the formation of tenacious external Al₂O₃ scales to prevent internal oxide growth and slow the degradation of mechanical properties [8–10]. While dilute alloys generally adhere to the Wagner criterion for exclusive outward Al₂O₃ growth, two-phase MPEAs tend to follow more complicated two-phase descriptions [23–25].

Earlier work in model superalloys showed that ternary element additions could improve oxidation performance by locally gettering oxygen and that secondary phases could provide an effective reservoir of solute to allow for exclusive outward growth, even when the bulk composition was less than Wagner expressions had predicted [26–31]. In these alloys, under the proper circumstances, the precipitates act as solute reservoirs and preferentially oxidize before the parent matrix forming an external oxide scale. The continued growth of the scale, which is fed by internal precipitates, is dependent on the balance of solute flux from the precipitates to the metal-oxide interface. Over time, these precipitates are locally consumed, leaving behind a wake of precipitate free material below the components surface, ultimately leading to the exhaustion of solute supply and failure to maintain the growing oxide.

A natural progression of this idea is consideration of the role of secondary phase morphology (i.e., size and shape, volume fraction, distribution, etc.) on the successful use of the reservoir effect. Research conducted by Gil et al. on TiAl-based intermetallics indicated relationships between phase morphology and oxidation resistance [32, 33]. A preliminary model to characterize a secondary phase’s ability to maintain an oxide scale was devised in terms of precipitate chemistry and volume fraction [29]. While this relationship is more of a modification to the original Wagner criteria, it has proven to be a reasonable predictor of oxide products for concentrated alloys containing multiple phases [30, 34]. To delve further into the kinetic basis for the reservoir effect, the diffusion columns above the secondary phases were considered [35]. It was determined that the amount of bulk solute required to exclusively form some oxide was impacted by the volume fraction and the shape of the secondary precipitates, which dictates the interfacial area through which outward solute flux occurs. With the advent of advanced characterization techniques such as atom probe tomography (APT), the chemical and morphological aspects of nanoscale phases are even more determinable which may lead to better predictive oxide models [36, 37].

This study explored the influences of precipitate size and volume fraction on the oxidation behavior the single MPEA, Ni₄₅Co₁₇Cr₁₄Fe₁₂Al₇Ti₅. This alloy, which belongs to a newer group of high entropy superalloys (HESAs), has a two-phase FCC + L1₂ microstructure like traditional nickel-based superalloys but employs higher concentrations of iron and cobalt to promote the formation of constituent phases that could also satisfy the empirical criteria defining HEAs (i.e., phase is a solid solution containing five or more components, each constituting greater than 10 at%, with a phase configurational entropy greater than 1.5R) [1, 4, 5, 38–42]. Though the high entropy alloy community has tended to favor single phase materials, multi-phase high entropy alloys are a necessity that can provide chemical breadth and compatibility with commercially viable processes.

Material Synthesis

The material used for analysis was first fabricated as an approximately 60 g rod via arc-melting from pure elements (99.9 at% purity or better) on a water-cooled copper hearth in an inert ultra-high purity (UHP) argon atmosphere. Bulk chemistry was analyzed via energy dispersive x-ray spectroscopy (EDS) and APT and is summarized in Table 1. The EDS measured composition was determined using multiple point spectra from a polished specimen within each sample group. Group-to-group averages were well within the accepted tolerance for non-quantitative EDS, with an average range (minimum to maximum spread) among all measurements and species of 1.4%. The standard deviation among those APT measurements are heavily influenced by the non-representative volume fractions observed within each tip.

Table 1

Expected and measured sample chemistry
Atomic Percent	Ni		Co		Cr		Fe		Al		Ti
Expected	45		17		14		12		7		5
Measured (EDS)	44.3 ± 0.4		17.5 ± 0.2		14.2 ± 0.2		12.3 ± 0.2		6.5 ± 0.2		5.2 ± 0.1
Measured (APT)	45.2 ± 7.4	16.9 ± 3.1		12.3 ± 5.2		10.4 ± 3.7		8.4 ± 1.6		6.7 ± 3.1

Alloy Design/Thermodynamic Modeling

The alloy used in this study was designed via thermodynamic modelling predictions using the CALPHAD method [43]. The calculations were conducted using Thermo-Calc™ and a combination of the high entropy alloy (TCHEA6) and nickel superalloy (TCNI12) thermodynamic databases [44–46]. Thermo-Calc’s TC-PRISMA precipitation module was used to model precipitation kinetics [47]. The interfacial energy used to simulate precipitation of the intermetallic phase, ${\sigma }^{\gamma /\gamma {\prime }},$ was defined as $17 \text{m}\text{J}/{\text{m}}^{2}$, determined through iterative comparison with experimental results and is in line with traditional superalloys for the given temperature range [48]. The resulting phase equilibria and precipitation kinetics are shown in Figs. 1 and 2, respectively.

Thermal Processing

Based upon the simulated phase equilibria and precipitation kinetics, a solution heat treatment of 1200°C for 35 hours in UHP argon followed by water quenching was selected to fully dissolve

any tertiary phases formed during solidification. Phase dissolution was validated via optical microscopy and x-ray diffraction analysis. The solution heat-treated rod was then sectioned into six bulk pieces which were annealed in UHP argon at 800°C, 900°C, and 1000°C respectively for two distinct times to generate microstructures containing identical volume fractions of precipitates but with different precipitate sizes. A complete listing of the annealing temperatures and times is provided in Table 2. Samples are identified using a sequence of numbers representing the annealing temperature followed by a letter representing either a long or short anneal.

Table 2

Thermal processing schedule used to create all six sample groups
Sample ID	Processing Temp. / Time (°C / h)	Expected Precipitate Radius (nm)	Expected Fraction (vol. %)
1000L	1000 / 124	352	23
1000S	1000 / 0.17	25	23
900L	900 / 124	142	36
900S	900 / 2	36	36
800L	800 / 432	75	43
800S	800 / 40	34	43

Thermogravimetric Analysis

All oxidation experiments were performed at 1000°C in a Setaram Setsys Evolution thermogravimetric analyzer (TGA) in an atmosphere consisting of 79% UHP Ar and 21% O₂ to approximate the oxygen partial pressure found in air without nitrogen. Rectangular test specimens with approximate dimensions of 7 mm × 4 mm × 2 mm were ground through 800-grit SiC paper and ultrasonically cleaned in isopropyl alcohol prior to heating. Combined nonisothermal-isothermal TGA tests and individual cyclic TGA tests were conducted using the testing parameters listed in Table 3. In the combined nonisothermal-isothermal TGA tests, specimens were exposed to flowing Ar + O₂ during heating from room temperature up to 1000°C capture the early-stage oxidation behaviors for known precipitate morphologies and to avoid any microstructural changes such as precipitate coarsening that could occur during heating. The samples were then held at 1000°C and oxidized isothermally for 100 h. Multiple samples from each heat treatment were tested to reduce sample-to-sample variance caused by differences in grain size and crystallographic orientation. The collected TGA data was corrected by subtracting blank experiments to account for buoyancy forces and normalized by individual sample starting surface area, measured via calipers [49]. Repeated measurements were averaged and compared using standard deviation error bars. Parabolic oxidation constants were calculated by linear regression of the squared normalized mass gains versus time during the static oxidation period [50]. During the cyclic TGA tests, specimens were also exposed to flowing Ar + O₂ through the duration of the tests.

Table 3

TGA oxidation test parameters used in this study
	Non-Isothermal/Isothermal	Cyclic
Duration	100 Hours	50 cycles
Temperature profile	Ramp from R.T. to 1000°C and hold for duration	Ramp to 1000°C and hold 15 min. Cool to 50°C and hold 2 min. Repeat
Heating rate Cooling rate	Heat: 100 K/min Cool: - - -	Heat: 50 K/min Cool: 50 K/min
Gas Flow	Total: 20 mL/min
Working Gas	21%O₂, 79% Ar

Characterization Methods

Cross sectional electron micrographs and EDS measurements were taken on a JEOL-7000 F scanning electron microscope (SEM) equipped with an Oxford X-max EDS Detector. Base metal specimens were metallographically ground and polished through 0.02 µm colloidal silica while oxide cross sections were only polished through 0.05 µm colloidal silica to minimize edge rounding. Select oxide cross sections were created via focused ion-beam (FIB) milling using a Quanta FEI Quanta 3D Dual Beam FIB-SEM with successively smaller beam currents to finely polish the observed surface while minimizing damage and cracking in the metal-oxide interface.

To additionally quantify the influence of microstructure on properties, Vickers microhardness was measured using an automated Clemex CMT in 3×10 arrays with equal 0.5 mm spacing. Intermetallic precipitates were further revealed through swab etching with Marble’s Reagent and quantified using ImageJ thresholding and particle counting modules [51]. For comparison with TC-Prisma calculations, measured precipitate areas were converted to equivalent circle diameter (ECD) values.

Oxide layer thickness was measured using the Size of Oxidation Feature from Image Analysis (aka SOFIA) package [52], a python program developed by the Oak Ridge National Laboratory which measures the shortest distance between specified contours of a highly contrasting micrograph. A representative example is shown in Fig. 3. To supply the program with the most definitively segment-able oxide scale, colored EDS maps were separated into red-green-blue (RGB) stacked images. A green or inverted green channel image was found to demarcate the boundary most clearly between TiO₂ and the base metal / internal Al₂O₃. The contrast band

providing separation was further enhanced by performing a despeckling noise reduction in ImageJ which eliminated bright spots within the border region. As SOFIA only considers the distance between upper and lower contour bands, any local variation in brightness within the layer of interest does not impact the final measurements. Comparisons between scale thicknesses and all other statistical measures were calculated using two sample t-tests in Minitab with $\alpha =0.05$ [53].

Atom probe tomography was performed on a Cameca LEAP 6000-XR in laser mode (30 K, 40 pJ, 170 kHz). Samples were lifted out from bulk on the FEI Quanta 3D Dual Beam and sharpened on the TESCAN LYRA FIB-SEM. Reconstruction was performed using Cameca’s IVAS analysis program (version 6.3) with precipitate chemistry determined by isoconcentration surfaces and selective voltage regimes [54].

Initial Microstructure

The average precipitate morphologies in each sample were quantified with the use of ImageJ on the backscattered electron (BSE) micrographs shown in Fig. 4. Consistent with published literature on similar alloys [42, 55–58], all the microstructures were found to consist of nearly spheroidal low atomic number contrast precipitates in a higher atomic number contrast matrix. The precipitates appeared to be uniform within each specimen and, generally, increased in size and volume fraction with increased annealing time and decreased annealing temperature, respectively, as is shown in Fig. 5. These findings were consistent with the overall trend as calculated by TC-Prisma, with most predicted average diameters falling within the measured 95% confidence interval. To confirm the changes in microstructure, 30-point arrays of Vickers hardness indents were made and measured (Fig. 6). The median sample hardness increased with both increasing precipitate volume fraction and decreasing precipitate size as expected from first principles calculations [59].

To further characterize the chemistry of the precipitate phase, APT tips were extracted from bulk polished samples. Subsequent data reconstruction and analysis, summarized in Fig. 7 and Table 4, highlighted the significant chemical segregation between the matrix and intermetallic precipitates. The results are summarized in Table 4. The precipitate chemistry, determined by isoconcentration surfaces from selected regions of interest, was found to be similar to classic superalloy ${{\gamma }}^{{\prime }}$-Ni₃(Al,Ti) phase but with some additional substitution of cobalt [60, 61]. The matrix was found to contain high concentrations of nickel, cobalt, iron, and chromium. The configurational entropy, $\varDelta {S}_{conf}$, of the total alloy and matrix phase as a function of mole fraction, ${X}_{i}$, was calculated using Eq. 1:

$$\varDelta {S}_{conf}=-R\sum _{i}{X}_{i}\text{ln}\left({X}_{i}\right)$$

Both the bulk alloy and matrix conform to the empirical high entropy alloy definition with an average $\varDelta {S}_{conf}$ of $1.54R$ and $1.57R$, respectively [4]. Further analysis of the APT data showed little-to-no enrichment of the phase boundaries, indicating that the elements within the precipitates and matrix were uniformly distributed and that a variation of the inverse lever rule could be used to estimate each samples volume fraction more accurately. If the nominal and precipitate atomic concentrations are taken as ${X}_{\text{n}\text{o}\text{m}}$ and ${X}_{P}$, respectively, then (Eq. 2):

$${X}_{\text{n}\text{o}\text{m}}={\phi }_{P}{X}_{P}+\left(1-{\phi }_{P}\right){X}_{P}$$

where ${\phi }_{P}$ is the volume fraction of precipitate phase [60, 61]. Plotting $\left({X}_{\text{n}\text{o}\text{m}}-{X}_{P}\right)$ vs. $\left({X}_{P}-{X}_{\text{M}\text{a}\text{t}\text{r}\text{i}\text{x}}\right)$ for each atomic species should yield an approximately linear relationship, the slope of which is the volume fraction of precipitate phase (Fig. 8).

Table 4

Mean atomic concentrations for the original casting calculated by mass spectrum analysis of 1000L, 1000S, 800L, and 800S APT specimens
Ion	Average Phase Composition (at%)		Calculated Bulk Composition (at%)
Ion	PPT	Matrix	–
Ni	60.1 ± 2.4	32.8 ± 3.8	45.2 ± 7.4
Al	12.2 ± 0.7	5.8 ± 0.9	8.4 ± 1.6
Ti	11.9 ± 0.4	2.4 ± 0.9	6.7 ± 3.1
Cr	2.6 ± 0.8	19.9 ± 2.3	12.3 ± 5.2
Fe	3.1 ± 0.7	16.3 ± 1.6	10.4 ± 3.7
Co	9.9 ± 1.7	22.1 ± 1.8	16.9 ± 3.1

Comparison of the EDS and APT measurements as well as examination of the inter-precipitate spacing indicated that the sampling distribution of the APT may be over sampling the matrix. To obtain more representative volume fractions, ${X}_{nom}$ was taken as the atomic concentrations measured through bulk EDS for the specific sample group (Table 1), rather than what was measured from the total APT volumes. The resulting phase fractions correlated well the values determined from backscattered SEM images and those predicted by ThermoCalc. The bulk concentration measured by APT indicates that the samples were significantly leaner in nickel than originally synthesized which may indicate some sampling bias in the selected areas or poor separation of overlapped mass spectrum peaks.

Oxidation Behavior

Figure 9 shows a representative FIB trench milled from sample 800L. All the investigated samples formed a similar tri-layer oxide structure consisting of a faceted external layer consisting of

TiO₂ + Fe_xO_y, an underlying continuous Cr₂O₃ layer, and a discontinuous internally oxidized Al₂O₃ subsurface region.

Figure 10 shows (a) nonisothermal-isothermal and (b) cyclic oxidation results for the samples annealed at 1000°C. No statistically significant change in overall mass gain was observed in the nonisothermal-isothermal TGA tests (Fig. 10a). However, there was a measurable difference in the parabolic oxidation rate between the two groups. The alloy that contained smaller precipitates (i.e., 1000S) exhibited a lower average ${K}_{p}$. Samples 1000L and 1000S behaved similarly in terms of total mass gain with each reaching steady oxidation, defined as the time until parabolic oxide growth is achieved, in approximately 10 hours. Under cyclic loading conditions, 1000S outperformed 1000L in terms of oxidation resistance and gained less specific mass overall (Fig. 10b).

Figure 11 shows BSE cross sections, EDS maps, and surface oxide morphologies for TGA specimens of 1000L and 1000S. Both groups displayed similar three-layered microstructures as described above, however, there was a difference in the Al₂O₃ morphology and subsequently a measurable change in the outer Cr₂O₃ layer thickness. Externally, no appreciable difference was observed in outer scale that formed after 100 hours of oxidation. Closer inspection of the metal-oxide interface and the internally grown Al₂O₃ showed that the internal oxide layer of sample 1000S was more continuous than the one in 1000L and had begun to grow a mixed titanium – aluminum oxide that was reminiscent of the beginnings of internal-to-external scale conversion (shown in the magnified inset). The Cr₂O₃ scale in sample 1000L was found to have a thickness of $8.83\pm 0.97 {\mu }\text{m}$ while the scale in sample 1000S was found to be thinner at $7.95\pm 1.23 {\mu }\text{m}$.

Figure 12 shows results from nonisothermal-isothermal and cyclic oxidation tests on samples annealed at 800°C. The smaller precipitate containing samples (i.e., 800S) gained less mass for the given oxidation time with lower parabolic oxidation rates in both nonisothermal-isothermal and cyclic tests. Examination in cross section, the nonisothermal-isothermal test specimens (Fig. 13) exhibited the same three-layered oxide structure as the 1000°C specimens, with sample 800S having a more contiguous Al₂O₃ layer than sample 800L. As observed in the other sample groups, a systematic variation in Cr₂O₃ layer thickness was observed with the larger precipitate containing material displaying a thicker Cr₂O₃ scale after 100 hours accounting for the observed increase in mass gain for the 800L samples.

To elucidate the microstructural evolution during earlier stages of oxidation, several nonisothermal-isothermal oxidation samples were removed from the TGA after approximately 30 minutes (see Fig. 14). The 800S samples formed a nearly continuous inner Al₂O₃ layer and a more cohesive outer TiO₂ + Fe_xO_y scale as compared to the 800L samples after the same oxidation time. The 900°C annealed sample group (900L and 900S) displayed similar behavior to that of the 800L and 800S samples with smaller precipitate containing samples performing better. Several of the samples in this group were found to contain shrinkage cavities which subsequently caused some samples to crack during sample preparation. This led to an increase in total oxide mass gain over the prescribed time in nonisothermal-isothermal testing and produced inconsistent results in cyclic testing (Fig. 15).

While the inconsistent mass gains may have obscured the true oxidation reaction rates, the microstructural changes observed in the samples mirror those of previous specimens (Fig. 16). The samples containing smaller precipitates (i.e., 900S), consistently exhibited a more continuous Al₂O₃ sublayer than the larger precipitate containing samples (i.e., 900L). In addition, the 900L samples also exhibited more spallation and cracking of the oxide scale. As such, only small regions of those samples contained cohesive, measurable layers.

Oxidation Kinetics and Modelling

To understand the kinetic oxidation behavior of each sample group, a generalized reaction rate model, expressed in Eq. 3, was fit to the specific mass gains for each sample.

$${\left(\text{S}.\text{M}.\text{G}.\right)}^{n}={k}_{n}t$$

The degree of the reaction (i.e., the reaction kinetics exponent), $n$, should vary between ~ 1 and ~ 3, representing the spread from linear through parabolic and logarithmic growth (Fig. 17) [20, 62]. The reaction products which formed and controlled further diffusion through each sample were similar for all sample groups. Therefore, $n$ was also consistent across the sample groups. However, there was a consistent decrease in the reaction order with decreasing precipitate size for the 900°C and 800°C sample groups (i.e., 900L, 900S, 800L, and 800S).

To allow for comparison with other high temperature oxidation experiments, the parabolic reaction rate was calculated for the steady state portion of the mass gain curves (see Fig. 18). The parabolic oxidation rate constant, ${K}_{p}^{{\prime \prime }}$, was determined through calculation of the best fit curve of the mass gain data using Eq. 4 [63]:

$$\text{S}.\text{M}.\text{G}. =\sqrt{{K}_{p}^{{\prime \prime }}\bullet t}+{m}_{0}$$

To more accurately capture the transition from linear to parabolic growth and asses the variability in the parabolic rate constant throughout the experiment, a sliding window analysis approach was used to measure ${K}_{p}^{{\prime }{\prime }}$ as a function of the starting time ($t$) of the data range. Through an iterative process the range of data used to estimate the fitting parameters, ${K}_{p}^{{\prime \prime }}$ and ${m}_{0}$, was reduced by increasing the starting time considered. For example, iteration 1 considered the mass gain over the entire time range 1 minute to 100 hours, iteration 2 considered only 2 minutes to 100 hours, iteration 3 considered 3 minutes to 100 hours, and so on until only the final portion of the mass gain curve was considered. During the multi-oxide growth process, the initial oxidation front does not conform to the steady-state, diffusion-controlled region until some time, ${t}_{p}$, whereupon the parabolic growth model becomes valid. The determination of ${t}_{p}$ is still qualitative, but the data suggests that the time to reach steady state oxidation is reduced with decreasing precipitate size. The values for ${K}_{p}^{{\prime }{\prime }}$ that are most comparable to other literature are in the flat regions from approximately 40 hours onward and steadily decrease with both increased precipitate volume fraction and decreased precipitate size. In general the HESAs ${K}_{P}^{{\prime }{\prime }}$rates are on the order of ${10}^{-11} {\text{g}}^{2}/\text{c}{\text{m}}^{4}\text{s}$ which falls in line with many other MPEAs and Ni-based superalloys [11, 62, 64, 65].

The results highlight a clear trend in oxidation behavior with respect to precipitate size for a given volume fraction. Apart from the 1000°C annealed, nonisothermal-isothermal series, materials that contained smaller precipitates outperformed their larger precipitate counterparts in terms of overall mass gain for both oxidation tests. This effect seems to stem from the coalescence of internal Al₂O₃ that is forming beneath the Cr₂O₃ layer as oxidation progresses which may act to block further oxide development [30, 34]. If the initial Ni₃(Al,Ti) precipitate distribution is taken to be the nucleation sites for Al₂O₃ growth, their growth rate, $dD/dt$, should follow classical Lifshitz-Slyozov-Wagner coarsening and is therefore proportional to $1/{r}^{2}$ [66]. At the same time, for a fixed area and volume fraction $\left(V.F.\right)$with equal particle size and spacing, as the number of particles ($N$) increases, the particle width (${D}_{ppt}$) must decrease (Fig. 19a):

$${D}_{ppt}=\sqrt{\frac{4\bullet \left(Area\right)\bullet \left(V.F\right).}{\pi \bullet N}} \text{a}\text{n}\text{d} \frac{dD}{dt}\propto 4/{D}_{ppt}^{2}$$

Conversely, considering regularly spaced circular precipitates, as the number of precipitates increase, both the lateral, ${L}_{lat}$ (Eq. 6a), and diagonal, ${L}_{diag}$ (Eq. 6b), distances between precipitates must decrease (Fig. 19b):

${L}_{lat}=\frac{\sqrt{Area}-\sqrt{N}\bullet {D}_{ppt}}{\sqrt{N}-1}$	(6a)
${L}_{diag}=\sqrt{2{\left({L}_{lat}+{D}_{ppt}\right)}^{2}}-{D}_{ppt}$	(6b)

The increased growth rate and decreased lateral diffusion distance in the small precipitate containing samples leads to a faster overall coalescence of the Al₂O₃ layer and a quicker transition to steady state oxidation. This lateral growth phenomena, modeled in Fig. 19 and highlighted in Figs. 11, 13, and 14, has been observed and described for other ternary systems in which Al₂O₃ eventually formed, coalesced, and grew outward [13, 67–70]. When the Al₂O₃ layer becomes more contiguous, even internally, it restricts further oxidation as evidenced by the decrease in outer Cr₂O₃ scale thickness, parabolic oxidation rate, time to reach steady state, and overall mass gain of the samples [68]. It is likely that the effect has dependence on volume fraction of the reservoir phase, which may partially explain the diminished effect in the 1000°C annealed nonisothermal-isothermal test specimens (1000L and 1000S). If the lateral growth of oxide precipitates is considered the dominant mechanism for coalescence and protection, a bi-modal distribution of prior precipitates obtained through nonisothermal heat treatment may provide even shorter pathways for compaction as the inner precipitate pathways are filled more efficiently.

During cyclic oxidation testing, approximately 80% of mass gain occurs during the elevated temperature hold (Fig. 20). However, the time spent at lower temperatures can still slowly allow for coalescence of the Al₂O₃ layer without significant accumulation of any additional oxide products. This continued lower temperature Al₂O₃ growth explains why samples containing small precipitates gained less mass under cyclic conditions, even in low volume fraction samples (1000L and 1000S).

The most direct illustration of the influence of phase volume fraction on oxidation behavior can be discerned from a comparison of the 1000S and 800S groups, which both had an approximate precipitate size of 40 nm (Fig. 21). Although the higher volume fraction material gained less mass overall and had a lower average parabolic oxidation rate, the difference is relatively small. It is believed that the lack of cross sample comparisons stem from two key issues: texture effects and the inability to form an external Al₂O₃ layer. The samples within an annealing group came from the same section of the original casting and, post-heat treatment, exhibited the same microstructures in terms of grain size and crystallographic orientation. As the samples moved further from each other on the original casting, this distribution changed and likely caused some difference in the bulk performance of the sample [71, 72]. To further study this effect, it would be beneficial to move to a higher aluminum content composition to suppress the formation of Cr₂O₃ altogether. This would more directly measure the efficacy of precipitate size and volume fraction without having to parse out secondary effects. Substituting the titanium entirely for a different FCC stabilizer would likely help as well by removing the influence of the outer TiO₂ layer and reducing the growth rate, and therefore forming potential, of Cr₂O₃ [64]. Additionally, samples from the 900°C annealing group (900L and 900S) had porosity that was uniform within the group but was unique among the three annealing temperatures, leading to a baseline elevation in mass gain. The similar microstructural change among oxidized samples leads us to believe the intra-sample data comparing 900L and 900S is valid, however drawing comparisons between 900L and 900S and the other two groups is a bit more challenging.

The impact of microstructural features on the oxidation behavior of a well-behaved transition metal MPEA has been investigated. The results show that samples containing smaller, highly concentrated, precipitates gain less mass overall under both nonisothermal-isothermal and cyclic oxidation conditions at 1000°C. Each annealed sample group exhibited a three-layered oxide structure of external (TiO₂ + Fe_xO_y), intermediate Cr₂O₃, and internal Al₂O₃ with variations in the morphology of each. Specimens containing smaller precipitates on average, formed external TiO₂ layers much earlier, thinner Cr₂O₃ layers, and more uniform and continuous internal Al₂O₃ layers than their larger precipitate containing counterparts. This effect is attributed to the elevated coarsening and coalescence rates that smaller of Al₂O₃ nuclei possess, which leads to an earlier blocking of oxidation in the samples. This effect has been observed in other ternary systems as well as in recent developments in percolation theory for oxidation of single-phase materials which may be viewed as the same mechanism on the microstructure scale rather than atomic, short-range ordering scale [73].

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work utilized equipment owned by the Alabama Analytical Research Center (AARC), which is housed at the University of Alabama. This work was supported by the National Science Foundation (DMR-2105364).

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Microstructural Impacts on the Oxidation of Multi-Principal Element Alloys

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