ALLOYS AND METHODS OF MAKING ALLOYS

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application entitled “Methodology of Designing Alloys with Preferable Physical Properties and Corrosion Resistance and Related Compositions Thereof” and having Ser. No. 63/718,294, filed Nov. 8, 2024, which is herein incorporated by reference in its entirety.

FEDERAL SPONSORSHIP

This invention was made with government support under N00014-23-1-2441 and N00014-20-1-2368 awarded by the Office of Naval Research. The government has certain rights in the invention.

BACKGROUND

The enhancement of corrosion resistance through the addition of Cr in ferrous and Ni-based alloys has been extensively studied. Many Cr-containing compositionally complex alloys (CCAs) have been developed in accordance with (though not defined by) the traditional Cr content threshold for robust corrosion resistance through passivity. However, this approach has its limitations and there is a need for other approaches.

SUMMARY

The present disclosure provides for alloys and methods of making alloys, and the like.

In an aspect, the present disclosure provides for an alloy comprising: Cr_xFe_yNi_zAl_qSi_rTi_s, wherein x is 9-20, y is 1-80, z is 0-50, q is 0-30, r is 0-15, and s is 0-12, wherein x+y+z+q+r+s=100, wherein at least 1 of q, r, and s are not equal to 0.

BRIEF DESCRIPTION OF THE DRAWINGS

Further aspects of the present disclosure will be more readily appreciated upon review of the detailed description of its various embodiments, described below, when taken in conjunction with the accompanying drawings.

FIG. 1.1A illustrates X-ray diffraction patterns of Fe-8Cr-8Al-xTi and Fe-xCr-{16-x}Al-8Ti (at. %) alloys using a Cu K-α (0.154 nm) source. FIG. 1.1B illustrates back-scattered electron micrographs and energy dispersive spectroscopy elemental line profiles of Ti, Al, Cr, and Fe of Fe-8Cr-8Al-8Ti (at. %) alloy sample after solutionization heat treatment.

FIGS. 1.2A-B illustrate weighted average alloy (A) density, and (B) estimated cost in US dollars per kg of Fe-8Cr-8Al-xTi and Fe-xCr-{16-x}-8Ti (at. %) alloys tested in this work.

FIGS. 1.3A-B illustrate CSRO Warren-Cowley (a) values for the like-element pairs across the (A) Fe-8Cr-8Al-xTi and (B) Fe-xCr-{16-x}Al-8Ti compositional space as calculated from the simplified first nearest-neighbor Monte Carlo approach at 1.3 T_c. Positive values indicate a like-pair clustering tendency, whereas negative values indicate ordering is preferred between like pairs. Unconnected data points are for ternary compositions.

FIGS. 1.4A-D illustrate potentiodynamic polarization results of Fe-8Cr8Al-xTi alloys in deaerated 0.1 M Na₂SO₄(aq) adjusted to (A) pH 4 and (B) pH 1; and Fe-xCr-{16-x}Al-8Ti alloys in deaerated 0.1 M Na₂SO₄(aq) adjusted to (C) pH 4 and (D) pH 1; compared to 304L stainless steel and pure α-Ti. The scan rate was about 0.52 mV/s. i_pass is passive current density defined at 0 V while i_crit is the critical current density. The jitter in the cathodic region of the curves is due to the manual removal of hydrogen gas bubbles formed below E_corr from the alloy surface.

FIGS. 1.5A-C illustrate extracted parameters i_crit and i_pass vs. (A) Ti composition for Fe-8Cr8Al-xTi alloys, and (B) Cr/Al ratio for Fe-xCr-{16-x}Al-8Ti alloys from the potentiodynamic polarization behaviors in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 1. (C) i_crit of all the alloys tested in this work compared to that of known binary Fe—Al [47] in deaerated 0.0126 M H₂SO_4(aq), Fe—Cr—Al [26] in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 1, Fe—Ti [48] and Fe—Cr [3] alloys, alloys in deaerated 0.1 M H₂SO_4(aq).

FIG. 1.6A illustrates number of dissolved monolayers (h) obtained from chronoamperometry experiments at −0.7 V for Fe-8Cr-8Al-xTi, Fe-xCr-{16-x}Al-8Ti, and 304L stainless steel alloy samples in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 1, FIG. 1.6B representing the h-value results of Fe-xCr-{16-x}Al-8Ti versus Cr/Al ratio in the alloys. Thickness of the grey line for 304L represents the error bar.

FIGS. 1.7A-D illustrates bode impedance magnitude (|Z|) and phase (Z_phz) plots of (A) Fe-8Cr-8Al-xTi and (B) Fe-xCr-{16-x}Al-8Ti alloys where, x={0,4,8,12,16}including 304L, (C) Electrical circuit model (ECM) used for fitting obtained impedance data where R_s, R_fle and Q_fle, R_f and Q_f, and W represent the resistance of the solution, resistance and CPE of film/electrolyte interface, film resistance and CPE, and Warburg diffusional impedance element, respectively (D) Polarization resistance (R_p) defined as R_p=R_s+R_fle+R_f from ECM fitting impedance data plotted against alloy compositions, after potentiostatic hold at 0 V vs. MMSE for 10 ks in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 1.

FIGS. 1.8A-C illustrate (A) Potentiodynamic E-log(i) curves, and (B) Bode impedance (|Z|) and phase (Z_phz) plots of performed after potentiostatic hold at 0 V for a period 10 ks for Fe-8Cr-8Al-8Ti (Ti8) alloy. All exposed in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 1, pH4, pH 7, and pH 10. (C) Bode impedance and phase plots of Fe-8Cr-8Al-8Ti alloy after exposure time up to 105 seconds in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4. The solid lines represent fits of the impedance data using the ECM shown in FIG. 7c.

FIG. 1.9 illustrates XPS spectral deconvolution peak fitting of O 1s, Cr 2p_3/2, Al 2p, Fe 2p_3/2, and Ti 2p core shells of the potentiostatically grown passive film of Fe-8Cr-8Al-4Ti (at. %) after 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4.

FIGS. 1.10A-B illustrate XPS passive film cationic enrichment factors (f) vs. alloy composition of the alloy series (A) Fe-8Cr-8Al-xTi and (B) Fe-xCr-{16-x}Al-8Ti passive films grown for 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4.

FIG. 1.11 illustrates selected XPS sputter relative intensity depth profiles of elemental cations for passive films grown for 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) pH 4. Here, Fe is Fe(II), Cr is Cr(III), Al is Al(III) cations, and O is O 1s, respectively. Relative intensity is defined as the ratio of area under the peak fits and core-shell relative sensitivity factor. Fe/5 and O/10 suggest the relative intensity divided by 5 and 10, respectively.

FIG. 1.12A illustrates thermoCalc generated CALPHAD results of Fe-8Cr-8Al-xTi (at. %) alloy compositions using TCFE9 thermodynamic database and FIG. 1.12B Table S1: Compositions of the Fe—Cr—Al—Ti alloys in Wt. %.

FIG. 1.13 illustrates thermoCalc generated CALPHAD results of Fe-xCr-{16-x}Al-8Ti (at. %) alloy compositions using TCFE9 thermodynamic database.

FIG. 1.14 illustrates back-scattered secondary electron micrographs and energy dispersive spectroscopy elemental maps of second-phase containing regions within Fe-8Cr-8Al-12Ti (at. %) and Fe-8Cr-8Al-16Ti (at. %) samples. Both after solutionization heat treatment.

FIG. 1.15 illustrates TEM results of Fe-8Cr-8Al-16Ti (at. %) alloy. (A) HAADF image, (B) Elemental maps and spectrum of Fe, Cr, Al, and Ti across the two phases of BCC and Fe₂Ti (Fe is lower than BCC phase). (C) SAED patterns of the Fe₂Ti (space group: P6₃/mmc) confirming its presence following the reported structure in materials project phase mp-2454

FIG. 1.16 illustrates current density (i) and imaginary impedance (−Z″) plots obtained from single frequency potentiodynamic polarization of Fe-8Cr-8Al-xTi alloys in deaerated 0.1 M Na₂SO_4(aq) pH 4.

FIG. 1.17 illustrates current density (i) and imaginary impedance (−Z″) plots obtained from single frequency potentiodynamic polarization of Fe-8Cr-8Al-xTi alloys in deaerated 0.1 M Na₂SO_4(aq) pH 1.

FIG. 1.18 illustrates current density (i) and imaginary impedance (−Z″) plots obtained from single frequency potentiodynamic polarization of Fe-xCr-{16-x}Al-8Ti alloys in deaerated 0.1 M Na₂SO_4(aq) pH 4.

FIG. 1.19 illustrates current density (i) and imaginary impedance (−Z″) plots obtained from single frequency potentiodynamic polarization of Fe-xCr-{16-x}Al-8Ti alloys in deaerated 0.1 M Na₂SO_4(aq) pH 1.

FIG. 1.20 illustrates E vs. log(i) plot obtained from potentiodynamic polarization of pure Fe, Cr, Al, and a Ti (HCP), in deaerated 0.1 M Na₂SO_4(aq) pH 1 after cathodically reducing their native oxide films. Scan rate 1 mV/s.

FIG. 1.21 illustrates bode impedance and phase plots of Fe-8Cr-8Al-xTi alloys after potentiostatic hold at 0 V for 10 ks in 0.1 M Na₂SO_4(aq) pH 4.

FIG. 1.22 illustrates bode impedance and phase plots of Fe-xCr-{16-x}Al-8Ti alloys after potentiostatic hold at 0 V for 10 ks in 0.1 M Na₂SO_4(aq) pH 4.

FIG. 1.23 illustrates polarization resistance (R_p) calculated from ECM fitting of Fe-8Cr-8Al-8Ti (Ti8) alloy EIS data obtained after (left) different potentiostatic hold times at 0 V in deaerated 0.1 M Na₂SO₄ pH 4 solution; (right) 10 ks of potentiostatic hold at 0 V in deaerated 0.1 M Na₂SO₄ adjusted to different pH values.

FIG. 1.24 illustrates XPS spectral deconvolution peak fitting of O 1s, Cr 2P_3/2, Al 2p, Fe 2p_3/2, and Ti 2p core shells of the potentiostatically grown passive film of Fe-8Cr-8Al (at. %) after 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4 using H₂SO_4(aq).

FIG. 1.25 illustrates XPS spectral deconvolution peak fitting of O 1s, Cr 2P_3/2, Al 2p, Fe 2p_3/2, and Ti 2p core shells of the potentiostatically grown passive film of Fe-8Cr-8Al-8Ti (at. %) after 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4 using H₂SO_4(aq).

FIG. 1.26 illustrates XPS spectral deconvolution peak fitting of O 1s, Cr 2p_3/2, Al 2p, Fe 2p_3/2, and Ti 2p core shells of the potentiostatically grown passive film of Fe-8Cr-8Al-12Ti (at. %) after 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4 using H₂SO_4(aq).

FIG. 1.27 illustrates XPS spectral deconvolution peak fitting of O 1s, Cr 2p_3/2, Al 2p, Fe 2p_3/2, and Ti 2p core shells of the potentiostatically grown passive film of Fe-8Cr-8Al-16Ti (at. %) after 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4 using H₂SO_4(aq).

FIG. 1.28 illustrates XPS spectral deconvolution peak fitting of O 1s, Cr 2p_3/2, Al 2p, Fe 2p_3/2, and Ti 2p core shells of the potentiostatically grown passive film of Fe-16Al-8Ti (at. %) after 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4 using H₂SO_4(aq).

FIG. 1.29 illustrates XPS spectral deconvolution peak fitting of O 1s, Cr 2P_3/2, Al 2p, Fe 2p_3/2, and Ti 2p core shells of the potentiostatically grown passive film of Fe-4Cr-12Al-8Ti (at. %) after 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4 using H₂SO_4(aq).

FIG. 1.30 illustrates XPS spectral deconvolution peak fitting of O 1s, Cr 2P_3/2, Al 2p, Fe 2p_3/2, and Ti 2p core shells of the potentiostatically grown passive film of Fe-12Cr-4Al-8Ti (at. %) after 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4 using H₂SO_4(aq).

FIG. 1.31 illustrates XPS spectral deconvolution peak fitting of O 1s, Cr 2P_3/2, Al 2p, Fe 2p_3/2, and Ti 2p core shells of the potentiostatically grown passive film of Fe-16Cr-8Ti (at. %) after 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 4 using H₂SO_4(aq).

FIG. 1.32 illustrates normalized XPS sputter depth profiles of elemental cations of the passive films of Fe-8Cr-8Al-xTi alloys grown for 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) pH 4. Here, normalized intensity of a cation is defined as to divide the relative intensity by its maximum relative intensity for any sputter time.

FIG. 1.33 illustrates normalized XPS sputter depth profiles of elemental cations of the passive films of Fe-xCr-{16-x}Al-8Ti alloys grown for 10 ks at 0 V in deaerated 0.1 M Na₂SO_4(aq) pH 4. Here, normalized intensity of a cation is defined as to divide the relative intensity by its maximum relative intensity for any sputter time.

FIG. 1.34 illustrates comparison of CSRO as calculated from cluster expansion (CE) and the coherent ordering descriptor-based Monte Carlo (COD-MC) method for the ternary Al—Cr—Fe system. (Left) Cluster expansion: 137 training structures, initialized with ferromagnetism, with a cross-validation score of 26.4 meV/atom. Monte Carlo simulations used 20×20×20 atom simulation cells and 1,000 equilibration steps, followed by 32,000 steps from which thermodynamic averages were obtained. CSRO was calculated at 3,400 K to ensure a single phase disordered region across the composition space. This overestimation of phase boundaries is well-known when excluding vibrational entropy. (Right) COD-MC: Computed using the method described in the main text. Results shown were calculated at T_red=4, where q²)/k_B, where k_B is Boltzmann's constant, and J_ij are the effective cluster interactions for T_red≡^P_ij(J_ij the nearest neighbor pairs. J_ij are converted from the chemical pairwise interactions, V_ij as in [14] using the basis function definition of ATAT [15], [16]. Visually, there is good qualitative agreement between the CE and COD-MC methods, with clustering and ordering regions generally in agreement, which is remarkable given the simplicity of the COD-MC model. One notable exception where agreement is questionable is the α_Cr-Fe pair, which changes sign from positive (clustering) to negative (ordering) in the Fe-rich region of the ternary diagram when computed from CE but remains clustering everywhere when computed from COD-MC. Cr—Fe is a relatively unique binary alloy known to change sign in CSRO around 10 at. % Cr [17]-[19]. The origin of this phenomenon is too complex for a simple nearest-neighbor model to capture, so it is not surprising it is not reproduced in COD-MC.

FIG. 1.35 illustrates computed Warren-Cowley SRO values for the Fe-8Cr-8Al-xTi alloys as calculated using the first nearest-neighbor interaction only model as a function of reduced temperature, T_red. Here, q²)/k_B, where k_B is Boltzmann's constant, and J_ij are the effective cluster interactions for T_red≡^P_ij(J_ij the nearest neighbor pairs. J_ij are converted from the chemical pairwise interactions, V_ij as in [14] using the basis function definition of ATAT [15], [16]. (a-b) x=16, (c-d) x=12, (e-f) x=8, and (g-h) x=4. Left plots display dissimilar elemental SRO pairs, while right plots give the like-pairs. Significant changes in the SRO parameter magnitudes are indicative of phase transitions and are verified by considering discontinuities in the heat capacity.

FIG. 1.36 illustrates computed Warren-Cowley SRO values for the Fe-xCr-{16-x}Al-8Ti alloys as calculated using the simplified first nearest-neighbor interaction only model as a function of reduced temperature, q²)/k_B, where k_B is Boltzmann's constant, and J_ij are the effective cluster T_red. Here, T_red=^P_ij(J_ij interactions for the nearest neighbor pairs. J_ij are converted from the chemical pairwise interactions, V_ij as in [14] using the basis function definition of ATAT [15], [16]. (a-b) x=12, (c-d) x=8, and (e-f) x=4. Left plots display dissimilar elemental SRO pairs, while right plots give the like-pairs. Significant changes in the SRO parameter magnitudes are indicative of phase transitions and are verified by considering discontinuities in the heat capacity.

FIG. 1.37 illustrates CSRO values for the dissimilar-element pairs as calculated from the simplified first nearest-neighbor Monte Carlo approach at 1.3 T_c. Positive values indicate a clustering tendency, whereas negative values indicate ordering is preferred. Unconnected data points are for ternary compositions.

FIG. 2.1 illustrates XRD spectra of all post-solutionized Ni₄₃Fe₃₇Cr₁₀(Al_xSi_yTi_z) CCAs studied, with FCC peaks indicated by stars.

FIG. 2.2 illustrates representative SEM/EDS image of the homogenous microstructure reflected by sample Al5Ti5, as well as all other samples barring Si₅Ti_s and Si₇Ti₃.

FIG. 2.3A illustrates density of alloys as a function of composition measured using an Archimedes method following solutionization. Each concentric radial axis tick represents an increase of 0.1 g/cc, with the center reflecting a density of 7.4 g/cc. FIG. 2.3B illustrates hardness of alloys as a function of composition measured using Vickers microhardness with a 0.5 kg load. Each concentric radial axis tick represents an increase of 100 HV0.5, with the center reflecting a hardness of 0 HV0.5. All error bars represent one standard deviation of measured values. Color gradients between red and green represent compositions varying from 10 at % Al to 10 at % Ti, color gradients between red and blue represent compositions varying between 10 at % Al to 10 at % Si, and color gradients between green and blue represent compositions varying between 10 at % Ti to 10 at % Si. Bold black circles represent the control alloy value, with concentric gray bands representing the standard deviation of measured values for that sample.

FIGS. 2.4A-C illustrate representative potentiodynamic E-logi curves for (A) Al—Ti, (B) Al—Si, (C) Ti—Si LWE sweeps performed in N₂(g)-bubbled 0.1 M H₂SO₄ following cathodic pretreatment as described herein. Black dashed lines indicate the potential used in the chronoamperometric and potentiostatic passive film growth experiments.

FIGS. 2.5A illustrate representative chronoamperometry curves obtained by stepping a reduced sample to +0.15 V_SHE. (B) Resulting h value distributions across all alloys, where error bars indicate one standard deviation. Each concentric radial axis tick represents an increase of 5 monolayers, with the center being 5 monolayers and the first ring being 10 monolayers. The bold black line in (B) indicates the average h value for the control alloy, with gray shading indicating one standard deviation of measured values.

FIGS. 2.6A-C illustrate representative potentiostatic (+0.15 V_SHE) logi−logt and −Z_imag−logt curves for (A) Al—Ti, (B) Al—Si, and (C) Ti—Si LWE sweeps. Data represented by dots refer to the right side −Z_imag axis.

FIG. 2.7 illustrates resulting t_0.5 distribution of Al—Ti (dotted), Si—Al (dashed), and Si—Ti (dot-dashed) LWE sweeps. Error bars indicate one standard deviation of measured values, and the bold black solid line indicates the average value for the control, with the gray shaded region representing one standard deviation.

FIGS. 2.8A-G illustrate bode (A-C) and Nyquist (D-F) plots from EIS taken after 10 ks film growth at +0.15 V_SHE for the Al—Ti (A, D), Al—Si (B, E), and Ti—Si (c, f) LWE sweeps. (G) A schematic of the circuit used to fit the EIS data. Rp is calculated by the sum of film/electrolyte charge transfer and film resistances (i.e. R_p=R_fle+R_f). The circuit parameters used for the fits displayed in d-f can be found herein.

FIG. 2.9 illustrates resulting R_p relations for Al—Ti (dotted), Si—Al (dashed), and Si—Ti (dot-dashed) LWE sweeps. The control alloy's (Al0Si₀Ti₀'s) R_p is represented by the solid bold black line. All error bars and light gray bands represent one standard deviation of fitted values across multiple film growth experiments. R_p is calculated by the sum of film/electrolyte charge transfer and film resistances (i.e. R_p=R_fle+R_f)

FIG. 2.10 illustrates actual (ie) and convoluted (i*e) current density profiles, spectral actual (vM) and congruent (vcg) dissolution rate profiles of Ni, Fe, Cr for CCAs (A) Al0Si₀Ti₀, (B) Si₁₀ along with Si, and (C) Ti₁₀ along with Ti, all obtained via AESEC-LSV (anodic direction) experiments in deaerated 0.1 M H₂SO₄. Here, ΘM represents the enrichment or depletion of the metallic species for its actual dissolution rate compared to when it would have dissolved congruently. A boxcar averaging (N=10) was used for all curves to improve the signal-to-noise ratio. Note the decrease in the scale used for the y-axis between sub-figures and also within elements.

FIG. 2.11 illustrates percent total enrichment normalized to the total dissolution (% ΘM) of Cr, Si, and Ti in the potential range of E_corr to +0.6 V obtained from AESEC-LSV experiments in deaerated 0.1 M H₂SO₄.

FIG. 2.12 illustrates XPS spectral deconvolution peak fits for all species present in sample Ni₄₃Fe₃₇Cr₁₀Ti₁₀ following potentiostatic film growth at E_app=+0.15 V_SHE for 10 ks.

FIG. 2.13 illustrates cation fractions of all species following 10 ks potentiostatic film growth at E_app=+0.15 V_SHE, as calculated from Equation (6).

FIG. 2.14 illustrates metal cation fractions of passivating species following 10 ks potentiostatic film growth at E_app=+0.15 V_SHE, as calculated from Equation (6).

FIGS. 2.15A-C illustrates phase boundary plots for generic alloy platforms Fe_balNi₄₃Cr₁₀— (FIG. 2.15A) —Al_xSi_y, (FIG. 2.15B) —Al_xTi_y, and (FIG. 2.15C) —Ti_xSi_y. The gray envelope indicates binary combinations of each LWE pair which yield a predicted single-phase FCC microstructure at each alloy's solidus temperature. The black dashed line indicates the condition where the pairwise sum of LWE is equal to 10 at %. The orange dashed line illustrates the single-phase compositional boundary, with the gap between the black and orange lines indicating the relative phase stability of the alloy set. Darkening shades of blue represent increasing numbers of phases.

FIG. 2.16A illustrates multiple linear regression (MLR) log 10Rp coefficients for each passivating component. Inlaid plot describes MLR fitting performance, garnering a R2 value of 0.980. FIG. 2.16B illustrates Rp plotted against the combination of Cr and Ti cation fraction in log scale. Resulting correlation highlights the positive MLR coefficients for both Cr and Ti and synergistic (10×) effects of Cr and Ti oxide species' expression.

FIG. 2.17A illustrates multiple linear regression (MLR) t_0.5 coefficients for each passivating component. Inlaid plot describes MLR fitting performance, garnering a R2 value of 0.973. FIG. 2.17B illustrates t_0.5 plotted against the combination of Cr, Si and Ti cation fraction. Resulting correlation highlights the negative MLR coefficients for both Ti, Si and Cr.

FIG. 2.18 illustrates film growth speed and film growth characteristics of all samples made for this study. The resulting 4-mean cluster centroids are plotted as open circles and labeled. Inlaid is an elbow plot, indicating that k=4 clusters is an apt choice.

FIG. 2.19 illustrates STEM image and line profile of grain boundary found in sample Al10.

FIG. 2.20 illustrates SEM/EDS image of homogeneous, single-phase microstructure observed for sample Al5Ti5, and also seen in all samples barring Si5Ti5 and Si7Ti3.

FIG. 2.21 illustrates the OCP of samples Al0Si0Ti0 and Ti10 monitored over a span of 24 hours following cathodic reduction and an EIS scan.

FIG. 2.22 illustrates bode and Nyquist representations of alloy impedance over the span of a 31 day immersion experiment.

FIG. 2.23 illustrates optical microscopy of the exposed areas of samples A10Si0Ti0 and Ti10 after 31 days of immersion in 0.1M H₂SO₄.

FIG. 2.24A illustrates Table 1 in Supplemental information of Example 2.

FIG. 2.24B illustrates Table 2 in Supplemental information of Example 2.

FIG. 2.24C illustrates Table 3 in Supplemental information of Example 2.

DETAILED DESCRIPTION

The present disclosure provides for alloys and methods of making alloys, and the like.

Before the present disclosure is described in greater detail, it is to be understood that this disclosure is not limited to particular embodiments described, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting, since the scope of the present disclosure will be limited only by the appended claims.

Where a range of values is provided, it is understood that each intervening value, to the tenth of the unit of the lower limit (unless the context clearly dictates otherwise), between the upper and lower limit of that range, and any other stated or intervening value in that stated range, is encompassed within the disclosure. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges and are also encompassed within the disclosure, subject to any specifically excluded limit in the stated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the disclosure.

Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. Although any methods and materials similar or equivalent to those described herein can also be used in the practice or testing of the present disclosure, the preferred methods and materials are now described.

As will be apparent to those of skill in the art upon reading this disclosure, each of the individual embodiments described and illustrated herein has discrete components and features which may be readily separated from or combined with the features of any of the other several embodiments without departing from the scope or spirit of the present disclosure. Any recited method can be carried out in the order of events recited or in any other order that is logically possible.

Embodiments of the present disclosure will employ, unless otherwise indicated, techniques of chemistry, material science, and the like, which are within the skill of the art. Such techniques are explained fully in the literature.

The following description and examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how to perform the methods and use the compositions and compounds disclosed and claimed herein. Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.), but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in ° C., and pressure is in bar or psi. Standard temperature and pressure are defined as 25° C. and 1 bar.

Before the embodiments of the present disclosure are described in detail, it is to be understood that, unless otherwise indicated, the present disclosure is not limited to particular materials, reagents, reaction materials, manufacturing processes, or the like, as such can vary. It is also to be understood that the terminology used herein is for purposes of describing particular embodiments only, and is not intended to be limiting. It is also possible in the present disclosure that steps can be executed in different sequence where this is logically possible.

It must be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a support” includes a plurality of supports. In this specification and in the claims that follow, reference will be made to a number of terms that shall be defined to have the following meanings unless a contrary intention is apparent.

General Discussion

The present disclosure provides for alloys and methods of making alloys, and the like. In an aspect, the present disclosure provides for non-equiatomic alloys that exhibit excellent corrosion resistance at low pHs (e.g., about 1 pH) afforded by passive films. In an aspect, alloys of the present disclosure include lightweight elements (LWEs) (e.g., Al, Si, and/or Ti) to produce lower-density austenitic alloys. For example, a greater than 10-fold increase in film resistance and 4-fold increase in passive film growth rate relative to the control alloy can be achieved using the alloys of the present disclosure.

Example 1 provides for two series of Ti-containing FeCrAl alloys with varying and fixed Cr/Al ratios were synthesized and characterized for structure, chemical short-range order, corrosion resistance, and passive film composition in 0.1 M Na₂SO_4(aq) containing solutions. Example 2 provides for a set of single-phase alloys with abundant Co-free FCC elements Ni₄₃Fe₃₇Cr₁₀—(Al,Si,Ti)₁₀ that were designed using a high-throughput CALPHAD technique to further explore and define the specific physical and corrosion-resistance impacts of lightweight elements Al, Si, Ti while controlling for a single-phase microstructure. Additional details are provided in Examples 1 and 2.

The present disclosure provides for alloys having the following formula: Cr_xFe_yNi_zAl_qSi_rTi_s. In an aspect, the alloy is free of cobalt (Co). Subscript x is 9-20, subscript y is 1-80, subscript z is 0-50 or 1-50, subscript q is 0-30 or 1-30, subscript r is 0-15 or 1-15, and subscript s is 0-12 or 1-12, where x+y+z+q+r+s=100 and where at least 1 of q, r, and s are not equal to 0. In an aspect, y+z=80 and q+r+s=10. In an aspect, x+y+z>80 and q+r+s<20. In an aspect, x+y>80, x+z>80, or y+z>80.

The present disclosure provides for alloys having the following formula: Cr_xFe_yAl_qTi_s. In an aspect, the alloy is free of cobalt (Co). Subscript x is 9-20, subscript y is 1-80, subscript q is 1-30, and subscript s is 1-12.

The present disclosure provides for alloys having the following formula: (Fe_yNi_z)Cr_x(Al_qSi_rTi_s). In an aspect, the alloy is free of cobalt (Co). Subscript x is 10, subscript y is 1-80, subscript z is 0-50 or 1-50, subscript q is 0-10 or 1-10, subscript r is 0-10 or 1-10, and subscript s is 0-10 or 1-10. In an aspect, y+z=80 and q+r+s=10. In an aspect, one of q, r, and s is equal to 0, wherein the other two q, r, and s are 1 to 10. In an aspect, two of q, r, and s are equal to 0 and the remaining one of q, r, and s is 10.

The present disclosure provides for alloys having the following formula: (Cr_xFe_yNi_z)(Al_qSi_rTi_s). In an aspect, the alloy is free of cobalt (Co). Subscript x is 9-20, subscript y is 1-80, subscript z is 0-50 or 1-50, subscript q is 0-30 or 1-30, subscript r is 0-15 or 1-15, and subscript s is 0-12 or 1-12. In an aspect, x+y+z>80 and q+r+s<20. In an aspect, one of x, y, and z is equal to 0 and x+y>80, x+z>80, or y+z>80. In an aspect, one of q, r, and s is equal to 0 and two of the following are present: q is 1-18, r is 1-15, and s is 1-12. In an aspect, two of q, r, and s are equal to 0 or one of the following is present: q is 1-18, r is 1-15, and s is 1-12.

In an aspect, the alloy is a single phase alloy or a duplex alloy. In an aspect, single phase refers to an alloy comprised of a single crystal structure, without any other crystal structures present throughout the microstructure. In an aspect, the duplex alloy refers to an alloy comprised of two crystal structure phases. In this (and usual) context, “duplex” refers to a material containing both face-centered cubic (FCC) and body-centered cubic (BCC) crystallographic phases.

In an aspect, the present disclosure provides for one of the following formula: Ni₄₃Fe₃₇Cr₁₀—(Al_qSi_rTi_s)₁₀, where q is 0-30, r is 0-15, and s is 0-12, wherein at least 1 of q, r, and s are not equal to 0; Fe₈Cr₈Al_xTi where x was varied from 0 to 16; and Fe,Cr_{16-x}Al₃Ti, where x was varied from 0 to 16.

In an aspect, the alloy has an excellent corrosion resistance. In particular, the alloy has electrochemical parameters describing overall corrosion resistance as compared to those of 304L stainless steel (an industry standard widely used corrosion resistant alloy). For example, the parameters of the efficiency of passive film formation (h, icrit) of the alloy are compared the efficiency of passive film formation is lower in value as comparted to that of 304L stainless steel. Also, protectiveness of the passive film (ipass) from LSV smaller for the alloy is better (|Z| after 10 ks of film growth experiments higher the better) than 304L stainless steel.

In an aspect, the alloy has a lower density than 304K stainless steel (304K has densities <7.8 g/cm³)

In an aspect, the synthesis of the alloy of the present disclosure includes a melting and casting method, i.e., electric arc melting of pure Fe, Cr, Al, Ti nuggets following the alloy composition and then casting the molten alloy into an ingot. The processing step includes heat treating the individual ingots at an elevated temperature (see Table S1) for a set period of time (depends of thickness of the sample, 6 h for our samples) and then to quench into water at room temp. This allows for the retaining of the desired phase formed at elevated temperatures. Illustrative examples of methods of making the alloys of the present disclosure are provided in Examples 1 and 2.

EXAMPLES

Now having described the embodiments of the disclosure, in general, the examples describe some additional embodiments. While embodiments of the present disclosure are described in connection with the example and the corresponding text and figures, there is no intent to limit embodiments of the disclosure to these descriptions. On the contrary, the intent is to cover all alternatives, modifications, and equivalents included within the spirit and scope of embodiments of the present disclosure.

Example 1

Passivation induced corrosion resistance of non-equiatomic BCC Fe—Cr—Al—Ti alloys, including critical passivator concentration, the roles of each alloying element, and possible synergies between the passivating components, i.e., Ti, Cr, and Al are presented. Two solid-solution BCC alloy series: Fe-8Cr-8Al-xTi and Fe-xCr-{16-x}Al-8Ti where x was varied from 0 to 16 at. %, were investigated in acidified 0.1 M Na₂SO_4(aq) solutions. Short and long-term passivation behaviors and oxide passive film chemistry were characterized. Alloys with at least 4 at. % Ti with 8 at. % both Cr and Al; or 8 at. % Ti with a Cr/Al ratio higher than 0.5 exhibited excellent corrosion resistance in pH 1 solution with a lower density than 304L stainless steel. Ti additions to Fe—Cr—Al alloys were predicted to not only function as a passivating species but also to act as a species that alters the chemical short-range order by clustering of Cr—Cr pairs in their 1st nearest neighbors' arrangement. This could be forecast using a “Coherent Ordering Descriptor” based on Monte Carlo simulations supported by the first principles Density Functional Theory calculations. The possibility of a new Ti containing highly corrosion-resistant low-cost stainless steel with only 4 at. % Ti and 8 at. % Cr while using 88 at. % inexpensive Fe and Al is suggested. Two underlying mechanisms describing the enhanced passivation behaviors are discussed based on the chemical short-range ordering of Cr atoms, and passive film stability provided by mixed oxide species, suggesting concepts useful for designing new lightweight corrosion-resistant alloys.

The addition of Cr to Fe-based alloys has been a long-established strategy for ensuring passivity, with a distinct improvement in corrosion resistance at Cr concentrations above 12-13 at. % [1]. Above this threshold, critical concentrations in the alloy are obtained to ensure a Cr-dominated passive film, either through combinations of percolation [2]-[5], preferential oxide film nucleation [6]-[8], and/or incongruent or selective dissolution of iron [9]. Alloying with other passivating elements at low concentrations may exploit elemental synergies to reduce this threshold [4], [10]. However, a mechanistic interpretation of helper passivators in such simplified systems is critically underexplored. The Fe—Cr—Al system is often considered for nuclear applications [11]-[15], being valued for its high-temperature oxidation resistance coupled with corrosion resistance in water at 300° C. [16]. A beneficial “third-element effect” is observed between Cr and Al [17]-[19]. However, the governing mechanism is unknown. One of the mechanisms of Cr—Al synergy might be related to the extensive solid solubility of Cr(III) and Al(III) cations in a common corundum structure to form a mixed oxide. Wagner [20] conjectured that this solubility in oxidation helps in the formation of a uniform protective Al(III) oxide scale as Al(III) can diffuse through the initial (unstable) Cr(III) oxide scale in a Fe—Cr—Al alloy at elevated temperatures [21].

While “third element effects” with Al and Cr oxidation are well studied at high-temperature oxidation whereby adding Cr, Al₂O₃ formation is favored at lower Al concentrations. However, there is little evidence explaining beneficial Cr—Al interactions during room temperature aqueous passivation. Zhu and Zhang [22] suggested the simultaneous addition of 7% Cr and 3% Al to Fe-24% Mn (wt. %) alloys was more beneficial to corrosion resistance in chloride and sulfate solutions than either element's independent contribution. Notably, Auger electron spectroscopy depth profiling revealed outer layer Al enrichment and Cr inner layer enrichment within the passive film formed on the Fe-25% Mn-4% Al-5% Cr (wt. %) alloy in 1 M Na₂SO₄ solution, despite the corundum oxides of Cr and Al having complete solid solution solubility [23]. Rebak et al. [24] evaluated the corrosion behavior of BCC Fe—Cr—Al type alloys produced with powder metallurgy via immersion, polarization, and electrochemical impedance spectroscopy in sulfuric, hydrochloric, and nitric acids. Adjustments in the composition, most noticeably an increase in the Cr content, were shown as a viable strategy for improving passivity and, hence corrosion resistance. Springer et al. [25] surveyed a range of ferritic Fe—Cr—Al alloys via salt spray corrosion testing. The addition of 8 at. % Al lowered the Cr concentration necessary to avoid severe corrosion from 12 to 10 at. %, verifying Al addition can effectively enable the formation of protective oxides despite lower Cr contents. Passive film depth profiling revealed Al outer layer enrichment at low Al concentrations and a homogeneous distribution with Cr at increasing Al concentrations suggesting potential beneficial interactions between these elements. Lynch et al. have shown that Al additions in Fe—Cr—Al alloys suppress the formation of Fe(III) oxides [26].

Alloying Cr and Al-containing Fe-based alloys with small amounts of Ti has also been explored. Luu et al. [27] showed independent 2 at. % Cr, and 2 at. % Ti additions to an ordered Fe₃Al intermetallic improved corrosion resistance by lowering the passive current densities in sulfate and chloride solutions, with Ti having a stronger additive effect than Cr. Likewise, the addition of 2.5 at. % Ti to Fe-40A1 by Diaz et al. [28] increased polarization resistance and pitting potential in simulated human body fluids while an equal addition of Cr had similar effects on pitting potential but increased the rate of uniform corrosion. However, Fe—Ti binary alloy passivation requires a rather high Ti threshold of 18-20 at. % [29]. Fe, Cr, Ti, and Al were all suggested to be present in the passive film. Both Cr and Al doping of a Ti-dominated oxide film have been suggested to improve corrosion resistance [30], [31]. Additionally, significant Al presence has been shown within Ti-dominated films formed on Ti-6Al-4V [32], [33]. Al, Cr, and Ti are often jointly added to multi-principal element alloys targeting corrosion resistance [10], [34]-[44]. While Ti is capable of independent passivation in Fe—Ti alloys [45], [46], it also may coexist in the passive film of such multi-principal element alloys typically as Ti(IV, III) with Cr(III) and Al(III) [10], [43], [44]. Coexistence in the passive film has suggested interaction between the cations, allowing for passivity at concentrations below traditional thresholds for binary alloys [10](i.e., 12-13 at. % for Fe—Cr [1], [3], 15-25 at. % for Fe—Al [47], and 18-20 at. % for Fe—Ti [48]). However, there has been little work to establish whether the behavior indicates synchronous behavior as opposed to mere coexistence and additive benefits.

While Al and Ti may improve the passivity of Fe—Cr alloys, undesirable second-phase formation often constrains practical secondary element concentrations. In particular, increased Al and Ti concentrations can initiate second phases when added to Fe—Cr alloys including FeAl [49], FeTi₂ [49], TiCr₂ [50], Heusler (L₂₁) [49], Ti₅Cr₇Fe₁₇ [51], mixed Laves phases [51], and spinodal clustering during aging [52], [53]. Such phases can lead to increased strength [25], [54] at the expense of decreased ductility [25], [55] and significant localized corrosion [56]. Thus, efforts to evaluate the effect of Ti addition to single-phase Fe—Cr—Al alloys whether multi-principal elemental alloys [57] or conventional solvent-solute alloys would benefit from an understanding of its effects on passivity within composition ranges informed by the well-studied solubility limits of the system [58]-[60].

Micro-alloyed Al and Ti additions in steels have been considered for improvements in physical and mechanical properties, especially in the automotive alloy steel design. [61], [62]. The low density of both elements may decrease alloy density. Al has been added to a series of advanced high strength steels targeting transformation induced plasticity or as grain refiners [62]. Additionally, Al added oxide dispersion strengthened (ODS) steels where Al2O₃ formation at high temperatures has been shown to protect the steel in harsh environments [63] while in aqueous environments Al is beneficial but lacks a mechanistic understanding [64]. However, the additions of Al and/or Ti in low or large contents to steels may promote the formation of undesirable oxide inclusions or other additional phases [65]. Phases such as FeAl (B2 type) and Fe₂Ti (Laves phase) may form with the addition of Al and Ti to Fe—Cr alloys. However, limited research has been conducted on their electrochemical corrosion behavior and aqueous passivation ability.

This example describes the corrosion resistance and interactions between Al, Cr, and Ti in Fe-based tertiary and quaternary alloys. Corrosion behavior in sulfate-containing solutions was evaluated using electrochemical methods and passive film oxide characterization by surface sensitive methods. Two series of alloys, Fe-8Cr-8Al-xTi (at. %), and Fe-xCr-{16-x}Al-8Ti (at. %), where x={0, 4, 8, 12, 16} were studied and compared with 304L stainless steel. Here, the effects of varying Ti content were studied by fixing concentrations at 8 at. % Cr+8 at. % Al, along with the effects of varying Cr/Al ratio with a constant level of 8 at. % Ti in a single-phase microstructure. By varying the composition within these alloy series, this study aims to identify critical thresholds for passivation. Furthermore, passive film oxide chemistry, molecular identity, composition, and depth profiling were evaluated using X-ray photoelectron spectroscopy. Chemical Short Range Ordering (CSRO) predictions were made for each elemental pair in these alloys using first principles Density Functional Theory (DFT) calculations and a newly defined parameter known as the “Coherent Ordering Descriptor” based on Monte Carlo Simulations. Synergistic effects between elements are investigated, offering a framework for understanding passivation when designing future Fe—Cr—Al—Ti containing alloys.

Methods

Experimental

Two series of alloys composed of Fe, Cr, Al, and Ti were fabricated through vacuum arc melting using pure metals (Fe, Al, Ti purity about 99.9%, Cr about 99.2%) and were cast into 1 cm diameter and thickness 5 mm buttons using suction casting. Samples were remelted and flipped five times to ensure homogeneity. The alloys were then solutionized for 6 hours at temperatures across a range 1000-1300° C. and quenched in water to room temperature. Temperatures for solutionizing were selected with ThermoCalc (TCFE9: Steels/Fe-Alloys v9.3 database) to promote a single-phase BCC microstructure while remaining well below the predicted melting temperatures. The alloy compositions and their solutionization temperature are listed in Table 1 with compositions in weight percent listed in Table S1 (FIG. 1.112B). CALPHAD predictions are shown in FIGS. 1.12A and 1.13 of the supplementary material. To prevent extensive oxidation during solutionization, the buttons were encapsulated in a quartz tube purged with Ar gas. As-homogenized samples along with samples of commercial grade 304 L stainless steel (Fe-7Ni-20Cr in at. %, McMaster Carr) and pure α-Ti (purity 99.996%, Fischer Scientific) were epoxy cold mounted. Surfaces to be electrochemically tested were mechanically ground with SiC paper up to #1200 grit and cleaned with iso-propanol. For microstructure and post-exposure surface analyses, up to 1 μm finish was achieved using diamond suspension.

Alloy microstructures were identified from x-ray diffraction (XRD) phase analysis using a Malvern Panalytical Empyrean diffractometer with Cu ka (0.154 nm) radiation at an acceleration voltage of 45 kV and a scan rate of 0.05°/sec. A FEI Quanta 650 field emission scanning electron microscope (SEM) with Energy Dispersive Spectroscopy (EDS) capability was used for phase chemical composition analyses. For Ti-16, where a second phase was observed, the structure was further identified via transmission electron microscopy (TEM) using methods discussed further in the supplementary material.

Electrochemical testing was conducted with a Gamry Instrument Reference 600+TM potentiostat in a conventional three-electrode electrochemical cell having an exposed sample area of 0.06 cm² defined by a rubber O-ring. A platinum mesh counter electrode, mercury-mercury sulfate reference electrode (MMSE, E=+0.640 V vs. standard hydrogen electrode), and the sample as the working electrode was used. All potentials in this Example will be referenced vs. MMSE unless mentioned otherwise. Electrolyte solutions of 0.1 M Na₂SO₄(aq) were made using ultrapure water (Millipore Sigma) and titrated to pH 1, pH 4, pH 7, and pH 10 using stock H₂SO₄(aq) or NaOH(aq). The solutions were continually bubbled with N₂(g) throughout all experiments to minimize the effects of dissolved oxygen. The N₂ bubbling occurred at sufficient distance from the oxide-electrolyte interface to not affect the electrolyte boundary layer. All electrochemical experiments were repeated at least three times to ensure reproducibility.

A series of electrochemical experiments were utilized to evaluate the passivity and overall corrosion behavior of the alloys. First, potentiodynamic polarization experiments were performed for all alloys in the anodic direction from −2.14 V to +0.66 V after cathodically reducing the air-formed oxide at −2.14 V for 120 s. Hydrogen gas bubbles generated on the alloy surface during the cathodic hold as well as at significantly negative (i.e., not affecting the passivity process) potentials of the potentiodynamic polarization experiments were manually removed. In addition to current density, the imaginary component of impedance (Z_imag) was also monitored for every 5 mV using a sinusoidal signal of 20 mV (RMS) and a single frequency of 10 Hz to evaluate qualitative trends in the passive film thickness using relationships developed elsewhere [66]-[68]. In a second procedure, potentiostatic electrochemical impedance spectroscopy (EIS) was performed after the cathodic reduction pre-treatment described above (−2.14 V, 120 s) and a potentiostatic hold of 10 ks at 0 V. A sinusoidal signal of 20 mV (RMS) was applied at a 0 V DC potential across a frequency range of 100 kHz to 1 mHz at 8 points per decade of frequency. Finally, Chronoamperometry was performed for all BCC Fe—Cr—Al—Ti alloys and 304L stainless steel after the cathodic reduction pre-treatment described above (−2.14 V, 120 s). This test was used to calculate the number of dissolved monolayers (h) at an applied potential of −0.7 V, a potential selected to be within the primary passive region for all evaluated alloys while recording the current density of every 0.01 s for 600 s. h was calculated using the relation [3]:

h = ∫ 0 t i · dt [ q · ( 2 · X F ⁢ e + 3 · X C ⁢ r + 3 · X A ⁢ l + 4 · X T ⁢ i ) ρ · a 2 ] - 1 Eq . ( 1 )

where i is the magnitude of current density with time (t=300 s) obtained during the chronoamperometry experiment, q is the electronic charge, x_M is the mole fraction of constituent M in the alloy, P is a constant equal to square root 2/2 for BCC (110) or square root 3/4 for FCC (111), and a is the lattice constant of the alloys calculated using XRD pattern analysis. The BCC (110) close-packed plane was assumed for Fe—Cr—Al—Ti alloys. Given the slight change in lattice parameters of the alloys, it was assumed for all to be equal to 0.290 nm for all alloys. For these calculations, the valence states of Fe, Cr, Al, and Ti were assumed to be +2, +3, +3, and +4 respectively. Alloys with lower h-values indicate rapid efficient re-passivation such that there is less oxidative dissolution required before the accumulation of enough passivator elements on the surface to form a stable passive film [3]. For 304L stainless steel, an FCC close-packed plane (111) and lattice parameter of 0.35 nm was used to calculate h values using Eq. 1. Possible changes in macro-texture do not challenge the qualitative comparisons between alloys evaluated in this work. Oxide passive film chemical compositions were characterized using single-step potentiostatic film growth experiments and x-ray photoelectron spectroscopy (XPS). The alloy surface with a native oxide was cathodically minimized as mentioned above, and then the applied potential was stepped immediately to 0 V vs. MMSE (inside the passive range) and held for 10 ks, as described above. Cationic species in the electrochemically grown passive film for 10 ks at 0 V were analyzed using a PHI VersaProbe-III XPS Analyzer. The instrument was calibrated with an Au standard to the 4f_7/2 core level at 84.00 eV binding energy. C 1s (284.8 eV) was used as a reference to shift spectra. The details of the XPS instrument settings for high-resolution spectra, and sputter depth profiles are available elsewhere [10], [69]-[71], and in the supplementary section. Core-shell spectra of O 1s, Fe 2p_3/2, Cr 2p_3/2, Al 2p, and Ti 2p were deconvoluted to obtain cationic compositions (X^S_M), enrichment factors (f_M) and concentration (relative intensity) depth profiles of the passive films on the basis of binding energy, full-width half-max, and multiplet splitting from reference spectra obtained elsewhere [72], [73]. The procedures for X^S_M, f_M, and concentration calculations along with the steps taken for accommodating the overlap of Cr 3s within the Al 2p spectra are described in the supplementary material.

Computational—Chemical Short-Range Order Derived from Ordering Descriptors

From first-principles, Warren-Cowley CSRO parameters [74], [75] were calculated given the effects of CSRO on corrosion behavior previously established via a percolation model of passivating elements [2]-[4]. For multicomponent alloys, Warren-Cowley CSRO parameters α_ij^p are defined [76] as

a ij p = { P ii ( p ) - c _ i 1 - c _ i , i = j 1 - P ij ( p ) c _ i , i ≠ j Eq . ( 2 )

where P_ij(p) is the conditional probability of finding an atom of type j within shell p, given an atom of type i is at the origin, and c_j is the average composition. In the binary case, the expressions in Eq. 2 are equivalent. CSRO of the experimental compositions was computed using a combination of DFT [77], [78] and Monte Carlo (MC) simulations. MC is frequently used as a statistical sampling technique in combination with a method to evaluate the energies of various solid solution configurations. One such method that can be used is the cluster expansion (CE) [79]-[82], which has been extensively used to study CSRO in a variety of both binary [83]-[86] and multicomponent alloy systems [87]-[90]. The CE is a generalized Ising model that is dependent on many-body clusters (i.e., pairs, triplets, quadruplets, etc.), the weightings of which are usually determined from training on DFT data, that can accurately describe the energy of various atomic configurations. Determination of these effective cluster interactions can be computationally costly, involving hundreds to thousands of DFT calculations for multicomponent alloys, and is subject to complicating factors such as dynamical instabilities [91]-[93] and size-mismatches [29], [85], [94].

Instead, a simplified, first nearest neighbor interaction only, approach was selected based on qualitative ordering types. These ordering types are articulated by Wolverton et al [85]. Namely, the pairwise chemical interactions V are parameterized based on the “ordering energy,” δE_ord=ΔH_R−ΔH_O, and “coherent phase-separation energy,” δE_CPS=ΔE_CS^min−ΔH_R, as described in Ref. [85]. These quantities respectively give the coherent ordering or coherent phase-separation fluctuation tendency of a disordered alloy and thus account for long-ranged strains. This method was hypothesized to capture qualitative alloy behavior at vastly reduced computational cost when compared to the CE (see supplementary material), despite its much more quantitatively approximate nature. To compute δE_ord and δE_CPS, only three energetic quantities are required: (1) The energy of the random alloy, ΔH_R; for this, special quasi-random structures [95] of 16 atoms were calculated, the atomic positions of which are taken from Ref. [96]. (2) The coherency strain energy, ΔE_CS^min as obtained from epitaxial minimization (see, for instance, Refs. [85], [97]). (3) The lowest energy ordered compound at a given composition, ΔH_O. Only the equiatomic binary composition prototypes of B2 (CsCl) and B32 (NaTl) were considered; not only are these commonly stable BCC lattice decorations but they have ordering wavevectors at the special points of the Brillouin zone and are ground states of the Ising model with first and second nearest neighbor pair interactions [98]. The B2 structure has an ordering wave vector at (100), the H point of the Brillouin zone, and the B32 structure peaks at (½½½), the P point. DFT calculations were performed with settings in accordance with the Open Quantum Materials Database [99], [100] standard, the specifics of which are given in the supplementary material.

The chemical pairwise interactions for first nearest neighbors were then taken as V_ij=δE_CPS if ΔE_CS^min<ΔH_O and V_ij=δE_ord if ΔE_CS^min>ΔH_O and are mentioned in Table 2 for each binary sub-alloy of Fe—Cr—Al—Ti system. Thus, V_ij<0 indicates a repulsive (phase separating) interaction while V_ij>0 indicates an attractive (ordering) interaction. The pairwise V_ij were then used to parameterize Monte Carlo simulations of the experimental quaternary alloys and extract CSRO parameters using the Alloy-Theoretic Automated Toolkit (ATAT) code package [101]-[103]. This approach has been termed as “Coherent Ordering Descriptor-based Monte Carlo” (COD-MC). While some comparison of this method to CE approaches is presented in the supplementary material, extensive validation will be deferred to a future paper. Typically, beyond any ordering transition, the magnitude of CSRO decreases as temperature was increased. CSRO values were thus referenced to a constant amount above each composition's respective critical temperature, T_c, which ensured a more equitable comparison of the effect of composition on CSRO. The determination of T_c can be found in the supplementary material.

Results

Alloy Microstructure, Density, and Cost

XRD patterns suggest a single-phase BCC matrix for the majority of the synthesized alloys after the solutionization heat treatments, with additional peaks present only within the Ti16 pattern shown in FIG. 1.1A. Notable texture variations were present within the BCC alloys, however, no clear trends in texture were present with composition. For all the alloys, a minimal variation was observed in their calculated XRD-based lattice parameter of 0.290 nm. XRD phase analyses generally match the calculated CALPHAD microstructures shown in Table 1. SEM imaging and EDS elemental analysis revealed that all single-phase alloys exhibited a homogeneous microstructure and chemical composition, with a representative analysis of Ti8 presented in FIG. 1.1B. For Ti16, second-phase was confirmed to be the C14 Laves phase (Fe₂Ti) through BSE micrographs in combination with elemental mapping and selected area electron diffraction analysis using TEM, see FIGS. 1.14 and 1.15 of the supplementary material. For Ti12, CALPHAD suggests the microstructure to be single phase BCC A2 but small regions enriched in Ti are observed post solutionization at 1300° C. with SEM imaging and EDS mapping, shown in FIG. 1.14 of the supplementary material. These features were only present at grain boundaries at area fractions that were insufficient to be observed in the XRD patterns. This could be due to the very small window between the solidus and solvus temperatures at this composition of ≈5° C., leading to some occurrences of liquidation.

Alloy densities calculated from weighted averages of pure elements densities (see FIG. 1.2A) show decreasing densities with increased Ti and Al concentrations, indicating each element's light-weighting ability. The density of the Fe—Cr—Al—Ti alloys in this Example was found to be within a range of 6.75-7.50 g/cm³, lower than that of 304 L stainless steel which has a density of ≈7.8 g/cm³. Further, the weighted average costs associated with sourcing the alloy compositions using pure element price ($/kg) (see FIG. 1.2B) exhibits an increasing trend with increasing Ti content as well as Cr content despite a decrease in Al content. This is due to the costs of pure Ti which is the most expensive among Cr, Al, and Fe [104]. Despite this, a majority of the alloys showed lower costs than the standard 304L stainless steel ($1.83/kg), except for Ti16. Alloys such as Fe-8Cr-8Al-8Ti (at. %) remained a BCC solid solution (see FIG. 1.1) and produced a weighted average density of ≈7.13 g/cm³ and an average source cost of ≈$1.43/kg.

Chemical Short Range Order from Coherent Ordering Descriptor-Based Monte Carlo

FIGS. 1.3A-B exhibit CSRO parameters for the first neighbor shell, α_ij, of the Al—Al, Cr—Cr, Fe—Fe, and Ti—Ti pairs as a function composition for the Fe-8Cr-8Al-xTi and Fe-xCr-{16-x}Al-8Ti alloys as computed from first principles MC simulations for BCC lattice decorations (i.e., no secondary phases are considered). For fixed Cr and Al contents at 8 at. %, FIG. 1.3A shows α_Cr-Cr is clustering-type (α_ij>0) and slightly increases with Ti addition as Fe is exchanged for Ti up to 8 at. %, after which it decreases in magnitude but remains clustering. Al—Al shows ordering behavior (α_ij<0) with a maximum magnitude at 4 at. % Al after which it decreases but remains ordering. A strong ordering tendency was exhibited by Ti—Ti and Fe—Fe pairs at all compositions. FIG. 1.3B shows that as Al is exchanged for Cr at a fixed Ti content of 8 at. %, there is a relatively constant increase in α_Cr-Cr (becoming more positive) and decrease in α_Al-Al (becoming more negative). This indicates increasing Cr alloy content enhances Cr—Cr pairs to cluster and Al—Al pairs to order which follows previously reported results by Diawara et al [7], [8]. Further, it can be seen that Ti—Ti pairs and Fe—Fe pairs tend to become less ordered.

The observed CSRO effects shown in FIGS. 1.3A-B can be rationalized by considering the coherent ordering tendencies of the binary alloys, given by δE_ord (see Table 2). δE_ord^Fe-Ti is nearly twice as large as the next strongest competing binary δE_ord^Al-Fe and nearly three times larger than δE_ord^Al-Cr. Thus, while most of the binary alloys form ordered compounds, FeTi has by far the strongest coherent ordering fluctuation. Therefore, it seems the strong ordering between Fe—Ti, Al—Fe, and Al—Cr, prevents Cr and Ti from interacting. This is reflected in the ordering-type CSRO parameters for α_Fe-Ti, α_Al-Fe, and α_Al-Cr and the clustering-type CSRO parameters for α_Cr-Ti as given in the supplementary material. This phenomenon of competing ordering pairs inducing clustering of passivating elements has been demonstrated before in FCC (FeCoNi)_1-x-yCr_xAl_y alloys [4].

Al—Ti, which is known to form a variety of ordered compounds, exhibited negligible ordering tendency within our COD-MC model. This is because the known stable ordered phases of Al—Ti are not BCC decorations (e.g., at the equiatomic AB composition, the L1₀ (CuAu) prototype is experimentally observed [105], and DFT predicts L1₀ to be nearly degenerate in energy with the E11 (CuTi) phase [99]), but the simple model used in this work assumed an underlying BCC lattice. It should be noted that lattice-based models like the CE trained only on BCC data would also likely not capture this behavior. Given that the COD-MC model description of the ordering tendency for the Al—Ti pair carried some uncertainty, we investigated the effect of increasing the strength of the V_AlTi interaction. A negligible impact on the calculated CSRO parameters was found, provided this interaction was not significantly stronger than that of Fe—Ti. In particular, the Cr—Cr pair from which the conclusions were drawn via the percolation model [2], [3] was largely unchanged. Given the formation enthalpy of the B2 phase for Fe—Ti is approximately 150 meV/atom lower in energy than that of Al—Ti and the overall convex hull depths are similar [99], it seems unlikely the Al—Ti interaction uncertainty affects the results.

Electrochemical Evaluation

Anodic Polarization

FIG. 1.4A shows the E-log(J) curves of Fe-8Cr-8Al-xTi alloy samples in deaerated 0.1 M Na₂SO_4(aq) pH 4. All E-log(J) plots indicate an active-passive transition, passivity, and onset of trans-passivity at ˜0.5 V. The in-situ monitored imaginary component of impedance (−Z_img) at 10 Hz to measure an impedance parameter proportional to oxide thickness obtained during polarization can be found in the supplementary section. The results generally indicated improved passivity with Ti concentration at a fixed level of 10 at. % Cr regarded as non-passivating [106]. Most alloys demonstrated the ability to passivate prior to transpassive dissolution in upward scans similar to Cr containing binary alloys (such as Fe—Cr). The exceptions were Ti16 and Cr0 with high Ti and Al contents, respectively. Ti8 showed the lowest passive current density (i_pass), defined here as the current density at a 0 V applied potential. All alloys showed a similar corrosion potential (E_corr), and similar cathodic and anodic behaviors near the E_corr. Ti0 and Ti4, alloys with lower Ti levels, showed increased critical current densities (i_crit) at potentials below −0.5 V, suggesting slower passive film formation processes [3]. A significantly stronger trend in passivation behavior with Ti content can be observed in deaerated 0.1 M Na₂SO_4(aq) adjusted to pH 1, as shown in FIG. 1.4B, where Fe-based passive species are thermodynamically unstable. Therefore, passivity is comparatively more dependent on metastable Al, Cr, and/or Ti passive species [107].

E-log(J) plots of the Fe-xCr-{16-x}Al-8Ti alloys with varying Cr/Al ratios and fixed 8 at. % Ti in deaerated 0.1 M Na₂SO₄(aq) adjusted to pH 4 and pH 1 are shown in FIG. 1.4C and 1.4d, respectively. E-log(i) plots for the pure constituent elements under acidic conditions can be found in the supplementary material. In pH 4, current densities in the active-to-passive transition region generally decreased with the substitution of Al with Cr but were still higher than that of 304L stainless steel. Despite higher i_pass values, the −Z_imag for Cr8, Cr12, and Cr4, (i.e., three alloys with both Al and Cr in the passive film), was greater (see the supplementary section). For both electrolytes, minimal changes in E_corr were observed for these alloys in both electrolytes. Further, Ti16 showed an increase in i_pass despite the comparatively lower i_c,magnitude, which suggests a detrimental role of the second phase (C14 Laves) containing microstructure.

FIG. 1.5A-B shows the extracted i_crit and i_pass values determined based on the anodic polarization results in the pH 1 condition. Increased Ti content generally led to a decreased i_crit with minimal changes in i_pass comparable to 304L stainless steel as shown in FIG. 1.5A. An increase in i_pass and i_crit values occurred with a decrease in Cr/Al ratio, as shown in FIG. 1.5B. The alloys Cr8, Cr12, and Cr16 showed similar low i_crit, while i_crit for Cr4, alloy was significantly higher, suggesting a threshold concentration between the Cr4 and the Cr8 composition. Alloys with Cr/Al ratio of greater than 1 indicated an i_crit that was comparable range while the i_pass was very similar to that of 304L. In both electrolytes, Cr16 alloy exhibited the lowest i_pass while those of the Al-rich alloys were generally higher. This potentially indicates a film that was more porous and/or had a higher defect concentration. FIG. 1.5C places into perspective the significant synergistic benefits of Al+Cr+Ti addition to Fe with smaller i_crit values compared to that of binary Fe—Al, Fe—Ti, Fe—Cr, and ternary Fe-10Cr—Al (at. %) alloys in sulfate containing acidified solutions obtained from previous reports. This indicates the quaternary alloy passivated at lower contents of Al, Cr, and Ti below their individual binary critical concentrations required for passivation.

Number of Dissolved Monolayers (h)

FIG. 1.6A shows the calculated values of h for Fe-8Cr-8Al-xTi and Fe-xCr-{16-x}Al-8Ti alloys in deaerated 0.1 M Na₂SO_4(aq) pH 1 following the chronoamperometry procedure discussed above. For the alloys with varying Ti (e.g., ≤16 at. %) and fixed Cr and Al contents, the h values decreased exponentially with increasing Ti content from =600 for Ti0 to =20 or lower for Ti8 (i.e., 8 at. % Ti), Ti12, and Ti16. A threshold type behavior was observed where there is a minimal additional reduction in h above 8 at. % Ti. For alloys with fixed Ti and varying Cr/Al ratio, a similar threshold type behavior was observed with respect to varying Cr where h values decreased from =1500 for Cr0 to less than =20 for Cr8, Cr12, and Cr16. In terms of Cr/Al ratio, h values indicated minimal additional reduction for Cr/Al ratio higher than 1, as shown in FIG. 1.6B. Further, alloys Fe-8Cr-8Al-xTi and Fe-xCr-{16-x}Al-8Ti with x≥8 at. % had lower h values than the 304L stainless steel, indicating that repassivation was more efficient. This suggests that these alloys form passive films more efficiently by requiring fewer monolayers of metal dissolution to reach the conditions where passivation could be obtained similar to that of 304L stainless steel [3], [4].

Passive Film Impedance

FIGS. 1.7A-B show the Bode EIS impedance magnitude (|Z|) and phase (Z_phz) spectra of the passive films of Fe-8Cr-8Al-xTi and Fe-xCr-{16-x}Al-8Ti alloys grown at 0 V in 0.1 M Na₂SO_4(aq), adjusted to pH 1 following the single-step passivation procedure discussed above. The EIS spectra for both series of alloys in 0.1 M Na₂SO_4(aq), pH 4 can be found in the supplementary section. FIG. 1.7C shows the equivalent circuit model (ECM) reported by Jakupi et al. [108] used to fit all the EIS spectra to calculate the polarization resistance (R_p) of the alloy passive films plotted against alloy composition in FIG. 1.7D. Within the Ti series and including 304L, the Ti8 alloy showed the highest R_p, while Ti16 had the lowest R_p and the low-Ti alloys had a similar but superior performance. Notably, for Ti16, the dual peaks in the phase angle plots suggested two distinct constant phase elements (CPEs), which were not detected in the other alloys. Both Cr4 and Cr12, alloys with Cr and Al present at uneven ratios of 1/3 and 3, display inferior R_p and phase angle trends consisting of two time constants, possibly due to separation and oxide layering with different RC time constants in the pH 1 solution [109]. Such behavior was not observed in the Ti8 sample. In pH 1, R_p was noticeably higher for the three alloys with the greatest Cr concentrations, whereas the values for the Al-dominated alloys were significantly lower. Compared to 304L with 20 at. % Cr, alloys with fixed 8 at. % Ti but Cr/Al ratio greater than 1 showed higher R_p with much lower Cr alloying contents, suggesting significant benefits due to the combination of Cr with Ti and/or Al below or better than the classical Fe—Cr threshold of 12-13 at. % Cr.

Alloy Ti8 was further explored for its passivation behavior under different pH conditions. FIG. 1.8A contains the polarization behavior of Ti8, where i_pass was found to be lowest at pH 4, followed by pH 7, pH 10, and pH 1. Despite increases in E_corr, polarization in pH 1 yielded the highest i_pass values, indicating inferior corrosion resistance. Higher i_pass values were attributed to the thermodynamic chemical instability of passivating oxides, in particular those formed with Cr(III), Al(III), and Fe(II) oxides, in strong acids [107]. Likewise, the EIS, after 10 ks of potentiostatic film growth suggested Ti8 had the lowest |Z| at 1 mHz in pH 1 as shown in FIG. 8B. See FIG. 1.23 of the supplementary material for R_p values obtained after EIS fitting using the ECM shown in FIG. 1.7C. R_p was highest under pH 10 conditions, followed closely by pH 4 and pH 7 suggesting slight improvement in performance in increasingly basic solutions. EIS plots of films formed during longer film growth times from 10 s to 100 ks (27.7 h) upon single-step potentiostatic exposure at pH 4 are shown in FIG. 1.8C. Calculated R_p values can be found in FIG. 1.23 of the supplementary material. Both |Z| values at 1 mHz and R_p continuously increases with growth time. Additionally, broad capacitive regions suggested by phase angles approaching 90° indicated the film remained capacitive at lower frequencies, further suggesting a continually improving film in pH 4 sulfate containing environment. Despite evolving time constants, which vary over exposure time, passive film formation time did not appear to affect the number of dominant CPE terms in the Bode plot.

Passive Film Oxide Characterization

The presence of passive species containing Al, Cr, Fe, and Ti cations that are predicted to form on the basis of thermodynamic stability was evaluated with XPS. Fit spectra for films grown on each alloy in the pH 4 solution identified Al(III), Ti(III), Ti(IV), Cr(III), Fe(III) and Fe(II) oxides, Cr(III) and Fe(III) hydroxides and oxyhydroxides, and potentially FeCr₂O₄ spinel in all cases where the mentioned elements were present. Representative spectral deconvolution peak fits from the Ti8 sample are shown in FIG. 1.9, while the same for all the other alloy samples can be found in the supplementary section. Passive film cationic enrichment factor trends for the Fe-8Cr-8Al-xTi and Fe-xCr-16-xAl-8Ti alloys are shown in FIG. 11.0A-B. The cation fractions used to calculate the enrichment factors can be found in Table S2 of the supplementary material. As expected, Ti had a greater cation fraction in the films as well as an enrichment factor, formed on alloys with higher Ti alloying concentrations, and was highly enriched relative to bulk composition (f between 1.5 and 3). While Cr and Fe cation fractions decreased with increasing Ti content, those of Al(III) increased, potentially indicating mixed or complex oxides containing both Ti(IV, III) and Al(III), (FIG. 1.10A).

Furthermore, the passive films of alloys with higher Cr contents (e.g., Cr18, Cr16), except Cr12, contained a proportionally greater fraction of Cr(III) in the passive film (f_Cr≈1.5 compared to f_Ti≈0.5 for Cr16 alloy). A smaller fraction of Ti(IV) was found, indicated by less enrichment (f_Ti≈2.5) relative to the fixed 8 at. % bulk composition (also see Table S2) for alloys with higher Cr/Al ratios. This suggests that instead of promoting Ti presence in the passive film, Cr may effectively compete with Ti, thus reducing its proportion of the overall passive film composition.

XPS depth profiling shown in FIG. 1.11 for the cations of Fe, Cr, Al, Ti, and O suggests but does not prove cationic mixing as opposed to phase separation of oxides within the passive films which would be indicated by a distinct inner and outer oxide marked by separate peaks for each cation. Cationic mixing was further suggested from nearly identical profile peaks with overlapping relative intensity versus depth profiles, but would need additional diffraction data for proof. Sputter profiles of all the other alloys can be found in the supplementary section. In the passive film of Ti-free Ti0 alloy, the maximum Cr and Al signals were also observed at similar sputtering times and the profiles only varied from one another as indicated by a slightly deeper depth of Al(III) oxide distinct from other elements. With gradual increases in Ti concentration, the sputtering depths for which maximum Cr and Al intensities were observed began to differ. However, oxidized Ti appears to occur at similar intensities in both the Cr and Al peak regions. Depth profiles also indicated that the maximum intensities of Ti cations were often observed at similar depths as the maximum Cr intensity. However, oxidized Ti still followed similar concentration profiles as Al at deeper depths. For all alloys, the highest intensity of Fe cations was observed at the minimum sputtering times (i.e. the outer region of the film). Thus, enrichment factors obtained from high-resolution XPS scans, which disproportionately observe photo-electrons from the outer regions of the film, may have slightly over-reported Fe intensities relative to the global film composition.

Discussion

The study shown herein has highlighted three important findings. They are that (i) microstructural effects are important in that the formation second phase can alter the passivation behavior due to the phase partitioning of passivating elements. (ii) in solid-solution alloys, synergistic composition effects are present such as Cr—Cr clustering brought about by effects of other alloying elements, special characteristics of the ‘third’ element effects passive film which cannot be ruled out. Additionally, (iii) the binary alloys Fe—Al, FeCr, and Fe—Ti, or ternary Fe—Cr—Al alloys, are not equal to Fe-8Cr-8Al-xTi and Fe-xCr-16-xAl-8Ti. Consider the findings in FIG. 1.5A-C. The performance of the latter in sulfuric acid cannot be matched by any additive or adaptation of the minimum nor weighted i_crit values based on composition. It is observed that an inexpensive iron base alloy with only 16 at. % as the sum of Ti and Cr behaves similarly to 304L stainless steel containing 20 at. % Cr.

Microstructural Effects

The microstructures of the alloys can be observed to be single phase BCC up to the addition of 8 at. % Ti (see FIG. 1.1 and Table 1). The theoretical maximum solubility of Ti in BCC Fe is estimated to be ˜12 at. %, beyond which the Laves phase (C14, Fe₂Ti type) is expected to follow the CALPHAD predictions (see FIG. 1.12) and confirmed using TEM selected area electron diffraction (see FIG. 1.15). The formation of a second phase can alter the passivation behavior due to the segregation of passivating elements such as Ti[10]. Intermetallic second phases such as the C14 Laves can have a more deleterious effect due to Ti being bound more strongly to Fe than in the solid solution BCC matrix. Such an effect is observed for the alloy Ti16, which showed higher i_pass and a lower R_p after 10 ks compared to the single phase alloys with lower Ti concentrations. Although multiple phases were present in Ti16, the single-phase microstructure of the remaining alloys indicates the observed trends with Ti content are likely governed by either Ti as an agent affecting local CSRO of constituents in the alloy substrate or elemental effects of Ti on passivating Cr and Al-rich oxides.

Thermodynamic and Kinetic Factors Influencing Alloy Passivation

The passivation behavior of the alloys is strongly affected by the thermodynamic stability and formation kinetics of their constituent oxides and hydroxides governed by their potential miscibility, and other factors such as the electrolyte pH and anion. Firstly, Al and Ti, unlike Cr and Fe, can form their oxides at more negative electrochemical potentials than the Fe—Cr—Al—Ti alloys' E_corr. Comparing the formation energies for all the possible oxides such as Fe, Cr, Al and Ti using open source databases [110] shows that Al2O₃ (−3.45 eV/atom) is the most stable compared to TiO₂ (−3.35 eV/atom), Cr₂O₃ (−2.45 eV/atom) and then Fe₂O₃ (−1.65 eV/atom) [99], [100], all of which are stable in pH 4 and 0.56 V vs. SHE according to their pure metal-water Pourbaix diagrams [107]. In addition to single-cation oxide species, multi-cation species such as Ti₂Cr₂O₅ (−2.94 eV/atom), Ti₃AlO (−1.395 eV/atom), FeCr₂O₄ (−2.286 eV/atom), Al₂FeO₄ (−2.806 eV/atom), Ti₂FeO₅ (−2.855 eV/atom), Fe₂TiO₅ (−2.257 eV/atom), Ti₂Fe₂O₄ (−2.315 eV/atom), and Fe₂AlO₄ (−2.238 eV/atom) all have more negative formation energy than the compositionally weighted averages of the pure element oxides and elemental species (i.e., the convex hull) [99], [100]. Thus, the possibility of complex oxides must also be considered. However, the low availability of XPS reference spectra and the difficulty of electron diffraction in thin films renders fitting to many of the complex oxide species listed above impractical.

The miscibility of certain oxides either due to similar crystal structures or comparable ionic radii (substitutional type) might promote oxide stability and better protection aided by the selective absence of excluded weak passivators. Al(III) cations were observed to be enriched in the passive films when there were more Ti(III) and Ti(IV) cations present (FIG. 1.9, 1.10, and Table S2), suggesting Ti sub-oxides such as Ti(III) might be compatible with Al(III) cations and favor oxide miscibility during the passivation. Al2O₃ doped with Ti[111], TiO₂ doped with Al [112], or Cr₂O₃ both by Al[113], or Ti[114] have interesting electronic properties. The electrical conductivity of the mixed oxides is reported to slightly increase when Cr₂O₃ [114] or Al₂O₃ [111] are doped with Ti or TiO₂ when doped with Al[115] or Cr[116]. This is because of cationic vacancy creation in order to achieve charge balance for the oxidation states of Ti⁺⁴ and Al⁺³ and Cr⁺³. Only in the case of Cr₂O₃—Al₂O₃, is the mobility of the mixed oxide expected to decrease as there is no creation of charged vacancy or interstitial to maintain charge balance [117]. This agrees with a comparable R_p observed for single phase Fe-8Cr-8Al-xTi (at. %) alloys with and without Ti added after 10 ks of passive film growth at 0 V, see FIG. 1.7.

Passive film formation kinetics as linked to h and i_crit indicate the elements in combination in Al—Cr—Ti alloys improve self-healing over binary alloys Fe—Cr, Fe—Al, Fe—Ti and ternary Fe-10Cr—Al (at. %) alloys (FIG. 1.5C). The passive film formation is driven by the formation kinetics of the elements and oxides. The more negative corrosion potential of pure Al suggests that Al₂O₃ can be expected to form before Cr and Ti form their oxides in upward scans over the potential range used (see FIG. 1.20). However, all of these alloy components should have significant potential driving for formation based on the performance difference between the applied potential during the LSV (see FIG. 1.20) even at potentials below reversible hydrogen ion/hydrogen evolution potentials. However, the oxide kinetics and dissolution of these pure oxides differ substantially where oxides of Cr and Ti show similar passive current densities that are significantly lower than those of Al, and Fe in acidic media. An example of such a behavior can be observed in Cr0, which shows delayed passivation kinetics (i_crit of 30 mA/cm², h of 1500) in pH 1 even with 8 at. % Ti addition. Thus, it is evident that for all the alloys containing 8 at. % Ti, that some presence of Cr₂O₃ is necessary for rapid passivation, even if Cr concentrations are below the traditionally established 12-13 at. % threshold for Fe—Cr alloys[1].

Effect of Chemical Short-Range Ordering

Following the percolation model for passivation [2], [3] as well as the nucleation and growth models [7], [8], another possible mechanism for the added Ti benefit would be the alteration of CSRO of the primary passivating element in a binary alloy. Individually for each binary combination of Fe-based alloys in the FeCr—Al—Ti system, compared to Cr (12 at. % [1]) in Fe, Al (=25 at. % [47]) as well as Ti (=18 at. % [48]) in Fe have a higher critical passivity threshold required to achieve an Al(III) or Ti(IV, III) oxide rich passive film in acidified sulfate environments. Thus, Cr is the superior primary passivating element. Moreover, Cr can be induced to cluster via Ti as the clustering agent. As observed from the addition of Ti, see FIG. 1.3A-B, only Cr—Cr pairs tend to cluster, while Ti—Ti and Al—Al pairs atoms showed a tendency to order in their 1^st nearest neighbor shell. This scenario would reduce the Cr—Cr nearest neighbor distance, allowing nucleation [7], [8] or percolation of Cr oxides to occur rapidly [2], effectively reducing the alloy dissolution required during the early stage passive film formation process for the same nominal Cr content and achieve faster passivation [118](see FIGS. 1.5A-C and 1.6A-B). Thus, herein, Ti and potentially Al [4], [5] act as the agents for introducing clustering type CSRO in Cr—Cr pairs, decreasing the critical passivity threshold of Cr in these alloys. This indicates the “third element effect” type behavior of Ti on Cr passivation in Fe base alloys, both in the presence or absence of Al in the alloy. [25], [26].

Further investigation into the self-healing ability of Fe—Al—Cr—Ti alloys in chloride containing solutions seems essential, as the constituent oxides particularly TiO₂, more so than Cr₂O₃, and Al₂O₃ demonstrate greater resistance to chloride induced localized breakdown. This complex interplay of these oxides could offer enhanced passive film stability at lower concentrations than those required for individual Al, Ti or Cr passivation in Fe, providing further insights into developing more corrosion resistance against chloride attack.

CONCLUSIONS

Two series of Ti-containing FeCrAl alloys with varying and fixed Cr/Al ratios were synthesized and characterized for structure, chemical short range order, corrosion resistance, and passive film composition in 0.1 M Na₂SO_4(aq) containing solutions. Parameters such as h values, E_crit, i_crit, i_pass, and R_p after 10 ks were used to compare the effects of composition and structure on aqueous passivation over short and long term exposure. The following conclusions were observed and can be used to further study the effect of synergies and designing lightweight corrosion resistant Al—Cr—Ti containing alloys:

The maximum solubility of Ti in the evaluated Fe—Cr—Al alloys herein was found to be 8 at. %. Greater content led to intermetallic formation such as the C14 Laves phase (Fe₂Ti type) in the case of Fe-8Cr-8Al-16Ti, which negatively impacted passivity.

Passivation behaviors of Fe-8Cr-8Al-xTi (at. %) alloys in 0.1 M Na₂SO_4(aq) (both pH 4 and pH 1) were found to be strongly enhanced with Ti additions. With just 4 at. % Ti, 8 at. % Cr and 8 at. % Al, the alloy passivated more efficient (i.e., smaller i_crit and h-values) with increasing Ti content. The passive films grown show better performance in both the short term (i_pass) and long term (R_p after 10 ks exposure) with increasing Ti content, except for 16 at. % Ti. The alloy with Ti at 16 at. % likely leads to the partitioning of passivators to the second phases formed in the microstructure. Moreover, the alloys Fe-8Cr-8Al-8Ti and Fe-8Cr-8Al-12Ti showed greater corrosion resistance in acidified sulfate solutions than 304L containing 20 at. % Cr.

Passivation behaviors of Fe-xCr-{16-x}Al-8Ti (at. %) alloys in sulfate containing acidic conditions (both pH 4 and pH 1) were strongly enhanced by a higher Cr/Al ratio. With increasing Cr/Al ratio greater than 0.5, the alloy passivated with lower i_crit and h-values, and the passive films grown showed better corrosion resistance in both the short term (i_pass) and long term (R_p after 10 ks) testing. A ratio of 8 at. % Cr: 8 at. % Al was found to be the threshold composition such that these alloys with equal or higher Cr/Al ratio showed better corrosion resistance than 304L.

Ti alloying in Fe—Cr—Al alloys functioned as a facilitator of a third element effect for introducing the ordering type CSRO for Al—Al, Ti—Ti, Fe—Fe pairs and clustering type CSRO for Cr—Cr pairs, which can promote faster alloy passive film formation in the Fe-8Cr-8Al-xTi and Fe-xCr-{16-x}Al-8Ti alloys, effectively decreasing the critical threshold of Cr content needed for passivation. Further, Ti, as well as Al, played the role of secondary and tertiary passivators across pH ranges. The alloys with 8% Cr8% Al-8% Ti passivated whereas binary Fe—Al, Fe—Ti, Fe—Cr, and ternary Fe-10Cr—Al alloys required much more i_crit at higher concentrations.

In the absence of Cr(III), Al(III), and Ti(IV) did not appear to exhibit mutual miscibility in the passive films evident from their peak-separated cation depth profiles with subsequent and poor corrosion resistance. However, in the presence of Cr(III), some miscibility was indicated via the XPS sputter depth profiling. Increasing alloy Ti concentrations increased the surface cation fraction of Al in the passive film but decreased the overlap and presence of Cr(III), suggesting a potential stabilization of Al₂O₃ by Ti sub-oxides.

Developing corrosion resistant Fe-based alloys using Al—Ti—Cr, can lead to being lighter and inexpensive than 304L stainless steel. They showed potential in reducing Cr and Ti dependency for passivation by lowering their required alloy concentrations when used in combination with Cr—Ti—Al.

Tables for Example 1

TABLE 1
List of all the Fe—8Cr—8Al—xTi and Fe—xCr—{16 −
x}Al—8Ti alloy compositions and their predicted and observed microstructure
post solutionizing heat treatment at the temperature for which single-
phase BCC structure without melting (when possible) is suggested by CALPHAD.

	Fe	Cr	Al	Ti	Solutionizing	Microstructure	Microstructure
Alloy	(at. %)	(at. %)	(at. %)	(at. %)	Temp. (° C.)	(CALPHAD)	(XRD)

Ti0	84	8	8	0	1350	BCC_A2	BCC
Ti4	80	8	8	4	1350	BCC_A2	BCC
Ti8/Cr8	76	8	8	8	1350	BCC_A2	BCC
Ti12	72	8	8	12	1300	BCC_A2	BCC
Ti16	68	8	8	16	1250	BCC_A2 +	BCC +
						C14 Laves	C14 Laves
Cr0	76	0	16	8	1250	BCC_A2	BCC
Cr4	76	4	12	8	1300	BCC_A2	BCC
Cr12	72	12	4	8	1350	BCC_A2	BCC
Cr16	76	16	0	8	1350	BCC_A2	BCC

TABLE 2
Binary alloys and their ordering tendencies.

Qualitative

Binary Alloy	δEord	δECPS	Ordering Type

AlCr	96	meV/atom	−159	meV/atom	Ordering
AlFe	149	meV/atom	−365	meV/atom	Ordering
AlTi	−21	meV/atom	−428	meV/atom	“Ideal” *
CrFe	−5	meV/atom	−71	meV/atom	Clustering
CrTi	9	meV/atom	−131	meV/atom	Ordering
FeTi	279	meV/atom	−374	meV/atom	Ordering
Bold indicates values taken as pairwise chemical interactions Vij, as determined by min(ΔECSmin, ΔHO) as described in Sect. 2.2, within the simplified nearest-neighbor interaction Monte Carlo model. Positive values of Vij indicate an ordering (attractive) tendency and negative values indicate a clustering (repulsive) tendency.
* AlTi has ΔECSmin > ΔHO, indicating the ordering fluctuation δEordAl—Ti is dominant over δECPSAl—Ti, but δEordAl—Ti is negative.
This could be a result of complications in the structural relaxations due to dynamical instabilities of Ti or the presence of (unknown) ordered BCC lattice decorations lower in energy than the considered B2 and B32 prototypes. We thus set VAlTi = 0 in the Al—CrFe—Ti Monte Carlo simulations. We tested the effect of increasing the strength of this ordering interaction and found negligible impact on our conclusions with the proviso that the interaction is not markedly stronger than that of δEordFe—Ti.

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Supplemental Information for Example 1

TEM Experimental

The transmission electron microscopy (TEM) sample of the Ti-16 alloy sample was prepared via Focused Ion Beam (FIB) lift-out in a Thermo Fischer Scientific Helios UC G4™ Dual Beam system. The lift-out site was selected to ensure the presence of the Fe₂Ti phase, which is not representative of global phase area fractions. A 0.4 μm Pt layer was first deposited with the electron beam operating at 5 keV followed by a 1.5 μm Pt layer deposited with the ion beam operating at 30 keV. The lift-out was cut with a Ga⁺ beam at a 30 keV accelerating voltage, attached to a tungsten lift-out needle, and placed on a copper grid using Pt deposition with the ion beam. The sample was then thinned with subsequent passes at 30 keV followed by cleaning with 5 keV ion beam energy down to a final thickness below 100 nm.

The foil was then transferred to a ThermoFisher Scientific 60-300 kV Themis Z TEM system. The Fe₂Ti phase was first imaged in High-Angle Annular Dark-Field mode (FIG. 1.15A) at a 200 kV and a 350 μA beam current with probe correction. The composition of each phase was confirmed via scanning transmission electron microscopy (STEM) with a Super-X detection system and Velox analysis software (FIG. 1.15B). Finally, selected area electron diffraction patterns (FIG. 1.15C) were collected over an approximately 165 nm diameter region to confirm the Fe₂Ti structure. The diffraction patterns were acquired along specific zone axes of the hexagonal crystal structure.

XPS Experimental

Sputter depth profiles were taken using a 1 keV Ar ion beam over a 3 mm×3 mm area, while capture core shell spectra every 0.25 min using 112 eV pass energy x-rays with 0.2 eV and 50 ms energy and time interval per step, respectively. Kolxpd software was used to peak fit every spectra to obtain area under the peaks corresponding to the species of Fe 2p_3/2[1], Cr 2p_3/2[1] Al 2p [2], and Ti 2p [3]. The Cr 3s overlap in the Al 2p region was also adjusted for every spectra such that Cr 3s region was assumed as one Voigt peak with a fixed area and position in relative proportion to the total area under the peaks of the Cr 2p_3/2 region using the corresponding relative sensitivity factors of these regions [4]-[6].

XPS Analysis: Oxide Surface Cation Fractions

To obtain the oxide cation fractions from the surface XPS core-shell spectra peak fitting, first the relative contributions (R_MS) of each metal constituent M, where M: {Fe,Cr,Al,Ti} were calculated by dividing the area under the peaks from Fe 2p₃n, Cr2p₃₂, Al 2p and Ti 2p₃₂ by its corresponding relative sensitivity factors, as listed in below.

• • Fe 2p_3/2: 1.964
  • Cr 2p_3/2: 1.623
  • Cr 3s: 0.08
  • Al 2p: 0.256
  • Ti 2p_3/2: 1.385

Next, to achieve oxide cation composition of each metal constituent (χ^S_M) in the passive film, individual relative contributions are divided by the total contribution from all the constituents as shown below.

χ M S = R M S ∑ R M S ( 1 )

here, M={Fe,Cr,Al,Tl}

The enrichment factor (f) described in the manuscript FIG. 1.9, was determined as the ratio between the surface cation fraction (χ^S_M) and bulk microstructural composition (x_M) as shown below:

f M = χ M S χ M ( 2 )

TABLE S2
XPS based passive film cation fractions (mol. %) obtained for the
Fe—8Cr—8Al—xTi and Fe—xCr-{16 − x}Al—8Ti (at. %) alloys
after 10 ks of potentiostatic hold at 0 V vs. MMSE
in deaerated 0.1M Na2SO4 adjusted to pH 4 using H2SO4.

	Alloy	Fe	Cr	Al	Ti

	Ti0	89	11	0	—
	Ti4	65	19	4	12
	Ti8/Cr8	45	27	8	20
	Ti12	64	12	6	18
	Ti16	39	15	10	35
	Cr0	50	—	10	40
	Cr4	72	6	3	19
	Cr12	25	29	8	38
	Cr16	71	24	—	5

DFT Settings: DFT calculations were performed using the Vienna Ab-initio Simulation Package (VASP) [7]-[10]. The projector-augmented wave (PAW) method [9], [11] and the Perdew, Burke, and Ernzerhof (PBE) implementation of the generalized gradient approximation (GGA) exchange-correlation functional [12] were used. A plane-wave energy cutoff set at the maximum defined by the VASP potentials for a given element in the structure (VASP INCAR tag PREC=ACC) was used during relaxation, with the final static calculation using an energy cutoff of 520 eV. Methfessel-Paxton smearing of order 1 [13] with a smearing width of 0.2 eV was used. Gamma-centered k-point grids of 6000 k-points per reciprocal atom (KPPRA) were used during relaxation, and grids of 8000 KPPRA were used during the final static calculation. Calculations were initialized ferromagnetically with initial magnetic moments of 5 μ_B for all elements with 3d electrons.

REFERENCES FOR EXAMPLE 1 SUPPLEMENTAL INFORMATION

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Example 2

The emergence of compositionally complex alloys (CCAs) and phase-predictive software has enabled the microstructure-informed optimization of corrosion-resistant elements to promote stainless behavior. The relatively high solubility of lightweighting elements (LWEs) Al, Si, and Ti in face-centered cubic (FCC) CCA microstructures offers a promising path toward lower-density austenitic alloys. In this Example, a set of single-phase FCC alloys based on Ni₄₃Fe₃₇Cr₁₀—(Al,Si,Ti)₁₀—excluding Mn and Co—was designed using high-throughput CALPHAD modeling and fabricated via arc melting. This composition space enabled a controlled study of LWE influence on relevant properties while maintaining chemical homogeneity. LWE additions reduced density and increased hardness relative to a control alloy without LWEs, with Al and Ti producing the most pronounced effects on each property, respectively. Two key electrochemical parameters—passive film growth rate and resistance—were quantified, with Ti showing the strongest per-atom effect: a greater than 10-fold increase in film resistance and 4-fold increase in growth rate relative to the control alloy. Both unsupervised machine learning methods applied on XPS results and elemental dissolution rates determined in operando reveal rapid surface enrichment by Si and Ti, likely retarding early-stage electrochemical dissolution of non-passive elements and providing mechanistic insight to the observed bulk LWE enhancement of passivation kinetics and charge efficiency. Finally, unsupervised clustering analysis identified simple quantitative design rules for corrosion: Ti greater than 3 at % promotes both fast film growth and higher passive film resistance, while Si greater than 5 at % or Ti at 3 at % yields rapid growth but lower resistance.

Introduction

Compositionally complex alloys (CCAs) are a class of alloys characterized by the presence of multiple elements at substantial concentrations such that traditional solvent/solute descriptors of alloys are no longer sufficient [1]. By including more elements in a given alloy composition, the configurational entropy of the alloy is increased relative to that of a traditional alloy made up of one principal element. This increase in entropy allows for the enhanced solubility of species often only microalloyed in traditional alloys, such as Ti in steel added to reduce the effect of Cr carbide sensitization through TiC formation [2]. CCAs offer a way to design new alloys which take advantage of multiple elemental effects simultaneously, and many alloys have been developed for enhanced mechanical strength [3, 4], thermal stability [5, 6], and corrosion resistance [7, 8, 9]. In parallel, many CCA designers have turned to this alloy design strategy for lightweighting, or reducing the density of a high-performance alloy through the introduction of elements with low density, or lightweighting elements (LWE) [10, 11]. The practical benefits of light-weighting alloys such as steels or Ni-based alloys are myriad and especially potent in the transportation sector, as lighter-weight vehicles require less force (and therefore fuel) to accelerate. One application of particular interest is the design of lighter alloys for use in corrosive environments such as seawater and harsh chemical storage containers.

For structural components, a ductile face-centered cubic (FCC) matrix phase is highly desirable due to the large number of accessible crystal slip systems, allowing for greater alloy ductility and a reduced likelihood of sudden, catastrophic, and brittle failure. Traditionally, Fe, Ni, and Co are used as FCC “matrix elements”—i.e., elements which stabilize the FCC phase, and Al also adopts the FCC structure in Al-based alloy systems [12, 13]. To impart corrosion resistance to these matrix elements (particularly when employing “phase stabilizers” Fe, Co, and Ni), Cr is added, as Cr forms a passive protective oxide over the alloy, protecting the corrosion-prone matrix elements from further dissolution. However, although Al itself is mildly corrosion resistant and adopts the FCC structure as an element, other corrosion-resistant species, such as Cr, reflect sparing solubility within FCC Al when utilized as a solute element as in stainless ferrous alloys [14]. Furthermore, although Co forms the FCC phase at high temperatures, it is often prohibitively ex-pensive for large-scale adoption and is impacted by human rights violations in mining Co ore [15]. Therefore, in this Example, Fe and Ni were employed for FCC stabilization, FCC matrix elements on which many commercial alloys rely for phase stability and which allow appreciable Cr and LWE solubility. Using this initial design constraint, the only LWEs with consequential solubility and relative environmental abundance within these matrix elements are Al, Si, and Ti, greatly narrowing the elemental palette of interest.

Furthermore, these LWEs tend to form protective passivating oxides in their own right, and exploiting the combinatorial effect of a Cr+LWE-based film has been a recent design strategy to enhance alloy corrosion resistance while also synthesizing a lower-density alloy [16, 17, 18, 19, 20]. Al and Ti-based alloys, primarily used for aerospace and biomedical applications, respectively, are known to be inherently corrosion resistant due to the formation of alumina and titania passive oxide films [21, 22]. Si, being a brittle metalloid not suitable for structural applications, nevertheless displays a silica passive film that has been long exploited in the electronics industry to create high-impedance patterns on printed circuits, protecting the underlying circuit from electrical shorts and chemical attack [23]. Therefore, the co-utilization of Cr (as the primary passivator), already used for corrosion resistance, and such LWE (also termed secondary passivators, third elements, or promoters [24, 25, 26]) which strongly passivate in their own right is an attractive prospect, assuming that all species are dissolved in the same phase in a high enough amount to be a meaningful secondary passivator.

To aid in the development of alloys of a desired microstructure, the thermodynamic framework known as the CALculation of PHAse Diagrams (CALPHAD) has emerged as a critical tool to predict the phase stability of a given alloy composition at a given temperature or temperature range [27, 28]. This predictive method has facilitated the targeted design of alloys that incorporate Cr and LWE into an FCC matrix without generating second phases that may confound the observed increase or decrease in the resistance to corrosion imparted by LWE [9, 29, 30, 31]. However, few studies exploring the corrosion resistance of Cr+LWE CCAs while controlling for structure have been published.

The enhancement of corrosion resistance through the addition of Cr in ferrous and Ni-based alloys has been extensively studied, and a traditional critical Cr concentration threshold of approximately 12 at % has been observed to impart corrosion resistance in acidic environments, with concentrations less than 12 at % showing incomplete or insufficient protection [32, 33]. This threshold has been observed to be lower if other passivating species are present [24, 26]. Many Cr-containing FCC CCAs have been developed in accordance with (though not defined by) the traditional threshold, including the original Cantor alloy (CoCrFeMnNi), which contains 20% Cr [34, 35]. On one hand, such heavy Cantor-adjacent alloys display strong passivating films and general corrosion resistance, but are not designed with reduced density in mind. On the other, lightweight (ρ<5 g/cc) multiphase alloys based on an AlTiVCr composition space have been developed which similarly display strong corrosion resistance (containing 25% Cr), but lack the ductile FCC matrix so desirable for structural applications.

Next, the corrosion effects of utilizing binary combinations of Cr and Al, Si, or Ti in amounts exceeding the single-phase solubility limits have been explored in some select systems [9, 36, 37, 38]. In most cases, the generation of the second and third phases has been shown to be detrimental to corrosion resistance through the formation of a corrosive galvanic couple between phases of dissimilar nobility or the sequestration of primary or secondary passivating elements into one phase to the detriment of other phases [9]. A set of alloys based on AlxCoCrFeNi demonstrated a reduction in corrosion resistance with an increase in Al concentration, due to further Al additions stabilizing a second phase that was depleted of Cr [9, 36]. In such alloys where LWE additions induce second phases which either sequester Cr, protecting the matrix phase, or themselves lack Cr, any possible benefits of copassivating LWE are confounded by either phase being depleted of Cr below the threshold necessary for Cr passivation. Similarly, the addition of Ti to a CoCuFeNiMn composition indicated a decrease in corrosion performance as the addition of Ti increased, due to the formation of a second Ti-rich phase that formed a galvanic couple with the FCC matrix [37]. Finally, the addition of Si to HEA for corrosion resistance has not been extensively studied to date. A pair of alloys AlCoCrCuFeNiSix demonstrated a possible increase in corrosion resistance with increasing Si addition, but the lack of additional alloys in this set (including an x=0 at % Si alloy) makes this assertion difficult to make confidently [38]. Although such exploratory studies are necessary to probe the phase stability of early CCA compositions, no studies seeking to leverage the enhanced phase stability of CCAs and recent advances in CALPHAD technology to explore Cr+LWE passivation while controlling for a single-phase microstructure or consistent matrix composition have been reported. The utilization of such predictive methods toward the end of devel-oping consistent test sets for the determination of alloying elements' effects represents a largely unexplored opportunity for the eventual development of optimal CCA compositions.

In this example, a consistent alloy set was designed around the stoichiometry NiaFebCr₁₀AlxSiyTix, where a+b=80 at % and x+y+z=10 at %. This alloy platform was designed to maintain a reasonably large testable range of LWE while limiting the amount of Ni, the densest element in the system. The amounts a and b of Ni and Fe (respectively) in the base of the alloy set were chosen to dissolve binary combinations of LWE summing to 10 at % in the austenite phase without generating confounding second phases. Here, the microstructure was held as an experimental constant to consistently explore the effects of LWEs on physical properties, such as density and hardness, as well as on aqueous passivation. The primary objective of this Example is to develop initial design rules and considerations for the addition of these LWEs to an FCC matrix for both enhanced corrosion resistance and lightweighting using unsupervised data science methods confined to a consistent data set. Toward this end, alloys were fabricated, homogenized, and tested using Vickers microhardness and the Archimedes method of density measurement. In addition, a suite of electrochemical techniques, including in-operando atomic emission spectroelectrochemistry (AESEC), were utilized in order to generate consistent and descriptive corrosion parameters that can be further analyzed and compared in compositional variations to develop quantitative design rules. Furthermore, the composition of the passive films of select alloys was analyzed using ex situ X-ray photoelectron spectroscopy (XPS). The combination of in-operando measurements, observed corrosion predictors, and passive film compositional data was used to discern whether the presence of a given LWE oxide species imparts inherent benefits to the growth speed of the passive film (self-healing rate) and its impedance, or whether any benefit of a given LWE is due to the enhancement of the Cr content in the passive film. This family of alloys is intended to provide an introduction to the rational co-design of lightweight, ductile, and corrosion-resistant alloys using CALPHAD and the LWE design rules developed herein.

Experimental Methods

CALPHAD Calculations

Equilibrium information derived from the CALPHAD methodology was used to design the alloys of this study (as described herein). CAL-PHAD was employed in large part due to its rapid computational time (1-4 alloys/s), making it a powerful high-throughput tool for the prediction of important parameters, including, but not limited to, phase stability and solidus temperature. To make use of the computational speed of CALPHAD, single-point equilibrium calculations using the TCHEA3 database were run for a set of discrete compositions at the chosen homogenization temperature, as well as at the solidus temperature of each composition, discussed in more detail in herein. These calculations yield the equilibrium phases of the given composition under atmospheric pressure and at either the user-defined homogenization temperature or the material-defined solidus temperature. The homogenization temperature calculations were used to design the alloy platform (described herein). The solidus temperature was chosen as the temperature at which a given alloy would have the largest probability of showing a disordered single-phase microstructure because of the maximization of the entropic energy-saving contribution to mixing free energy, −TS. More specific details on this method can be found in herein.

Alloy Design, Synthesis, and Microstructural Characterization

To control for structure and auxiliary elemental effects, a general com-position of Ni_aFe_bCr₁₀Al_xSi_yTi_x, where a+b=80 at % and x+y+z=10 at % was designed subject to maintaining a solubility of LWE Al, Si, and Ti in binary combinations limited as a sum to 10 at %. These a and b values were calculated using the CALPHAD method (also described above), employing Thermo-Calc software to determine a pair (a, b) which leads to wide (deltaT>100 K) single-phase temperature ranges for all combinations of Al, Si, and Ti adding to 10 at %. Ni was minimized (subject to previously mentioned phase stability concerns) to minimize the resulting alloy density. Cr was limited to 10 at % in order to highlight the specific effects of LWE on passivation within a subcritical alloy, where Cr is kept below its traditional percolation threshold in binary and ternary alloys [32, 33]. This design process led to a “platform” composition of Ni₄₃Fe₃₇Cr₁₀, to which any binary combination of Al, Si, and Ti summing to 10 at % could be added, and homogenized to form a single phase microstructure. Thus, the complicating effects of two-phase corrosion metallurgy are avoided, and protection is conferred by the passive film, which regulates dissolution.

Once designed, thirteen alloys with the general composition of Ni₄₃Fe₃₇Cr₁₀Al_xSi_yTi_x, where x+y+z=10 at % (specific compositions listed in Table 1) were made into samples of 1 cm diameter by arc-melting high-purity elements under an argon atmosphere. The samples were flipped and remelted at least five times to ensure complete melting. The samples were then encapsulated in quartz purged with Ar gas and homogenized at 1150 C for either 24 hours (for all samples except Si₅Ti₅ and Si₇Ti₃) or 72 hours (for samples Si₅Ti₅ and Si₇Ti₃) before quenching in room temperature water. Also, a sample of 304L stainless steel was acquired from McMaster-Carr to serve as a relevant industrial stainless alloy comparison.

TABLE 1
Targeted alloy compositions and their abbreviated names considered
in this study, alongside their measured densities.

Alloy	Ni	Fe	Cr	Al	Si	Ti	Density
Name	(at %)	(at %)	(at %)	(at %)	(at %)	(at %)	(g/cc)

Si10	43	37	10	0	10	0	7.92
Al3Si7	43	37	10	3	7	0	7.79
Al5Si5	43	37	10	5	5	0	7.78
Al7Si3	43	37	10	7	3	0	7.69
Al10	43	37	10	10	0	0	7.51
Al7Ti3	43	37	10	7	0	3	7.56
Al5Ti5	43	37	10	5	0	5	7.69
Al3Ti7	43	37	10	3	0	7	7.73
Ti10	43	37	10	0	0	10	7.82
Si3Ti7	43	37	10	0	3	7	7.87
Si5Ti5	43	37	10	0	5	5	7.92
Si7Ti3	43	37	10	0	7	3	7.87
Al0Si0Ti0	48	42	10	0	0	0	8.06
304L	7.5	73.3	19.2	0	0	0	8
Inconel625*	59.0	5.3	24.4	0.9	1.1	0.5	8.44
Comparable corrosion-resistant alloys 304L (McMaster-Carr) and Inconel 625 are included as density comparisons. EDS-measured compositions can be found herein. Alloys were homogenized at 1150° C. for 24 hours (all samples, barring Si5Ti5 and Si7Ti3) or 72 hours (samples Si5Ti5 and Si7Ti3).
*Inconel 625 also contains 5.5 at % Mo, 2.3 at % Nb and 1 at % Co.

Following homogenization, the compositions and microstructures of the samples were characterized using a scanning electron microscope (SEM), equipped with energy-dispersive X-ray spectroscopy (EDS). SEM and EDS analysis was performed using the FEI Quanta 650 and Thermo Scientific Phenom XLG2 scanning electron microscopes in backscattered electron imaging (BEl) mode. The images and EDS elemental maps were acquired with a consistent accelerating voltage of 15 keV and a working distance of roughly 10 mm for the Quanta 650 or 6 mm for the Phenom XLG2, according to each machine's specifications. EDS maps and point measurements were analyzed using Oxford Instruments Aztec software, and multiple EDS map measurements were performed on each alloy at different locations in the sample to confirm the bulk composition. Although chemical inhomogeneity along the grain boundaries was not observed at the SEM level, TEM imaging and EDS analysis were performed to confirm chemical homogeneity in regions close to the grain boundaries. The results of this TEM analysis, where homogeneity across a grain boundary is observed, can be seen in herein. Phase analysis of X-ray diffraction (XRD) patterns was performed using a Bruker D2 Phaser X-ray diffractometer which utilizes Cu Kα radiation (λ=1.54 Å). The scans were completed between 20° and 120° with a step size of 0.01°/step and a dwell time of 0.1 s/step. Peaks were indexed using Python, utilizing peak finding packages to identify peaks and Bragg's law to confirm that all peaks indeed belong to an FCC crystal structure with the same lattice parameter. The estimated lattice parameters were then compared with the FCC Fe and Ni lattice parameters to ensure that the lattice parameters were approximately a Vegard's law average of the FCC Ni and Fe lattice parameters.

Evaluation of Density and Hardness

Following microstructural evaluation, density and hardness were measured. The density of each of the alloys was measured in a microbalance using a standard Archimedes setup, measuring each sample's dry mass (m_dry) and mass suspended in DI water (m_sub) multiple times to ensure accuracy. The alloy density was then calculated using Equation (1), derived from a buoyancy force balance.

ρ = ρ H 2 ⁢ O * m dry m dry - m s ⁢ u ⁢ b ( 1 )

Alloy hardness was measured using a Tinius Olsen Hardness Tester, initialized to measure Vickers microhardness under a load (P) of 0.5 kgf (HV0.5). Prior to hardness testing, samples were polished to a #1200 grit. Indents were taken throughout the sample using an inverted pyramid with an angle (α) of 136° between adjacent faces. Indents were taken far from each other to ensure independent measurements. Resulting indents were measured in situ using Tinius Olsen software and an optical micrograph, adjusting the indents' vertices when necessary. These width and length measurements were used to calculate an average diagonal length (d, in mm), which is related to hardness through Equation (2) from ASTM E92-23 [39]. Each sample received a minimum of 5 indents for accuracy and to develop a statistical distribution of values.

H ⁢ V 0 . 5 = 2 ⁢ P ⁢ sin ⁢ a 2 d 2 ( 2 )

Electrochemical Corrosion and Passivity Characterization

The corrosion behavior and performance of the alloys were characterized using a standard three-electrode cell, with potential controlled by either a Gamry Instrument Reference 600+ potentiostat or a Biologic SP-300 potentiostat. The experimental design focus was on passivity, as this phenomenon regulated corrosion in this set of alloys in the chosen harsh sulfuric acid environment. A platinum counter electrode, saturated mercury-mercurous sulfate reference electrode (+0.640 V versus SHE), and an electrolyte of 0.1 M H2SO4 with a pH of approximately 0.76 were used for all experiments, and the sample exposure area was controlled using a circular rubber O-ring, with an area of 0.062 cm². Furthermore, N₂ gas was bubbled during all tests to maintain the hydrogen evolution reaction (HER) as the dominant cathodic reaction, as any dissolved O₂ could lead to the oxygen reduction reaction (ORR) becoming a second prevalent cathodic reaction, potentially confounding kinetic analysis.

Prior to all electrochemical testing, any surface oxide formed as a result of atmospheric exposure was reduced and removed electrochemically by applying a series of cathodic potentiostatic holds. A bias of −0.76 V_SHE was applied for 300 s, followed by a hold at −1.26 V_SHE for 3s, before a final bias of −0.76 V_SHE, which was applied for 60 seconds, as in Xie et al. [33]. Variable-frequency impedance measurements were taken after the application of this procedure to ensure that the low-frequency magnitude of the impedance across the metal-solution interface was approximately equal to the system's measured high-frequency impedance, indicating the complete reduction and lack of any protective film.

First, potentiodynamic polarization was employed to confirm the formation of passive films on the surface of the alloys under an anodic bias. After the application of the previously mentioned oxide reduction holds, the sample's open circuit potential (OCP) was measured for 3 s, then the sample's potential was varied between −0.05 V relative to the sample's open circuit potential to +1.24 V_SHE, with a scan rate of 1.667 mV/s (100 mV/min).

The passivation efficiency, represented by the number of dissolved mono-layers needed to percolate a passive film, was characterized through chronoamperometry, as described by Xie et al. [33]. After the application of the previously mentioned oxide reduction routine, the potential was increased to 0.15 V_SHE, a potential chosen to be representative of early (or primary) passivation, and the current response was measured for 300 s with a sampling period of 0.01 s. This rapid measurement time for a given alloy has led h to be considered as a high throughput (HtP) experimental measure of bulk alloy corrosion resistance. The integral of this current with respect to time represents the total charge passed during passivation and can be converted to the number of monolayers dissolved through Equation (3), assuming an FCC (111) plane as the exposed face:

h = 3 2 ⁢ a 2 ⁢ ∫ i ⁡ ( t ) ⁢ dt 2 ⁢ e ⁢ ∑ z i x ⁢ i ( 3 )

where α is a FCC lattice constant, calculated using XRD, i is the measured current density, e is the elementary charge, and zi and xi being a species i's assumed valence and bulk concentration in at %, respectively. All alloys had nearly identical measured lattice parameters, close to a Vegard's Law ap-proximation between FCC Ni and Fe, so the same value of 3.595 Å was used for all alloys. A +2 valence was assumed for Fe and Ni and a +3 valence was assumed for Cr, as described in Xie et al. [33]. A +3 valence was assumed for Al and a +4 valence was assumed for Si and Ti, based on their most commonly observed valence and in accordance with the respective Pourbaix diagrams of Al, Si, and Ti for the conditions (pH and potential range) of this study. The h value is intended to be used as a structure- and composition-controlled parameter that describes the ease of an alloy in self-healing during sudden loss of film, such as during localized corrosion or mechanical damage. Finally, passive film growth kinetics and impedance were characterized using potentiostatic single-frequency electrochemical impedance spectroscopy (SF-EIS) and variable-frequency electrochemical impedance spectroscopy (EIS).

Following oxide reduction, the applied potential was increased to 0.15 V_SHE, and a single frequency potential wave was applied with a frequency of 5 Hz and an amplitude of 10 mV_RMS each time step, similar to analyses reported elsewhere [8, 40, 25, 26]. A frequency of 5 Hz was chosen to generate a maximally complex impedance response, allowing the resulting Z_imag measured to be proportional to film thickness, similar to a parallel plate capacitor [41]. From this, the complex impedance of the film and the AC current passing through the surface were measured as a function of time for 10 ks. However, this proportionality is subject to a number of assumptions, including a constant permittivity, making the specific −Z_imag values found imprecise and subject to variation from test to test. Although the specific maximum −Z_imag values varied from experiment-to-experiment, this data was used in order to define a time constant for the alloys. This was performed by finding the time t_0.5 where the alloy's complex impedance is half of the final (max) value. Thus, a consistent metric for film growth speed can be determined from in-consistent and qualitative data, and a distribution of t_0.5 values measured relative to the specific final −Z_imag values can be ascertained.

Following 10 ks of monitored oxide growth, potentiostatic EIS was completed in a wide frequency range at 0.15 V_SHE, applying a potential wave with an amplitude of 10 mV_RMS in a frequency range of 100 kHz to 10 mHz, with 8 measured points per decade of frequency. The complex and real impedance components of the grown film were measured as a function of frequency. Following spectrum measurement, the resulting spectra were fit using a representative circuit (FIG. 2.8g), and Rp was calculated as the sum of the charge transfer resistance of the metal/film/electrolyte interfaces (from mass conservation) and film (R_fle and R_f, respectively, from FIG. 2.8g) following Sur et al. and others [26, 42]. The fitting was performed with Python and the same circuit was utilized for all alloys to facilitate com-parison [43]. Fitting was performed in order to separate charge-separative and local diffusion-related components (represented by the constant-phase elements (CPE) and Warburg elements) from the resistance to charge transfer from bulk solution to the bare metal surface, a proxy parameter for describing a film's strength or resistance in protecting the bare metal from further corrosion, mathematically represented by resistors with purely real impedance.

Atomic Emission Spectroelectrochemistry (AESEC) Analysis

Specific elemental dissolution rates (vM) of Ni, Fe, Cr, including Si and Ti, were tracked for samples Al0Si₀Ti₀, Si₁₀ and Ti₁₀ during linear sweep voltammetry (LSV) in deaerated 0.1 M H₂SO₄, using an on-line inductively coupled plasma atomic emission spectrometer (ICP-AES, Horiba France, Ultima 2C), also known as atomic emission spectroelectrochemistry (AESEC), as described elsewhere [44]. A polychromator with a focal length of 0.5 m and a monochromator with a focal length of 1.0 m were used to detect elements dissolved in the electrolyte. Cr signal at 267.72 nm was obtained by the monochromator to achieve a better detection limit. Emission intensities at characteristic wavelengths of each element were used to calculate equivalent dissolution rates and the convoluted current density (i*e) elaborated further elsewhere [44]. Congruent dissolution rates (v_cg) for Fe, Cr, Si and Ti were calculated assuming that Ni undergoes congruent dissolution for all potentials using the following relation.

v M c ⁢ g = X M X N ⁢ i · v N ⁢ i ( 4 )

where XM is the mole fraction of metal ‘M’. The difference between the congruent and actual dissolution rate would indicate the enrichment rate of the element, and the area between the curves would indicate the elemental enrichment (ΘM) at the surface. The percentage of elemental enrichment (Θ′M) is normalized to the total congruent dissolution of the element as described below:

% ⁢ Θ M ′ = { 1 - ∫ a b v M ⁢ dt ∫ a b v M c ⁢ g ⁢ dt } × 100 ⁢ % ( 5 )

here, a and b are the lower and upper time limit values that represent the active-to-passive transition region for all CCAs. In potential terms, this region is defined from the corrosion potential (E_corr) to +0.6 V. This specific region was chosen to calculate the 8 M of Cr, Si, and Ti during the early-stage alloy passivation of select alloys.

XPS Analysis of Passive Film

CCAs Al0Si0Ti0, Al₁₀, Si₁₀, Ti₁₀, Al₅Ti, Al₅Si_s and Si₅Ti_s were selected to characterize the composition of the film grown on a cathodically reduced surface for 10 ks at +0.15 V_SHE using X-ray photoelectron spectroscopy (XPS). Following the aforementioned film growth procedure, the samples were rapidly transported to a PHI VersaProbe III XPS system under a N2 atmosphere to minimize atmospheric effects on the oxide. High resolution scans were taken using Al source X-rays (1468.7 eV) of the O 1s, C 1s, Ni 2p3/2, Fe 2p1/2, Cr 2p3/2, Al 2p, Si 2p and Ti 2p (when present) core shells, with a 26 eV pass energy, 0.05 eV step size and 100 μm spot size.

The resulting spectra were fit using KoIXPD software, first employing a Shirley background substitution, then utilizing Voigt peaks for nonzero-valence cation peaks, and Doniach-Sunjic peaks for zero-valence (metal) species peaks. Peaks were defined using reference spectra obtained from various trusted sources, using the sources' binding energies (graphically rep-resented as peak positions), widths, amplitudes, and multiplet splitting (indexing peaks relative to each other) to ensure the physical meaning of the resulting fits [45, 46, 47]. Finally, the total intensity of each oxidized species (li) was normalized relative to that species' relative sensitivity factor (Ri) using Equation (6). Once all species were normalized, the total cation fraction of each metal species was similarly calculated by dividing the species' normalized intensity by the sum of all other normalized intensities.

X M S = I M R M ∑ I i R i ( 6 )

Results

Microstructure

FIG. 2.1 displays the XRD patterns of all CCAs explored in this study. The spectra reflect a single-phase microstructure for all of the alloys, with no obvious second-phase peaks. However, after further SEM examination, a small distributed particulate phase with an approximate composition of Ni2SiTi was observed in Si5Ti5 and Si7Ti3. The relatively small volume fraction of the particles, evidenced by the absence of identifiable XRD peaks and confirmed through SEM image analysis, combined with testing in non-localized corrosion-inducing environments, minimizes the electrochemical im-pact of this second phase. A further evaluation of the stoichiometry, phase, and volume fractions of the particles found in these two samples can be found herein, and follow-up studies on the effect of the particulates on the corrosion properties in localized corrosion-inducing environments are in progress.

All other alloys in this set presented a single phase homogeneous solid solution microstructure determined by XRD and SEM, and an example single phase SEM/EDS map, representative of all samples excluding Si5Ti5 and Si7Ti3, can be seen in FIG. 2.2.

Density and Hardness

FIG. 2.3a reports the density of the alloys as a function of LWE con-centration. Results indicate that all LWE additions lower the overall alloy density. Moreover, Al is more effective in lowering alloy density relative to Si and Ti. Between Al and Ti, this trend can be explained by taking into consideration the higher density of elemental Ti in a similarly close-packed crystal structure (HCP) at high temperatures. However, in comparison with Si, the trend highlights a discrepancy between the lower elemental density of Si and its relatively muted impact in lightweighting. This discrepancy is due to the fact that Si's low elemental density is largely defined by its non-close-packed diamond cubic crystal structure.

FIG. 2.3B reports the hardness of the alloys as a function of LWE content. These measurements indicated that Al additions achieve marginal hardness improvements relative to the control, in line with the results reported by Li et al. which describe alloy hardness increasing with Al content in HEA coatings and claddings designed for wear resistance [48, 49]. Furthermore, the trends displayed in FIG. 2.3B suggest that the increase in hardness is roughly equivalent between the additions of Al and Si. The marginal and similar increases in hardness from the addition of Al and Si match other results reported for similar HEAs and high-entropy nitrides [50, 51, 52]. The addition of Ti, relative to Si or Al, further increases the hardness of the alloy, as seen in works studying similar alloys [53, 54]. In summary, while Si additions achieve marginal density and hardness improvements relative to the control, Al and Ti highlight the possibility of maximizing a given alloy composition for density or hardness, because of the consistently powerful effects Al has on lowering alloy density relative to Si and Ti additions and Ti on increasing alloy hardness relative to Si and Al additions.

Evaluation of LWE Effects on Passive Film Growth Kinetics

To determine the specific performance effects of the LWE species, potentiodynamic polarization was performed in a solution of 0.1 M H2SO4, pH 0.76. FIG. 2.4 displays the resulting Elogi curves for each binary variation among LWE. All alloys demonstrate robust passivity in the aggressive testing environment, with a distinct critical current density (i_crit) occurring at a potential anodic with respect to Ecorr and an extended passive region. Furthermore, the Al—Ti (FIG. 2.4B) and Ti—Si (FIG. 2.4C) sweeps indicate that early passivation kinetics are generally improved by adding Ti relative to Al and Si, as i_crit decreases with increasing Ti. Between samples Al₁₀ and Ti₁₀, i_crit decreased from 273 μA to 73 μA, with as little as 3 at % Ti (7 at % Al, Al7Ti3) achieving a factor of 2 reduction in critical current density compared to 10 at % Al. The sample Si₁₀ displays an i_crit comparable to the control alloy, 448 μA, but as little as 3 at % Ti (7 at % Si, Si₇Ti₃) achieved another factor of 2 reduction in critical current density compared to 10 at %. Between Al and Si, there seems to be no strong improvement as the Al concentration is varied with Si, but all alloys in the set outperformed the control alloy in terms of early passivation kinetics.

Once passivated, the passive current density (i_pass) of most alloys (including the control and only barring the Si₁₀ sample) is comparable to 304L stainless steel (FIGS. 2.4A-C), and the transpassive breakdown potentials of all tested samples are comparable. The similarity in passive current densities indicates that the steady-state films being formed are likely similarly protective to the stalwart 304L grade stainless steel, which contains far higher amounts of Cr. The higher passive current density of the Si₁₀ sample and the small, repeatable current fluctuations indicate that the overall film that is formed may be defective, allowing for easier charge-transfer kinetics. To further explore this behavior, the passive film composition will be analyzed in greater detail herein. However, the addition of Si in combination with other LWE, even at high (xSi=7 at %) Si amounts, seems to counteract the high passive current density effect observed when Si is added alone (i.e. in sample Si₁₀).

To further analyze the apparent difference in the early passivation kinetic efficiency, the alloys were subjected to chronoamperometry, and individual h values were calculated per Equation (3). Here, higher h values represent less efficient passivation, requiring more charge to passivate. The step-up potential of +0.15 VSCE after cathodic reduction was chosen to be representative of the end of the primary passive region for all samples. Representative chronoamperometry logi−logt curves are plotted alongside the resulting h value distribution of each of the LWE sweeps in FIG. 2.5 to highlight the connection between CA shape and h. Representative chronoamperometry curves (FIG. 2.5A) indicate that the control, Al₁₀, and Ti₁₀ samples passivate strongly in the primary passivation regime, with the Si₁₀ sample exhibiting stronger early passivation characteristics than the control, only to level off to a higher, seemingly steady state current after approximately 10 s, further evidence of a defective, incomplete, or otherwise less protective film. Other alloys in this series performed similarly in logi−logt graph shape to the control, with a decreasing current over time.

h value calculations indicate that additions of Ti relative to Al decrease the amount of dissolved monolayers needed to passivate. This result indicates that Ti and Al may not have an additive effect on passivation efficiency during early passivation because Ti additions monotonically improve performance relative to Al. This result, though surprising at first, is further discussed herein by deconvoluting the specific effects of LWE on passivity. However, the resulting h value distribution from adding Si relative to Al indicates a possible local minimum h value, hinting at an optimal Al—Si balance to achieve minimal dissolved monolayers for passivation. Finally, adding any amount of Ti relative to Si decreases the h value dramatically. However, with any amount of Si present in combination with Ti, the resulting h value remains roughly constant and higher than Ti without Si present. Overall, similarly to the potentiodynamic results, Ti additions were found to improve early passivation kinetic efficiency, decreasing the number of monolayers needed to passivate relative to those of Al and Si.

Lastly, longer-term (10 ks) potentiostatic passivation experiments were performed to track the growth speed of the film. Here, while the potential was fixed to the same potential used in the chronoamperometry experiments, the DC current was monitored alongside Z_imag, measured using a 5 Hz, 10 mV_RMS signal for the single-frequency impedance analysis. This complex impedance may be directly proportional to the film thickness, assuming a maximally capacitive behavior at that frequency with a largely invariant dielectric constant. The time constant values (t_0.5) were observed to follow a tight distribution for each alloy in many experiments, with notable and significant differences between groups. Representative runs of the resulting logi−logt and −Z_imag−logt curves are shown in FIG. 2.6. First, current-time relations indicate that adding Ti relative to both Al and Si decreases the passive current density following 10 ks of growth, indicating that Ti additions may lead to a higher-impedance passive film. Second, all LWE additions except Si₁₀ decreased the passive current density relative to the control. Lastly, all samples with xSi<7 at % form strong, steady-growing passive films, with samples containing xSi>=7 at % showing signs of instability after 10 ks of growth. FIG. 2.7 reports the resulting t_0.5 values, with error bars reporting the standard deviation of t_0.5 values. Results indicate that Ti and Si both increase the film growth kinetics when added relative to Al. Between Si and Ti, the results indicate that Ti may increase film growth kinetics marginally when added relative to Si. Furthermore, similar trends between alloy composition and both h and t_0.5 further highlight the ability of the HtP h value to capture trends described by higher-fidelity measures (and lower throughput).

In summary, all LWE enhance passive film kinetics (increasing film growth rate and charge efficiency) when added relative to Ni and Fe. Furthermore, the addition of Ti relative to other LWE was shown to further increase the passivation efficiency and passivation rate, and although Si improves the film growth rate relative to Al, it does not uniformly improve the passivation efficiency. The results indicate that relatively large additions of Si tend to form a film faster but less efficiently, and current fluctuations during chronoamperometric and potentiostatic film growth indicate that the resulting film may have decreased strength relative to samples with modest or no Si additions.

Evaluation of LWE Effects on Passive Film Resistance

Electrochemical impedance spectroscopy (EIS) was used after 10 ks of potentiostatic film growth (E_app=+0.15 V_SHE) to assess the resistance to charge transfer (hereby termed the “strength”) of the film formed at a low overpotential representative of early passivation. The resulting Bode (a-c) and Nyquist (d-f) plots are reported in FIG. 2.8. In FIG. 2.8a-c, the addition of any LWE results in an increase in the magnitude of the low-frequency impedance relative to the control alloy. Ti additions increase the low-frequency magnitude of the film impedance when added relative to Al and Si. Between Al and Si, impedance reaches a local maximum at roughly equal additions of Al and Si. This local maximum further suggests interplay between Al and Si species during early stage film formation, with an optimal Al—Si balance that outperforms both Al₁₀ and Si₁₀. However, since many Al— Si alloys show a low-frequency “tail” in their Nyquist representations, some of the low-frequency impedance magnitude may be due to local diffusion phenomena, rather than the real charge-transfer resistance of the film.

Therefore, to better highlight these trends, a representative circuit (FIG. 2.8G) was used to further decouple different sources of “film strength.” The total real impedance from the bulk electrolyte to the bare metal (here termed Rp) was determined by adding the real-valued charge transfer resistance between the electrolyte and the film and the real-valued impedance of the film itself, as in Sur et al. [26]. In this way, the real-valued resistance to charge being passed from oxidizing species in solution to further corrode the bare metal was chosen as a general proxy measurement for “film strength.” The semi-infinite Warburg element (W in the circuit diagram) describes the impedance to transport by electromigration and diffusion through the electrolyte and film. All circuit parameters for the fits shown in FIG. 2.8D-F can be found herein. Notably, all CPE reflected a values close to or above 0.9, indicating largely capacitive behavior across interfaces and the passive film. FIG. 2.9 compares the Rp values for all three elemental sweeps. The trends across sweeps remain the same as the low-frequency magnitude of overall impedance, with all LWE improving Rp relative to the control, Ti increasing Rp when added relative to both Al and Si, and Al and Si not increasing or decreasing consistently when added relative to one another. Interestingly, adding as little as 3 at % Ti can produce a film that outperforms an alloy containing Al and/or Si without Ti. Therefore, of all LWE, Ti remains the best option for forming a stronger and more robust film compared to Al and Si. To further connect these impedance findings into longer-term passivity at OCP, 30-day immersion testing on samples Al0Si0Ti0 and Ti₁₀ with weekly intermittent EIS measurements was performed and detailed herein.

In-Operando Elemental Dissolution Rates During Passivation

Distinct behaviors were observed in the elemental dissolution rates of Cr, Si, and Ti between the Al0Si0Ti0, Si₁₀, and Ti₁₀ CCAs from the AESEC-LSV experiments, as shown in FIGS. 2.10A-C. The electrical current density profiles (ie) for these CCAs are similar to those observed in the LSV experiments described in FIG. 2.4 with lower i_crit and i_pass observed for Ti₁₀ compared to Si₁₀ and Al0Si₀Ti₀. In the cathodic region, the current density profiles for the three samples are similar. Under large negative overpotentials where the cathodic HER reaction dominates, all the CCAs show dissolution, indicating the dissolution of the native oxides formed prior to the cathodic potential sweep. No such dissolution is observed as the negative overpotential decreases with polarization in the anodic direction. Ni and Fe exhibit congruent dissolution behavior in the anodic region and under small positive overpotentials, while Cr and other LWEs showed a lower dissolution rate than their congruent dissolution rate, i.e., surface enrichment, further highlighting their roles as passivators in this system. In general, Ni, Fe, and Cr dissolved at lower rates in the presence of LWEs, as can be seen from the nu_diss values at the anodic dissolution peak in active-passive transition, corresponding to i_crit. CCA Ti₁₀ exhibited the lowest dissolution rates, dissolving 20 times less than Al0Si0Ti0, while Si₁₀ dissolved approximately 1.5 times less than A10Si0Ti0. The addition of Ti and Si shows a clear decrease in i_crit[55, 56]. The percentage of enrichment normalized to the total dissolution (theta prime_M) in the active-passive transition region (E_corr to +0.6 V) is shown in FIG. 2.11. CCAs Al0Si₀Ti₀, Si₁₀, and Ti₁₀ exhibited approximately 36%, 7%, and 31% of Cr enrichment out of their total Cr dissolution, respectively. Si₁₀ also reflected an approximate 30% Si enrichment, while Ti₁₀ displayed approximately 59% Ti enrichment relative to their respective total dissolution. These results indicate that in the presence of Si, enrichment of Si is favored more than Cr enrichment, while in the presence of Ti, the significant enrichment of both Ti and Cr is favored.

Composition and Chemical Properties of Early Passive Film

In order to connect the electrochemical results to film chemistry, high-resolution XPS was performed after a potentiostatic film growth procedure of 10 ks at +0.15 V_SHE following the cathodic reduction mentioned previously on selected alloys. The alloys were selected as follows: the control alloy, Ti₁₀, Al₁₀, Si₁₀, Al₅Ti₅, Al₅Si₅, Si₅Ti₅. These alloys were selected to best represent general trends for unary and binary additions of LWE. Example fitted spectra for all species measured for the Ti₁₀ sample are found in FIG. 2.13.

Furthermore, the fraction of individual chemical species was calculated similarly, using the individual intensities of the chemical species.

FIG. 2.13 reports the compositions of the oxide films measured using high-resolution XPS. Compared with the relative film composition to the bulk composition, all LWE-containing CCAs display oxides where Fe and Ni oxide species are depleted, while Cr oxide and LWE oxide species are enriched. Such enrichment supports Cr and all LWE's designation as passivating species, while Fe and Ni are not due to their relative depletion. Furthermore, while the presence of Al and Si oxide species was limited to their low energy oxides Al2O₃ and SiO₂, Ni, Ti, and Cr reflect the presence of multiple oxide and hydroxide species. Although Ni and Cr reflect a meaningful expression of their hydroxide species, the vast majority of Ti expression is confined to TiO₂, with some Ti₂O₃ also consistent with fitting. Of all LWE, Si shows the largest cation fraction, followed by Ti and Al. To highlight this discrepancy, FIG. 2.14 graphically describes the relative surface metal cation fractions of all passivating species across each elemental sweep compared to the control alloy. Moreover, films grown from alloys containing LWE express a greater Cr cation fraction in the passive film than in the control.

This increased Cr expression in combination with LWE species' passive film expression indicates that LWE may have two effects on passive film chemistry, either of which can alter corrosion performance: (1) increasing the ability of Cr to form a protective oxide and (2) passivating and integrating into the protective oxide in their own right. Further analysis and deconvolution of these specific effects are described herein.

Discussion

Solubility of LWE in a FCC Matrix and CALPHAD-Based Design of Alloys

Despite the beneficial physical and electrochemical effects that LWE have on a typical FCC alloy, their usage is limited by LWE solubility within the FCC matrix, which differ from species-to-species and among species added in concert. To visualize the relationship between the pairwise solubility of Al—Ti (FIG. 2.15A), Al—Si (FIG. 2.15B), and Si—Ti (FIG. 2.15C) combinations on the alloy platform, the maximum combined solubility of each species combination is plotted as a phase map in FIG. 2.15. Here, each point is colored by the number of solid phases at equilibrium at each alloy's solidus temperature, where the −TS term is maximized for high-entropy phase stabilization. The gray interior envelope bounded by the orange dashed line indicates a region where binary combinations of LWE yield a single-phase FCC microstructure, as predicted by Thermo-Calc. The dashed black lines in FIG. 2.15 indicates the final balance between LWE (xLWE1+xLWE2=10 at %), and as all black dashed lines lie inside the single-phase envelopes (bounded by orange dashed lines), it was predicted that all alloys have a single-phase microstructure. However, each binary combination has a tendency, when outside the envelope, to generate up to 4 additional phases.

Taking into account the sets Fe_balNi₄₃Cr₁₀Al_xSi_y and Fe_balNi₄₃Cr₁₀Al_xTi_y first (shown in FIGS. 2.15A and 2.15B), there is a broad single phase region defined by a concave-down single phase boundary, where the combination of Al and Si or Ti produces a higher net solubility (xAl+xSi or xAl+xTi) than the maximum solubility of each of the LWE alone. Furthermore, alloy compositions just outside the single-phase envelope are largely predicted to form one additional phase, indicating a smooth transition between a single-phase and a dual-phase microstructure. This relatively smooth transition may facilitate the design of precipitate- or second-phase-strengthened alloys on the basis of a similar composition, using Al+Ti and Al+Si amounts and/or ratios as tuning knobs.

Next, considering the Fe_balNi₄₃Cr₁₀Si_xTi_y set, the single-phase boundary adopts a concave-up shape, where the addition of Si and Ti in combination achieves a lower total LWE solubility than Si or Ti alone. This is likely due to the affinity of Si and Ti for forming intermetallic phases, such as the G-phase phase seen in Si5Ti5 and Si7Ti3, or the Heusler phase seen in other similar alloys [7, 8]. Furthermore, alloys just outside the single-phase boundary tend to form an additional 2 phases, usually a C14 laves or G-phase, where Ti and the combination of Si and Ti are enriched, respectively. This indicates that the Fe_balNi₄₃Cr₁₀Si_xTi_y system may have a sharper compositional transition between single- and multiphase behavior than experienced by the Fe_balNi₄₃Cr₁₀Al_xSi_y and Fe_balNi₄₃Cr₁₀Al_xTi_y systems and may indicate a more difficult path toward the controlled development of a targeted microstructure by varying Ti+Si amounts and/or ratios.

Connecting Passive Film Chemistry and Performance

Source of Beneficial Performance Deconvolution through Multiple Lin-ear Regression

As described herein, the observed film chemistry benefits offered by the inclusion of LWE in this system are twofold, as both LWE participate in passivation in their own right and also promote greater molar fractions of Cr species in the passive film compared to the LWE-less control alloy (from FIG. 2.14). To deconvolute the different effects of each LWE on the film resistance, multiple linear regression (MLR) was performed between each passivating species' (Cr, Al, Si, Ti) cation fraction xfilm, from FIG. 2.14 and the base-10 logarithm of Rp, from FIG. 2.9. MLR employs a least squares regression procedure to fit a hyperplane defined by Equation (7) to the measured Rp data.

log 10 ⁢ R p = ∑ b i ⁢ x i f ⁢ i ⁢ l ⁢ m ( 7 )

Here, the sign of coefficients bi describes whether or not the presence of a specific species i is positively or negatively correlated with log 10Rp. In the case where a species has a negative coefficient, it can be suggested that that species' benefit (relative to the other passivating species) toward film resistance is likely not due to that species acting as a particularly potent secondary passivator, where its oxide species contribute to film impedance.

FIG. 2.16A shows the resulting coefficient distribution for all passivating species. Firstly, the large positive coefficient for Cr indicates that Cr's commonly known status as a primary passivator is appropriate, as it is strongly and overwhelmingly correlated with the overall film log 10Rct. Furthermore, Ti's positive coefficient suggests that Ti's presence in the oxide film probably imparts some resistance in the film beyond Ti promoting the enhanced Cr proportion in the passive film, highlighting Ti's role as a true secondary passivator, also reflected in FIGS. 2.11 and 2.14. This is also not unexpected, as Ti-based alloys are widely considered to be extremely corrosion resistant due to Ti forming a strong passivating oxide in many harsh environments when it is used as the principal element. [57, 58, 59]. To highlight the beneficial aspect of the inclusion of Cr and Ti in the film, the sum of their cationic fractions against alloy log 10Rct is plotted in FIG. 2.16B. The strong linear dependence between Ti and Cr cation fraction and log 10Rct further highlights that Cr and Ti improve the resistance of the film through their inclusion in the film. This defensibly synergistic effect on film impedance is shown to be more than additive, with Cr and Ti cation fractions being linearly related to the log 10-transform of Rp. In contrast, Si and Al demonstrate negative MLR coefficients, indicating that their inclusion alone in the passive film prob-ably does not impart resistance, at least in relation to Cr and Ti species. Therefore, it can be concluded that the benefit in film impedance due to the addition of Al and Si can be attributed primarily to Al and Si promoting Cr expression in the passive film.

In order to deconvolute LWE oxide presence and enhanced chromia expression from oxide growth speed, a similar MLR analysis was performed between cation fraction (FIG. 14) and t_0.5 (FIG. 2.7). The resulting coefficients are plotted in FIG. 2.17. The coefficients suggest that inclusion of Cr, Si, and Ti species in the passive film is correlated with a faster-forming film (evidenced by their negative MLR coefficients) with respect to Al, which has a positive MLR coefficient. Therefore, in comparison to all of the LWE species considered in this study, films containing Si and/or Ti will have formed faster than films containing a similar amount of Al. To further highlight this trend, the sum of Cr, Ti, and Si cation fractions is plotted against t_0.5 in FIG. 2.17B. The strong negative correlation between the sum of Cr, Ti, and Si cation fractions and t_0.5 further supports the notion that it is the Cr, Ti, and Si oxide species' presence that accelerates film formation. Although Si₁₀ and Si₅Ti₅ alloys seem to deviate from the linear trend, this can be explained by observing that Si cations are expressed in significantly higher amounts (45%) in the passive film than Ti cations (31%) (see FIG. 2.14), and the MLR coefficient of Si is approximately half that of Ti. A summary of the MLR-based performance sources for each LWE is tabulated in Table 2.

TABLE 2
Summary table of performance benefit sources for each LWE
and passive film performance metric from MLR analysis.

	Film Resistance	Film Growth Speed
	Performance Enhancement	Performance Enhancement
LWE	Source	Source
Al	Enhancing Cr(III) Proportion	Enhancing Cr(III) Proportion
Si	Enhancing Cr(III) Proportion	Si Oxide Presence
Ti	Ti Oxide Presence	Ti Oxide Presence

Thermodynamic and Kinetic Factors Influencing Passivity and Passivation Mechanism

Although MLR provides a beneficial and data-driven decoupling of the bulk corrosion performance improvements afforded by the inclusion of LWE in the passive film, the possible thermodynamic and kinetic factors rationalizing such mechanistic behaviors must be considered.

First, the beneficial relationship between the Ti and Cr oxide fractions and Rp reflected in the above MLR analysis can be explained by examining the mutual oxide solubility between Cr₂O₃ and each of the dominant LWE oxide species. Although Al₂O₃, Ti₂O₃, and Cr₂O₃ have mutual solid solution solubility due to their shared corundum structure, TiO₂ and SiO2 are nearly insoluble in Cr₂O₃ [60, 61, 62]. Therefore, it is unlikely that alloys containing Si or Ti form a continuous film with Cr, rather forming a layered or other-wise phase-separated film. This film may combine the inherent resistance of Cr₂O₃, TiO₂, and SiO₂ in series, since the species would need to trans-port through each film separately and across interphase boundaries. This behavior would explain the additive effect of the Cr and Ti oxide fraction on the total film impedance, as suggested by the MLR analysis. However, since Al₂O₃ and Cr₂O₃ are mutually soluble, it is reasonable that a film composed of soluble Al₂O₃ and Cr₂O₃ would average the intrinsic resistances of Al₂O₃ and Cr₂O₃, as species would have to transport through a more homogeneous corundum film where most of the cation sites are occupied by Cr (III), but some are occupied by Al (III) [63]. This mutual solubility of Al₂O₃ and Cr₂O₃ leading to a nonlayered film has been described elsewhere, lending credence to this idea [8, 25]. Definitive evidence of such layering or phase separation of Cr₂O₃ and Si and Ti oxides during aqueous passivation has not been observed due to the thin (<10 nm) nature of electrochemically grown films. However, layered Cr₂O₃—TiO₂ films have been grown through atomic layer deposition (ALD) on corundum, with planar interphase boundaries observed between Cr₂O₃ and TiO₂ layers even when films were deposited at 375° C. [64].

Second, the MLR analysis describing Cr, Si, and Ti film expression being correlated with faster film growth kinetics can be rationalized by comparing the formation energies of each LWE passive component normalized by LWE element. While TiO₂ and SiO₂ have similar per-cation formation energies of −960 kJ/mol and −923 kJ/mol, respectively, Cr₂O₃ and Al2O₃ have a more positive per-cation formation energy of −579.4 kJ/mol and −791.15 kJ/mol, respectively [65, 66]. Therefore, on a per-cation basis, Si and Ti oxides have a higher thermodynamic driving force for formation under the condition of excess oxidant and limited Cr/LWE species, as is likely true for an alloy with limited bulk Cr/LWE alloy amounts in an aggressive, oxidizing solution.

Such driving forces may allow for the formation of LWE oxides (particularly TiO₂ and SiO₂) before Cr₂O₃ and allow less dissolution of non-passivating elements such as Ni and Fe while allowing Cr₂O₃ to form following the passivation models based on site percolation of Cr [33, 67] and/or nucleation of Cr₂O₃ islands [68, 69]. This can be termed as the “early-dissolution blocking” mechanism of secondary passivation. Further, the protective nature of the early-stage LWE oxide may define the efficiency of this mechanism, as stronger LWE films would block more non-passivating elemental dissolution. The enrichment of both Ti and Cr on the surface of Ti₁₀, unlike in the case of Si₁₀ during early-stage passive film formation (active-passive transition in AESEC-LSV; see FIGS. 2.10 and 2.11), suggests that this mechanism is in play and that the greater protective nature of Ti oxides compared to Si oxides may govern the efficiency of film formation, characterized by h (FIG. 2.5).

Development of Design Rules for Optimal Film Growth Rate and Resistance

Finally, in order to better understand the effect of LWE on the balance between film resistance and growth speed, Rp and t_0.5 are plotted against each other for all alloys in the set in FIG. 2.18 as proxy measurements. In order to develop general compositional guidelines for corrosion-resistant CCA design, k-means clustering was performed between Rp (log scaled) and t_0.5, with an elbow plot (FIG. 2.18, inlaid) indicating that k=4 clusters is an appropriate choice. These four clusters, defined by their centroids, are plotted in FIG. 2.18 alongside the data. These four clusters can be characterized as forming: (1) fast growing, strong films, (2) fast growing, weak films, (3) slow growing, weak films, and (4) slowest growing, weakest films (the control alloy). These clusters, while mathematically defined by different values of Rp and t_0.5, also vary consistently by their bulk composition.

A summary of the resistance and growth rate characteristics and the compositional rules of each group can be found in Table 3. Group 1 alloys, characterized by both fast growth kinetics and strong film impedance, are compositionally characterized by containing a high amount of Ti of 5 at % or more. This result can be rationalized by considering the strong correlation between Ti film content and film impedance and film growth speed, as discussed herein.

Group 2 alloys, characterized by fast growth kinetics and a weaker film, are characterized by having a low (3 at %) Ti amount or a silicon content of at least 5 at %. Again, this can be explained through the discussion herein, where both Si and Ti are correlated to faster film growth. Film impedance remains relatively weak in this group as a result of the lack of or small amount of Ti (and therefore Ti oxide species), which is suggested to have an additive effect on impedance with Cr, unlike Si and Al.

Group 3 alloys, composed of LWE-containing alloys with the lowest impedance and the slowest film growth, are characterized by containing Al in at least 7 at % without Ti present. This result coincides with the previously stated MLR analysis, as relative to other LWE, Al is correlated to slower and weaker film growth.

Finally, it is important to note that all judgments on the efficacy of LWE in growing stronger films faster are relative to each other, since Group 4 contains only the control alloy, which exhibits the slowest forming and weakest film due to the presence of no LWE. Therefore, while the inclusion of any LWE will improve corrosion properties relative to similar alloys not containing LWE, the bulk Ti content should be maximized in order to optimize an alloy for both quick healing and strong passivation. However, Si can be considered a more abundant additive that quickens self-healing but imparts no film impedance beyond promoting enhanced Cr passivation.

TABLE 3
Summary table of compositional, film growth speed, and film
resistance characteristics of 4-means clustered data.

Group	Compositional	Film Growth Rate	Film Resistance
Number	Characteristics	Characteristics	Characteristics
1	High Ti: xTi > 3 at %	Fast	Strong
2	Low Ti: xTi <= 3 at %	Fast	Weak
	High Si: xSi >= 5 at %
3	High Al: xAl >= 7 at %	Slow	Weak
4	No LWE	Slowest	Weakest

Conclusion

A set of single-phase alloys with abundant Co-free FCC elements Ni₄₃Fe₃₇Cr₁₀—(Al,Si,Ti)₁₀ was designed using a high-throughput CALPHAD technique to further explore and define the specific physical and corrosion-resistance impacts of lightweight elements Al, Si, Ti while controlling for a single-phase microstructure. Alloys were analyzed for density, Vickers mi-crohardness, and corrosion resistance. Corrosion resistance was further di-vided into kinetic (i.e. passive film growth rate) and strength-based (i.e. passive film resistance) effects, and select alloys' passive film chemistry and in-operando elemental dissolution were analyzed using XPS and AESEC, respectively. The following conclusions were reached: All LWE lower alloy density compared to the LWE-less control, but Al decreased alloy density most effectively. Further, all LWE increase alloy microhardness relative to the control alloy, but Ti increased alloy hardness more effectively than Al and Si.

All LWE improve passive film growth rate (parametrized by t_0.5) in 0.1 M H₂SO₄ relative to the control alloy, but Si and Ti improve growth rate more effectively than Al. Adding any amount of Ti greater than or equal to 3 at %, or Si at 5 at % or more was found to increase the passive film growth rate most effectively according to k-means clustering results reported in FIG. 2.18.

The addition of LWE increased passive film resistance (parametrized by Rp) relative to the control, but Ti was found to be the most effective LWE toward this goal. Adding Ti above 5 at % with either Al or Si as balance improved alloy passive film resistance most effectively according to k-means clustering results reported in FIG. 2.18.

XPS analysis indicates that LWE both express their oxides in the alloys' passive films and also increase the amount of Cr(III) species in the passive film. These chemical effects were deconvoluted with respect to the growth rate and resistance of the passive film using MLR. MLR analysis suggests that Ti's utility is derived from both its oxide's presence in the alloy passive film and increasing Cr(III) expression, while Al and Si derive the bulk of their respective utility through the increase of Cr(III) species in the passive film.

LWE were shown to have synergistic effects with Cr during passivation when confined in a single-phase microstructure, demonstrating a greater than 10-fold increase in passive film impedance and a 4-fold increase in passive film growth speed compared to the LWE-less control alloy.

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Supplemental Information for Example 2

Additional Detail on CALPHAD Alloy Design

All CALPHAD calculations were performed using Thermo-Calc 2022b software and Thermo-Calc's TCHEA3 database created specifically for HEA and CCA alloys. Additionally, these calculations were further accelerated by utilizing a Python script to create lean and streamlined MACRO files which can run unsupervised in Thermo-Calc's console mode. The script takes a generic list of any elements represented in the TCHEA3 database, as well as a list of [min at %, max at %, step at %] for each species. All possible combinations of defined elements and compositional ranges are then compiled into a list, and a Thermo-Calc MACRO file is generated which performs a single-point equilibrium calculation at either a set temperature or at each alloy's solidus temperature. These single-point calculations ran at a speed of about 1-4 alloy composition(s)/second, and all resulting output files were accumulated into a custom SQL database, collecting the important thermodynamic and phase data in a tractable format across three tables storing bulk, phase, and constituitive information recorded following each simulation. The phase information of the alloys was used in order to design the alloys in this study, specifically the balance between Fe and Ni necessary to achieve a single phase, but other alloy “scans” were used to rapidly discover other single-phase alloy systems the study of which is currently ongoing at the time of writing.

EDS Compositions

Alloy compositions were measured using EDS, as described in § 2.2. EDS map scans were performed multiple times on samples, varying locations be-tween scans. The resulting average compositions for each sample can be found in Table 1. Table 1: EDS-measured alloy compositions and their abbreviated names considered in this study. Values are averages taken over multiple EDS area scans.

TEM Imaging and EDS Analysis of the Grain Boundary

Chemical inhomogeneity along grain boundaries, most commonly observed in stainless steel sensitization, can be detrimental to corrosion resistance. Sensitization, or the formation of chromium carbides in stainless steel along grain boundaries, leads to a local depletion of chromium in the alloy, opening the alloy up to enhanced attack in the regions adjacent to grain boundaries. Furthermore, any chemical inhomogeneity or second phase along a grain boundary could induce a microgalvanic couple between the bulk and grain boundary region, further enhancing corrosion damage in areas close to the grain boundary. Although carbon is not considered in this set of alloys, the tendency for CCAs to segregate certain elements or to form secondary phases along grain boundaries, which may induce a microgalvanic couple, necessitates a closer inspection to ensure that the alloys presented lack such potentially deleterious and confounding features.

To this end, higher-resolution STEM in combination with EDS analysis was performed, since no chemical inhomogeneities were observed in SEM/EDS analysis. A representative STEM-EDS line profile across a grain boundary within sample Al10 is presented in FIG. 2.19. The analysis of this grain boundary and several other grain boundaries represent no obvious signs of any elemental inhomogeneity, providing further evidence of a fully homo-geneous microstructure as seen in the SEM.

G-Phase Reflected in Si5Ti5 and Si7Ti3

As mentioned in the main text, two alloys, despite reflecting single-phase XRD patterns, were found to have a small distributed particulate phase upon SEM imaging. From the SEM images shown below in supplementary FIG. 2.20, the particulate phase is enriched in Ni, Si, and Ti, while deficient in Fe and Cr. In addition, it is likely that the second phase precipitated during quenching. This is indicated by the appearance of the second phase being small particles, despite homogenization at a temperature of 1150° C. for 72 hours. At such a high temperature for that amount of time, it would be expected that the second phase would coarsen if it were in equilibrium with the surrounding FCC matrix during homogenization. Furthermore, after homogenizing different Si5Ti5 and Si7Ti3 samples for 24 and 72 hours, the particles appeared to have a similar size and area fraction. The total phase fraction and composition, measured via the area scan EDS, and the relative compositions of each phase, measured using the point scan EDS, are reported in Table 2 for the samples Si5Ti5 and Si7Ti3.

Table 2: Compositions of regions of interest for selected 2-phase alloys Si5Ti5 and Si7Ti3 after homogenization. Matrix and particulate phase compositions are the average of mul-tiple EDS point scans, and the overall is the result of an area map. Percentages represent the average measured area fractions over 10 SEM images taken throughout the sample. Area fractions were determined using ImageJ image processing software.

Thermo-Calc predictions on Si5Ti5 and Si7Ti3 at lower temperatures in combination with the stoichiometry of the particulate phase reported in Table 2 indicate that the second phase is likely G-phase with an approximate composition of Ni₂SiTi, similar to G-phases phases reported in similar FCC-based intermetallic alloys [1]. Moreover, the relatively small volume fractions of the second phases explain the lack of clear G-phase peaks in Si5Ti5 and Si7Ti3's XRD patterns. As electrochemical measurements were performed in this initial study in the absence of chloride ions, which are known to induce localized corrosion at interphase boundaries, these particles were not considered to have a large effect herein on the electrochemical properties measured [2]. Furthermore, as the majority of the exposed area (>90%) in both samples is the desired FCC matrix phase (which has a composition close to designed), all current measurements (normalized by area) are largely dominated by this phase, further lessening the effect of the second phase presence on uniform corrosion measurements. Lastly, the particulate phase is heavily enriched (˜45 at %) in passivating species Al and Ti, and, in agreement with electrochemical measurements described in § 3.3 and § 3.4, is not expected to induce preferential dissolution [2].

EIS Fitting Parameters

To deconvolute different sources of impedance, the circuit shown in main text FIG. 2.8G was utilized to fit the EIS data. Table 3 reports the circuit parameters used in the fits displayed in main text FIG. 2.8D-F. Note the relatively high α for both the film and interfacial CPEs, indicating that the film and interface act approximately to pure capacitors.

Immersion Testing

In order to provide evidence of the longer-term stability of the oxides grown in the chosen environment, the best- and worst-performing alloys, Ti10 and Al0Si0Ti0, respectively, were subjected to a 31 day immersion test in 0.1M H₂SO₄. Following the cathodic reduction routine described in § 2.4, a high-resolution EIS scan was performed at each alloy's open circuit potential (OCP). After this initial EIS scan, a 24 hour OCP hold was completed, monitoring each alloy's OCP as a function of time. EIS scans were then repeated weekly until 31 total days of immersion. Following immersion, optical microscopy was performed to illustrate each alloy's surface damage.

The OCP results are presented in FIG. 2.21. The OCP of Al0Si0Ti0 remained within 5 mV of its initial value, but displayed a decrease in OCP toward the end of the 24 hour period, indicating a possible lack of passivity and enhanced corrosion attack. In contrast, Ti1O displays an OCP that increases over time, indicating the growth and maintenance of a noble passive film over time. Consistent with these findings, the impedance results over time (FIG. 2.22) indicate that Ti10 displays a much more consistent impedance over time, only diminishing slightly over the 31-day period. Al0Si0Ti0's impedance, when viewed in the Bode representation, appears to grow over time. However, this apparent growth is likely due to the formation of an nonprotective salt film, evinced by the large growth in capacitive impedance. Further evidence of the disparity in protectiveness of each alloy's film can be seen in the real impedance of both alloys overtime. Ti10's real impedance remains far larger than Al0Si0Ti0's. Finally, optical imaging of each alloy's surface (FIG. 2.23) supports the conclusions of both the OCP and EIS monitoring results, with Al0Si0Ti0's surface reflecting grain faceting in-line with uniform corrosive attack and lack of passivity and Ti10's surface remaining largely unchanged, with pre-testing polishing scratches still visible.

Table 3: EIS circuit parameters used to parametrize the fits displayed in main text FIG. 2.8D-F.

REFERENCES FOR SUPPLEMENTAL INFORMATION FOR EXAMPLE 2

• 1. X. Yan, A. Grytsiv, P. Rogl, V. Pomjakushin, X. Xue, On the crystal structure of the Mn—Ni—Si G-phase, Journal of Alloys and Compounds 469 (2009) 152-155.
• 2. S. B. Inman, D. Sur, J. Han, K. Ogle, J. R. Scully, Corrosion behavior of a compositionally complex alloy utilizing simultaneous Al, Cr, and Ti passivation, Corrosion Science 217 (6 2023).

It should be noted that ratios, concentrations, amounts, and other numerical data may be expressed herein in a range format. It is to be understood that such a range format is used for convenience and brevity, and thus, should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. To illustrate, a concentration range of “about 0.1% to about 5%” should be interpreted to include not only the explicitly recited concentration of about 0.1 wt % to about 5 wt %, but also include individual concentrations (e.g., 1%, 2%, 3%, and 4%) and the sub-ranges (e.g., 0.5%, 1.1%, 2.2%, 3.3%, and 4.4%) within the indicated range. In an embodiment, the term “about” can include traditional rounding according to significant figures of the numerical value. In addition, the phrase “about ‘x’ to ‘y’” includes “about ‘x’ to about ‘y’”. In addition, “about 0” is greater than 0 but not 0.

It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations, and are set forth only for a clear understanding of the principles of the disclosure. Many variations and modifications may be made to the above-described embodiments of the disclosure without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure.