Structural Characterization of Phase Separation in Fe-Cr: A Current Comparison of Experimental Methods

All the experiments presented in the present work (TEM, APT, and SANS) were conducted on the same three binary Fe-Cr alloys with different Cr contents, see Table I. The alloys were prepared by vacuum arc melting and solution treatment at 1373 K (1100 °C) for 2 hours in a slight overpressure of pure argon before being quenched in brine. Thereafter, samples were aged at 773 K (500 °C) for different times and quenched in brine.

Samples for SANS measurements were cut into plates with the approximate dimensions 5 × 5 × 1.5 mm³, and the oxide layer was removed by grinding and polishing. SANS data were then recorded on the LOQ diffractometer at the ISIS pulsed neutron source, Oxfordshire, UK. The wavelength, λ, range of the incident neutron beam was 2.2 to 10 Å, allowing a range of the scattering vector (Q) from 0.006 to 1.4 Å⁻¹ (Q = 4πsinθ/λ, where 2θ is the scattering angle) to be measured simultaneously. Samples were fixed at around 11 m from the moderator. Two detector banks were used to collect data. An ORDELA multi-wire proportional gas counter located at 4.15 m from the sample, and an annular scintillator area detector located at 0.6 m from the sample. The active area of the former detector was 64 × 64 cm² with 5 mm square pixels, whilst the latter had 12 mm pixels.[41] All the measurements were performed at ambient temperature using a neutron beam collimated to 4 mm diameter. Scattering data of as-quenched samples were collected for 2 hours per sample and that from the aged samples were collected for 30 minutes per sample.

The raw SANS data were corrected for the measured neutron transmission of the samples, illuminated volume, instrumental background scattering, and the efficiency and spatial linearity of the detectors to yield the macroscopic coherent differential scattering cross section (dΣ/dΩ) using the MantidPlot framework (version 3.2.1). These reduced instrument-independent data were then placed on an absolute scale using the scattering from a standard sample (a partially deuterated polymer blend of known molecular weight) measured with the same instrument settings.[42] dΣ/dΩ describes the shapes and sizes of the scattering bodies in the sample and the interactions between them.[41]

The final preparation of samples for APT measurements was performed by the standard two-step electro-polishing method. APT analyses were conducted using a LEAP 3000X HR^TM at 55 K (−218 °C). The ion detection efficiency is about 37 pct. The 3D reconstructions were performed by IVAS 3.4.3 software with evaporation field of 33 V/nm, field factor (k _f) 3.8 and image compression factor 1.8. Most of the analyses have been presented earlier and further details can be found in the following references.[29,32,43] To complement these data, new measurements were conducted for sample 35Cr1.

The first part of the TEM study was conducted using phase contrast in a JEOL 2000F TEM[16] operating at 200 kV. The samples were prepared by electro-polishing and subsequently immediately transferred to the high vacuum system to avoid any oxide formation that could obstruct the visualization of the phase contrast arising due to coherency strains. The second part of the TEM study was performed using a double Cs corrected JEOL ARM 200F TEM operating at 200 kV.[17] The samples were prepared in two different ways: (i) electro-polishing and subsequent gentle Ar ion beam polishing, (ii) lift-out technique in a Helios NanoLab focused ion beam scanning electron microscope (FIB-SEM). The TEM analyses, conducted using the JEOL ARM 200F microscope, were performed by mainly electron energy loss spectroscopy (EELS) spectrum imaging (SI).

The chromium and iron elemental maps were extracted by performing windowed elemental mapping on the 3D data cube. Multi-linear least squares (MLLS) fitting was performed using the extracted background of the high-loss region and reference spectra for the chromium and iron signals over the energy range from 400 to 900 eV. The periodic length-scale was investigated using auto-correlation analysis on the compositional maps in Digital Micrograph^TM.

SANS data for the different alloys and aging conditions are shown in Figure 1. It can be seen that peaks appear in the SANS patterns of all the aged samples. This arises from correlations in density within the alloy nanostructure and is a characteristic of phase separation. The patterns of solution treated (as-quenched) samples have no clear peak. They are flat in the Q range larger than 0.1 Å⁻¹ and they almost overlap with each other (Figure 1(d)).

In order to assess the peak position Q _m and peak intensity dΣ(Q _m)/dΩ, the scattering from the decomposed structure was evaluated according to the method illustrated in Figure 2. Since the patterns of the as-quenched samples, i.e., structures without decomposition, show a flat behavior beyond Q = 0.1 Å⁻¹ and no interaction peak, their scattering function was taken as the scattering pattern of a homogeneous sample. dΣ(Q)/dΩ of the as-quenched sample was fitted by a power function (I _b ), as shown in Figure 2(a), and subsequently the background of each condition was subtracted, see Figure 2(b). dΣ(Q)/dΩ was normalized by I _b , I _n  = dΣ(Q)/dΩ/I _b (Figure 2(c)) and I _n vs log Q was fitted by a Gaussian function, I _G. Finally, the intensity characteristic of phase separation, I _PS, was obtained by I _PS = I _b (I _G − 1), see Figure 2(d). Q _m and dΣ(Q _m)/dΩ were determined from the pattern of I _PS. The procedure explained here is similar to the procedure used in Hörnqvist et al.[25] with the exception of the fit of the background which was performed for each condition in the present study since the scattering behavior of the initial states was different.

As can be seen from Figure 3, dΣ(Q _m)/dΩ increases with aging time (Figure 3(a)) and Q _m moves to smaller reciprocal length-scale (Q), i.e., longer real-space length scales (Figure 3(b)), as phase separation progresses. This is also seen from Figure 1. Since the initial stages of phase separation are particularly difficult to address experimentally, it is interesting to turn the attention to what happens with the scattering function beyond the peak position. The value of dΣ(Q)/dΩ decreases in the high-Q range for all the aged samples, but, as mentioned, the scattering patterns of the unaged samples are flat (Figure 1). The Q-dependence of the scattering functions for samples 25Cr1000, 30Cr200, and 35Cr100 in the high-Q range is similar to each other, at about −4. The Q-dependence of the scattering patterns for samples 25Cr100, 30Cr20, and 35Cr10 is, on the other hand, close to −2, while the Q-dependence of sample 35Cr1 is about −1.3. Thus, it is clear that the slope of the scattering function in the high-Q range is a rather sensitive probe of the early-stage phase separation. The slope increases gradually from zero for the solution-treated sample to -4 for all the samples that are significantly decomposed, i.e., after long time aging at 773 K (500 °C). This Q-dependence is related to the degree of segregation in the emerging interface (through e.g., the surface fractal dimension), a more negative slope representing greater segregation.

If it is assumed that all alloys decompose via SD, the wavelength of decomposition can be calculated by the formula generated by substituting Q = 4πsinθ/λ into Bragg’s Law:where Q _m is the scattering vector at the peak position.

The calculated wavelengths are shown in Table II together with the wavelengths calculated from APT using the radial distribution function (RDF) and the auto-correlation function (ACF),[32] and from TEM using the ACF.[16,17] The amplitude for the 35Cr alloy from APT and TEM is also shown.

It should be noted that it has previously been found by APT that the three investigated alloys are in the transition region between NG and SD at 773 K (500 °C)[29] and although Pareige et al.[10] claimed that Fe-25 at. pct Cr decomposed via SD, isolated particles have been shown on 3D atom maps in both References 10 and 29. It is therefore believed that the dominant decomposition mechanism in alloy 25Cr is non-classical NG.[29] Henceforth, it may be better to treat this condition using a precipitate analysis. The Guinier approximation (ln(dΣ(Q)/dΩ) vs Q ²) is commonly used to estimate the size of particles in alloys, and relies on the fact that at low Q values the scattering law for a sphere may be approximated by an exponential series expansion.[44] The radius of gyration or the Guinier radius, R _g, can be calculated from the slope of the plot, which is equal to −R _g ² /3. If we assume that the microstructure consists of monodisperse spherical particles, the radius of the particles, R, is equal to \( \sqrt {5/3} R_{\text{g}} \).[44] The same particle approximation was also applied to the other alloys in this work for comparison. The appearance of the Guinier plots for the different alloys was similar and the behavior is exemplified for alloy 25Cr in Figure 4. The particle radii calculated from the Guinier plots are presented in Table III. The calculated particle size shows the same trend as the spinodal wavelengths presented in Table II, namely, that the apparent domain size increases as phase separation progresses.

It is interesting to evaluate the evolution of the structural parameters with time in comparison with theoretical works. The theory of Binder et al.[45] and the Monte Carlo simulations of Marro et al.[46,47] have demonstrated that the time evolution of the peak position and the peak intensity obey power laws: where t is the aging time.

The a′ and a″ parameters were evaluated for the 35Cr alloy since this is the only alloy where a sufficient number of sample conditions were investigated to provide a fair description of the kinetic coefficients. The values of a′ and a″ are 0.16 and 0.64, respectively. Since the wavelength is proportional to Q _m ⁻¹ , the wavelength is proportional to t ^a’ , and thus, the wavelength of alloy 35Cr at 773 K (500 °C) has a t ^0.16 dependence. The values of a′ and a″ in the present work are in good agreement with the work by Katano et al.[19] Ujihara et al.[24] measured a′ = 0 − 0.35 and they also observed that a′ was smaller at lower aging temperature for the same alloy. Moreover, they found that Q _m did not always have a power law dependence with t, and a′ was smaller in the early stages of decomposition. Theoretically, Binder et al.[45] predicted a′ = 1/6 and a″ = 1/2 for low temperatures, while Marro et al.[46,47] obtained a′ = 0.2 − 0.28 and a″ = 0.65 − 0.74 below the critical temperature T _c. The value of a′ obtained in the present work is slightly smaller than the theoretical estimations. The reason may be that the decomposition is still in the early stage. If, instead, the kinetics is evaluated based on the particle size showed in Table III, the particle size evolves with a simple power law according to R∝t ^0.27. The theory of Lifshitz–Slyozov–Wagner[48,49] indicates a′ = 1/3 in the coarsening stage occurring after long-term aging when the diffusion is mainly through the bulk. Huse[50] argued that smaller a′ observed at short aging times was due to the contribution of the diffusion along the interface. Some later simulation works showed agreements with their theories.[10,51,52] The above results illustrate that in order to reveal the mechanism of decomposition, it may be necessary to make careful comparisons of the kinetic evolution of the microstructure characteristic length-scale with physical models.

TEM elemental mapping (EELS) results for alloy 35Cr in unaged and aged conditions are presented in Figure 5. There is already a slight indication of elemental segregation after 1 hours of aging at 773 K (500 °C) and after 10 hours aging and onwards phase separation is evident. These results presented comprehensively in Reference 17 were surprising, since it was generally believed that the many overlapping domains that the electron beam was traveling through would cause an averaging of the elemental, Cr and Fe, signal and that the nanostructure could not be visualized. It should be mentioned that the elemental mapping in Figure 5 was conducted on rather thick samples (thickness ≈ 42–100 nm) and still it was possible to resolve the decomposed regions of about 2 nm in sample 35Cr1. The reason was hypothesized to be that the main part of the signal arises in the top surface (<5 nm) of the sample before the electron beam has spread out significantly, reducing the signal notably.[17] The estimation of the wavelength of decomposition was found to be insensitive to the thickness of the TEM sample, whereas the amplitude of decomposition was only possible to estimate using a much thinner sample of about 32 nm thickness and for the sample aged for 100 hours.[17]

2D Cr concentration maps sectioned from the APT measurements on the 35Cr alloy are presented in Figure 6. It can be seen that there is greater segregation, i.e., into α and α′, after 10 and 100 hours of aging at 773 K (500 °C), compared to the unaged sample and the sample aged for 1 hour. By applying statistical analysis, it is possible to distinguish a difference also between the unaged sample and the sample that has been aged for 1 hour at 773 K (500 °C). It has been found that one of the most sensitive ways to represent minor decomposition is by generating the radial concentration profiles from each and every Cr atom in the analyzed volume and then averaging these concentration profiles. This treatment is called RDF analysis and example results are given in Figure 7 for the 35Cr alloy aged at 773 K (500 °C). It is clear that all alloy conditions are distinct from each other and the wavelength and amplitude of the concentration fluctuations can be evaluated from these curves using the method suggested by Zhou et al.[32] The results from the RDF analysis of wavelength and amplitude are included in Table II. It should be noted that when the nominal alloy composition is not in the center of the miscibility gap, as in the case of the alloys in the present work, an asymmetric compositional amplitude develops.

The decomposition after 1 hour aging of alloy 35Cr is clearly seen from the SANS measurements (Figure 1), demonstrating the sensitivity of SANS to small degrees of decomposition. Studies of the early stages of decomposition require good resolution at the high-Q range, since the change in slopes of dΣ/dΩ is a good indicator of decomposition. A similar type of scattering behavior has been found previously by Furusaka et al.[20] They studied phase separation in Fe-Cr alloys and Al-6.8pctZn at different aging conditions (aging times up to 50 hours for Fe-40pctCr and up to 60 minutes for Al-6.8pctZn at different temperatures). They observed only Q ⁻² and Q ⁻⁴ dependences of the scattering function at high-Q ranges. It was believed that early and late stages of phase separation can be distinguished clearly by these two features. They argued that the Q ⁻² dependence is a feature of the early stages of phase separation, and the Q ⁻⁴ dependence characterizes the later stages of phase separation when the inhomogeneities in the alloys have sharp interfaces with the matrix. Ujihara et al.[24] also observed the same Q ^-n dependence. However, a recent in-situ SANS work shows a gradual increase of the slope with aging time from 0 to 2 at 773 K (500 °C) and from 0 to 2.5 at 798 K (525 °C) for alloy 35Cr.[25] The results presented here agree well with this in-situ work. It should be pointed out that a sharp interface, defined here as either NG or coarsening of SD, is not a pre-requisite for the Q ⁻⁴ dependence since it is known from APT[29,32] that all conditions in the present work are far from the late stage with a fully developed amplitude and the interfaces between Fe-rich and Cr-rich domains are still diffuse. Therefore, one must not draw too far-reaching conclusions on interfaces based on the slopes since they can be affected by several factors.[24]

It is interesting to note that no distinct difference in scattering function evolution could be found for the different alloys. It is believed that the three investigated alloys are located in the transition region between NG and SD, but alloy 25Cr, which is decomposing via non-classical NG, displays a similar scattering function evolution as the two other alloys, i.e., 30Cr and 35Cr, which are decomposing via SD.[29] Similar scattering functions for particle and spinodal microstructures have also been found before.[24,53,54] Furthermore, it seems like the analysis of structural parameters, using either the particle or composition wave assumption, is reasonable for all alloy conditions. This may indicate that these alloys have features of both NG and SD. On the other hand, it may also indicate that SANS is not able to distinguish between different mechanisms of decomposition, unless kinetics is considered.

It is generally believed that TEM is not a suitable technique[27] to investigate the early stages of phase separation in Fe-Cr since the concentration fluctuations are minute, both in length-scale and in concentration amplitude. TEM has instead mainly been used as a qualitative probe[5] though in some cases the mechanism of decomposition has been distinguished, for example, where the phase contrast is larger, enabling the observation of particles or mottled contrast characteristic for SD.[55] Comparing the results herein from TEM and APT with the SANS, it is clear that all techniques are capable of detecting the early stages of phase separation in the Fe-Cr system.

Table II and Figure 8 show the comparison between the wavelengths obtained from SANS, TEM, and APT data. It can be seen that the spinodal wavelength calculated from the SANS measurements is consistent with both prior TEM and APT results. The wavelengths obtained from the RDF analysis of APT data are, however, generally larger than the values from SANS while wavelengths obtained from the ACF are generally smaller than that from SANS. Zhou et al.[32] suggested that the RDF is a good tool for estimating the wavelength and amplitude of phase separation. However, for the very early stages of, for example, 35Cr1, the wavelength obtained by RDF seems incorrect. It is larger than that from SANS and even slightly larger than the wavelength of 35Cr10 from the RDF. As mentioned earlier, the APT measurements are only performed on a very small volume and there are some uncertainties regarding the 3D reconstruction, and thus the good agreement with SANS validates the use of the APT technique for determining the wavelength even though SANS is deemed to be more reliable. The ACF analysis of the APT data was only performed in 1D but still the agreement is good, and thus the assumed isotropic nature of the microstructure seems reasonable. On the other hand, it should be noted that the thickness of the thin-foils used for analytical TEM is in the order of 100 nm, which is much larger than the wavelength measured.[17] Moreover, the wavelength quantified by TEM remains constant for different thicknesses. Therefore, as Westraadt et al.[17] have indicated, the EELS signal is not averaged through the thickness of the samples.

For quantifying the amplitude of phase separation, APT is a good choice. Different methods have been proposed for estimating the amplitude from APT data. RDF was suggested as a promising method to give accurate results on the composition amplitude in Fe-Cr alloys.[32] Westraadt et al.[17] used the standard deviation in the relative quantification maps from TEM to represent the amplitude of a 35Cr alloy as shown in Table II. Nevertheless, the composition fluctuation amplitude measured from the EELS analysis varies with the foil thicknesses and the acquisition parameters. Only approximate numbers were given from the EELS analyses, since the electron-sample interaction volume generates some uncertainty between the elemental distribution in the sample and the compositional measurement. The required thickness for obtaining a reasonable amplitude is related to the mean free path for inelastic scattering of electrons.[17,56] The reasonable agreement is achieved only when the thickness was reduced to 32 nm for 35Cr100. Further reduction in the sample thickness reduces the probability of a scattering event, resulting in a low signal-to-noise elemental map. To determine the amplitude for samples with less decomposition is even harder since preparing thinner samples is a challenge. In the present work, the amplitude was not calculated from the SANS data because of the lack of an effective method for doing so.

Despite the shortcomings in determining composition amplitudes, both TEM and SANS are competitive tools for characterizing phase separation. TEM provides microstructure images which reflect the microstructure directly and are helpful in interpreting APT and SANS results. With TEM crystal orientations are available, which is hard to acquire from APT. Crystal orientations are of significant importance when investigating anisotropic decomposition, e.g., decomposition under coherency strains.[57‐61] When there are coherency strains, phase separation prefers to develop along specific crystal directions, the soft directions.[59] This leads to anisotropic decomposition in materials. Soriano-Vargas et al.[5] observed that α′ aligned in the <110> direction of α by TEM. Although anisotropic decomposition in single crystalline or textured polycrystalline materials can be analyzed by SANS, orientations of the single crystal or the texture of the polycrystal should be determined before measurements and measurements should be done along known orientations to quantify the analyses.[60,61] Otherwise, TEM is still needed after SANS measurements to confirm the reason for the anisotropy. This also applies to APT when using it to study anisotropic decomposition. Therefore, combination of TEM, APT, and SANS can give an unambiguous view on anisotropic phase separation. Moreover, combining microstructure images from TEM and APT (especially the 3D atom map) may give more impartial views when drawing conclusions on the decomposed microstructure from SANS data since from SANS it is hard to distinguish between different morphologies during phase separation as discussed above. On the other hand, SANS can collect data efficiently and has great advantages over the other two techniques for in-situ analyses, which enable us to continuously track the development of phase separation.[22,25,62] These advantages of SANS can be utilized for effective kinetic analysis to provide a more comprehensive understanding of the kinetics of phase separation at an early stage of embrittlement.

One of the major benefits of SANS is arguably the direct mapping of the reciprocal space structure, which can also be obtained from modeling e.g., by LBM.[63‐65] A recent example of investigations on the kinetics of the early stage of phase separation can be found in Hörnqvist et al.[25] They used in-situ SANS measurements to study the evolution of the microstructure at 773 K (500 °C) and 798 K (525 °C) and compared the results with modeling using the Cahn–Hilliard–Cook (CHC) model. They found a good agreement of the length scale of decomposition between experiments and modeling. The linearized CHC theory is not sufficient to accurately describe the phase transformation. Nonetheless, the examples from Bley[23] and Hörnqvist et al.[25] demonstrate the link between the Cahn-Hilliard model and SANS experiments. Hence, by simulating the structure factor evolution using the non-linear Cahn-Hilliard model with proper physical input data, and making direct comparisons to the structure factors from SANS where the nuclear scattering has been deconvoluted,[23] it could be possible to significantly advance our understanding, and the quantitative modeling, of the phase separation process. The recent development in phase-field modeling of SD[43,66] enables physical descriptions of binary as well as multicomponent alloy systems considering all the physical parameters and thermodynamics appropriately.