Solving Ambiguity in EBSD Indexing of Long-Period Stacking Ordered (LPSO) Phase in Mg with Template Matching Approach

Abstract

Magnesium (Mg) alloys with long-period stacking ordered (LPSO) phases are receiving increasing interest because of their excellent mechanical performance. The close similarity in atomic stacking sequences between different LPSO polytypes and Mg lattice often leads to ambiguous indexing in electron backscatter diffraction (EBSD), a commonly used material characterization technique. Instead of the Hough transformation approach used in commercial software, an alternative indexing approach, which can catch subtle differences by matching experimental patterns with simulated ones, is explored in this study. Our results, showing ~94% of mapping data being correctly indexed as the target phase, 14H LPSO, demonstrate the capability of not only resolving the LPSO phases but also distinguishing different LPSO polytypes. This approach offers a valuable, if not unique, solution for the microscale characterization of LPSO phases, enabling precise microstructure tuning to further promote the mechanical properties of Mg alloys.

1. Introduction

As the lightest structural materials, magnesium (Mg) and its alloys hold great promise as replacements for conventional structural materials like iron and aluminum, especially in weight-sensitive applications like aerospace and automobiles [1]. However, Mg faces inherent challenges due to its hexagonal close-packed (hcp) structure, which causes issues such as low ductility and high deformation anisotropy [2,3,4]. To overcome these limitations, solutions like tuning the chemical composition [3], grain refinement [5], precipitate hardening [6], etc., have been explored. While adjusting the chemical composition is a universal approach to enhancing material performance, the addition of specific elements, particularly, rare-earth elements (REs, e.g., Y and Gd) combined with transition metal elements (TMs, e.g., Zn, Ni, and Cu), has proven exceptional in strengthening Mg. These alloys, first introduced by Kawamura [7], owe their excellent performance to a group of intriguing phases known as long-period stacking ordered (LPSO) phases [8]. In addition to increased strength, LPSO-contained Mg alloys also exhibit improved ductility due to the presence of the LPSO phase [9]. LPSO phases exhibit periodic stacking of alloying element-enriched layers, a characteristic often revealed through transmission electron microscopy (TEM). A few LPSO polytypes, such as 10H, 14H, 12R, 18R, and 24R [10,11], are categorized by their periodicity and often co-exist in one alloy.

While TEM successfully identifies LPSO phases, its limited field of view—typically less than one micron—hinders the direct link to macroscopic mechanical properties. Alternatively, electron backscatter pattern (EBSD) analysis, as a powerful tool for crystallography and phase characterization at the micron to millimeter scale, is frequently adopted to study LPSO. However, direct EBSD indexing and analysis of LPSO phases remain scarce. To the best of the authors’ knowledge, most EBSD analyses either exploit the orientation relationship (OR) between LPSO and indexed Mg phases for unindexed LPSO phases or completely neglect the LPSO phases, treating the unindexed black area in EBSD maps as LPSO phases [12,13,14,15,16]. To bridge this gap, a few attempts have been made by combining EBSD and energy-dispersive spectroscopy (EDS), utilizing composition differences resolved from simultaneously acquiring EDS to identify LPSO in EBSD maps [17,18], or combining EBSD and backscatter electron (BSE) imaging, leveraging BSE contrast differences stemming from composition changes [13,15,16]. However, this strategy fails when multiple LPSO polytypes exist, as the elemental differences and associated BSE contrast differences become less pronounced in different LPSO polytypes.

Given the fact that LPSO phases form by the periodic stacking of alloying element-enriched layers and the associated stacking faults (SFs), it is understandable that the difficulty in EBSD indexing of LPSO phases lies within their crystal structures which share great similarities between each other and with the Mg matrix. As a result, the projected EBSD patterns appear remarkably alike, with minor differences mainly in the intensities of corresponding Kikuchi lines. Traditional indexing approaches, commonly found in commercial software, such as the Hough transformation approach, primarily consider the position of Kikuchi lines and tend to overlook subtle changes in line intensities [18]. Apart from structural similarity, the indexing difficulty also comes from their complex structure, leading to deteriorated pattern quality and blurred/weaker Kikuchi lines [17] which are hard to index by traditional Hough transformation. Consequently, correctly indexing EBSD patterns for LPSO becomes challenging. Moreover, achieving high-quality sample preparation is another hurdle in experimentally catching these subtle differences. EBSD is sensitive to surface quality, and ensuring acceptable sample conditions is crucial for accurate characterization.

To develop a robust approach for EBSD indexing of LPSO phases, an alternative approach, template matching, has been adopted in this study. This approach matches individual experimental patterns with simulated ones; in principle, it will be sensitive to subtle changes in EBSD patterns. Using single-phase 14H LPSO alloys, we optimized sample preparation techniques, applied the template matching approach, and successfully indexed most experimental patterns in individual EBSD maps, where our commercial software failed. Our results eliminate ambiguity in the EBSD analysis of LPSO phases, unlocking new insights for advancing Mg alloys with LPSO phases.

2. Experimental Procedure

Pure Mg (99.99 wt.%), Ni (99.99 wt.%), and Gd (99.9 wt.%) metals were melted, mixed, and then poured into a steel mold under a protective gas atmosphere (1 vol.%SF₆ + 99 vol.%CO₂). The cast temperature of all ingots was 700 °C. The ingots were then solid solution-treated at 500 °C for 20 h. The alloy with a nominal composition of Mg₉₀.₅Gd₅.₅Ni₄ (at.%), showing as a single phase, was used for EBSD indexing. Optical microscopy (OM) samples were polished using SiC grinding paper until no obvious scratches were visible and etched for <10 s using a mixed solution of 4% nitric acid and 96% ethanol before observation. TEM samples were first wire-cut from the cast ingot into thin slices of ~1 mm in thickness, followed by mechanical grinding to ~80 mm. ϕ 3 mm disks were punched out of pre-thinned slices before being subjected to twin-jet polishing with a mixed solution of 10% perchloric acid and 90% methanol. All TEM observations were conducted on an FEI Talos TEM operated under 200 kV.

EBSD samples were first mechanically polished using a series of SiC grinding papers, followed by fine polishing using diamond suspension solutions of 3 μm, 1 μm, and 0.25 μm on a polishing cloth. The final polishing was carried out using a 0.04 μm silica suspension (Allied High Tech, Cerritos, CA, USA). It is worth mentioning that the samples were found to be extremely sensitive to the polishing duration of the final polishing; a reduced polishing time (e.g., 30 s) is recommended. EBSD mapping was carried out under 30 kV and a spot size of 3 (with a probe current of ~60 pA) on an FEI Nova scanning electron microscope (SEM) equipped with an EBSD detector (EDAX TEAM^TM, Pleasanton, CA, USA). Because of the large grain size (~a few hundred microns), the step size was set to be 5–10 μm. The “pattern centre”, describing the relative position of the EBSD detector, was recorded during each map acquisition. The “pattern centre” for the illustrated map was [0.506 0.692 0.681]. During map acquisition, experimental patterns were saved and then exported for further indexing. To enhance the pattern quality, a binning of 1 × 1, which yields a pixel size of 463 × 463 for each pattern, was applied. The refined template matching (RTM) algorithm [19] was adopted for off-line EBSD indexing, using an open-source AstroEBSD code, developed by Britton’s group [20]. Corresponding EBSD maps were generated using the MTEX 5.10.2 package in MATLAB R2021b [21].

3. Methods: A Guideline for Applying a Template Matching Approach

3.1. Flowchart of Applying Template Matching Approach

The refined template matching (RTM) algorithm compares experimental EBSD patterns with a library of simulated patterns generated under identical experimental conditions. For any given phase, the library is created from the master backscatter pattern, which covers the entire Edward sphere using many-beam dynamical simulation. The master pattern can be generated by Bruker Esprit, DynamicS (as detailed in the AstroEBSD manual), or AZtecCrystal MapSweeper. A custom MATLAB script accounts for the differences in projected screens of the master pattern used by these different software packages. The atomic models of given phases are needed to simulate their complete backscatter pattern. As shown in blue arrows in Figure 1, atomic models of LPSO candidates [22], 14H (Mg₃₅Zn₃RE₄, hexagonal, P6₃/mcm) and 18R (Mg₂₉Zn₃RE₄, trigonal, P3₂12), were adopted by replacing Zn and REs with Ni and Gd for generating complete backscatter patterns. It should be noted that different stacking sequences may cause very slight differences in lattice parameters, which is not considered in the current study.

Depending on the complexity of the involved phases and the quality of EBSD patterns, the template matching approach can be computationally demanding even for an EBSD map containing ~1000 data points on a high-end personal computer. It takes ~25 min to index 50 patterns with a pixel size of 463 × 463 on the author’s computer with an 8-core 16-thread AMD Ryzen^TM7 5700X CPU and 32 Gb RAM. The RTM algorithm addresses this by splitting such a time-consuming process into two steps: rough and fine matching. As illustrated by black arrows in Figure 1, rough matching is the initial step, involving a broad comparison between the experimental pattern and a library of simulated ones. With lower orientation resolution or fewer details, this step aims to quickly narrow down the potential matches. The fine-matching step involves a detailed and precise comparison between the experimental pattern with the potential matches. Thus, a balance between the efficiency and accuracy of EBSD indexing is achieved, greatly reducing the time and storage space needed for template matching [19].

3.2. Tips for Obtaining EBSD Experimental Pattern

As the sample preparation and resulting surface quality significantly influence the acquired EBSD patterns, obtaining an acceptable surface quality of Mg samples is quite challenging mainly due to their softness and their strong tendency to oxidize. The introduction of LPSO phases makes Mg alloys even more prone to oxidation compared to pure Mg. Consequently, the recommended approach in the literature [12], such as the use of diamond suspension and polishing procedures, which yield satisfactory polishing without surface degradation on other Mg alloys, is no longer applicable to the current samples. Following such procedures, a thin brown layer was found to quickly form on the sample surface.

To remove possible oxidation layers during polishing, the polishing rate, which refers to the removal rate of the topmost surface materials, needs to be balanced with the oxidization rate of the sample. It comes as no surprise that the polishing rate is higher when using coarser suspensions, larger applied loads, and faster rotation speeds. Therefore, the final polishing step, during which the finest suspension is applied, needs to be carefully tuned to achieve acceptable surface quality. After testing different combinations, a silica suspension of 0.04 μm and a rotation speed of 350 rpm were chosen for the final polishing of the under-studied samples. It is worth noting that different materials may require different polishing procedures, which should be tested on a case-by-case basis.

The operating conditions of scanning electron microscopy also influence the obtained EBSD patterns. Besides these standard parameters such as high-tension voltage and working distance, the camera setting is also critical. Higher binning for pattern acquisition can be employed to reduce the pixel dimension of obtained pattern images, leading to shorter scanning and indexing times. Depending on the quality of experimental patterns, one can test to determine the threshold of binning, at which the template matching algorithm starts to produce unreliable indexing results.

4. Results and Discussion

4.1. The Type of LPSO Phase in the Sample

Based on the calculated Mg-Gd-Ni phase diagram [23], the LPSO single-phase structure exists within the range of 1–5 at.% Gd, 1–4 at.% Ni, and Mg (balance). Additionally, increasing the contents of RE and TM elements compared to Mg is believed to lead to an increased volume fraction of LPSO phases [24]. Based on this research, a single-phase LPSO alloy with a nominal composition of Mg₉₀.₅Gd₅.₅Ni₄ (at.%) is manufactured. Figure 2a shows the OM image of the current alloy. Except for a few precipitates and black pits, a uniform contrast can be clearly observed, indicating a single-phase microstructure. The SEM second electron (SE) image of the current alloy is shown in Figure 2b. Similar to the OM image, a smooth and uniform contrast can be observed, confirming the single-phase nature of the studied material. Precipitates with regular shapes can be occasionally observed as indicated by the red arrow, and they are enriched with Ni, as suggested by EDS analysis. Due to their limited volume percentage and rather small size compared to the LPSO grain, the precipitates in the current study are considered negligible in EBSD scanning and thus will not be discussed further in this study.

To rule out the possibility of co-existing LPSO polytypes, TEM observation has been carried out to identify the exact type of LPSO in the current study. As shown in selected area electron diffraction (SAED) in Figure 2c, the diffraction pattern shows 13 extra characteristic reflections between the incident beam and (0002)_Mg, in all grains, indicating the manufactured materials are indeed 14H LPSO. This result agrees with the past study which states that 14H has better thermal stability and can be transformed from 18R when being subjected to heat treatment [25,26].

4.2. The Comparison Between Template Matching and Commercial Software

The indexing results using template matching and Hough transformation are shown in inverse pole figure (IPF) maps in Figure 3 for comparison. These IPF maps represent the sample surface’s normal direction with respect to the crystallographic orientations of the indexed phase. Mg along with 14H and 18R (the two most likely co-existing LPSO phases) are imported as phase candidates for both methods. The on-site TEAM^TM software (V4.4), based on Hough transformation, incorrectly recognizes most EBSD patterns as Mg. The confidence index (CI) from TEAM^TM software, representing the accuracy of indexing using the Hough transformation approach, is very low (~0.04) and thus likely unreliable. It should be noted that TEAM^TM software frequently fails to index most experimental patterns and produces incoherent maps for the current alloy. A similar situation where LPSO is incorrectly indexed as Mg due to lower CIs has been reported in the literature [17]. On the other hand, the template matching successfully resolves over 94% of the scanned area to be 14H LPSO, agreeing with the previous OM, SEM, and TEM observations. It should be noted that the unindexed patterns can be caused by Ni-rich precipitates or grain boundaries. An undesirable surface is also believed to be another reason for the indexing failure of the template matching. This new approach not only successfully resolves LPSO phases from Mg, but also distinguishes different LPSO phases.

One example of the indexed EBSD pattern from the template matching algorithm is shown in Figure 4. The correlation coefficients (s) [19], which indicate how good the matching between the experimental and simulated pattern is, of the three candidate phases (Mg, 14H, and 18R) are 0.2270, 0.3003, and 0.1030, respectively. This indicates that the experimental pattern shown in Figure 4a belongs to 14H LPSO. The patterns of these three phases resemble each other closely in terms of the position of major Kikuchi lines, which can be hardly distinguished from the traditional Hough transformation approach [18]. The extra periodicity introduced by difference stacking sequences in LPSO phases mainly introduces extra lines with low intensity and line intensity changes, which are correctly captured by the template matching algorithm. The correlation coefficients of most indexed patterns are relatively lower (~0.2–0.4). Although the poor surface and inherently lower pattern quality of LPSO is surely the main culprit, it should also be noted that the shape of the on-site EBSD detector is also another reason. As can be seen in the experimental pattern in Figure 4a, any pattern signals that fall out of the round detector (four corners) are lost, while the simulated pattern covers the entire squared image, meaning that ~21.5% area of the experimental pattern is always inherently different to the simulated patterns. Although it reduces the exact correlation coefficient value of each pattern, it can be regarded as a systematic error and should have no effect on the final indexing result.

5. Conclusions

In this study, we demonstrate the successful use of the template matching approach in indexing the EBSD patterns from phases with identical atomic structures but different stacking sequences, such as LPSO polytypes. Using the 14H LPSO single-phase alloy as the model system, ~94% of the EBSD patterns from a single map were correctly indexed as 14H LPSO phases, whereas these patterns were misidentified as Mg by on-site commercial software. In solving the ambiguity in EBSD analysis of LPSO phases using such a technique, we anticipate advancements in clarifying microstructure–property relationships of Mg alloys involving LPSO phases, thereby aiding the development of high-strength and high-ductile Mg alloys.

Author Contributions

The single-phase alloy was fabricated by J.Y.; characterization was carried out by Y.L.; data analysis was conducted by Y.L. and G.-z.Z.; and the manuscript was written by Y.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Acknowledgments

The authors thank Xiaopeng Yang for his assistance in generating the master patterns of the involved phases.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures

Figure 1. Images illustrating the principles of RTM. Three candidate phases (Mg, 14H, and 18R) are input into the AZtecCrystal MapSweeper to obtain the master patterns. Pattern libraries are then generated based on these master patterns, which can be compared to the experimental pattern. The corresponding best match is subjected to a refined matching to obtain the final indexing result. Master patterns shown in the top right part are viewed along the identical direction; while the overall distribution is quite similar for all three phases, clear intensity differences in Kikuchi lines can be observed.

Figure 2. Microscopy characterization and phase identification. (a) Optical and (b) SEM micrographs showing continuous and uniform contrast; (c) TEM SEAD pattern giving clear evidence of 14H LPSO.

Figure 3. A comparison of the same area indexed using commercial software and RTM. (a) Commercial software, with most areas being indexed as Mg with low averaged CIs (~0.04); (b) RTM, correctly indexing ~94% area as 14H LPSO. Corresponding inverse pole figures (IPFs) are shown on the right of each map. The average Image Quality (IQ) of the area is ~839.

Figure 4. Indexing results from the RTM algorithm’s (a) experimental pattern; best-matching results for (b) Mg, (c) 14H, and (d) 18R. Red values are the corresponding correlation coefficients.

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