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Article

Efficient Implementation of the Binary Common Neighbor Analysis for Platinum-Based Intermetallics

by
Wenming Tang
1,
Xianxian Zhang
1,
Jianfeng Tang
1,
Xingming Zhang
1,
Liang Wang
1,2,
Wangyu Hu
3 and
Lei Deng
1,*
1
School of Chemistry and Materials Science, Hunan Agricultural University, Changsha 410128, China
2
The Peac Institute of Multiscale Sciences, Chengdu 610207, China
3
College of Materials Science and Engineering, Hunan University, Changsha 410082, China
*
Author to whom correspondence should be addressed.
Metals 2024, 14(6), 614; https://0-doi-org.brum.beds.ac.uk/10.3390/met14060614
Submission received: 15 April 2024 / Revised: 18 May 2024 / Accepted: 21 May 2024 / Published: 23 May 2024
(This article belongs to the Section Computation and Simulation on Metals)
Browse Figures
Versions Notes

Abstract

:
The common neighbor analysis (CNA) for binary systems is a powerful method used to identify chemical ordering in intermetallics by unique indices. The capability of binary CNA, however, is largely restricted by the availability of indices for various ordered phases. In this study, CNA indices of 11 ordered phases derived from a face-centered cubic structure were introduced on a case-by-case basis. These phases, common in intermetallics containing platinum-group metals, include C11b, MoPt2, C6, B11, AgZr, A2B2[111], A2B2[113], Pt3Tc, A3B[011], A3B[111], and A3B[113]. The chemical order in static chemical perturbation, dynamic phase competition, and experimentally reconstructed nanophase alloys were identified using binary CNA. The results indicated that the proposed version of binary CNA exhibited significantly higher accuracy and robustness compared to the short-range order, polyhedral template matching, and the original binary CNA method. Benchmarked against available methods, the formation, decomposition, and competition of specifically ordered phases in bulks and nanoalloys were well reflected by present CNA, highlighting its potential as a robust and widely adopted tool for deciphering chemical ordering at the atomic level.

1. Introduction

Atomic simulations provide detailed insights into material equilibrium structures, thermodynamic properties, and dynamic processes at the atomic scale, primarily through methods such as molecular statics, molecular dynamics (MD), and Monte Carlo (MC) simulations [1,2,3,4]. One of the most challenging aspects of atomic simulations lies in analyzing the vast amounts of generated data [3]. Typically, accurate and effective algorithms are needed to identify local structures within atomic configurations, such as crystal phases, crystal defects, or structural motifs in liquid and glass. Voronoi analysis [5], for instance, utilizing Voronoi polyhedra to reflect the characteristics of the topology of neighboring atoms, is often used in the analysis of liquid and glass [5,6,7]. However, even slight disturbances can cause fluctuations in the morphology of Voronoi polyhedra, making it difficult to identify thermalized crystals and distinguish hexagonal close-packed (HCP) structures from face-centered cubic (FCC) ones [8,9]. The common neighbor analysis (CNA) makes full use of the topology of atom pairs in common neighbors of the reference atom and one of its first nearest neighbors (first NNs) [10,11]. With specific CNA signatures, this method can distinguish HCP, FCC, body-centered cubic (BCC), icosahedral structures, and extended surfaces, and it is more robust to thermal fluctuation than Voronoi analysis. The geometrical symmetry of the atomic configuration is also a common criterion. The central symmetry parameter, for example, quantifying the local loss of central symmetry in atomic positions, can be applied to determine symmetric lattices, including BCC and FCC, but not HCP [12,13,14].
The identification of chemically ordered phases in binary and multi-component alloys remains a challenge in atomic simulations. Warren–Cowley long-range order (LRO) and short-range order (SRO) are classical parameters focusing on global or local chemical ordering, respectively. In fact, the former characterizes the averaged occupation probabilities of each component on sublattices that are well defined for single crystalline but not for polycrystalline and nanostructured alloys. In contrast, the latter focuses on the occupation probabilities of each component around an atom. Thus, the SRO is still indeterminate intrinsically as it usually considers the number and composition of first NNs, but not their spatial arrangements [15,16,17,18,19,20]. Interestingly, some of the topological analysis methods originally developed for monoatomic systems can be further extended to deal with chemically ordered phases in alloys [21,22]. For example, inspired by Voronoi analysis, the polyhedral template matching (PTM) method utilizes the convex hulls formed by the neighbor set of an atom and thus allows for the analysis of not only HCP, FCC, and BCC structures but also B2, L10, and L12 ordered phases [23,24]. By taking into account the topology of common first NNs for heterogeneous chemical species, the CNA method for binary alloys was proposed and implemented, so that the L10, L11, L12, and L60 LRO phases can be recognized with additional three indices [25,26]. This binary CNA method was further extended to the second nearest neighbors (second NNs) and can thus distinguish similar LRO phases from each other, such as D1/D7, “CH”/40, L10, L11, L12, L13, and D022 [26].
Among various LRO phases spanning vast amounts of intermetallic compounds, herein, we focus on the FCC-derived superstructures with four atoms per cell or fewer due to their combinatoric and geometric simplicity [27,28,29]. As suggested by exhaustive enumeration and confirmed by high-throughput computation, such as cluster expansions, there are only 17 LRO phases [27,29]. Figure 1 gives a bird’s eye view of the comparison and correlation of composition arrangement among these superstructures. Furthermore, Table 1 gives a broad overview of all occurrences of a given LRO phase in binary alloy systems based on platinum-group metals (PGMs). This unique chemical ordering provides plenty of room for tuning the catalytic efficiency or stability of the platinum (Pt) shell or skin by a Pt-based intermetallic core or substrate through the ligand or strain effects [30,31]. Therefore, the capability to identify these LRO phases is important to the rational design of PGM nanocatalysts with reduced cost and high performance [32,33,34,35]. Although the binary CNA method has been applied to identify several common ground states, the CNA signatures of remaining 11 LRO phases need to be analyzed in detail to complement the entire landscape. In this study, CNA signatures along with additional criteria were obtained for the following LRO phases: C11b, MoPt2, C6, B11, AgZr, A2B2[111], A2B2[113], Pt3Tc, A3B[011], A3B[111], and A3B[113]. The robustness and accuracy of binary CNA were verified through chemical perturbation, dynamic phase competition, and experimentally reconstructed nanophase alloys. It was demonstrated that binary CNA can be effectively applied to atomic configurations involving chemical or thermal perturbation, as well as a wide range of surfaces and defects. Consequently, the proposed version of the binary CNA method represents a valuable resource for comprehensive investigation into the identification of ordered phases in processes, such as the ordered–disordered transition and the formation and competition of ordered phases in binary alloys.

2. Model and Method

The parameters of the extended binary CNA only consider the first and second NNs of atoms. Considering the similarities between the structures of different ordered phases, for example, the atomic environments within the second NNs of atoms with lower stoichiometry in MoPt2 and A3B[011] are identical, which leads to situations where the types of ordered phases cannot be distinguished within the range of second NNs. Therefore, it is necessary to introduce additional criteria to distinguish these ordered phases, involving as few nearest neighbors as possible. This section clarifies the genesis of all parameters in the proposed binary CNA and provides clear additional distinguishing conditions so that similar ordered phases can be accurately differentiated.

2.1. CNA for Binary Alloys

The original CNA method involves geometric analysis of atom pairs, considering three key factors: (i) whether two atoms are first NNs, (ii) the number of common first NNs shared by two atoms, and (iii) the topological relationship among these common first NNs [25,26]. The criteria for identifying first NNs involve assessing whether the distance between a reference atom and another atom is below a critical threshold, typically defined as the minimum value between the first and the second peaks on the radial distribution function. If two atoms are first NNs to each other, they are considered to be geometrically connected by a geometry bond rather than a chemical bond. Figure 2 shows the arrangements of a reference atom and its first NNs, second NNs, and common first NNs for determining CNA signatures. The CNA method utilizes three parameters, namely, ijk, to describe atom pairs that are first NNs. Here, i represents the number of common first NNs, j indicates the number of bonds among these common first NNs, and k denotes the number of bonds in the longest chain formed by these j bonds. The combination of these three indices constitutes a representative signature for a specific crystal phase. For example, an atom’s ijk signature of 12 × 421 corresponds to the FCC structure. Various signatures for different crystal phases can be found in reference [37].
For intermetallic systems, a binary CNA method was proposed, which introduced three indices, namely, t, u, and v, as supplementary criteria to describe the ordering types of atom species within common first NNs [23]. For these three indices, t represents the chemical type of the chosen reference atom, u represents the chemical types of first NNs of the reference atom, and v encompasses the distribution information of the common first NNs. The details of the CNA signature, ijk-tuv, were analyzed for L10, L11, L12, and L60 ordered phases [24,25]. However, challenges arise when dealing with LRO structures, like L12 and “CH”/40. To address this challenge, the heterogeneity or homogeneity of the atom pair (the reference and its second NNs) was introduced as extra to ijk-tuv signatures, which was proved effective in distinguishing D1/D7, L10, L11, “CH”/40, L12, L13, and D022 structures, at least [26].
When dealing with varied superstructures spanning Pt-based intermetallics, it will be necessary to further incorporate additional criteria into binary CNA signatures. As illustrated in Figure 3, for instance, repetitive binary CNA signatures may occur among similar LRO phases. Herein, specific configurations of extended NNs were incorporated as the extra criteria, as depleted in Figure 4. Therefore, these 17 superstructures can be differentiated and accommodated in the same framework, which has been concluded in Figure 3 and will be detailed case by case in subsequent sections.

2.2. Binary CNA Parameters for C6, A2B2[111], and A3B[111] Phases

The C6 phase consists of two layers of A atoms alternating with one layer of B atoms along the [111] direction. The atomic ratio between A and B in this phase is 2:1. In contrast, the A2B2[111] phase involves two alternating layers of A and B atoms along the [111] direction, with an equal atomic ratio (1:1) within the phase. The A3B[111] phase is formed by stacking three layers of A atoms followed by one layer of B atoms along the [111] direction, resulting in an A-to-B atom ratio of 3:1. It is important to note that there are two different types of A atoms within the A3B[111] phase, each with a distinct surrounding environment. These include A-layer atoms located between the A and B layers, as well as A-layer atoms positioned between the two A layers. The A atom type A1, located between the A and B layers, has a comparable atomic environment to the A atoms in the C6 and A2B2[111] phases.
When atom A is taken as the reference atom (Aref and t = type A), the topological relationship of the twelve first NNs of A is discussed in Figure 5, Figure 6 and Figure 7 (The geometric bond between the reference atom in the center of cells and the first NN atom is colored in green with a dashed line, while connected common first NNs are shown in pink with dotted lines), as well as Tables S1 and S2. Within the surrounding twelve first NNs, there are nine atoms of type A, three of which form A-A pairs in common first NNs (v = type A), while the remaining six form A-B pairs in common first NNs (v = type G). Additionally, the common first NNs of three type B atoms (u = type B) also form A-A and B-B pairs (v = type F).
According to the description provided, the binary CNA parameters for A atoms in these three phases consist of three 421-AAA patterns, six 421-AAG patterns, and three 421-ABF patterns. To differentiate between these three phases with identical binary CNA signatures, additional conditions were introduced. Firstly, atoms of a different type are identified within the first NNs of the Aref. Subsequently, their first NNs are examined among these identified atoms of a different type. The next step is to count the number of atoms that belong to the same type as Aref among these first NNs. If there are three atoms of the same type as Aref, the phase is identified as A2B2[111]. If there are six atoms of the same type as Aref, the phase can be either C6 or A3B[111]. To further distinguish between the C6 phase and A3B[111], it is necessary to identify three second NNs of type A. Next, three sets of pairs of second NNs form among the three second NNs, with shares two common second NNs. In addition to the Aref, there are three other distinct second NNs. If these three identified atoms are of the same type as the Aref, the phase corresponds to A3B[111]. Conversely, if these three identified atoms differ in type from the Aref, the phase indicates the C6 phase.

2.3. Binary CNA Parameters for L11, C6, and A3B[111] Phases

The L11 structure is formed by alternative stacking of one layer of A atoms and one layer of B atoms along the [111] direction. Although the ordered arrangements of C6 and A3B[111] have been mentioned earlier, in all three of these structures, B atoms are situated between two layers of A atoms, resulting in identical first NNs and second NNs environments for B atoms. When considering B as the reference atom (Bref and t = type B), if A is the first NN (u = type A), the resulting configuration yields six 421-BAF patterns. However, if the first NN is another B (u = type B), the resulting configuration yields six 421-BBE patterns.
To distinguish between these three types of Bref, additional criteria based on the original parameters must be included. First, it is necessary to identify the first NNs that differ from the Bref. Then, within this set of distinct first NNs, it is necessary to determine their respective first NNs. If there are six atoms of the same type as the Bref among these further identified first NNs, it indicates an ordered L11 phase. If only three atoms of type B are present, it is necessary to ascertain whether there exist twelve atoms of type A among these additionally found first NNs. If all twelve first NN atoms are type A, this ordered phase can be classified as A3B[111]. Otherwise, it corresponds to a C6-ordered phase.

2.4. Binary CNA Parameters for “CH”/40, C11b, and Pt3Tc Phases

The “CH”/40 phase consists of two alternating layers of A atoms and two alternating layers of B atoms along the [201] direction. The C11b phase is formed by alternating two layers of A atoms and one layer of B atoms along the [001] direction. The Pt3Tc phase is formed by alternating three layers of A atoms and one layer of B atoms along the [001] direction. The CNA parameters for the B atom in all three cases are as follows. When the reference atom is B (Bref and t = type B), its surrounding A atoms (u = type A) form eight 421-BAE patterns, while its surrounding B atoms (u = type B) form four 421-BBA patterns.
To distinguish these three types of B atoms, it is necessary to identify four atoms in the first NNs that are of the same type as the Bref. If these atoms are not coplanar, the phase corresponds to “CH”/40. In cases of coplanarity, the phase is either C11b or Pt3Tc. To distinguish between C11b and Pt3Tc phases, it is necessary to identify the second NNs of type A. If there are four coplanar atoms of type B among these two sets of first NNs, they correspond to the C11b phase. On the other hand, if all twelve first NNs atoms are type A, then they correspond to the Pt3Tc phase.

2.5. Binary CNA Parameters for MoPt2 and A3B[011] Phases

The MoPt2 phase is formed by alternating two layers of A atoms and one layer of B atoms along the [011] direction. Similarly, the A3B[011] phase is created by alternating three layers of A atoms with one layer of B atoms along the same direction. The binary CNA parameters for B atoms in both phases share a common feature: the reference atom (Bref, type B) has ten first NNs of A atoms (u = type A), two of which form 421-BAA patterns, while the remaining atoms form 421-BAG patterns. Additionally, there are two first NNs of B atoms (u = type B) forming 421-BBA patterns within the first NNs.
To distinguish between these two phases based on the B atoms, it is necessary to follow these steps. First, locate the first NNs for the Bref that belong to a different type. Then, search for type B atoms within the first NNs of the first NNs. If the number of atoms belonging to the same type as the Bref is exactly five, the phase can be identified as MoPt2. Otherwise, it should be denoted as A3B[011].

2.6. Binary CNA Parameters for L13 and A3B[113] Phases

The L13 phase is analogous to the L11 phase, as it replaces every other layer of B atoms with A atoms along the [111] direction. The A3B[113] phase is formed by stacking three layers of A atoms alternating with one layer of B atoms along the [113] direction. The CNA parameters for the B atoms in both structures are as follows: the reference atom is B (Bref, t = type B), with ten A atoms forming two 421-BAA patterns and eight 421-BAG patterns in the first NNs, while the remaining two B atoms form 421-BBG patterns.
To differentiate the B atoms in the two phases, first, it is necessary to identify the second NNs of Bref. Then, it is necessary to find the common second NNs of these second NNs, excluding the central atom. If all of the common second NNs are type B, then the phase is classified as L13. If there are six type B atoms among these common second NNs, then the phase is classified as A3B[113].

2.7. Other Repetitive Cases

Since this paper only focuses on the properties of atomic geometric positions, the extended binary CNA parameters obtained by interchanging the types of A and B in the phases of equimolar phases, such as L10, L11, B11, AgZr, A2B2[111], “CH”/40, and A2B2[113], are identical. For example, if we consider AgZr with Bref, interchanging all A and B types would result in a CNA signature identical to that with Aref. In these cases, additional methods of distinction are no longer needed.

3. Validation and Application

For the first test of the present CNA method, atomic configurations containing 4000 atoms of the perfect single phases are generated and analyzed. For these 17 superstructures, binary CNA signatures, along with extended NN information, are able to correctly identify each single phase in the same framework. However, the robustness to chemical perturbation and lattice distortion, as well as the performance compared with available methods, still need to be further validated.

3.1. Robustness to Chemical Perturbation

Starting with perfect L10 (Fe0.5Pt0.5) or L12 (Fe0.25Pt0.75) bulks containing 4000 atoms, 1% of atoms were randomly chosen and subsequently exchanged the chemical identity. Then, a chemically perturbated Fe0.5Pt0.5 sample and an off-stoichiometric Fe0.275Pt0.725 sample were created, respectively. Within both samples, the chemical ordering was reassessed and compared to the PTM method implemented in OVITO [38]. As shown in Figure 8, the percent of the L10 phase recognized by the PTM method is 87.17%, while it is 81.70% with the present binary CNA method. In the off-stoichiometric sample, the percent of the L12 phase recognized by the PTM method is 87.97%, while it is 82.95% with the binary CNA method. This discrepancy arises from the fact that the criteria of binary CNA are stricter than those of the PTM method. When the chemical type of an atom changes, the bonding relationships between that atom and its NNs also change. For instance, a single anti-site defect will create twelve chemical disordered sites at a range of first NNs and an extra six disordered sites in the range of first NNs to second NNs. It is reasonable to assume that the anti-site defects are isolated when only 1% of atoms are randomly exchanged. Therefore, we can infer that 88% of the L10 phase remains, as suggested by the PTM method that focuses on the topology of first NNs, while 82%, according to the binary CNA method, takes into account the influence of second NNs. For binary systems far from LRO or stoichiometry, however, such an accurate estimate will be challenging, and thus detailed analysis is needed.

3.2. Dynamic Phase Competition in a Thermalized System

Due to the difference in formation energies, varied LRO phases exhibit different ordering trends and compound-forming possibilities over the parameter space of components and stoichiometries. The formation and decomposition of specific LRO phases in thermalized (at 300 K) Fe0.5Pt0.5 bulks were examined. The starting configuration is a L10/A2B2[111] composite consisting of 4096 atoms. The MC-MD coupling simulations with embedded atom potential were carried out to search over large portions of configuration space [39,40,41,42]. Figure 9 shows the evolution of LRO phases in Fe0.5Pt0.5 bulks, where chemical disordering and lattice distortion were introduced by thermalization and relaxation. At the beginning, both the A2B2[111] phase and L10 phase completely disappear. As the simulation progresses, the L10 phase subsequently reappears and gradually increases to about 85%. It is worth noting that other metastable LRO phases are also involved in these dynamic competitions. That is to say, the “CH”/40 and A2B2[113] phases appear after the decomposition of A2B2[111] and compete with not only each other but also the L10 phase. According to our static calculation based on embedded atom potential, the formation energy of A2B2[111], A2B2[113], and “CH”/40 is −0.219, −0.546, and −0.622 eV/atom, respectively, higher than that of the L10 phase (−0.628 eV/atom). Despite similar thermodynamic stability, however, the amount of the “CH”/40 phase is much lower than that of the L10 phase. This interesting discrepancy may be attributed to lattice mismatch induced by the favorable stacking direction of Fe and Pt, as illustrated in Figure 1. Therefore, there are a small number of “CH”/40 and A2B2[113] residuals. It is evident that the present binary CNA can be applied to characterize and extract LRO phases from thermalized and relaxed systems, especially metastable ones that cannot be identified by available tools. The capability to characterize metastable phases is important for utilizing PGM alloys as promising catalysts, and most of which are difficult to access kinetically in the bulk but may be exhibited in epitaxial films or nanophase alloys.

3.3. Partial Ordering in an Experimentally Reconstructed Nanophase Alloy

Perfectly ordered alloys that are thermodynamically favorable may not be commonly found in practice. During synthesis, chemical ordering that is usually hindered by kinetic diffusion can be achieved upon high-temperature annealing. Taking the Fe-Pt system as an example, when annealed at high temperatures, chemically disordered Fe-Pt thin films or nanoparticles can transform into L10 or L12 phases, depending on the chemical compositions [43,44,45,46]. Herein, LRO phase analysis was performed on Fe0.28Pt0.72 nanophase alloys, as illustrated in Figure 10. The atomic configuration of nanoparticles was reconstructed by ADF-STEM, which is composed of 23,196 atoms, as depicted in Figure 10a [47]. The resultant LRO phases identified by the SRO parameter, PTM method, and the original or present version of binary CNA are given in Figure 10b–e, while an overall comparison across these methods is illustrated in Figure 10f. The SRO parameter reveals a content of 33% in the L12 phase and 2% in the L10 phase in the nanoparticle. A total of 30% of the L12 phase and 1% of the L10 phase are recognized by the PTM method. According to the original binary CNA, a content of 20% of the L12 phase and 0.5% of the L10 phase coexist in the nanoparticle. The present binary CNA method also discovers a content of 7.2% in the L12 phase and a minor presence of the D022 phase (0.5%) but not the L10 phase.
The difference in the amount of the major LRO phase and the L12 superstructure among these identification methods greatly depends on their degree of strictness. The SRO parameter and PTM analysis focus on the number and composition or topology of equivalent neighboring atomic sites of an atom, usually its first NN. Therefore, they tend to overestimate the occurrence of FCC-derived superstructures. The original version of binary CNA further takes into account the bonding relationship among the common first NN of a pair of atoms. In contrast, the extended version considers configurations of second NNs, resulting in improved precision in distinguishing ordered phases compared to the original one. Therefore, this modification further reduces the occurrence of specific ordered phases when compared to the original method. Furthermore, the present extended version considers various long-ranged NNs, depending on chemical ordering, and thus is the strictest method. It works well for bulk materials, as illustrated previously, but seems to underestimate the amount of LRO phases in nanomaterials. For nanoparticles, there is a significant proportion of surface and dispersed defects, as illustrated in Figure S1. In the present framework, both the under-coordinated atoms themselves and their long-ranged NNs cannot be assigned to a specific ordered phase.

4. Conclusions

This work expands upon the existing framework of extended binary CNA by incorporating additional structures. Eleven new binary CNA parameters are introduced, expanding the original set of six structures to include C11b, MoPt2, C6, B11, AgZr, A2B2[111], A2B2[113], Pt3Tc, A3B[011], A3B[111], and A3B[113]. The methodology for distinguishing repetitive binary CNA parameters among these 17 structures is also established. After correctly identifying the perfectly ordered phases, three types of atomic configurations with various degrees of imperfection were selected to validate the robustness and accuracy of the proposed binary CNA method. Firstly, the atomic configurations of L10-PtFe and L12-Pt3Fe with slight chemical perturbations (1%) were processed. Compared with the PTM method, the proposed binary CNA method is more stringent, as it considers the second NNs. Next, the evolution of ordered phases in the L10/A2B2[111]-PtFe composite was identified in real time. In this system, exhibiting lattice distortion due to thermal perturbation, the ultimate dominant phase is L10, aligning with the trend observed in the formation energies of ordered phases from static calculations. Finally, the experimentally reconstructed nanophase alloy was processed, which is chemically and thermally perturbated, and thus exhibits numerous surface and internal defects. Despite the fact that D022 shares the same first NN with L12. The proposed binary CNA is capable of distinguishing D022 from L12, beyond the ability of the PTM method, the original or extended version of the CNA method, and the SRO parameter. For defect-rich nanophase alloys, the proposed binary CNA can be further enhanced in fault tolerance to defects, thereby obtaining a reasonable amount of ordered phases. In principle, the proposed binary CNA can be applied to FCC-derived superstructures, and it requires a comprehensive analysis of all CNA parameters and additional criteria.

Supplementary Materials

The following supporting information can be downloaded at https://0-www-mdpi-com.brum.beds.ac.uk/article/10.3390/met14060614/s1, Table S1: Extended binary CNA feature parameters for new N = 3 derived structures. Includes MoPt2, C6, and C11b; Table S2: Extended binary CNA feature parameters for new N = 4 derived structures. Includes B11, AgZr, A2B2[111], A2B2[113], Pt3Tc, A3B1[011], A3B1[111], and A3B1[113]; Figure S1: FCC structure and atomic distribution without structure type in Fe0.28Pt0.72 nanoparticles. The atoms are colored according to their coordination number.

Author Contributions

Conceptualization, W.T.; methodology, W.T. and J.T.; writing—original draft preparation, W.T. and X.Z. (Xianxian Zhang); validation, X.Z. (Xianxian Zhang) and L.W.; writing—review and editing, X.Z. (Xingming Zhang), W.H. and L.D; software, W.T. and X.Z. (Xingming Zhang); investigation, X.Z. (Xingming Zhang) and L.W.; visualization, X.Z. (Xianxian Zhang) and L.W.; resources, J.T.; data curation, J.T. and L.D.; supervision, W.H. and L.D; funding acquisition, W.H. and L.D; project administration, L.D. All authors have read and agreed to the published version of the manuscript.

Funding

We acknowledge the support of the Natural Science Foundation of Hunan Province (Grant Nos. 2023JJ30309, 2019JJ50221, and 2020JJ5260), the Funding of the Hunan Education Department Project (Nos. 20A248 and 22B0225), and the Ministry of Science and Technology of the People’s Republic of China (National Key Research Project of China, Grant 2023YFB3003000).

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors upon request.

Acknowledgments

We acknowledge the support of the computation platform of the National Super Computer Center in Changsha (NSCC).

Conflicts of Interest

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

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Metals 14 00614 g001
Figure 1. The set of all FCC-derived binary LRO phases with unit cell sizes that are two, three, and four times larger than the parent lattice. For some superstructures (denoted by the star *) among the 17, the binary CNA parameters are available. Reprinted with permission from ref. [27], 2024, American Physical Society.
Figure 1. The set of all FCC-derived binary LRO phases with unit cell sizes that are two, three, and four times larger than the parent lattice. For some superstructures (denoted by the star *) among the 17, the binary CNA parameters are available. Reprinted with permission from ref. [27], 2024, American Physical Society.
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Figure 2. Arrangements of a reference atom and its (common) NNs utilized to determine the signatures of binary CNA.
Figure 2. Arrangements of a reference atom and its (common) NNs utilized to determine the signatures of binary CNA.
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Figure 3. Additional criteria about NNs used for LRO phases with the same CNA signatures. (a) Corresponds to Section 2.2, (b) corresponds to Section 2.3, (c) corresponds to Section 2.4, (d) corresponds to Section 2.5, (e) corresponds to Section 2.6.
Figure 3. Additional criteria about NNs used for LRO phases with the same CNA signatures. (a) Corresponds to Section 2.2, (b) corresponds to Section 2.3, (c) corresponds to Section 2.4, (d) corresponds to Section 2.5, (e) corresponds to Section 2.6.
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Figure 4. Arrangements of varied NNs considered for identifying LRO phases with the same signatures. (a) Schematic of the positions of the first NNs of the first NNs, (b) schematic of the positions of the second NNs of the first NNs, (c) schematic of the positions of the second NNs of the second NNs.
Figure 4. Arrangements of varied NNs considered for identifying LRO phases with the same signatures. (a) Schematic of the positions of the first NNs of the first NNs, (b) schematic of the positions of the second NNs of the first NNs, (c) schematic of the positions of the second NNs of the second NNs.
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Figure 5. Arrangements of twelve common first NNs for the C6 phase (a) with Aref and (b) with Bref. The geometric bond between the reference atom in the center of cells and one first NN atom are colored in green (dashed line) and those connected common first NNs in pink (dotted line).
Figure 5. Arrangements of twelve common first NNs for the C6 phase (a) with Aref and (b) with Bref. The geometric bond between the reference atom in the center of cells and one first NN atom are colored in green (dashed line) and those connected common first NNs in pink (dotted line).
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Figure 6. Arrangements of twelve common first NNs for the A2B2[111] phase (a) with Aref and (b) with Bref. The color scheme for the dotted line is identical to that of Figure 5.
Figure 6. Arrangements of twelve common first NNs for the A2B2[111] phase (a) with Aref and (b) with Bref. The color scheme for the dotted line is identical to that of Figure 5.
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Figure 7. Arrangements of twelve common first NNs for the A3B[111] phase (a,b) with Aref and (c) with Bref. The color scheme for the dotted line is identical to that of Figure 5.
Figure 7. Arrangements of twelve common first NNs for the A3B[111] phase (a,b) with Aref and (c) with Bref. The color scheme for the dotted line is identical to that of Figure 5.
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Figure 8. L10 and L12 phases in off-stoichiometric Fe0.495Pt0.505 and Fe0.245Pt0.755 bulks, respectively. Yellow indicates Fe atoms and gray indicates Pt atoms. (a,d) Show the atomic configurations, (b,e) present the identification results for (a,d) using the PTM method, and (c,f) show the identification results for (a,d) using the proposed binary CNA method.
Figure 8. L10 and L12 phases in off-stoichiometric Fe0.495Pt0.505 and Fe0.245Pt0.755 bulks, respectively. Yellow indicates Fe atoms and gray indicates Pt atoms. (a,d) Show the atomic configurations, (b,e) present the identification results for (a,d) using the PTM method, and (c,f) show the identification results for (a,d) using the proposed binary CNA method.
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Figure 9. Evolution of LRO phases in the FePt L10/A2B2[111] composite during MC simulations. Yellow indicates Fe atoms and gray indicates Pt atoms.
Figure 9. Evolution of LRO phases in the FePt L10/A2B2[111] composite during MC simulations. Yellow indicates Fe atoms and gray indicates Pt atoms.
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Figure 10. Atomic configuration of the Fe0.28Pt0.72 nanoparticle and LRO phases recognized by different methods: (a) atomic configuration from ADF-STEM, where yellow indicates Fe atoms and gray indicates Pt atoms, (b) SRO based on the composition of first NNs, (c) PTM, (d) extended binary CNA, (e) present version of binary CNA, (f) overall comparison of resultant concentration of LRO phases.
Figure 10. Atomic configuration of the Fe0.28Pt0.72 nanoparticle and LRO phases recognized by different methods: (a) atomic configuration from ADF-STEM, where yellow indicates Fe atoms and gray indicates Pt atoms, (b) SRO based on the composition of first NNs, (c) PTM, (d) extended binary CNA, (e) present version of binary CNA, (f) overall comparison of resultant concentration of LRO phases.
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Table 1. The occurrence of common FCC-derived LRO phases in PGM-based binary alloys. Adapted from Ref. [36].
Table 1. The occurrence of common FCC-derived LRO phases in PGM-based binary alloys. Adapted from Ref. [36].
ScTiVCrMnFeCoNiCuZnYZrNbMoTcRhPdAgCdHfTaRe
L10-IrPtPtPtPt-Pt-Pt--Pt-----Pt-Pt-
L11--------Pt-------PtPt----
C11bRuIrOs--------Pt-------Pd--
MoPt2--Pt---------PtPt------Pd-
C6------------Pt---------
L12PtIr-PtPtPt--PtPtPtPtRu---PtPtPtIrIr-
L13--------PtPt--------Pt---
B11--------------------Pd-
AgZr----------------------
A2B2[111]----------------------
“CH”/40---------------Pt------
A2B2[113]---------------Ir------
Pt3Tc--------------Pt------Pt
A3B[011]------Pd-------------Ru-
A3B[111]----------------------
D022--Pt--Ir-Pt-Pt-----Pt--Pd-Pd-
A3B[113]---------------Ir------
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Tang, W.; Zhang, X.; Tang, J.; Zhang, X.; Wang, L.; Hu, W.; Deng, L. Efficient Implementation of the Binary Common Neighbor Analysis for Platinum-Based Intermetallics. Metals 2024, 14, 614. https://0-doi-org.brum.beds.ac.uk/10.3390/met14060614

AMA Style

Tang W, Zhang X, Tang J, Zhang X, Wang L, Hu W, Deng L. Efficient Implementation of the Binary Common Neighbor Analysis for Platinum-Based Intermetallics. Metals. 2024; 14(6):614. https://0-doi-org.brum.beds.ac.uk/10.3390/met14060614

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Tang, Wenming, Xianxian Zhang, Jianfeng Tang, Xingming Zhang, Liang Wang, Wangyu Hu, and Lei Deng. 2024. "Efficient Implementation of the Binary Common Neighbor Analysis for Platinum-Based Intermetallics" Metals 14, no. 6: 614. https://0-doi-org.brum.beds.ac.uk/10.3390/met14060614

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