Advanced Electron Microscopy Image Processing for Analyzing Amorphous Alloys: Electron Microscopy Image Cluster Analyzer (EMICA). Tool and Results

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1. INTRODUCTION

Electron microscopy has been a powerful tool in materials science research, allowing us to explore the atomic-scale structure and properties of various materials. Amorphous alloys, known for their disordered atomic structure, have attracted significant attention due to their unique characteristics and potential applications [1–3]. This article introduces EMICA, a Python-based software tool developed to enhance electron microscopy image processing for the analysis of amorphous alloys.

2. BACKGROUND

Amorphous alloys, characterized by their lack of long-range order, present challenges in terms of structural analysis. The need to understand the atomic-scale structure and physicochemical properties of these materials has driven the development of specialized tools. EMICA has made valuable contributions to this field, by simplifying and automating cluster analysis and spatial pattern recognition.

3. EMICA: AN ELECTRON MICROSCOPY IMAGE CLUSTER ANALYSIS TOOL

EMICA is a versatile and open-source software tool designed to streamline electron microscopy image processing. Its user-friendly interface makes it accessible to researchers in materials science and related disciplines. At its core, EMICA automates cluster analysis and spatial pattern recognition, significantly improving the efficiency of electron microscopy data analysis.

4. MATERIALS AND EXPERIMENTAL TECHNIQUES

In this study, we employed electrochemical deposition to fabricate samples of three distinct amorphous alloys: CoP, CoNiP, and NiW. The examination of the atomic structures of these samples was carried out via high-resolution transmission electron microscopy (HRTEM) on an FEI Titan 80–300, instrument operating at both 300 and 80 kV with aberration correction [4; 5].

The thinness of the samples, ranging from 2 to 10 nm, enabled us to conduct a detailed investigation of the local atomic structure, revealing varying degrees of ordering within the alloys. HRTEM images were acquired over a range of temperatures, from 20 to 300 °C.

 

Fig. 1. Original electron microscopy image of the amorphous alloys CoP and NiW

 

After high-resolution transmission electron microscopy (HRTEM) images were acquired, an extensive post-processing phase was conducted using GPU software. The initial steps involved precise image calibration to ensure accurate measurements. Denoising techniques were subsequently applied to enhance clarity and reduce noise. Subsequently, the Particle Analyzer tool was employed for particle detection, with additional filtering procedures refining the identification based on factors such as size and circularity. The generation of coordinate points for each particle yielded a robust dataset.

The processing entailed cross-correlation using a double-core function represented mathematically as follow:

$H_{\phi ,r_0}\left(x,y\right)=h\left(x,y\right)\sum _{\phi }h\left(x-r_0\sin \phi ,y-r_0\cos \phi \right),$

The function h(x, y) was defined as h(x, y) = = sin c (ρ/ρ₀) – h₀, with specific parameters selected: r₀ = 0,25 nm, ρ₀ = 0,15 nm). The value of h₀ was determined based on the condition

$\sum _{x,y}h\left(x,y\right)\approx 0.$

This meticulously designed experimental setup and analytical approach allowed us to investigate and understand the intricate atomic structures and ordering in amorphous alloys, offering valuable insights into their material properties [6].

5. METHODOLOGY

The method employed by EMICA represents a systematic and comprehensive approach to electron microscopy image analysis, tailored to the unique challenges presented by amorphous alloys. This section outlines the key steps involved in processing electron microscopy data and extracting valuable insights into the atomic-scale structure and physicochemical properties of materials [7].

5.1. Euclidean Distance-Based Clustering Approach

In the Euclidean distance-based clustering approach employed by the software, the identification of atomic or particle clusters within electron microscopy images is achieved through a sequential process. The process involves the calculation of pairwise distances between all points or particles in the image, with each point treated as a potential cluster center.

Distance calculation

The application determines the Euclidean distance between each pair of points in the image, considering their spatial coordinates. Points that fall within a predefined range, defined by the minimum radius (RADIUS\_MIN) and maximum radius (RADIUS\_MAX), are considered neighbors.

Cluster formation

If the distance between two points is within the specified range, they are clustered together. This process is iteratively repeated until no more points can be added to the cluster, ensuring that all neighboring points within the defined radius are grouped together.

In general, this clustering approach enables EMICA to uncover the structural orderliness at various length scales within the material. It is particularly effective at capturing both local and extended atomic arrangements, making it well-suited for the analysis of amorphous alloys.

5.2. Angle calculation methods

Angle calculations are a crucial aspect of software tools and offer valuable insights into the structural orderliness of atomic or particle arrangements. In instances where EMICA detects a closed loop within a cluster, it employs a specialized angle calculation method. This method takes into account the Euclidean geometric rules based on the shape formed by the connected points and edges within the closed loop. By analyzing the geometric properties of the enclosed area, EMICA computes the angles between adjacent edges or bonds.

For clusters that do not exhibit a closed loop, EMICA calculates the angle between every possible triplet of particles within the cluster. This approach assesses the angular variations within the cluster, providing insights into the local atomic arrangements.

Implication: Closed-loop angle calculations are particularly relevant when identifying ring-like structures or closed shapes within a material. This method aids in quantifying the angular relationships between particles that constitute closed structural motifs.

However, non-closed loop angle calculations are versatile and applicable to a wide range of cluster configurations. These methods help uncover structural irregularities, deviations from ideal geometries, and variations in local orderliness.

5.3. Cluster visualization

EMICA provides a visual representation of identified clusters through undirected graphs for each cluster. These graphs illustrate the connectivity between particles within a cluster, offering a clear depiction of the structural organization.

Consequently, cluster visualization aids researchers in understanding the spatial arrangement of particles within each identified cluster. This approach provides a basis for further analysis and interpretation of cluster properties.

5.4. Angle statistics

EMICA computes statistical measures for the angles calculated within each cluster. These measures include the mean, median, and standard deviation, allowing a quantitative characterization of the angle distri-butions.

Overall, angle statistics provide researchers with insights into the degree of structural orderliness within clusters. Deviations from ideal angles and angular variations are quantified, contributing to a deeper understanding of material properties.

5.5. Cluster point distribution and visualization

EMICA also facilitates the visualization of point distributions within clusters through scatterplots. The points of each cluster are depicted, allowing researchers to observe the spatial distribution of particles within the cluster.

Therefore, scatterplots enable researchers to assess the distribution of particles within clusters, helping identify trends, patterns, and irregularities. This visualization aids in the exploration of material properties and structural motifs.

By incorporating these methodologies, EMICA empowers researchers in materials science to conduct in-depth analyses of electron microscopy images, unveiling critical insights into the atomic-scale structure and physicochemical properties of amorphous alloys and related materials. Clustering, angular calculation, visualization, and statistical analysis constitute a powerful toolkit for advancing research in this field.

6. RESULTS

In this section, we present the outcomes of our electron microscopy analysis using EMICA, highlighting its ability to unravel the structural orderliness and physicochemical properties of amorphous alloys. Real-world case studies showcase the software’s proficiency in materials science research.

 

Fig. 2. Cluster point distribution

 

6.1. Cluster visualization

One of the key strengths of EMICA is its ability to visualize the identified clusters within electron microscopy images. For each analyzed sample, undirected graphs are generated to illustrate the connectivity between particles within different clusters. Fig. 3 provides examples of cluster visualizations for two distinct samples.

 

Fig. 3. Cluster visualizations for clusters

 

Overall, cluster visualizations offer a visual representation of the atomic or particle arrangements within each identified cluster. Researchers can observe connectivity patterns and structural organization, providing a foundation for further analysis.

6.2. Analysis of angle distribution

To gain insights into structural orderliness, EMICA computes the distribution of angles within each cluster. The angles are categorized into bins from 0 to 180 degrees, allowing us to assess the probability of finding angles within specific ranges. Fig. 4 presents angle probability charts for the selected files.

 

Fig. 4. Probability distribution of angle

 

Consequently, angle probability charts provide researchers with a quantitative understanding of the pre-valence of specific angular relationships within clusters. The observed peaks may correspond to preferred structural motifs or arrangements.

6.3. Analysis of the cluster point distribution

Understanding the distribution of points within clusters is essential for characterizing their sizes and densities. EMICA facilitates the analysis of cluster point distributions by categorizing clusters based on the number of points they contain. Figure 6 displays the probability of finding a certain number of points within a cluster.

As a result, cluster point distribution charts help researchers assess the variability in cluster sizes and identify the presence of smaller or larger structural units within the material. This information contributes to a more comprehensive understanding of material properties.

Our sample, which is representative of a complex amorphous alloy with intricate atomic arrangements, revealed multiple clusters with distinct structural features through EMICA analysis. These clusters displayed interconnected atomic groups, hinting at ordered domains within the amorphous matrix.

 

Fig. 5. Cluster point distribution probability chart

 

Angle distribution analysis demonstrated specific angle prevalence within clusters, suggesting favored atomic arrangements. This insight is crucial for understanding structural stability and potential applications.

Cluster point distribution analysis revealed variations in cluster sizes, indicating material heterogeneity and localized regions of higher atomic density.

The visualization of the EMICA cluster highlighted distinct clusters, some with ring-like or closed-loop structures. Specialized angle calculations unveiled unique angular relationships, indicative of ordered ring motifs.

Angle probability charts confirmed the preferred structural configurations in the sample, offering insights into material stability and potential transformations.

Cluster point distribution analysis of our sample revealed a diverse range of cluster sizes, implying that varying structural units may impact the mechanical and electronic properties of the sample.

6.5. Discussion of Findings

The results obtained through the application of EMICA offer significant insights into the atomic-scale structure and physicochemical properties of amorphous alloys. The combination of cluster visualization, angle distribution analysis, and point distribution assessment enhances our understanding of these materials.

In particular, the identification of preferred angles and structural motifs within clusters informs researchers about the potential stability and behavior of amorphous alloys. The observed variations in cluster sizes provide insights into the heterogeneity materials, which may influence their properties in practical applications [8; 9].

6.6. Implications

The implications of EMICA’s results extend to materials science research and development. By uncovering structural orderliness and characterizing local atomic arrangements, researchers have gained the knowledge needed to tailor amorphous alloys for specific applications. The software’s ability to handle complex structural analysis paves the way for innovations in materials design and engineering.

In conclusion, the capacity of EMICA for cluster visualization, angle distribution analysis, and point distribution assessment empowers researchers to explore the atomic-scale intricacies of amorphous alloys. The software’s significance lies in its ability to bridge the gap between complex material structures and real-world applications, fostering advancements in materials science and technology.

7. DISCUSSION

The results obtained through the application of EMICA offer valuable insights into the atomic-scale structure and physicochemical properties of amorphous alloys. The identified structural order provides a deeper understanding of the behavior and potential applications of these materials. The efficiency and accuracy of EMICA in electron microscopy analysis are noteworthy, demonstrating its significance in materials science research.

8. CONCLUSION

In conclusion, we addressed the research problem in this study, focusing on enhancing electron microscopy image processing for amorphous alloys through the development and implementation of EMICA. Summarizing our main points and findings, EMICA exhibited remarkable capabilities, elucidated through practical case studies, showcasing its efficacy in addressing the unique challenges posed by amorphous alloy analysis.

The implications and significance of our study lie in the potential transformation it brings to the field of electron microscopy image processing. EMICA stands as a valuable tool for us, researchers in materials science, offering specialized capabilities for cluster analysis and spatial pattern recognition in amorphous alloys. We underscore our confidence in urging researchers to adopt EMICA for their analyses. Our optimism regarding the tool’s contribution to fostering advancements and collaborations within the materials science domain is rooted in its boundless potential.

As we conclude, we emphasize the importance of looking forward. Future research, led by us, could expand upon the groundwork laid by EMICA, delving deeper into nuanced details of amorphous alloy structures. Additionally, addressing any limitations identified in our current study will further enhance the tool’s applicability and refine its role in advancing electron microscopy image processing for years to come.

About the authors

Dilla Dagim Sileshi

Far Eastern Federal University

Author for correspondence.
Email: dilla.d@dvfu.ru
ORCID iD: 0000-0002-9100-1257

PhD student, Institute of Mathematics and Computer Technologies, research engineer, Electron Microscopy and Imaging Laboratory

Russian Federation, Vladivostok

Evgeniy V. Pustovalo

Far Eastern Federal University

Email: pustovalov.ev@dvfu.ru
ORCID iD: 0000-0003-1036-3975

Dr. Sci. (Phys.-Math.), Professor, Department of Information and Computer Systems, Institute of Mathematics and Computer Technologies, Head of the educational program 09.03.02 “Information systems and technologies”, profile “Programming of robotic systems”

Russian Federation, Vladivostok

Alexander N. Fedorets

Far Eastern Federal University

Email: fedorec.an@dvfu.ru
ORCID iD: 0000-0001-9007-3171

senior lecturer, Department of Information and Computer Systems, Institute of Mathematics and Computer Technologie

Russian Federation, Vladivostok

References

Supplementary files