A review of emerging trends in Laves phase research: Bibliometric analysis and visualization

: The rapid development of modern aerospace and energy industries requires increasingly high service performance of metallic materials. Laves phase intermetallic compounds with the chemical formula AB 2 -type have attracted much attention due to their high melting point, excellent high-temperature strength, and oxidation resistance, and are regarded as one of the promising candidates for a new generation of high-temperature structural applications. Although it can be identi ﬁ ed that Laves phase alloy research has been an active research ﬁ eld in the last 20 years in terms of the trend of literature volume growth, there is still a lack of systematic descriptions and comprehensive overviews of the latest fron-tiers and hotspots in the ﬁ eld. In this article, a quantitative and visual knowledge mapping of the articles published in the ﬁ eld of Laves phase research in the last 20 years has been carried out based on the bibliometric analysis methodology of Cite Space software. Quantitative analysis of high-frequency key-words to understand the basic development of Laves phase and the evolution of the main research hotspots in each period of time identi ﬁ ed the hotspots of common concern seven themes: Laves phase, electronic structure, precipitation, Inconel 718 alloy, phase diagram, high-entropy alloys, and TiAl-based alloys. The analysis of the emergent keywords shows that electronic structure, high-entropy alloys, total energy calculations, and laser cladding can represent the research frontiers of Laves phases. This study provides systematic and valuable reference information to gain insight into the current state of Laves phase research and the evolution of the theme, which will be useful for further research.


Introduction
Laves phase alloys are the most diverse class of intermetallic compounds composed of AB 2 -type atoms with a topologically close-packed structure and have been an important research topic in the field of materials science.Laves phases are size compounds in which the atomic sizes of the transition metal group elements tend to have a definite atomic radius ratio of R A :R B = 1.225; in practice, there may be slight deviations from this atomic radius ratio, typically ranging between 1.05 and 1.68 [1].Laves phases with unique structural and physical properties have three structural types, namely densely packed hexagonal C14 type (also known as MgZn 2 -type hexagonal crystal system), densely packed cubic C15 type (MgCu 2 -type cubic crystal system), and double densely packed hexagonal C36 type (MgNi 2 -type hexagonal crystal system) [1,2].The atoms in the topologically close-packed structure of the Laves phase are tightly arranged, resulting in high coordination numbers and space utilization efficiency.Therefore, Laves phase alloys usually exhibit excellent properties, such as high-temperature strength, phase stability, exceptional oxidation resistance, and corrosion resistance.Consequently, Laves phase alloys are widely regarded as one of the most promising candidate materials for advanced ultra-high-temperature structures and are expected to be applied in fields such as aerospace, automotive, energy, and chemical engineering that require extreme environment resistance [2][3][4].
Although the properties and potential of Laves phase alloys have attracted considerable attention from numerous researchers, their brittleness, especially the room-temperature brittleness problem, has been the major obstacle that prevents them from moving towards practicality.In addition to this, a number of emerging research topics have continued to emerge.For instance, researchers are dedicated to significantly improving the mechanical properties and thermal stability of Laves phases through alloy design with doping and crystal structure modulation [2,5,6].The powder metallurgy preparation, additive manufacturing, and surface modification of Laves phase alloys have also attracted extensive attention [7][8][9].Therefore, given the continuous in-depth research on Laves phase alloys internationally, it is crucial to systematically review the relevant studies conducted in the past two decades in order to gain a profound understanding of the research hotspots and trends.This will help reveal the key unresolved issues in Laves phase alloys and provide researchers with targeted research directions, thereby further promoting their application and development in the field of ultra-high-temperature structural materials.
To the best of our knowledge, there has been no bibliometric study conducted on the literature review of Laves phase alloys so far.In this article, we aim to utilize bibliometrics and a systematic literature review to visualize and systematize the scientific literature knowledge of Laves phase research.As a new tool for scientometrics, knowledge mapping offers a novel approach to tracking hotspots in Laves phase alloy research.The CiteSpace literature visualization and analysis software can provide an efficient, reproducible, and rapidly applicable means of processing literature data, which has broad application prospects in the fields of bibliometrics and knowledge visualization [10,11].In this study, CiteSpace software was used to conduct quantitative analysis and draw knowledge maps of Laves phase research-related journal literature collected from Web of Science (WoS) over the past 20 years.This approach not only compensates for the subjective and one-sided nature of traditional literature-based research but also scientifically and effectively excavates hidden information in the literature, revealing the research hotspots and development frontiers of the Laves phases.By mining the key issues in Laves phase alloy research through knowledge graph exploration, we can promote its practical application and provide a valuable reference for the in-depth study of Laves phase alloys.

Search strategy and data collection methods
WoS is a globally renowned academic citation database developed and maintained by Clarivate Analytics.It offers powerful searching functions, allowing users to conduct searches using keywords, author names, journal titles, affiliations, cited references, and so on.Additionally, it provides various analytical tools and indicators, such as citation frequency, impact factor, h-index, etc., which can be used to evaluate and compare the impact and citation patterns of scholarly publications [12].The original data used in this study were sourced from the WoS Core Collection, using the search criteria with the subject "Laves phase" indexed in "all fields."The search time spanned from 2003 to 2023.Literature types were filtered to include "Article," "Proceeding Paper," and "Review."The search was conducted on June 28, 2023, resulting in 4,832 documents.Since this article primarily focuses on the research related to the application of the Laves phase as high-temperature structural materials, the literature related to the topic of hydrogen storage, catalysis, and magnetic functional materials was excluded.In order to ensure the accuracy of the research results, it is also necessary to perform data filtering and deduplication of the WoS format and finally obtain a total of 2,080 relevant and valid articles as the initial database.The citation frequency of these documents totaled 38,445 times during the period 2003-2023, with a citation count of 18.48 per article and an h-index of 83, indicating that up to 83 articles out of these 2,080 articles were cited at least 83 times, respectively, while the remaining 1,997 articles were cited no more than 83 times each.
Commonly used bibliometric visualization and analysis tools mainly include Hist Cite, Ref Viz, DIVA, VOS viewer, and CiteSpace.This study utilized the citation analysis-based literature mining and visualization software, CiteSpace 6.2.R4, to convert the Laves phase-related literature extracted from the WoS database into formats and perform visual analyses such as keyword co-occurrence and clustering mapping and other visualization techniques.The software's distinct time-zone view and keyword burst detection function can accurately assist in quickly discovering the research frontiers and future development trends of Laves phases [10,11].

Analysis of Laves phase research hotspots
The temporal evolution of publication output in a field can reflect its development status.In order to understand the research achievements of the Laves phase in the last two decades, an analysis of annual publication output was conducted for the retrieved relevant literature.Figure 1  As of June 28, 2023, there have already been 186 publications depicting the continuous and enthusiastic growth of Laves phase research.The sustained growth in Laves phase research may be attributed to its diverse functionalities and potential applications.Laves phases have found extensive applications in fields such as metal alloys, hightemperature alloys, magnetic materials, and catalysts [13,14].Exploring the properties and applications of Laves phases can also provide new insights and opportunities for material design and engineering.Furthermore, with the continuous advancements in experimental and computational methods, researchers are able to investigate the structure, synthesis, properties, and applications of Laves phases more comprehensively and in-depth.For instance, the utilization of cutting-edge techniques, such as ultra-high-resolution transmission electron microscopy, penetration analytical electron microscopy, atomic force microscopy, atom probe tomography, energy-dispersive X-ray spectroscopy (EDS/X-EDS), neutron diffraction, and high-throughput computational simulations, has enabled researchers to better comprehend, optimize, and manipulate novel Laves phase alloys [15][16][17].These advancements have also been pivotal in attracting increased attention from researchers in this field.
Keywords serve as important indicators that summarize the research content in the literature and, to some extent, reflect the main issues addressed in the literature.Analyzing keywords in the literature allows us to identify the core themes of sustained and popular research on Laves phases.The frequency information of keywords helps recognize knowledge associations in the research field and identify research hotspots, offering scientific predictions about the research frontier.The centrality of knowledge graph network nodes is one of the indicators for measuring node importance and degree of closeness [18].By analyzing high-frequency and high-centrality keywords, it is possible to understand the core hot topics that researchers have collectively focused on within a certain period of time.When analyzing the research hotspots of Laves phases, the network nodes were set as "Keywords."After running the software, a co-occurrence knowledge graph of keywords related to Laves phase alloys was obtained by merging synonymous keywords, as shown in Figure 2. As shown in Figure 2, each keyword is represented by a circular growth ring node, where the size of the growth ring is directly proportional to the frequency of appearance of the keyword.In other words, the thicker the growth ring of a node, the greater the number of citations within that specific time period.The different colored rings within the growth ring node indicate the corresponding year of occurrence.Through data analysis using CiteSpace, the information with N = 260, E = 878, and Density = 0.0261 can be obtained in the upper-left area of Figure 2.This indicates that there are a total of 260 node keywords appearing in 2,080 sample articles, forming 878 connections between the keywords.The density value of the keyword co-occurrence network is 0.0261.From the size of the nodes, it can be observed that compared to other keywords, "Laves phase," "Mechanical properties," "Behavior," and "Microstructure" are relatively more focused research topics.This is in line with the fundamental principles and development trends in materials science research.As Laves phase intermetallic compounds are used in high-temperature structural material applications, their mechanical properties and microstructure play a crucial role in the overall material performance.By persistently and deeply studying these core themes, scientific foundations can be provided for the development and application of new Laves phases.The connections between nodes represent the cooccurrence relationships between keywords.The nodes in the graph are tightly interconnected and intricately intertwined, with very few independent nodes appearing, indicating that research on Laves phases over the past 20 years has been relatively concentrated with a high degree of interconnectivity between the keywords of different themes [18].
All keywords with a frequency of occurrence greater than or equal to 135 and keyword centrality greater than or equal to 0.09 were selected through a software query to generate data in Tables 1 and 2. According to the node frequency statistics by CiteSpace, "Laves phase," "mechanical property," and "behavior" are ranked among the top three.Additionally, "microstructure," "microstructure evolution," "stability," "alloys," "strength," "precipitation," and "high temperature" are also ranked at the top, with their frequency of occurrence exceeding 200.These keywords are represented by larger nodes in Figure 2 and have more connections with other nodes, indicating high cooccurrence frequency and strong correlation.This suggests that they are the hot topic keywords in Laves phase research over the past 20 years.In addition to Laves phases, "mechanical property" is the most frequently occurring keyword.Laves phases with complex crystal structures often exhibit outstanding high-temperature structural material properties, such as high strength, high hardness, good hightemperature stability, and excellent corrosion resistance.These high-performance characteristics have attracted numerous researchers to extensively investigate the basic mechanical properties of Laves phases (e.g., hardness, elastic modulus, yield strength, and fracture toughness), dislocation behavior and deformation mechanisms (e.g., type of dislocations, dislocation formation mechanisms, slip systems, strain hardening, and plastic behavior), phase transition behavior (namely, the study of Laves phases under conditions of high temperature,  high pressure and external stress, phase transition paths, and metastable states), as well as multi-scale modeling and simulation (including first-principles calculations, molecular dynamics simulations, and finite element analysis) [19][20][21][22].These research topics are of great significance for a deeper understanding of the mechanical properties and engineering applications of Laves phase alloys.It is worth noting that the frequency of "high-entropy alloys," which is the latest emerging relevant field, also reached nearly 200 in 2019.The subsequent analysis in the keyword clustering graph will explore the association between high entropy alloys and the Laves phase research in detail.Additionally, there are some keywords with slightly lower frequencies in the cooccurrence network that still provide important references, such as "superalloy," "first principles," "total energy calculations," and "laser cladding."These keywords enrich our understanding of the Laves phases and expand the research directions.It is crucial to closely monitor these keywords and integrate them into the research and practice related to the Laves phases.The purple outer ring (i.e., the outermost ring) thickness of the yearly node in Figure 2 reflects the magnitude of betweenness centrality in keywords.The high centrality keywords serve as bridging links in the co-occurrence network and often possess significant research value.As shown in Table 2, "Laves phase," "mechanical property," "microstructure evolution," "behavior," and "total energy calculations" exhibit relatively high centrality.This implies that many keywords are connected through these five central nodes, reflecting their important positions in the field of Laves phase research.Upon comparison with Table 1, it is found that these five keywords possess both high-frequency and high-centrality characteristics.They play a crucial hub role within the entire network graph, accurately reflecting the current international research hotspots on Laves phases.It also demonstrates the close alignment between the hot topics of Laves phase intermetallic compound research and the fundamental paradigm of materials science research.In other words, synthesis and preparation, structural characterization, performance analysis, and theoretical simulation and calculations are interconnected, collectively promoting the development and innovation of the Laves phase.
Keyword clustering can further shed light on the research hotspots of Laves phases in the international community over the past 20 years.This can be achieved through clustering analysis of keywords with different weights using the LLR algorithm in the CiteSpace software.Figure 3 represents the visualized cluster knowledge map of research keywords related to Laves phases.Two important indicators, Modularity Q and Mean Silhouette S, are used to assess the credibility and reasonability of the obtained visualized map.From the upper-left corner of the clustering graph, the values of Q and S are 0.5418 and 0.8419, respectively.Modularity Q indicates the modularity of the network, with a larger value suggesting better clustering results.Silhouette value is a metric used to measure the homogeneity of the network after clustering, where a value closer to 1 reflects higher network homogeneity.According to the embedded algorithms in the software, the Q value of 0.5418 is greater than 0.3, indicating that the partitioned clustering structure is reasonable.The S value of 0.8419 is greater than 0.7, suggesting that the clustering is credible and convincing [18].From Figure 3, it can be observed that after clustering, there are seven clearly defined clusters, namely, #0 Laves phase, #1 electronic structure, #2 precipitation, #3 Inconel 718 alloy, #4 phase diagram, #5 high-entropy alloy, and #6 based on TiAl alloy.Clustering analysis is the process of aggregating and categorizing data in a complex network based on their similarity, helping identify and explore representative knowledge subgroups within a research field.In other words, the above clustering results also represent the hot topics of common interest in Laves phase research.
Figure 3 is sorted according to the number of keywords contained in each cluster, and the sequence indicates the importance of the cluster.The higher the ranking, the more prominent the importance of the cluster.The cluster labeled "Laves phase" naturally occupies the top position.To make the research hotspots more explicit and to better grasp the keyword information behind each cluster, the CiteSpace software was used to generate data in Table 3, which presents the keyword co-occurrence network clustering based on the aforementioned clustering network.From Table 3, it can be observed that the cluster size reflects the number of relevant keywords involved in each cluster.The S values of the seven clusters are all high, with 0.764 ≤ S ≤ 1, indicating the accuracy of using the LLR weighting algorithm for the keywords.The most representative identifying keywords in each cluster, as shown in Table 3, help identify the research hotspots of Laves phases that are the focus of international core research circles.The detailed information of the seven clusters is as follows: (1) The cluster labeled "Laves phase" includes keywords such as P92 steel, creep, microstructure, and G115 steel.The main identifying keywords, P92 and G115, that appear in the cluster labeled "Laves phase" are both new  martensitic heat-resistant alloys of steel [23].P92 steel is a Fe-Cr-Mo-V-type high-temperature alloy steel, also known as 9Cr-2W steel.G115 is a nickel-based steel.P92 and G115 have excellent high-temperature strength, low thermal expansion coefficients, and good oxidation resistance, with maximum operating temperatures of 620 and 650°C, respectively.They are widely used in supercritical and ultra-supercritical power generation boilers, gas turbines, petrochemical industries, and other applications.However, these heat-resistant alloy steels face challenges in manufacturing or long-term service, such as welding difficulties, selection and optimization of heat treatment parameters, stability and control strategies of microstructure, oxidation resistance, and stress corrosion cracking.The origins of these challenges are often related to the formation and evolution of Laves phase precipitates under high-temperature aging or thermal exposure conditions.In the case of P92 steel, the precipitates of Laves phase, (Mo, W)(Fe, Cr) 2 , MoFe 2 , WFe 2 , NbFe 2 , TiFe 2 , etc., during long-term creep at around 600°C, can deplete the crucial strengthening elements Mo and W from the matrix, reducing the solid solution strengthening effect [24].The growth of the Laves phase at high temperatures can also consume other small particle precipitates, further weakening the dispersion strengthening effect.Excessive precipitation or grain growth of Laves phase precipitates during long-term high-temperature service can significantly degrade the high-temperature properties of these heat-resistant alloy steels, leading to thermal embrittlement and premature failure [25].Therefore, controlling Laves phase precipitates and improving high-temperature creep properties (as mentioned above, "creep" and "microstructure" are also key labeled words) are important hot topics [26].
The inference that the "electronic structure" cluster is consistent with the previously mentioned "total energy calculations" is one of the five key terms with both high-frequency and high-centrality characteristics.They all reflect the growing interest in using first-principles or ab initio methods, such as electronic structure and energy calculations at the electronic level, to model and simulate typical material problems in Laves phase research.For instance, most Laves phase intermetallic compounds used in ultrahigh-temperature applications suffer from widespread room-temperature brittleness.The inherent brittleness of Laves phases is often related to the properties of electrons and energy bands, attributed to the directional covalent bonding nature, strong hybridization between specific orbitals, or the directional charge density distribution near the Fermi level [27].In order to improve the room-temperature brittleness of Laves phases, it is necessary to obtain basic mechanical property parameters, such as elastic constants, theoretical strength, and elastic modulus, which are also key indicators in the "electronic structure" clustering.These parameters are often challenging to measure experimentally for Laves phases with various crystal structures, such as C14, C15, and C36, but can be readily achieved through first-principles calculations.Additionally, it can be predicted that the most promising method to improve the room-temperature brittleness of Laves phases is to introduce doping or alloying elements to form multicomponent alloys, with a potentially large number of possibilities.Predictive studies on the electronic structure performance of multicomponent Laves phases using first-principles calculations will aid in screening a certain number of alloy systems for experimental investigations, saving resources and time.
The "Inconel 718 alloy" cluster indicates that the Laves phases, as important constituent phases, have a critical influence on the mechanical properties of the widely used and highly important nickel-based superalloy Inconel 718 (typical composition in weight percent is Ni-19Cr-18Fe-5Nb-3Mo-1Ti). The primary strengthening mechanisms of nickel-based superalloys include the precipitation strengthening of coherent intermetallic phases, γ′ and γ″, as well as solid solution strengthening [28].However, since the major alloying elements Cr, Fe, Mo, Nb, and Ti are also components of brittle Laves phases, the non-coherent harmful precipitates, such as Laves phases NbCr 2 , NbFe 2 , MoFe 2 , and TiCr 2 , tend to form [29].The presence of Laves phases in the form of continuous or semicontinuous grain boundary networks significantly reduces the room temperature tensile ductility, ultimate tensile strength, impact toughness, fracture toughness of as-forged Inconel 718, and even the high-temperature ductility at 649°C.The predominant cause of embrittlement is the brittle fracture of Laves phase precipitates [29].Furthermore, similar to the role of the Laves phase in the aforementioned heat-resistant alloy steels, the formation of the Laves phase consumes the strengthening elements Nb and Cr, thereby reducing the precipitation strengthening effect of γ″ phase Ni 3 Nb.Moreover, the liquid cooling process caused by melting solidification, welding, additive manufacturing, and other thermal processing methods exhibits significant sensitivity to the quantity, size, and morphology of Laves phase precipitates.Consequently, Inconel 718 alloys prepared through these methods are prone to the initiation and propagation of microcracks [30,31].This is also the reason why the terms "cooling rate" and "TIG welding" appear in this cluster.Tungsten inert gas (TIG) welding, known for its stable arc and low heat input, can achieve high-quality weld appearance and welding joint quality, making it more suitable for repairing or welding highmelting-point materials and thin plates.This is crucial for maintaining the excellent mechanical properties and heat resistance of nickel-based superalloys.4-6, it can be observed that in the early stage, closely related clusters include Laves phase, electronic structure, precipitation, phase diagram, and based on TiAl.The Laves phase itself possesses a unique multiphase structure, including C14, C15, and C36 structures.Both phase diagrams and electronic structures play essential roles in the early research on alloy systems associated with Laves phases, encompassing their phase behavior, phase stability, and solid-state transformations.In contrast, around the year 2000, there was a surge of research on TiAl intermetallic compounds, which drew attention to the Laves phases that appear as typical impurity phase precipitates.Over time, in addition to the "TiAl-based alloy" cluster, the "Inconel 718 alloy" cluster has also established extensive and profound connections with other clusters, indicating a sustained interest in the research hotspots represented by these clusters.It is worth noting that in the early period of 2003-2004, the "high-entropy alloy" cluster was only connected to the "Laves phase" cluster with a  single line.This is because it was not until 2004 that Yeh and Cantor simultaneously proposed the concept of high-entropy alloys with multiple-element mixtures and atomic compositions [32,33].Over the past 20 years, as time has progressed, the connectivity between these two clusters has gradually increased, establishing a complex and close relationship between these representatives of advanced structural materials.
Early high-entropy alloys can be understood as singlephase supersaturated solid solution alloys.Traditional alloy design concepts suggest that the more alloying elements there are, the more likely complex phases such as brittle intermetallic compounds will form.However, high-entropy alloys, due to their high configurational entropy resulting from near-equiatomic mixing, are less prone to the formation of hard and brittle intermetallic phases.As research has deepened over the past 20 years, it has become increasingly recognized that high-entropy alloys are complex and diverse.
Describing them solely as single-phase supersaturated solid solutions is not comprehensive and accurate enough.In addition to solid solution phases, high-entropy alloys can also contain supersaturated solutes, nano-scale precipitation strengthening phases, lattice defects, and others.Although the entropy of multiphase high-entropy alloys is lower than that of single-phase solid solutions, the high number of alloying elements in the multicomponent system still contributes to a relatively high level of mixing entropy.The composition of multiphase high-entropy alloys mainly includes phases such as FCC, BCC, and HCP, as well as intermetallic compounds like L12, B2, σ, Laves phases, and others.In particular, in the commonly present FCC-Laves phase (or BCC-Laves phase) eutectic or duplex high-entropy alloys, along with Laves phase precipitation strengthening, researchers have achieved synergistic optimization of alloy mechanical properties by precisely controlling the composition and atomic ratios of alloying elements to adjust the phase composition and structure in high-entropy alloys.This allows for synergistic enhancement of mechanical properties through the strengthening from Laves phases and toughening from solid solution phases [3,34,35].Typically, the strengthening effect of the second phase is generally higher than that of solid solution strengthening.Furthermore, the motion of dislocations in the solid solution phase plays a dominant role in the plastic deformation of the alloy, whereas the phase interfaces generated by the coherent or semi-coherent precipitation of nano-sized Laves phases act as potential barriers to dislocation motion.This induces the generation of ultra-high-density dislocations in the solid solution phase, resulting in a significant strengthening effect [36].Additionally, over-saturated solid solution high-entropy alloys commonly exhibit the possibility of modulation decomposition into duplex or multiphase structures, and deformation can induce phase transitions.Under the guidance of these rich strengthening and toughening strategies, many high-entropy alloys with outstanding simultaneous improvement in strength and good plasticity have been achieved.Examples include dual-phase high-entropy alloys or intermetallic compound precipitation-strengthened high-entropy alloys, such as CuCoNiCrFeAlx, AlCoCr-FeNi, and NiFeCrCoMn.At room temperature, the tensile yield strength can reach as high as 1.4-2.5 GPa, accompanied by corresponding tensile elongation of 20-50% and hardness ranging from 100 to 1,100 HV or reaching 14 GPa [37][38][39].These research studies aim to overcome the challenge of the inverse relationship between strength and ductility in the field of materials science and further A review of emerging trends in Laves phase research  9 explore a better balance between strength and ductility, imparting tremendous potential and application value to these alloys.The cross-combination of Laves phases and high-entropy alloys broadens the horizons for the development of new high-temperature structural materials.

Analysis of Laves phase research frontiers
Unlike research hotspots, the rapid increase in the frequency of occurrence of keywords in a short period reflects potential research frontier issues [40].One of the significant advantages of CiteSpace, compared to other knowledge mapping tools, is its ability to provide burst detection technology based on the burstiness algorithm for identifying emerging terms.By examining the temporal distribution of keyword frequencies, it can detect terms with highfrequency variation rates from a large set of keywords.
Exploiting the temporal distribution and dynamic changes of these burst terms, it is possible to uncover the research frontiers and development trends within the field of Laves phases.By setting the network nodes as "Keywords" in CiteSpace and utilizing the burst detection function to select "Burst Terms," the keyword burst map of Laves phase research from 2003 to 2023, as shown in Figure 7, can be obtained.The software automatically marks the annual rings of keyword nodes with burstiness, characterized by a sharp increase in citation counts starting from a specific year, with a red ring.The thickness of the purple outer ring represents the centrality of burst keyword nodes.Centrality reflects the strength of connections between the keyword node and other nodes in the network.A larger value indicates that the node has a prominent influence within the graph network.Consistent with the prior discussion, keywords with noticeable purple outer rings include "Laves phase," "mechanical property," "microstructure evolution," "heat treatment," "Inconel 718", "1st principles," etc., with centrality values ranging from 0.1 to 0.23.From Figure 7, it can also be observed that burst terms, such as "system," "transition," "constants," and "elements," do not hold much actual value.After excluding these terms from the graph, Figure 8 shows the top 20 burst keywords sorted by the year of their first occurrence, representing emerging research areas within the field of Laves phases from 2003 to 2023, which are at the forefront of research.The red area in the figure represents the duration of burst appearance for a specific keyword, indicating the period of burstiness."Strength" represents the intensity of the burst, with larger values indicating greater importance."Begin" represents the year of the first occurrence of the keyword burst, while "End" represents the year when the burst ends.From Figure 8, it can be observed that the burst keywords with a strength greater than 10 are "electronic structure" (14.22), "high entropy alloys" (11.12), "total energy calculations" (10.91), and "laser cladding" (10.08).This indicates that these four keywords have remained highly active and novel over the past 20 years, representing the forefront of Laves phase research during their respective time periods.Both expressions of "high entropy alloys" and "high-entropy alloys" have burst strengths greater than 10 (11.It is noteworthy that the burst keywords with the strongest citation intensity from 2021 to present, apart from the overlapping burst keyword of "high entropy alloys," are only "ductility." The division of these three stages reflects the continuous evolution of research frontiers related to the Laves phases, where new research perspectives or fields emerge periodically.It started with the initial emphasis on the theoretical foundation of Laves phase alloys, followed by studies of microstructure, mechanical properties, and thermodynamic properties in the middle stage.In recent years, there has been a profound development in novel fabrication techniques, performance evaluation, and the resolution of challenges related to room-temperature brittleness.Throughout this frontier trajectory, the performance of Laves phases plays a significant role that is concurrently intertwined with new types of steels or other popular hightemperature alloys (such as ferritic steels, martensitic steels, FeAl or TiAl intermetallic compounds, and high entropy alloys).The sole burst keyword "ductility" that has emerged since 2021 indicates that the issue of roomtemperature brittleness or the synergistic enhancement of strength and ductility in Laves phase alloys or Laves phasestrengthened multiphase high entropy alloys is the most active research frontier and development trend in recent years.Although Laves phase alloys have the potential for high-temperature structural material applications, their brittleness, especially at room temperature, has been one of the primary obstacles limiting their practical use.Addressing the improvement of room-temperature brittleness requires urgent research into fundamental issues such as phase transformations, phase stability, alloy doping, and plastic deformation mechanisms in Laves phases.For example, our research group has significantly improved the room-temperature brittleness of Laves phase TaCr 2 alloy, which is used in ultra-hightemperature applications, through synergistic toughening with alloy doping, refinement of grain size, and incorporation of soft secondary phases.The dense Laves phase-enhanced Cr-based alloy with a volume fraction of approximately 18% for the Laves phase was prepared using mechanical alloying and vacuum hot pressing powder metallurgy techniques, resulting in a density of 98.5%, compressive strength of 3,752 MPa, plastic strain of 28.6%, and fracture toughness value exceeding 6.12 MPa•m 1/2 .However, the microscopic mechanisms governing the synergistic enhancement of strength and ductility are not yet fully understood and require further systematic and in-depth investigation [41].First-principles calculations based on density functional theory (DFT) are an important approach for studying the fundamental properties of Laves phases.Starting from the essential electronic structure, these calculations can help uncover the microscopic mechanisms underlying phase transitions and plastic deformation in Laves phases.Additionally, by improving advanced powder metallurgy techniques and additive manufacturing methods, it is expected that the establishment of the electronic structuremicrostructure-mechanical property relationships at both macroscopic and microscopic scales will be achieved for Laves phase alloys.These research outcomes will provide theoretical and technological support for the development of new ultra-high-temperature structural materials.

Conclusions
Unlike existing descriptive reviews on Laves phases, this article, for the first time, employs bibliometric analysis.It utilizes a dataset of 2,080 bibliographic records retrieved from 2003 to 2023 WoS Core Collection database regarding Laves phase research, with a focus on high-temperature structural materials.The aim is to conduct data mining and construct a knowledge map, visually presenting quantitative research outcomes.The analysis reveals the hot topics and emerging frontiers in Laves phase research over the past two decades.The co-occurrence knowledge map of keywords demonstrates that Laves phase-related studies are highly concentrated in specific themes with strong correlations.The research focuses on Laves phases and aligns well with the fundamental paradigm of materials science research, encompassing synthesis and preparation, structural characterization, performance analysis, and theoretical simulation.These four aspects are interconnected and jointly propel the development and innovation of Laves phase research.Based on the co-occurrence and clustering analysis of keywords, the research on the Laves phase has identified seven major clusters of hot topics.They are Laves phase, electronic structure, precipitation, Inconel 718, phase diagram, high-entropy alloy, and TiAl-based alloys.Through frequent keyword emergence detection, the research on Laves phase in the past 20 years can be divided into three stages: 2003-2007, 2013-2015, and 2019-2023.Among them, the four keywords, namely electronic structure, high entropy alloys, total energy calculations, and laser cladding, with high burst strengths and active and novel research activities, can represent the forefront of Laves phase research in their respective time periods.In recent years, the room-temperature brittleness and the issue of strength-plasticity synergy enhancement in Laves phase alloys or Laves phase-strengthened multiphase high-entropy alloys have become the most active research frontier and development trend.
presents the annual publication volume in the field of Laves phase from 2003 to 2023.From Figure 1, it can be seen that the literature output of the Laves phase can be roughly divided into two stages over the past 20 years.The first stage spans from 2003 to 2009, during which the annual publication volume in Laves phase research is not more than 50 articles.Subsequently, until the search deadline of 2023, the second phase was observed.The red dashed line represents the fitted trend line, indicating an overall annual growth with occasional minor declines.By 2022, the number of published articles reached its peak at 255, which is nearly five times the annual publication count of the first phase of the literature.This substantial increase reflects the rapid development of Laves phase research.The growing volume of literature on Laves phases demonstrates its status as an active research field that has garnered widespread attention from scholars and is experiencing a surge in development.

Figure 1 :
Figure 1: Annual trend of publications related to the Laves phase in the past 20 years from 2003 to 2023.

( 2 )
The cluster labeled "Electronic structure" includes keywords such as elastic properties, microstructure, elastic constants, and ab initio calculations.(3) The cluster labeled "Precipitation" includes keywords such as precipitation, mechanical properties, sigma phase, and ferritic stainless steel.(4) The cluster labeled "Inconel 718 alloy" includes keywords such as alloy 718, segregation, cooling rate, and TIG welding.(5) The cluster labeled "Phase diagram" includes keywords such as ternary alloy systems, diffraction, and thermodynamic modeling.(6) The cluster labeled "High-entropy alloy" includes keywords such as highentropy alloys and laser cladding.(7)The cluster labeled "TiAlbased alloys" includes keywords such as oxidation, TiAl intermetallic compounds, and coatings.

Figure 3 :
Figure 3: Keyword clustering knowledge graph of Laves phase research.

Figures 4 -
Figures 4-6 show the temporal evolution of keyword clustering for Laves phase research, focusing on three typical time periods: early period (2003-2004), middle period (2009-2010), and recent period (2021-2022).By examining the connections and changing trends between clusters during different time periods, the temporal traversal of clustering graphs provides insights into the development and dynamics of research topics.The lines connecting the clusters in the figures represent the associations between two clusters, and the appearance, disappearance, or density of these lines help understand the evolution and intersection of research topics in different periods.From Figures 4-6, it can be observed that in the early stage, closely related clusters include Laves phase, electronic structure, precipitation, phase diagram, and based on TiAl.The Laves phase itself

Figure 4 :
Figure 4: Time traversal for keyword clustering of Laves phase research from 2003 to 2004.

Figure 5 :
Figure 5: Time traversal for keyword clustering of Laves phase research from 2009 to 2010.

Figure 6 :
Figure 6: Time traversal for keyword clustering of Laves phase research from 2021 to 2022.

Figure 7 :
Figure 7: Keywords emergent knowledge graph of Laves phase research.
12 and 10.82, respectively), confirming consistency with the clustering results of the aforementioned keywords.It suggests that dual-phase or multiphase high-entropy alloys strengthened by Laves phases are one of the most active research frontiers and development trends.From Figure 8, it can also be observed that Laves phase research over the past 20 years can be roughly divided into three stages: I.The first stage: Early research frontiers from 2003 to 2007 primarily focused on phase diagrams, deformation behavior, iron aluminides, electronic structure, total energy calculations, augmented wave method, and elastic constants.The burst keywords during this stage have generally spanned a long period of time, with durations of more than 10 years, and continue to have an impact to this day.Similar to the temporal traversal results of the aforementioned Laves phase research keywords, phase diagrams, deformation behavior, and electronic structure form the foundation for early studies on Laves phases.II.The second stage: Mid-term research frontiers from 2013 to 2015 mainly focused on first principles, ferritic steels, creep strength, thermodynamic property, martensitic steel, and phase stability.III.The third stage: The current burgeoning research frontiers from 2019 to 2023 mainly focus on high entropy alloys, laser cladding, corrosion resistance, alloy design, wear resistance, and ductility.These burst keywords with the latest onset reveal the newest keyword trends.

Figure 8 :
Figure 8: Top 20 keywords with the strongest citation bursts.

Table 3 :
Co-occurring keyword clusters of Laves phase researchCluster ID Cluster size Cluster silhouette Mean year Main label terms