Bibliometric review and recent advances in total scattering pair distribution function analysis: 21 years in retrospect

Abstract

Global research activities have been driven by the quest to develop and characterize novel materials for technological advancements. The total scattering pair distribution function (TSPDF) is a powerful and versatile characterization technique for examining the structural details of diverse complex materials including liquid, amorphous, disordered crystalline, and nanostructured materials. Thus, it is critical to keep track of research progress, identify research gaps, and future research directions of the application of the TSPDF technique in materials development and discovery. In this work, a bibliometric analysis of literature regarding the TSPDF technique between 2000 and 2021 was conducted using datasets retrieved from the Web of Science database. The research trends based on publication outputs, research subject distribution, co-authorships among institutions, countries/regions, co-citation of referenced sources, and keyword co-occurrence are evaluated and discussed herein. The impact of the TSPDF technique is projected to increase due to its importance in probing emerging functional materials, and the advances in specialized facilities and instrumentation among the scientific communities engaged with it. Finally, current and emerging research hotspots related to TSPDF technique such as catalysis, computer modeling and simulation, pharmaceutics, machine learning, hydrogen storage, battery materials, and layered structured materials are also identified and discussed.

Keywords:

• Total scattering
• pair distribution function
• local structure
• neutron diffraction
• X-ray diffraction
• bibliometric analysis

1. Introduction

The continuous search for new materials to provide technological solutions to the most challenging global problems facing humanity over the past decades—from health to transportation, renewable and clean energy, environmental sustainability, and climate crises—has caused rapid development of innovative materials while enlarging the materials landscape. A clear understanding of the atomic structure of materials is essential to develop a predictive process–structure–property– performance (PSPP) relationships, leading to the development of materials with optimal effectiveness for various applications. The significant progress in structure determination in almost all natural sciences has seen rapid advances in short-range crystallography techniques (Billinge & Kanatzidis, 2004). For crystalline materials, the approaches are founded on the ground-breaking work of Friedrich, Knipping, and Laue (1913) and Bragg, Bragg Apr, and Bragg (1913) on crystal diffraction. However, when the material of interest lack an average periodic structure or exhibits short-range ordering, traditional crystallography approaches become insufficient in characterizing the structure of such materials (Petkov, Ohta, Hou, & Ren, 2007; Proffen, Billinge, Egami, & Louca, 2003). Current technological devices and applications require using of advanced materials engineered with hierarchical and complex structures at atomic or nanometer length scales. Examples of such materials with advanced functionalities include relaxor ferroelectrics (Jeong & Lee, 2006; Jeong, Lee, and Heffner, 2008; Martin & Rappe, 2017), colossal magnetoresistance magnets (Božin et al., 2007; Shatnawi, Bozin, Mitchell, & Billinge, 2016), high-temperature superconductors (Frandsen et al., 2017; Yu et al., 2018), renewably-sourced battery anodes (García-Negrón et al., 2020; McNutt, Rios, Feygenson, Proffen, and Keffer, 2014; Tenhaeff, Rios, More, & McGuire, 2014), semiconducting quantum dots (Chen, Li, & Kanan, 2012; Li et al., 2015), and phase change materials for thermal energy storage (Goswami et al., 2021a, 2021b). Furthermore, large-scale design of soft materials, such as polymeric materials for energy harvesting, advanced structural materials, and drug-delivery applications relies heavily on a detailed understanding of structural information obtained from the total scattering pair distribution function (TSPDF) (Dhindsa et al., 2016; Goswami et al., 2010; Ho, Goswami, Chen, Keum, & Naskar, 2018; Lynch et al., 2017). Consequently, there is a growing need to develop more versatile techniques that transcend traditional crystallography and elucidate the structure and properties of these complex materials for improved and efficient material design.

Recently, the TSPDF method has proven to be a successful and versatile technique for structural analysis of complex functional materials by surpassing the capabilities of traditional X-ray diffraction (XRD). Relevant information can be discovered through the analysis of the atomic pair distribution function (PDF) data obtained from total scattering experiments (Egami & Billinge, 2003; Peterson, Olds, McDonnell, & Page, 2021; Prill, Juhás, Schmidt, & Billinge, 2015). For example, the XRD patterns of two phosphate materials are shown in Figure 1 in the left panels. The top-left pattern (a)(i) is from a crystalline sample, and the bottom-left pattern (b)(i) is from a similar nanocrystalline material that did not crystallize(Terban, Shi, Silbernagel, Clearfield, & Billinge, 2017). In the top-left pattern (a), sharp Bragg peaks were observed, meaning crystalline materials are discernible to XRD. However, the nanocrystalline sample, peaks are very broad and diffuse. This signifies that XRD provides limited insight into the structure of a sample and a small range of structural coherence. Signals that were obtained from the TSPDF approach on the top- and bottom-right patterns [(a)(ii) and (b)(ii)] exhibit well-defined pair correlations at low real-space distance, indicating a well-defined local structure. The peaks at the bottom-right diminish in amplitude with an increase in distance, and they disappear by approximately 40–50 Å, which signifies an absence of long-range order in the nanocrystalline material. Thus, the PDF data provides clearer structural information in the case of limited crystallinity, which makes it possible to characterize the atomic structure of the phosphate layers (Terban et al., 2017).

Figure 1. Powder XRD patterns of (a)(i) crystalline material and (b)(i) nanocrystalline material. [(a)(ii) and (b)(ii)] show the corresponding TSPDF data suitable for structural analysis in real space. The patterns’ PDF data show a clearer structural information for the nanocrystalline sample. Reproduced with permission from (Terban et al., 2017). Copyright 2017, American Chemical Society.

The PDF correlates atomic positions by measuring the probability of an atom being located at a specific distance from other atoms. Therefore, the PDF, it serves as a standard characteristic of the atomic structure and arrangement of a material (Petkov et al., 2007; Proffen et al., 2003). This method has been used to study a wide spectrum of materials predominantly liquids, and glasses as well as poorly crystalline, nanocrystalline, disordered crystalline, and well-ordered compounds (Dhindsa et al., 2016; Dmowski et al., 2010; Egami, 1990; Egami & Billinge, 2003; Goswami et al., 2010, 2021a; Ho et al., 2018; Lynch et al., 2017; Masadeh, 2016; Mauro et al., 2016; Petkov et al., 2002; Prill et al., 2015; Toby & Egami, 1992). Figure 2(a) shows the atomic distribution of a material and a hard-sphere model for measuring interatomic distances. Figure 2(b) shows a typical PDF pattern, G(r), with the diverse structural details that can be directly obtained from it. The peak position indicates the interatomic distance in the material, whereas the area of peaks is related to the number of neighboring atoms to the central atom. The peak width informs about the level of disorder inside the material, which can be a structural disorder effect and/or atomic thermal vibration (McNutt et al., 2014; Smith et al., 2008). The maximum distance at which peaks are observable gives insight into the material’s crystal size or its structural coherence (Chapman, 2016; Wang, Tan, Yang, & Hu, 2020).

Figure 2. (a) Atom distribution of CeO₂ in real space, and a sphere centered at an atom for evaluating radial distribution function (Wang et al., 2020), (b) TSPDF plot in real space, G(r), providing structural information in real space (Chapman, 2016).

TSPDF method was originally used for characterizing the structure and dynamics in liquids and glasses (Keen, 2020). The advances in these applications led to the recent extension of the TSPDF method to characterize more complex materials including disordered crystalline and nanocrystalline materials. The rich history of the applications of TSPDF methods to characterize liquid and glassy systems have been extensively discussed in the literature (Keen, 2020; Proffen et al., 2003; Shimakura, et al., 2001). The wide applicability of the TSPDF method in the past decades has been enhanced by a series of advances in techniques relating to synchrotron X-rays, intensely pulsed neutrons, and advanced computing. Despite the notable research interest and acceptance of the TSPDF method as a versatile technique for elucidating the structure and properties of complex functional materials, scientific publications on the TSPDF method have not been subjected to thorough bibliometric analysis. However, similar work has been published highlighting the progression of the TSPDF technique over time. Billinge (2019) made an effort to describe the key moments contributing to the TSPDF method’s recent growth and expanded the impact of the PDF technique in materials science today using data from the Web of Science (WoS) as an illustration. In a previous study, Billinge reviewed the history of the PDF method and discussed the major developments in the use of the PDF technique up till 2003 (Terban et al., 2017). Moreover, other published reviews describe using the PDF approach in probing the structure–property relationship of a wide range of advanced functional materials (Benmore, 2012; Keen, 2020; Mancini & Malavasi, 2015; Zhu et al., 2021).

Bibliometrics, the quantitative analysis of published information over time, has emerged as a useful tool for identifying research fronts, understanding the most recent developments in a field, providing insight and direction into future trends, and assisting funding agencies and policymakers with funding priorities, patent applications, and collaborations with other institutions (Elisha & Viljoen, 2021). For example, this form of analysis is poised to make significant contribution to the research and development activities in the field of materials science (Bello, Zhai, He, Xu, & Ni, 2021; Liu, Zhu, Gu, & Zhao, 2021). As a result, bibliometrics could be used to track and analyze publications that use the TSPDF method in a global context to provide relevant insight into the existing and future scholarly activity surrounding the TSPDF method.

In this article, the following variables are measured or evaluated: the volume of research output and the growth rate of publications and citations involving the TSPDF method between 2000 and 2021; research area categories based on the WoS database; contributions of leading countries/regions; productive institutions, co-citation of referenced sources; common keywords relevant to TSPDF method; and research hotspots and future directions based on common keywords. The focus on the last 21 years of research tips this study to predicting recent and future trends and impacts in the TSPDF field. The aim for this bibliometric study is to foster the development and heighten awareness of current global research trends in TSPDF techniques among individuals, collaborative researchers, and policymakers, and to inform future research decisions for the advancement of the TSPDF method.

2. Research methods

2.1. Data source

The WoS database was used to retrieve the publication data on TSPDF techniques over a 21 year period (2000–2021). The WoS platform was chosen as the source platform because it provides comprehensive access to natural sciences and engineering data. A search was conducted on 10 May 2022, and focused on documents indicative of research activities and effort in the form of full research articles, proceeding papers, and review papers. Although scholarly documents indexed outside the WoS databases were not included in our analysis, it should be mentioned that the WoS database is one of the most reliable tools for providing comprehensive citation data for many academic disciplines (Mongeon & Paul-Hus, 2016).

A comprehensive framework that considers relevant categories and keywords associated with TSPDF analysis was used for data search and retrieval. The search considers these keywords in the titles, abstracts, and author keywords in the documents published between 2000 and 2021. The search query resulted in 4,303 separate sets of data. An extensive screening of the retrieved materials was performed by manually examining the title and abstract sections. During this screening process, duplicates, and other irrelevant results (e.g., papers not based on TSPDF analysis) were excluded from the final records. As a result, the final record count consists of 3,205 sets of data. The collection strategy and results are detailed in Table S1 of the Supporting Information. It is possible that several impactful studies related to TSPDF research in the previous decades (1980s and 1990s) were left behind, this search only captures the recent publication records in the last 21 years to understand the recent research trends and further predict the future research direction.

Table 1. Top 20 productive countries with total publications and citations in TSPDF research (2000–2021).

Country	Total publications	Total citations	Avg. citation per publication	Collaboration strength^a	Most cited publication^b	No of citations
United States	1,521	50,346	33.10	1,039	Farrow et al. (2007)	1195
UK	442	13,070	29.57	533	Keen(2001)	428
Japan	423	5,533	13.08	230	Chapman et al. (2005)	105
China	409	6,704	16.39	356	Rong et al. (2018)	175
Germany	366	8,373	22.88	441	Dietrich et al. (2017)	137
France	359	8,284	23.08	452	Gaillac et al. (2017)	158
Italy	192	3,541	18.44	244	Bertolotti et al. (2017)	164
Spain	109	2,995	27.48	168	Fernández-García, Martínez-Arias, Hanson, and Rodriguez, (2004)	800
Denmark	102	2,273	22.28	125	Becker et al. (2010)	97
India	87	1,095	12.59	53	Cherukuvada and Nangia, (2014)	155
Russia	86	1,004	11.67	65	Gulyaev et al. (2014)	61
Switzerland	83	2,067	24.90	136	Derlet and Van Swygenhoven (2003)	74
Sweden	80	2,552	31.90	147	Samain et al. (2014)	160
Australia	76	2,307	30.36	92	Chapman et al. (2005)	171
Canada	72	1,539	21.38	101	Talaie, Duffort, Smith, Fultz, and Nazar (2015)	224
South Korea	69	1,115	16.16	69	Kim et al. (2008)	42
Poland	51	610	11.96	76	Molski, Hofkens, Gensch, Boens, and Schryver (2000)	39
Brazil	50	691	13.82	45	Rocha et al. (2016)	37
Hungary	42	705	16.79	38	Borbély et al. (2004)	75
Netherlands	38	766	20.16	45	Hiemstra (2013)	126

^a Collaboration Strength is calculated in VOSviewer software.

^bMost cited publication is based on country of affiliation of the corresponding author.

2.2. Data analysis and visualization

The datasets retrieved from WoS were saved as plain text files and exported to VOSviewer (v1.6.16) for further bibliometric analyses and generation of network maps for various research categories. VOSviewer is a free, user-friendly software that creates high-resolution visual images of bibliographic networks and offers opportunities for researchers to visualize and explore bibliographic work (Jan van Eck & Waltman, 2017; Jan van Eck & Waltman, 2010.) VOSviewer was operated mostly in the default mode with few instances of parameter adjustment for the construction and analysis of the network maps.

Explaining the relevant technical terms of this bibliometric study is crucial to properly understanding its contents. The bibliometric maps created using VOSviewer include items (i.e., nodes) that are usually the object of interest. Items include keywords, authors, journals, research organizations, and countries. A map usually contains only one set of items. There can be a link between any pair of items. A positive numerical value represents each link’s strength. Higher values represent a stronger connection between the items. Thus, the link strength is an indication of the strength of the relationship between items (van Eck & Waltman, 2013). For example, link strength could indicate the number of publications two countries have co-authored together. Associated items are linked together to form a network where the size of an item is directly proportional to the number of documents generated by the item/node in addition to the VOSviewer calculation of total link strength (Elisha & Viljoen, 2021). In the case of co-authorship analysis, the size of the node associated with an organization is the number of publications produced by the organization and the total strength of the co-authorship links of the organization with other organizations.

3. Results and discussion

The results of the bibliometric data analysis for TSPDF research between 2000 and 2021 are presented in the sections that follow. The results show the recent global trend of publications, global research subjects, participation of countries and their collaboration networks, the interaction between institutions, and referenced sources. Key insights into the future research trends in the TSPDF method are also highlighted.

3.1. Annual publication and citation trends

A total of 3,205 sets of data, including 2,842 articles, 290 proceedings, and 73 reviews were obtained from the WoS database and exported to VOSviewer for bibliometric analysis. Figure 3(a) shows the annual publication and citation trends of literature in TSPDF research. The annual output of global TSPDF research quadrupled, increasing from 60 documents in 2000 to 308 in 2021. The total citations trend also grew exponentially during the same period. However, there were decreases in the number of publications in 2004 and 2008 when compared to the preceding years. Conversely, there was a significant increase in the number of publications from 2008 to 2021, with 2,621 publications within that period representing 79% of the total publications. This increase could be because of the growth in the application of the TSPDF method not only for amorphous systems, but also disordered crystalline and nanostructured systems, including ferroelectric and thermoelectric materials (Lei et al., 2014). Another probable reason could be due to increased instrument availability for TSPDF research (Billinge, 2019). This underscores an overall increase in the interest and applicability of the TSPDF technique. Figure 3(a) displays that the application of the TSPDF technique will continue to grow and cause a continuous rise in the annual publication over the next decade.

Figure 3. Distribution of publications related to TSPDF research between 2000 and 2021 (a) Annual publication and citation trend of literature on TSPDF research (b) Web of Science research categories of publications on TSPDF research.

3.2. Research subject distribution based on WoS category

The WoS database was used to provide a bigger picture of the research subjects involved in the TSPDF technique. These research subjects are based on the classification of the publications on the WoS platform. Figure 3(b) depicts the top 15 WoS research categories of the publications on the TSPDF technique. Materials Science Multidisciplinary has the most publications (1,174), followed by Chemistry Physical (859), Chemistry Multidisciplinary (605), and Physics Applied (573). These research subjects make up 57% of the total, which indicates the multidisciplinary nature of TSPDF research that encompasses a wide breadth of areas including fundamental and applied research. In terms of the respective fields, chemistry and physics, and materials science are basic pillars, and categories such as physics condensed matter, nanoscience, physics multidisciplinary, physics fluids plasmas, chemical inorganic nuclear, instruments instrumentation, crystallography, metallurgy engineering, and materials science ceramics, meriting special consideration. These findings are consistent with the applications of TSPDF analysis in natural sciences. For instance, several advanced instrumentations are extensively used to characterize the nanostructure and nuances in short-range order of crystallographically-challenged materials through TSPDF analysis. Characterizing these attributes requires a solid understanding of nanoscience, crystallography, condensed matter physics, inorganic chemistry, and so forth.

3.3. Participation of countries/regions in TSPDF research

The participation of countries in TSPDF research provides key information about the relative application of the technique in different regions. Participation rates also reveal the research investments and trends in international research cooperation of the TSPDF method. The total publication output, citations, average citations, and collaborations related to TSPDF research of the leading countries are shown in Table 1. Based on these specific research output metrics, the top five most productive countries are the United States (1,521), the United Kingdom (442), Japan (423), China (409), and Germany (366). There is a small variation in the rankings when only total citations are considered, and the top five countries are the United States (50,346), the United Kingdom (13,070), Germany (8,373), France (8,284), and China (6,704). To provide a more encompassing view of the contributions of different countries, the average citations per publication was also considered. In this respect, the top five countries are United States (33.10), Sweden (31.90), Australia (30.36), United Kingdom (29.57), and Spain (27.48). These findings are indicative of these leading countries’ level of research influence. Furthermore, publications related to computational programs for modelling and fitting of atomic structures to PDF data were among the most cited articles in the respective countries. For instance, the most cited article related to PDF research in the United States focuses on the development of PDFgui, a refinement program for modeling the local structure and nanostructure in materials through atom PDFs (Farrow et al., 2007). Additionally, articles related to the application of the TSPDF technique in the research of lithium-ion batteries appeared among the most cited articles in the respective countries (Dietrich et al., 2017; Rong et al., 2018; Yamakawa, Jiang, Key, & Grey, 2009). This data point shows the importance of the TSPDF approach in elucidating the local structures and properties of battery materials for better energy storage and conversion.

The collaboration among countries involved in TSPDF research is illustrated with a network diagram in Figure S1 of the Supporting Information. To generate the figure, the minimum number of documents was set to 50. Out of the 78 countries involved in TSPDF research, only 28 met the set criteria. The sizes of the nodes denote the research output of individual countries to the TSPDF research, and the color of the nodes represents the respective cluster assigned to the node. The existence of a link between two countries implies that there is a collaborative relationship between them, and the thicker the visual link, the stronger the collaboration. Supporting Information Figure S1 demonstrates that there is a strong collaborative relationship among the leading nations in TSPDF research. In the red cluster, the United States shares the most co-authorship relationships with China, followed by the United Kingdom, Germany, France, and Japan. Other notable collaborative groups are represented by the yellow and blue clusters with predominantly European countries, where the United Kingdom, Germany, and France as the major drivers. Thus, the results validates the collaboration among the TSPDF community that could encourage continuous advancement of the field.

To gain a balanced perspective of regional participation in TSPDF research, the research output of the continents was compared as shown in Figure 4. The leading continent in TSPDF research is Europe (43.5%), followed by North America (31.6%), and then, Asia (21.4%). The significant contributions by these continents can be attributed in part to their access to large-scale scientific facilities and instruments for high-throughput TSPDF research. For example, notable research facilities in Europe include the European Synchrotron Radiation Facility (ESRF), ISIS Neutron and Muon Source, Diamond Light Source, German Electron Synchrotron (DESY), and so on. Also, North America possesses noteworthy infrastructures for TSPDF research, including the Advanced Photon Source (APS), Spallation Neutron Source (SNS), National Synchrotron Light Source (NSLS-II), and Canadian Light Source. Some of the notable facilities in Asia include the Super Photon ring-8GeV facility (Spring-8), China Spallation Neutron Source (CSNS), and Taiwan Photon Source (TPS). Furthermore, there is still room for enormous growth and expansion of TSPDF research for materials discovery and characterization in Australia, South America, and Africa.

Figure 4. Comparison of continents based on research output in TSPDF research.

3.4. Participation of institutions in TSPDF research

The participation of institutions in TSPDF research between 2000 and 2021 is discussed in this section. There are recommendations that the total publications, h-index, and average citations should be combined as metrics to obtain a more complete view of the contribution of institutions in a research field (Liu et al., 2021). The h-index, which refers to the number h of papers from an author, organization, or country/region that have been referenced at least h times (Mao, Huang, Chen, & Wang, 2018). The h-index is a common metric for evaluating publications because it captures research output based on the total number of publications and the total number of citations of those works. The reported h-index in this work is based not on all publications by a given institution, but rather those publications based on the parameters of the WoS search for this study. A total of 2,044 institutions are reported to be involved in TSPDF research, 40 having at least 30 publications. The top 15 institutions based on total publications are illustrated in Figure 5; the h-index and the average citation of each institution’s papers are also indicated. Argonne National Laboratory had the highest number of publications (390), followed by Oak Ridge National Laboratory (267), Brookhaven National Laboratory (214), Centre National de la Recherche scientifique (200), and then Rutherford Appleton Laboratory (192). h-index data were slightly different because Argonne National Laboratory occupied the first position (63), followed by Brookhaven National Laboratory (51), and then Los Alamos National Laboratory (42). In terms of average citations, State University of New York, Stony Brook stands out in the rank, followed by University of Cambridge, and then, Brookhaven National Laboratory. These leading institutions are either home to advanced facilities with one or more TSPDF instruments or they are in close proximity to these facilities (e.g., Columbia University and State University of New York, Stony Brook are 67.6 and 21 miles away, respectively from Brookhaven National Lab’s NSLS-II facility).

Figure 5. Top contributing institutions in TSPDF research based on their publication output, average citation, and h-index.

3.5. Co-citation analysis of referenced sources

The objective of co-citation analysis of referenced sources is to find the most significant journals cited by articles in the retrieved dataset. When two journals are referenced together by the same body of literature, a co-citation relationship is acknowledged. This type of analysis will not only highlight the key journals for researchers interested in the application of TSPDF techniques but it will also provide information on the relevant research themes, some of which are represented in the titles and major topical themes of the journals (Yang, Reniers, Chen, & Goerlandt, 2019). There are 8,738 publication sources cited by the 3,205 sets of data retrieved in this study, and 46 sources have been cited at least 600 times. Figure S2 (Supporting Information) depicts the co-citation map of the referenced sources with at least 600 citations. The cited sources are organized into three distinct color-coded clusters. The size and brightness of the circles are indicative of the citations received by these referenced sources. The red cluster includes journal in the chemistry discipline that received the most citations, including The Journal of American Chemical Society, Chemistry of Materials, and The Journal of Physical Chemistry C. This further exemplifies the important role of chemistry in TSPDF research, as highlighted in Subsection 3.2. Furthermore, the green cluster includes journals in the materials science and materials physics areas including the Journal of Applied Crystallography, Physical review B, and Journal of Physics: Condensed Matter. This depicts the fact that materials science is a key discipline engaged in TSPDF research. The blue cluster represents interdisciplinary and physics-based journals including Physics Review Letters, The Journal of Chemical Physics, Science, and Nature. This is attributed to the importance of understanding the structure-property relationships of the materials in TSPDF research, which spans across disciplines. The co-citation of referenced sources reveals that chemistry, physics, materials science, and interdisciplinary sciences are the prominent disciplines associated with TSPDF research and applications between the year 2000 and 2021.

3.6. Occurrence of keywords and research hotspots in the TSPDF field

To study the knowledge structure and trends in a research field, mapping the keywords therein is essential (Su & Lee, 2010). For a more holistic overview of the research hotspots in the TSPDF field, bibliometric data for the co-occurrence of keywords with at least five occurrences were collected, and 78 out of 3,685 author keywords met this threshold. These keywords are illustrated with 7 clusters in Figure 6. The size of the node denotes keyword occurrence frequency. The larger the node, the higher the frequency of occurrence. The results indicate that the top 10 most frequently occurring keywords include the following: pair distribution function (with 527 occurrences), followed by X-ray diffraction (213), neutron diffraction (128), total scattering (110), local structure (96), molecular dynamics (93), nanoparticles (68), structure (61), amorphous (56), and electron diffraction (51).

Figure 6. Network visualization of author keywords with a minimum of 5 occurrences appearing between 2000 and 2021. Node size represents the frequency of occurrence. The colored shapes with dash lines are drawn around the respective clusters as guide to the eye

After examining the network diagram in Figure 6, common trends among the items in the clusters become apparent. Several of the trends are discussed extensively here. The deep blue cluster illustrates the central role that pair distribution function analysis, neutron diffraction, and other scattering techniques play in the characterization of materials with structural inhomogeneities, including doped ceria, quartz, high-entropy alloys, bulk, and metallic glasses. Moreover, the application of TSPDF and diffused scattering techniques in the characterization of hydrogen storage materials were captured. It also shows the application of reverse Monte Carlo (RMC) techniques, in relation to TSPDF research to model disorder, short-range order, lattice distortion, and other phenomena in complex functional materials. The TSPDF technique is a relevant tool for providing insights into various phenomena such as lattice distortion, cation ordering, nanophase quantification, and others not easily distinguishable by traditional characterization techniques. Two hallmark examples include the application of TSPDF to uncover key details of the morphotropic phase boundaries in piezoelectrics and order-disorder transitions in colossal magnetoresistance (CMR) magnetic materials. For example, Neutron PDF was used to probe the structures of PbZr_1–xTi_xO₃ (PZT) near the piezoelectric morphotropic phase boundary (Zhang et al., 2014). It was reported that there are two types of monoclinic phase coexisting in long- and short-range structures of PZT and being separated by an additional phase boundary, which aids in using PZT for wide piezoelectric applications. Also, the TSPDF method was used to characterize CMR effects in magnetic materials (including Mn³⁺ - Mn⁴⁺ - based perovskites) under magnetic fields as they approach their respective Curie temperature. These materials are susceptible to the Jahn–Teller (J-T) effects, which lead to orbital ordering and distortion in the local structure of the materials. The TSPDF method revealed the variation in local structure across the orbital order/disorder transition that couples the J-T distortions in LaMnO₃ (Thygesen et al., 2017). In contrast to standard order/disorder descriptions, results demonstrate that a discontinuous transition in local structure occurs between ordered and disordered states. This further confirms the importance of TSPDF method in advancing the physics of CMR active materials for various applications, especially hard disk data storage.

The TSPDF technique plays a key role in the research and development of functional materials for hydrogen storage. The great intensity of synchrotron radiation makes in situ research possible, which can collect data with considerable speed and resolution to detect mechanistic properties or processes such as lattice defects—or disorder during hydrogen adsorption/desorption cycles—in hydrogen storage materials with precise detail. For instance, TSPDF analysis was used to probe the degradation mechanism in Mg_2–xPr_xNi₄ (x = 0.6 and 1.0) against hydrogenation cycles. The PDF pattern of Mg_1.0Pr_1.0Ni₄ showed peak broadening that became more significant with an increasing number of hydrogenation cycles. This was correlated with the accumulation of lattice strain or an increase of the dislocation density which led to the decrease in the hydrogen storage capacity of the material (Wang et al., 2020). PDF analysis was also employed to investigate the atomic structure and stability of bimetallic Pd_{1 − x}Pt_x for hydrogen storage (Kumara et al., 2017). The PDF analysis suggested the formation of a highly disordered structure with a high cavity–volume fraction for low-Pt content materials, a behavior that enhanced the stability of the materials for hydrogen charging/discharging cycles.

Furthermore, RMC modeling is an established approach used to simulate and interpret experimentally observed TSPDF data. This is a big-box approach in which a huge ensemble of atoms (i.e., up to tens of thousands) are moved at random with a defined acceptance criteria to find a satisfactory fit for the experimental PDF data. The aim is to create a sufficiently large configurational space for capturing atomic and nanoscale disorder and other structural information that matches available data. Modern adaptations allow fitting of multiple data types and incorporate chemical and physical constraints (Playford, Owen, Levin, & Tucker, 2014). The early application of RMC modeling was observed in the creation of atomistic models for liquid structures and glassy systems. However, the RMC approach has been extended to various nanostructured, and crystalline systems with significant structural, site occupancy, electron, spin, and atomic thermal vibrational disorders (Tucker, Keen, Dove, Goodwin, & Hui, 2007). For example, a pair distribution function study utilized RMC refinement to study the disorder in the Nb⁵⁺ - doped ceria system. The results revealed that the tiny pentavalent substituent is moved away from the ideal cubic coordination near four oxygens leading to under-coordinated oxygen, which explains the greatly increased oxygen storage capacity of redox catalysis-relevant materials (Hiley et al., 2018). RMC modeling was also used to provide short- and long-range structural information of the displacive α—β phase transition in quartz (Tucker, Dove, & Keen, 2000; Tucker, Keen, & Dove, 2001). These studies showed that local disorder occurs considerably below the transition temperature and that other features, such as the Si–O bond length, are immune to the phase transition. In other circumstances, RMC modeling has been used to provide comprehensive structural information in other material systems, including nanoporous materials (Goodwin et al., 2010), bimetallic nanoparticles (Li et al., 2017), electrode materials (Bréger, Kang, Cabana, Ceder, & Grey, 2007), and high-entropy alloys (Nygård et al., 2020), and so on. The above discussion has highlighted the central role TSPDF analysis plays in providing comprehensive structural details of a wide spectrum of complex materials with structural inhomogeneities.

The red cluster indicates the application of other complementary techniques such as electron diffraction, extended X-ray absorption fine structure (EXAFS), and transmission electron microscopy (TEM) with TSPDF analysis to investigate the structure and properties of complex materials. These include metallic glasses, nanomaterials, ferrihydrites, iron superconductors, silicon carbide, and alumina. The concept of magnetism for characterizing phenomena related to magnetic scattering and high-pressure PDF technique for measuring the structural features of materials with the aid of diamond anvil cells are also represented in the cluster.

The TSPDF technique and EXAFS have become methods of choice in characterizing nanostructured materials. The sensitivity of EXAFS to various elements and the capability to capture ordering in materials have caused it to be combined with TSPDF methods for the characterization of local structures of various functional materials, including nanostructured materials, and high temperature superconductors (Zhu et al., 2021). In one instance, PDF methods and EXAFS were combined to investigate the effect of lattice distortions on the superconductivity behavior of iron-based superconductors such as BaFe₂As₂ and LiFeAs (Li, Toyoda, et al., 2018). The results revealed that the local distortion in the FeAs planes of BaFe₂As₂ displayed a temperature-dependent characteristic that affected the superconductivity transitions. However, LiFeAs, showed no structural transition associated with the superconducting transformation at 18 K, and only a small deformation was found at temperatures below 200 K. For the first time, the real-space PDF modelling method was used to unravel the atomic structure of ferrihydrite, an iron oxyhydroxide material, which usually exist in the nanocrystalline form (Michel et al., 2007). It was found that ferrihydrite has a local structure consistent with a single phase (with hexagonal space group P6₃mc) consisting of 20% tetrahedrally coordinated iron and 80% octahedrally coordinated iron. Likewise, the TSPDF method was used in characterizing surface distortions, and local octahedral distortions, and gas adsorption in nanomaterials (Bertolotti et al., 2017; Goodwin et al., 2010; Tucker et al., 2001). Furthermore, the adoption of electron diffraction for crystal structure investigation has received more interest because of the advances in the data collection processes. When leveraging the strong interaction of electrons with matter, meaningful single-crystal electron diffraction data can be obtained from nanocrystals using TEM to conduct the electron diffraction experiments (Fujishima et al., 2008; Michel et al., 2007; Zhu et al., 2018). The structural details of a number of inorganic and organic compounds have been established through electron diffraction (Gemmi, Campostrini, Demartin, Gorelik, & Gramaccioli, 2012; Jiang et al., 2011; Willhammar et al., 2012). Recent advances in the total magnetic scattering (mPDF) through the interplay between neutrons and magnetic moments of atoms (Mühlbauer et al., 2019) have also provided insight into the magnetic inhomogeneities in complex functional materials such as spin liquid Gd₃Ga₅O₁₂ (Paddison et al., 2015) and Ising magnet, Dy₃Mg₂Sb₃O₁₄ (Paddison et al., 2016). Also, the impact of TSPDF analysis in the characterization of electrochemical materials are notable. The TSPDF method can provide insight into the atomic structure, and electrochemical reactions occurring in these complex materials (Grenier et al., 2017; Li, Toyoda, et al., 2018). Additional details of the application of the TSPDF in electrochemistry are provided later in this section.

TSPDF methods are also suitable for studying pressure-dependent processes, such as amorphization and structural changes. This is facilitated by the optimization of high-pressure PDF technologies (e.g. diamond anvil cell design, and data analysis procedures) for studying the local structure of complex functional materials within a pressure regime of 0–10 GPa (Chapman et al., 2010). For instance, the breakdown of SF₆ in the presence of glassy carbon, initiated in diamond anvil cells heated by a laser at 10–11 GPa and 2000–2100 °C was characterized using the high-pressure PDF method, Raman spectroscopy, and atomistic models (Rademacher et al., 2015). This further validates the importance of TSPDF methods in providing fundamental understanding of the interplay of structure, magnetism, and conductivity for complex materials characterization.

The yellow cluster indicates the application of the TSPDF technique (including Rietveld refinement) in probing the local structure and average structure of several functional materials including ferroelectrics, perovskite photovoltaics, cathode, and battery materials, and especially lithium-ion batteries, and sodium ion batteries. Ferroelectrics exhibit random polarization that is tunable in response to an external electric field (Zhu et al., 2021). Examples of ferroelectrics include perovskites oxides, PbTiO₃, BaTiO₃, and BiFeO₃. This ferroelectric behavior invokes several structural phenomena such as local lattice distortion and polar nanoregions (PNRs), which are structurally complex for traditional crystallography approaches. For example, relaxor ferroelectrics—a subclass of ferroelectrics exhibiting PNRs—are nanoscale aggregates initiated by random polarizations impacting the structural and dielectric characteristics of these materials. TSPDF methods have been used to characterize the PNRs phenomenon in this class of materials including Pb(Mg_1/3Nb_2/3)O₃ (Zhu et al., 2021), Pb(Zn _1/3Nb_2/3)O₃ (Jeong et al., 2008), and BaZr_xTi _1–xO₃ (Buscaglia, et al., 2014). Moreover, TSPDF has been proposed to provide relevant details on the structural analysis, phase evolution, and stability of perovskites including methylammonium lead iodide (MAPbI₃) thin film (Sanchez et al., 2019), methylammonium lead bromide (MAPbBr₃) hybrid perovskite (Page, Siewenie, Quadrelli, & Malavasi, 2016), and halide perovskite CsPbI₃ (Straus, Guo, Abeykoon, & Cava, 2020). This could provide insight for performance optimization of solar cells and photovoltaic systems.

The TSPDF technique has proven to be an effective approach in providing a fundamental understanding of important scientific phenomena related to battery materials, including lithium-ion batteries, sodium ion batteries, and cathode materials, which could help create a clean and sustainable future. The key reasons for the adoption of the TSPDF method for characterizing battery materials are as follows: (1) battery materials have components with poor crystallinity or amorphous structure; (2) the pronounced presence of static and/or dynamic disorder in the materials system; and (3) the chemical reactions and processes are influenced by nanoscale and mesoscale effects and domains (Mancini & Malavasi, 2015). To that end, several processes in cathode materials have been intensively researched for the sole purpose of increasing the energy density of these materials. For instance, the TSPDF technique has been used to characterize the following: structural evolution of electrode materials (Yang et al., 2019), hidden short-range order in high voltage spinel (Liu, Huq, Moorhead-Rosenberg, Manthiram, & Page, 2016), redox reaction mechanism (Rong et al., 2018), lithiation mechanism in battery materials (Key et al., 2011), and so on. Therefore, the TSPDF technique is a viable tool for probing the structures of various functional materials and providing essential insight into key material science issues.

The green cluster highlights the use of synchrotron radiations, Raman spectroscopy, X-ray absorption near edge structure (XANES) combined with TSPDF analysis to characterize the phenomena of interest (e.g., phase transitions, negative thermal expansion, etc.) among notable functional materials including metal organic frameworks (MOFs), catalyst oxides, nanoparticles, and thin films. The ability of XANES to be sensitive to the charge state of cations in nanostructured materials makes it a suitable method to be coupled with the TSPDF technique to provide details on the challenging scientific problems in materials science. For example, the TSPDF method has been combined with XANES and EXAFS to measure the local structure of nanoparticles across various length scales (Amidani et al., 2021; Gawai et al., 2019).

Moreover, the TSPDF technique has proven to be effective in providing important details on phenomena such as negative thermal expansion (NTE) in fundamental materials. NTE is observed when there is volume contraction with an increase in temperature. This phenomenon has shown relevance in optical components in aerospace materials, and optical fiber technology. To further optimize the properties of these NTE materials, understanding the origin of NTE is needed but is not explainable using traditional crystallography. TSPDF has revealed that it is due to the coupled vibration in the materials, the result is a thermally induced volume contraction even with the increase in bond length (Young & Goodwin, 2011). Several NTE materials such as zirconium tungstate, ZrW₂O₈ (Bridges et al., 2014), cyanides (Chapman, Chupas, & Kepert, 2005), oxides of Cu₂P₂O₇ (Shi et al., 2020), have been studied to understand the structure–property relationships. Some of these material relationships include pressure-induced amorphization, magnetovolume effect, and temperature-dependent atomic correlations. In the same vein, the TSPDF method has probed the local structure and shed new light on several relevant phenomena in layered framework materials including MOFs and zeolites. These materials are formed by regular metal clusters and organic ligands, and they are porous and geometrically flexible (Deng et al., 2020). These properties make them susceptible to structural disorder and low-energy dynamics that impact the following relevant processes: gas sorption and storage properties, pressure- and temperature-induced amorphization, and catalytic activity, all of which are discernible using TSPDF-based investigation (Young & Goodwin, 2011). TSPDF methods have been used successfully to characterize MOFs for various applications in the following areas: local structure of disordered or defective MOFs (Bennett et al., 2016; Orellana-Tavra et al., 2015), interaction of MOFs with gas molecules (Sava Gallis et al., 2016), or hazardous substance during uptake (Rangwani et al., 2018), in situ observation of structural modification in MOFs by chemical alterations (Simons et al., 2019). Hence, the TSPDF method is a versatile and powerful tool for characterizing a wide spectrum of materials.

The purple cluster brings attention to the application of computational approaches, such as molecular dynamics (MD) and density functional theory (DFT) with the TSPDF method in the characterization of processes (e.g., crystallization and stability) in a wide spectrum of materials from crystalline to highly disordered and amorphous materials including water. This cluster alludes to the established interest and advances in the application of these methods in analyzing the movements of atoms and molecules, thereby providing the structure and dynamic evolution of materials. MD simulations convey the structural details of materials through radial distribution function or pair distribution function plots that represent the atomic distribution as a function of distance. The application of MD simulation coupled with the neutron data and the TSPDF method to unravel the structural and dynamical properties of liquid water and amorphous ice in various conditions of temperature and pressure has been reported extensively in the literature (Amann-Winkel et al., 2016; Bakker & Skinner, 2010; Head-Gordon & Hura, 2002). An illustration is the measurement of the self-dynamics of water including translational and rotational diffusion in the gigapascal range (Bove et al., 2013). Another study reported the ultrafast probing of the structure of liquid water below the homogenous ice nucleation temperature which provides further information on the behavior of water (Sellberg et al., 2014). The polymorphic states of ice were also elucidated using experiments conducted at ambient pressure (Loerting et al., 2011). Furthermore, the behavior of water with other materials are captured including the study of the structure and metastability of SnO₂ nanoparticles with a few layers of water on the surface (Wang et al., 2013). MD can also be used to provide a starting structure for RMC modeling of disordered materials. For instance, MD simulation was combined with RMC modeling and high-energy XRD to resolve the structure of amorphous silicon monoxide (Grenier et al., 2017). Through the combination of these methods, silicon monoxide was found to transform into silicon- and silicon dioxide–like structures. Moreover, MD simulation was used to compare the interfacial water structure–property relationship on three different carbon substrates: namely, amorphous carbon, compressed expanded natural graphite, and pure graphite (Goswami et al., 2021a). The results show that the surface morphologies of these substrates determine the nanoscale properties of water and its interfacial interactions with the respective substrates. The TSPDF technique and computational simulation were coupled to provide a fundamental understanding of the supercooling mechanism in sodium sulfate decahydrate, a useful material for thermal energy storage applications (Goswami et al., 2021a).

The turquoise cluster signifies the application of the high-energy XRD technique with TSPDF to characterize the microstructure and atomic structure of materials. It also focuses on use of these techniques to provide key insights into processes such as adsorption of materials on surfaces. In addition to examples already introduced above, the TSPDF method also finds utility in the providing structural information on the surface adsorption mechanisms of arsenate oxyanions on γ-alumina nanoparticles (Li et al., 2011). The real-space PDF pattern showed the short-range atomic correlations between As–O and As–Al pairs. This could assist the removal of contaminants using metal (hydr)oxides. Also, the TSPDF method has been extensively used in catalysis to understand the structural relaxation mechanisms in nanoparticles due to the adsorption of gases (Lei et al., 2014). TSPDF and TEM techniques were used to characterize the microstructure and structural change and crystallinity of Pt nanoparticles due to particle size and adsorption of H₂/CO gases. The local structure reveals relaxation of Pt-Pt bonds, and the adsorption of H₂ improves the crystallinity of the materials while CO adsorption leads to structural disorder in the material. Thus, the TSPDF technique is suitable for characterizing the mechanisms and phenomena in various catalytic systems.

The orange cluster represents the application of the TSPDF technique for probing the structure of liquids, colloids, suspension, and other macromolecules. Notable examples include complex structures of electrolytes (Taylor, Davies, Hepplestone, Cheng, & Luo, 2019), the behavior of suspended nanoparticles in organic solvents (Zobel, Neder, & Kimber, 2015), and molecular processes guiding certain forms of carbohydrates (Petkov, Ren, Kabekkodu, & Murphy, 2013). Undoubtedly, the TSPDF technique is a powerful and viable tool for providing comprehensive structural details of a wide spectrum of functional materials and answering complex questions in materials science research.

4. Future research consideration

Co-occurrence and the evolution of keywords could be useful for providing a more comprehensive analysis of the development and future research directions emerging in the TSPDF field. To highlight the recent shift in research interests over the years, the relevant keywords used in the publications are observed in Figure S3 of the Supporting Information. Perspective on the themes for future research consideration are further discussed.

One of the emerging areas of interest in the TSPDF field is pharmaceutics and drug delivery. It is expected that the recent success in the application of PDF methods in drug delivery for the detection and analysis of nanoparticles of a pharmaceutical suspended in a solvent with a dilute concentration level as low as 0.25% (Terban, Johnson, Michiel, & Billinge, 2015) will enhance the wide applicability of the method for the characterization of phenomena (e.g., stability and dispersion) of more complex organic and inorganic pharmaceutical structures. Another notable area of interest is the development and incorporation of artificial intelligence (AI)-based approaches such as machine learning (ML) and database mining with TSPDF research. The current work in this area is concerned with the combination of ML with PDF methods to elucidate the process–structure–property relationships of various functional materials. For example, the ML approach has been applied to predict the space group of structures best matching the pair correlation of a measured atomic PDF (Liu, Tao, Hsu, Du, & Billinge, 2019). This is made possible by a model trained using more than 100,000 PDFs calculated from structures in the 45 most heavily represented space groups. The advancement of ML-based approaches to aid automated modeling and refinement of a large set of structures to experimental scattering data could give access to high-throughput TSPDF study for more novel materials discovery.

TSPDF data does not hold all the information needed to determine unique structural model or mechanisms in a material system. Therefore, the combination of the total scattering approach with other complementary techniques, such as solid-state NMR, computed tomography, TEM, EXAFS, XANES, Atom Probe Tomography, and Raman spectroscopy, could be vital for comprehensive characterization and description of phenomena that are significant to the contemporary materials science landscape. These approaches could provide new insight into processes such as sorption/desorption in gas storage materials, lattice and surface distortions, vibration modes, and phase transitions in complex hierarchical materials or devices. Other new technologies enabling high throughput acquisition of PDF data such as X-ray free-electron laser oscillator (XFELO) could also be explored (Halavanau et al., 2020). Additional burgeoning areas for research consideration are as follows: grazing incidence PDF, which is useful in the in situ characterization of thin/ultra-thin functional materials (Roelsgaard et al., 2019); thin-film PDF (tfPDF), which involves the local structure characterization of crystalline and amorphous thin films (Jensen et al., 2015); dynamic PDF (DyPDF) which is applicable for assigning vibrational modes to specific excitations in complex materials (Fry-Petit et al., 2015); 3D PDF for characterizing disorder in functional materials, especially single crystals (Weber & Simonov, 2012); and field-dependent PDF methods for characterizing several field-dependent ordering mechanisms in functional materials (Goetzee-Barral et al., 2017; Usher, Levin, Daniels, & Jones, 2015).

Furthermore, the advancement in instrumentation and computational approaches is expected to enhance the understanding of challenging mechanisms such as defect structure, or disorder in a wide class of complex functional materials including doped ceria, amorphous MOFs, macromolecules, perovskites, high-entropy alloys, battery materials, and so on. Specifically, considerable research effort is needed to improve and optimize the performance of computational modelling techniques such as RMC, MD, and DFT simulations. These simulations could help characterize complex polymorphous materials with structural, chemical, and magnetic inhomogeneities. A facile approach to model multiple phases in large-scale material systems would be beneficial for providing comprehensive details on the structure and mechanisms in complex functional materials such as those observed in photocatalysis, solid oxide fuel cells, and other energy storage systems.

Even with the rapid advances in the TSPDF field, there are still limitations that are worth extensive research consideration. For instance, conducting in situ and operando PDF experiments on some complex functional materials remains a daunting task. A typical example is the acquisition of in situ PDF for battery materials, in which ancillary battery cell components (which may include electrolytes, polymers, and carbon black) generate their own distinct and evolving scattering signals, making it difficult to detect the desired signal. This becomes even more difficult when a neutron source is used due to incoherent inelastic scattering from hydrogen-bearing species (Zhu et al., 2021). As a result, it is critical to address in situ battery cell design and the development of effective in situ neutron PDF techniques for characterizing battery materials. This could enable further understanding of the process–structure–property relationships of these materials for energy storage.

5. Conclusion

In an effort to characterize disordered materials, including many inorganic and organic materials whose structures are indiscernible by traditional crystallography techniques, researchers have developed the TSPDF technique for the investigation of complex hierarchical structures and materials limited to nanoscale or atomic order. To investigate the research effort of the relevant scientific community towards the progress and research direction in the application of the TSPDF method, a bibliometric assessment of the publications related to it during the past 21 years was conducted in this study. The results reveal that the application of the TSPDF technique is increasing, it involves a scientifically and geographically diverse community, and it is projected to continue this upward trend because of the need to understand the structural details and mechanisms in emerging functional materials in several multidisciplinary science fields.

Additionally, research consideration into pharmaceutics, catalysis, ML, magnetic scattering, and energy storage materials are among the emerging areas for structural analysis using the TSPDF method. Similarly, to keep up with the ever-increasing complexities in the new classes of functional materials, effective synergy between TSPDF methods with other complementary characterization techniques is expected. Specifically, computational modelling and AI-based approaches could be coupled with the TSPDF method to provide comprehensive structural details of polymorphous materials and enhance high-throughput structural analysis of complex functional materials. This study could be beneficial to researchers, policymakers, government agencies, industry, and PDF enthusiasts by informing future research decisions and collaborations, as well as by providing areas of further research exploration for the advancement of the TSPDF method.

Acknowledgment

This work was sponsored by the U. S. Department of Energy’s Building Technologies Office under Contract No. DE-AC05-00OR22725 with UT-Battelle, LLC.

Disclosure statement

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 article.