Multifunctional High Entropy Alloys Enabled by Severe Lattice Distortion

Since 2004, the design of high entropy alloys (HEAs) has generated significant interest within the materials science community due to their exceptional structural and functional properties. By incorporating multiple principal elements into a common lattice, it is possible to create a single-phase crystal with a highly distorted lattice. This unique feature enables HEAs to offer a promising combination of mechanical and physical properties that are not typically observed in conventional alloys. In this article, an extensive overview of multifunctional HEAs that exhibit severe lattice distortion is provided, covering the theoretical models that are developed to understand lattice distortion, the experimental and computational methods employ to characterize lattice distortion, and most importantly, the impact of severe lattice distortion on the mechanical, physical and electrochemical properties of HEAs. Through this review, it is hoped to stimulate further research into the study of distorted lattices in crystalline solids.

Atomic structure of an FeCrMoCBY metallic glass revealed by high energy x-ray diffraction

Amorphous bulk metallic glasses with the composition Fe₄₈Cr₁₅Mo₁₄C₁₅B₆Y₂have been of interest due to their special mechanical and electronic properties, including corrosion resistance, high yield-strength, large elasticity, catalytic performance, and soft ferromagnetism. Here, we apply a reverse Monte Carlo technique to unravel the atomic structure of these glasses. The pair-distribution functions for various atomic pairs are computed based on the high-energy x-ray diffraction data we have taken from an amorphous sample. Monte Carlo cycles are used to move the atomic positions until the model reproduces the experimental pair-distribution function. The resulting fitted model is consistent with ourab initiosimulations of the metallic glass. Our study contributes to the understanding of functional properties of Fe-based bulk metallic glasses driven by disorder effects.

Strategies and Considerations for Least-Squares Analysis of Total Scattering Data

The process of least-squares analysis has been applied for decades in the field of crystallography. Here, we discuss the application of this process to total scattering data, primarily in the combination of least-squares Rietveld refinements and fitting of the atomic pair distribution function (PDF). While these two approaches use the same framework, the interpretation of results from least-squares fitting of PDF data should be done with caution through carefully constructed analysis approaches. We provide strategies and considerations for applying least-squares analysis to total scattering data, combining both crystallographic Rietveld and fitting of PDF data, given in context with recent examples from the literature. This perspective is aimed to be an accessible document for those new to the total scattering approach, as well as a reflective framework for the total scattering expert.

Atomic arrangements in an amorphous CoFeB ribbon extracted via an analysis of radial distribution functions

We discuss the atomic structure of amorphous ferromagnetic FeCoB alloys, which are used widely in spintronics applications. Specifically, we obtain the pair-distribution functions for various atomic pairs based on high-energy x-ray diffraction data taken from an amorphous Co₂₀Fe₆₁B₁₉specimen. We start our reverse Monte Carlo cycles to determine the disordered structure with a two-phase model in which a small amount of cobalt is mixed with Fe₂₃B₆as a second phase. The structure of the alloy is found to be heterogeneous, where the boron atoms drive disorder through the random occupation of the atomic network. Our analysis also indicates the presence of small cobalt clusters that are embedded in the iron matrix and percolating the latter throughout the structure. This morphology can explain the enhanced spin polarization observed in amorphous magnetic materials.

Advantages of a curved image plate for rapid laboratory-based x-ray total scattering measurements: Application to pair distribution function analysis

The analysis and interpretation of the pair distribution function (PDF), as derived from total scattering measurements, is still seen by many as a technique confined to central synchrotron and neutron facilities. This situation has begun to change with a rising visibility of total scattering experiments reported in mainstream scientific journals and the modification of an increasing number of laboratory diffractometers. However, the rigor required during data reduction and the complexities of data interpretation mean the technique is still very far from being routine. Herein, we report the first application of a large area curved image plate system based on a Rigaku SPIDER (R-AXIS RAPID II) equipped with an Ag tube for collecting data amenable to high quality PDF refinement/modeling of crystalline, amorphous, and liquid samples. The advantages of such a system are the large Q range available without scanning (routinely in excess of 20 Å^-1) and the inherent properties of an image plate detector (single photon sensitivity, large dynamic range [1.05 × 10⁶], and effectively zero noise). Data are collected and structural models refined for a number of standard materials including NIST 640f silicon for which a R_wp ≤ 0.12 value was obtained with data collected in 60 min (excluding background measurements). These and other data are discussed and compared to similar examples in the literature.

Solid state chemistry for developing better metal-ion batteries

Metal-ion batteries are key enablers in today’s transition from fossil fuels to renewable energy for a better planet with ingeniously designed materials being the technology driver. A central question remains how to wisely manipulate atoms to build attractive structural frameworks of better electrodes and electrolytes for the next generation of batteries. This review explains the underlying chemical principles and discusses progresses made in the rational design of electrodes/solid electrolytes by thoroughly exploiting the interplay between composition, crystal structure and electrochemical properties. We highlight the crucial role of advanced diffraction, imaging and spectroscopic characterization techniques coupled with solid state chemistry approaches for improving functionality of battery materials opening emergent directions for further studies.

The development of high performing metal-ion batteries require guidelines to build improved electrodes and electrolytes. Here, the authors review the current state-of-the-art in the rational design of battery materials by exploiting the interplay between composition, crystal structure and electrochemical properties.

Structural properties of PbTe quantum dots revealed by high-energy x-ray diffraction

High-energy x-ray diffraction (HE-XRD) experiments combined with an analysis based on atomic-pair-distribution functions can be an effective tool for probing low-dimensional materials. Here, we show how such an analysis can be used to gain insight into structural properties of PbTe nanoparticles (NPs). We interpret our HE-XRD data using an orthorhombic Pnma phase of PbTe, which is an orthorhombic distortion of the rocksalt phase. Although local crystal geometry can vary substantially with particle size at scales below 10 nm, and for very small NPs the particle size itself influences x-ray diffraction patterns, our study shows that HE-XRD can provide a unique nano-characterization tool for unraveling structural properties of nanoscale systems.

Evolution of short-range order in chemically and physically grown thin film bilayer structures for electronic applications

Functional thin films are commonly integrated in electronic devices as part of a multi-layer architecture. Metal/oxide/metal structures e.g. in resistive switching memory and piezoelectric microelectrochemical devices are relevant applications. The films are mostly fabricated from the vapour phase or by solution deposition. Processing conditions with a limited thermal budget typically yield nanocrystalline or amorphous layers. For these aperiodic materials, the structure is described in terms of the local atomic order on the length scale of a few chemical bonds up to several nanometres. Previous structural studies of the short-range order in thin films have addressed the simple case of single coatings on amorphous substrates. By contrast, this work demonstrates how to probe the local structure of two stacked functional layers by means of grazing incidence total X-ray scattering and pair distribution function (PDF) analysis. The key to separating the contributions of the individual thin films is the variation of the incidence angle below the critical angle of total external reflection, In this way, structural information was obtained for functional oxides on textured electrodes, i.e. PbZr_0.53O_0.47O₃ on Pt[111] and HfO₂ on TiN, as well as HfO₂-TiO_x bilayers. For these systems, the transformations from disordered phases into periodic structures via thermal teatment are described. These examples highlight the opportunity to develop a detailed understanding of structural evolution during the fabrication of real thin film devices using the PDF technique.

Exact and fast calculation of the X-ray pair distribution function

A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.

Structure of Manganese Oxide Nanoparticles Extracted via Pair Distribution Functions

The structure of nanoparticles has been difficult to determine accurately because the traditional structure methods rely on large monocrystals. Here, we discuss the structure of nanoparticles based on real-space modeling of the pair distribution function obtained by a Fourier transformation of the high-energy X-ray scattering structure factor. In particular, we consider X-ray scattering data taken from colloidal manganese oxide nanoparticles used in Lithium-ion batteries, air-purification, and biomedical systems, which are known to exist in various nanometer-sized polymorphs. Insight is thus obtained into characterizing the structural relaxation of the MnO6 octahedra, which are the key building blocks of oxide nanoparticles, important in many technologies.

Time-resolved grazing-incidence pair distribution functions during deposition by radio-frequency magnetron sputtering

Characterization of local order in thin films is challenging with pair distribution function (PDF) analysis because of the minute mass of the scattering material. Here, it is demonstrated that reliable high-energy grazing-incidence total X-ray scattering data can be obtained in situ during thin-film deposition by radio-frequency magnetron sputtering. A benchmark system of Pt was investigated in a novel sputtering chamber mounted on beamline P07-EH2 at the PETRA III synchrotron. Robust and high-quality PDFs can be obtained from films as thin as 3 nm and atomistic modelling of the PDFs with a time resolution of 0.5 s is possible. In this way, it was found that a polycrystalline Pt thin film deposits with random orientation at 8 W and 2 × 10-2 mbar at room temperature. From the PDF it was found that the coherent-scattering domains grow with time. While the first layers are formed with a small tensile strain this relaxes towards the bulk value with increasing film thickness.

Local atomic structure of thin and ultrathin films via rapid high-energy X-ray total scattering at grazing incidence

Atomic pair distribution function (PDF) analysis is the most powerful technique to study the structure of condensed matter on the length scale from short- to long-range order. Today, the PDF approach is an integral part of research on amorphous, nanocrystalline and disordered materials from bulk to nanoparticle size. Thin films, however, demand specific experimental strategies for enhanced surface sensitivity and sophisticated data treatment to obtain high-quality PDF data. The approach described here is based on the surface high-energy X-ray diffraction technique applying photon energies above 60 keV at grazing incidence. In this way, reliable PDFs were extracted from films of thicknesses down to a few nanometres. Compared with recently published reports on thin-film PDF analysis from both transmission and grazing-incidence geometries, this work brought the minimum detectable film thickness down by about a factor of ten. Depending on the scattering power of the sample, the data acquisition on such ultrathin films can be completed within fractions of a second. Hence, the rapid-acquisition grazing-incidence PDF method is a major advancement in thin-film technology that opens unprecedented possibilities for in situ and operando PDF studies in complex sample environments. By uncovering how the structure of a layered material on a substrate evolves and transforms in terms of local and average ordering, this technique offers new opportunities for understanding processes such as nucleation, growth, morphology evolution, crystallization and the related kinetics on the atomic level and in real time.

Precise implications for real-space pair distribution function modeling of effects intrinsic to modern time-of-flight neutron diffractometers

Total scattering and pair distribution function (PDF) methods allow for detailed study of local atomic order and disorder, including materials for which Rietveld refinements are not traditionally possible (amorphous materials, liquids, glasses and nanoparticles). With the advent of modern neutron time-of-flight (TOF) instrumentation, total scattering studies are capable of producing PDFs with ranges upwards of 100–200 Å, covering the correlation length scales of interest for many materials under study. Despite this, the refinement and subsequent analysis of data are often limited by confounding factors that are not rigorously accounted for in conventional analysis programs. While many of these artifacts are known and recognized by experts in the field, their effects and any associated mitigation strategies largely exist as passed-down `tribal' knowledge in the community, and have not been concisely demonstrated and compared in a unified presentation. This article aims to explicitly demonstrate, through reviews of previous literature, simulated analysis and real-world case studies, the effects of resolution, binning, bounds, peak shape, peak asymmetry, inconsistent conversion of TOF to d spacing and merging of multiple banks in neutron TOF data as they directly relate to real-space PDF analysis. Suggestions for best practice in analysis of data from modern neutron TOF total scattering instruments when using conventional analysis programs are made, as well as recommendations for improved analysis methods and future instrument design.

Calculation of pair distribution functions for multiphase systems

The total scattering method is becoming increasingly popular because of its ability to investigate the structures of disordered crystalline and amorphous materials. Also, in recent years, significant development of total scattering instruments and sample environments has allowed for the study of increasingly complex materials, including multiphase samples. The total scattering formalism has already been well described in the paper by Keen [J. Appl. Cryst. (2001), 34, 172–177] but it was limited to the single phase case. In the present paper the formulae for multiple phase samples (consisting of a physical mixture of two or more distinct phases) are derived for the calculation of pair distribution functions for analysis using reverse Monte Carlo and other methods. The equations for conversion between different representations of the pair distribution function are also provided.

Neutron total scattering of crystalline materials in the gigapascal regime

Neutron total scattering of disordered crystalline materials provides direct experimental access to the local (short-range) structure. The ways in which this local structure agrees (or disagrees) with the long-range crystal structure can provide important insight into structure–property relationships. High-pressure neutron diffraction using a Paris–Edinburgh (P–E) pressure cell allows experimenters to explore the ways in which materials are affected by pressure, can reveal new synthetic routes to novel functional materials and has important applications in many areas, including geology, engineering and planetary science. However, the combination of these two experimental techniques poses unique challenges for both data collection and analysis. In this paper it is shown that, with only minor modifications to the standard P–E press setup, high-quality total scattering data can be obtained from crystalline materials in the gigapascal pressure regime on the PEARL diffractometer at ISIS. The quality of the data is assessed through the calculation of coordination numbers and the use of reverse Monte Carlo refinements. The time required to collect data of sufficient quality for detailed analysis is assessed and is found to be of the order of 8 h for a quartz sample. Finally, data from the perovskite LaCo0.35Mn0.65O3 are presented and reveal that PEARL total scattering data offer the potential of extracting local structural information from complex materials at high pressure.

Frontiers of water oxidation: the quest for true catalysts

Development of advanced analytical techniques is essential for the identification of water oxidation catalysts together with mechanistic studies.