Resolving the atomic-scale structure of defective high-entropy alloys (HEAs) containing interstitial species remains a major computational challenge due to the vast configurational space and the limitations of existing methods. Here we introduce PAIPAI (Package for Alloy Interstitial Predictions using Artificial Intelligence), a Monte Carlo framework coupled with machine-learning interatomic potentials (MLIPs) that searches for ground-state atomic configurations in HEAs with defects and interstitials. PAIPAI employs a dual-worker architecture-fast workers for rapid configurational screening and slow workers for high-accuracy refinement-coordinated through a shared waiting pool, enabling efficient parallel sampling. We demonstrate PAIPAI through three case studies: (i) surface segregation in a Ti-V-Cr-Re slab; (ii) interstitial oxygen and boron aggregation in bulk BCC Nb-Ti-Ta-Hf; and (iii) coupled metallic and interstitial segregation at grain boundaries in Nb-Ti-Ta-Hf. In all cases, Monte Carlo-optimized structures are significantly lower in energy than any configuration obtained by random sampling, and MLIP energy rankings are validated against density functional theory calculations. PAIPAI provides a general and efficient framework for predicting atomic ordering, segregation, and interstitial behavior in complex, defective HEA systems.
Based on BFS model and using Monte Carlo simulation we confirms the de-alloying in immiscible Au/Ni(110) system, and the critical Au coverage when de-alloying happens is also consistent with experiments. At the same time our simulation show that the structural phase transition will lead to the saturation of the number of alloying Au atoms.
November 2002, "Magister", Supervisors : Dr. H. Bouzar (Tizi-Ouzou, Algeria) with the collaboration of Dr. V. Pierron-Bohnes and Dr. C. Goyhenex (Strasbourg, France). Mouloud Mammeri University, Tizi-Ouzou (Algeria) and Louis Pasteur University, Strasbourg (France).
We present a methodology for the investigation of dislocation energetics in segregated alloys based on Monte Carlo simulations which equilibrate the topology and composition of the dislocation core and its surroundings. An environment-dependent partitioning of the system total energy into atomic contributions allows us to link the atomistic picture to continuum elasticity theory. The method is applied to extract core energies and radii of 60 degrees glide dislocations in segregated SiGe alloys which are inaccessible by other methods.
Avalanche photodiodes fabricated from AlInAsSb grown as a digital alloy exhibit low excess noise. In this paper, we investigate the band structure-related mechanisms that influence impact ionization. Band-structures calculated using an empirical tight-binding method and Monte Carlo simulations reveal that the mini-gaps in the conduction band do not inhibit electron impact ionization. Good agreement between the full band Monte Carlo simulations and measured noise characteristics is demonstrated.
The short and intermediate range order of an amorphous GeSe$_4$ alloy produced by Mechanical Alloying were studied by Reverse Monte Carlo simulations of its x-ray total structure factor and Raman scattering. The simulations were used to compute the $G^{\text{RMC}}_{\text{Ge-Ge}}(r)$, $G^{\text{RMC}}_{\text{Ge-Se}}(r)$ and $G^{\text{RMC}}_{\text{Se-Se}}(r)$ partial distribution functions and the ${\cal S}^{\text{RMC}}_{\text{Ge-Ge}}(K)$, ${\cal S}^{\text{RMC}}_{\text{Ge-Se}}(K)$ and ${\cal S}^{\text{RMC}}_{\text{Se-Se}}(K)$ partial structure factors. We calculated the coordination numbers and i…
Metropolis Monte Carlo simulations of the eutectic NaK alloy are performed using the Second Moment Approximation (SMA) model potential across a wide range of temperatures at constant pressure. The alloy structure and thermodynamics are analyzed along with the atomic level structures using a variety of structure identification methods. Both enthalpy and density are followed along an annealing process that reveals a clear melting point around 250 K. At lower temperatures, two thermodynamic branches are identified as crystalline and amorphous solids.
The short and intermediate range order of an amorphous Ge$_{30}$Se$_{70}$ alloy produced by Mechanical Alloying were studied by Reverse Monte Carlo simulations of its x-ray total structure factor, Raman scattering and differential scanning calorimetry. The simulations were used to compute the $G^{\text{RMC}}_{\text{Ge-Ge}}(r)$, $G^{\text{RMC}}_{\text{Ge-Se}}(r)$ and $G^{\text{RMC}}_{\text{Se-Se}}(r)$ partial distribution functions and the ${\cal S}^{\text{RMC}}_{\text{Ge-Ge}}(K)$, ${\cal S}^{\text{RMC}}_{\text{Ge-Se}}(K)$ and ${\cal S}^{\text{RMC}}_{\text{Se-Se}}(K)$ partial structure factors.…
An amorphous Ti50Ni25Cu25 alloy was produced by 19 h of mechanical alloying. Anomalous wide angle x-ray scattering data were collected at six energies and six total scattering factors were obtained. By considering the data collected at two energies close to the Ni and Cu K edges, two differential anomalous scattering factors around the Ni and Cu atoms were obtained, showing the chemical environments around these atoms are different. The eight factors were used as input data to the reverse Monte Carlo method used to compute the partial structure factors STi-Ti(K), STi-Cu(K), STi-Ni(K), SCu-Cu(K…
In this work, we study the equiatomic quaternary Heusler Alloy CoFeCrP using two methods: DFT and Monte Carlo simulations. The DFT method allowed us to illustrate the structural, electronic and magnetic properties of this alloy. The ground state phase diagrams have been presented to show the stable configurations in different physical parameter planes. On the other hand, the Monte Carlo simulations, performed under the Metropolis algorithm, permitted to deduce the critical the behavior of the equiatomic quaternary Heusler alloy CoFeCrP. The structural properties results show that the phase of …
We derive an Ising Hamiltonian for kinetic simulations involving interstitial and vacancy defects in binary alloys. Our model, which we term `ABVI', incorporates solute transport by both interstitial defects and vacancies into a mathematically-consistent framework , and thus represents a generalization to the widely-used ABV model for alloy evolution simulations. The Hamiltonian captures the three possible interstitial configurations in a binary alloy: A-A, A-B, and B-B, which makes it particularly useful for irradiation damage simulations. All the constants of the Hamiltonian are expressed in…
The high entropy alloy containing refractory metals Mo-Nb-Ta-W has a body centered cubic structure, which is not surprising given the complete mutual solubility in BCC solid solutions of all pairs of the constituent elements. However, first principles total energy calculations for the binaries reveal a set of distinct energy minimizing structures implying the likelihood of chemically ordered low temperature phases. We apply a hybrid Monte Carlo and molecular dynamics method to evaluate the temperature-dependent chemical order. At 300K a cesium-chloride ordering emerges between mixed (Nb,Ta) si…
High-entropy oxides (HEOs), as a new family of materials with five or more principal cations, have shown promising properties for various applications. In this work and inspired by inherent defective and strained structure of HEOs, photocatalytic CO2 conversion is examined on a dual-phase TiZrNbHfTaO11 synthesized by a two-step high-pressure torsion mechanical alloying and high-temperature oxidation. The HEO, which had various structural defects, showed simultaneous photocatalytic activity for CO2 to CO and H2O to H2 conversion without the addition of a co-catalyst. The photocatalytic activity…
The study of alloys using computational methods has been a difficult task due to the usually unknown stoichiometry and local atomic ordering of the different structures experimentally. In order to combat this, first-principles methods have been coupled with statistical methods such as the Cluster Expansion formalism in order to construct the energy hull diagram, which helps to determine if an alloyed structure can exist in nature. Traditionally, density functional theory (DFT) has been used in such workflows. In this work we propose to use chemically accurate many-body variational Monte Carlo …
In this paper, we study the critical magnetic properties of the Half Heusler alloy RhCrSi, using Monte Carlo simulations (MCS) under the Metropolis algorithm. In fact, to study this alloy, we apply an Ising model using the MCS simulations, we concentrate only on the magnetic atoms: Rh and Cr. For this purpose, these magnetic atoms are modeled by the spin moments S=5/2 for Rh atoms and sigma=2 for Cr atoms, respectively. In addition, we discuss the ground state phase diagrams in different planes corresponding to different physical parameters. On the other hand, for non-null temperature values, …
Zr and Sc precipitate in aluminum alloys to form the Al\_3Zr\_xSc\_{1-x} compound which, for low supersaturations of the solid solution, exhibits the L1\_2 structure. The aim of the present study is to model at an atomic scale the kinetics of precipitation and to build mesoscopic models so as to extend the range of supersaturations and annealing times that can be simulated up to values of practical interest. In this purpose, we use some ab initio calculations and experimental data to fit an Ising type model describing thermodynamics of the Al-Zr-Sc system. Kinetics of precipitation are studied…
The mobility of vacancies in alloys may limit dislocation climb. Using a combined density functional theory and kinetic Monte Carlo approach we investigate vacancy diffusion in Ni-Re, Ni-W, and Ni-Ta binary alloys up to 10 at.% solute concentration. We introduce an interaction model that takes into account the chemical environment close to the diffusing atom to capture the effect of solute-host and solute-solute interactions on the diffusion barriers. In contrast to an ideal solid solution it is not only the diffusion barrier of the solute atom that influences the vacancy mobility, but primari…
The growth rates and chemical ordering of ferroelectric alloys are studied with kinetic Monte Carlo (KMC) simulations using an electrostatic model with long-range Coulomb interactions, as a function of temperature, chemical composition, and substrate orientation. Crystal growth is characterized by thermodynamic processes involving adsorption and evaporation, with solid-on-solid restrictions and excluding diffusion. A KMC algorithm is formulated to simulate this model efficiently in the presence of long-range interactions. Simulations were carried out on Ba(Mg_{1/3}Nb_{2/3})O_3 (BMN) type mater…
We develop a Magnetic Cluster Expansion (MCE) model for binary bcc and fcc Fe-Cr alloys, as well as for fcc Fe-Ni alloys, and apply it to the investigation of magnetic properties of these alloys over a broad interval of concentrations, and over a broad interval of temperatures extending well over 1000 K. We show how an MCE-based Monte Carlo study describes the magnetic properties of these alloys, for example the composition and microstructure dependence of the Curie temperature, the non-collinearity of magnetic structures found in bcc Fe-Cr alloys, phase transitions between bcc and fcc in Fe-C…
The FCC structure of Pd$\rm_{1-x}$Ag$\rm_{x}$ ($\rm{x}=$ 0.25, 0.50, 0.75) alloys is considered as a fuel cell component in this study. We have looked into its qualities as a component of a fuel cell to see whether it could be potentially used as an alternative replacement of the Pt catalyst. We used Density Functional Theory (DFT) to study H and CO interaction with the surface, and Kinetic Monte Carlo~(KMC) to study H and CO desorption from the surface. The bulk modulus and equilibrium crystal structures of Pd$\rm_{1-x}$Ag$\rm_{x}$ alloys were computed using the GPAW code within plane wave ba…
Using Monte Carlo Simulations (MCS), based the Metropolis algorithm, we examine in this study, the magnetic properties of the rare earth based compound GdN. In a first step, we discuss and study the ground state phase diagrams explored in the different planes of physical parameter. The obtained stable configurations are illustrated by comparing the energies modeled by the Hamiltonian of Eq. (1). For non-null temperature values, we present and discuss the behavior the total magnetizations and susceptibilities as a function of: the temperature, the crystal field, the exchange coupling interactio…
Mo-Re-W Alloys for High Temperature Applications: Phase Stability, Elasticity, and Thermal Property Insights via Multi-Cell Monte Carlo and Machine Learning
A kinetic Monte Carlo simulations with model asymmetry in binary Fe-Cu alloy leading to the same microstructure are presented. A method based on thermodynamic data for calculation of interatomic potentials dependent on model asymmetry is presented and evaluated. Results show that kinetic pathways are sensitive to model asymmetry and are compared to the classical growth and coarsening theories. Experimental diffusion data is used and compared to simulation results to determine a realistic combination for simulations.
High-temperature, high-dose, neutron irradiation of W results in the formation of Re-rich clusters at concentrations one order of magnitude lower than the thermodynamic solubility limit. These clusters may eventually transform into brittle W-Re intermetallic phases, which can lead to high levels of hardening and thermal conductivity losses. Standard theories of radiation enhanced diffusion and precipitation cannot explain the formation of these precipitates and so understanding the mechanism by which nonequilibrium clusters form under irradiation is crucial to predict materials degradation and…
The earlier-developed ab initio model and the kinetic Monte Carlo method (KMCM) are used to simulate precipitation in a number of iron-copper alloys with different copper concentrations x and temperatures T. The same simulations are also made using the improved version of the earlier-suggested stochastic statistical method (SSM). The results obtained enable us to make a number of general conclusions about the dependencies of the decomposition kinetics in Fe-Cu alloys on x and T. We also show that the SSM describes the precipitation kinetics in a fair agreement with the KMCM, and employing the …
High entropy alloys (HEAs) are a series of novel materials that demonstrate many exceptional mechanical properties. To understand the origin of these attractive properties, it is important to investigate the thermodynamics and elucidate the evolution of various chemical phases. In this work, we introduce a data-driven approach to construct the effective Hamiltonian and study the thermodynamics of HEAs through canonical Monte Carlo simulation. The main characteristic of our method is to use pairwise interactions between atoms as features and systematically improve the representativeness of the …
Short-range order (SRO) in Fe-rich Fe-Cr alloys is investigated by means of atomistic off-lattice Monte Carlo simulations in the semi-grand canonical ensemble using classical interatomic potentials. The SRO parameter defined by Cowley [Phys. Rev. B 77, 669 (1950)] is used to quantify the degree of ordering. In agreement with experiments a strong ordering tendency in the Cr distribution at low Cr concentrations (~< 5%) is observed, as manifested in negative values of the SRO parameters. For intermediate Cr concentrations (5% ~< c_Cr ~< 15%) the SRO parameter for the alpha-phase goes through a m…
The estimator proposed recently by Delmas and Jourdain for waste-recycling Monte Carlo achieves variance reduction optimally with respect to a control variate that is evaluated directly using the simulation data. Here, the performance of this estimator is assessed numerically for free energy calculations in generic binary alloys and compared to those of other estimators taken from the literature. A systematic investigation with varying simulation parameters of a simplified system, the anti-ferromagnetic Ising model, is first carried out in the transmutation ensemble using path-sampling. We obs…
Pt-based bimetallic nanoparticles have attracted significant attention as a promising replacement for expensive Pt nanoparticles. In the systematic design of bimetallic nanoparticles, it is important to understand their preferred atomic structures. However, compared with unary systems, alloy nanoparticles present more structural complexity with various compositional configurations, such as mixed-alloy, core-shell, and multishell structures. In this paper, we developed a unified empirical potential model for various Pt-based binary alloys, such as Pd-Pt, Cu-Pt, Au-Pt, and Ag-Pt. Within this fra…
An amorphous Se$_{0.80}$S$_{0.20}$ alloy produced by Mechanical Alloying was studied by Raman spectroscopy, x-ray diffraction, extended x-ray absorption fine structure (EXAFS) and optical absorption spectroscopy, and also through reverse Monte Carlo simulations of its total structure factor and EXAFS data. Its vibrational modes, optical gap and structural properties as average interatomic distances and average coordination numbers were determined and compared to those found for an amorphous Se$_{0.90}$S$_{0.10}$ alloy. The results indicate that coordination numbers, interatomic distances and a…
Kinetics of homogeneous nucleation and growth of copper precipitates under electron irradiation of Fe_{1-x}Cu_x alloys at concentrations x from 0.06 at.% to 0.4 at.% and temperatures T from 290 to 450C is studied using the kinetic Monte Carlo (KMC) simulations and the statistical theory of nucleation (STN). The conventional assumption about the similarity of mechanisms of precipitation under electron irradiation and during thermal aging is adopted. The earlier-developed ab initio model of interactions in Fe-Cu alloys is used for both the KMC simulations and the STN calculations. Values of the …
The effect of grain size, easy magnetization axis and anisotropy constant distributions in the irreversible magnetic behavior of granular alloys is considered. A simulated granular alloy is used to provide a realistic grain structure for the Monte Carlo simulation of the ZFC-FC curves. The effect of annealing and external field is also studied. The simulation curves are in good agreement with the FC and ZFC magnetization curves measured on melt spun Cu-Co ribbons.
We present an extension of the semi-grandcanonical (SGC) ensemble that we refer to as the variance-constrained semi-grandcanonical (VC-SGC) ensemble. It allows for transmutation Monte Carlo simulations of multicomponent systems in multiphase regions of the phase diagram and lends itself to scalable simulations on massively parallel platforms. By combining transmutation moves with molecular dynamics steps structural relaxations and thermal vibrations in realistic alloys can be taken into account. In this way, we construct a robust and efficient simulation technique that is ideally suited for la…
We report on the structure and adsorption properties of Pd$_n$ ($n=1-4$) clusters supported on the rutile TiO$_2$ (110) surfaces with the possible presence of a surface oxygen vacancy or a subsurface Ti-interstitial atom. As predicted by the density functional theory, small Pd clusters prefer to bind to the stoichiometric titania surface or at sites near subsurface Ti-interstitial atoms. The adsorption of Pd clusters changes the electronic structure of the underlying surface. For the surface with an oxygen vacancy, the charge localization and ferromagnetic spin states are found to be largely a…
We introduce a simplified method to model the interatomic interactions of high entropy alloys based on a lookup table of cluster energies. These interactions are employed in replica exchange Monte Carlo simulations with histogram analysis to obtain thermodynamic properties across a broad temperature range. Kikuchi's Cluster Variation Method entropy formalism and high temperature series expansions are applied to directly calculate entropy from statistics on short- and long-range chemical order, and we discuss the convergence of the entropy as clusters of differing size are included.
The structural properties of the $Zn_xMg_{1-xS_ySe_{1-y}}$ solid solutions are determined by a combination of the computational alchemy and the cluster expansion methods with Monte Carlo simulations. We determine the phase diagram of the alloy and show that the homogeneous phase is characterized by a large amount of short-range order occurring among first-nearest neighbors. Electronic-structure calculations performed using the special quasi-random structures approach indicate that the energy gap of the alloy is rather sensitive to this short-range order.
In this paper we show that an effective Hamiltonian fit with first principles calculations predicts an order/disorder transition occurs in the high entropy alloy MoNbTaW. Using the Alloy Theoretic Automated Toolset, we find T=0K enthalpies of formation for all binaries containing Mo, Nb, Ta, and W, and in particular we find the stable structures for binaries at equiatomic concentrations are close in energy to the associated B2 structure, suggesting that at intermediate temperatures a B2 phase is stabilized in MoNbTaW. Our previously published hybrid Monte Carlo/molecular dynamics results for t…
Using an atom-vacancy exchange algorithm, we investigate the kinetics of the order-disorder transition in an fcc A_3B binary alloy model following a temperature quench from the disordered phase. We observe two clearly distinct ordering scenarios depending on whether the final temperature T_f falls above or below the ordering spinodal T_{sp}, which is deduced from simulations at equilibrium. For shallow quenches (T_f>T_{sp}) we identify an incubation time tau_{inc} which characterizes the onset of ordering through the formation of overcritical ordered nuclei. The algorithm we use together with …
A Magnetic Cluster Expansion (MCE) model for ternary face-centered cubic Fe-Ni-Cr alloys has been developed using DFT data spanning binary and ternary alloy configurations. Using this MCE model Hamiltonian, we perform Monte Carlo simulations and explore magnetic structures of alloys over the entire range of alloy compositions, considering both random and ordered alloy structures. In random alloys, the removal of magnetic collinearity constraint reduces the total magnetic moment but does not affect the predicted range of compositions where the alloys adopt low temperature ferromagnetic configur…
A first-principles derived approach is combined with the inverse Monte Carlo technique to determine the atomic orderings leading to prefixed properties in Pb(Sc_{0.5}Nb_{0.5})O_{3} perovskite alloy. We find that some arrangements between Sc and Nb atoms result in drastic changes with respect to the disordered material, including ground states of new symmetries, large enhancement of electromechanical responses, and considerable shift of the Curie temperature. We discuss the microscopic mechanisms responsible for these unusual effects.
We determine from first-principles the Curie temperature Tc for bulk Co in the hcp, fcc, bcc, and tetragonalized bct phases, for FeCo alloys, and for bcc and bct Fe. For bcc-Co, Tc=1420 K is predicted. This would be the highest Curie temperature among the Co phases, suggesting that bcc-Co/MgO/bcc-Co tunnel junctions offer high magnetoresistance ratios even at room temperature. The Curie temperatures are calculated by mapping ab initio results to a Heisenberg model, which is solved by a Monte Carlo method.
The local atomic order of an amorphous Ga$_{50}$Se$_{50}$ alloy produced by Mechanical Alloying (MA) was studied by the Extended X-ray Absorption Fine Structure (EXAFS) and X-ray Diffraction (XRD) techniques and by Reverse Monte Carlo (RMC) simulations of its total x-ray structure factor. The coordination numbers and interatomic distances for the first neighbors were determined by means of EXAFS analysis and RMC simulations. The RMC simulations also furnished the partial pair distribution functions $G^{\text{RMC}}_{\text{Ga-Ga}}(r)$, $G^{\text{RMC}}_{\text{Ga-Se}}(r)$ and $G^{\text{RMC}}_{\tex…
The generalized stacking fault energy is a key ingredient to mesoscale models of dislocations. Here we develop an approach to quantify the dependence of generalized stacking fault energies on the degree of chemical disorder in multicomponent alloys. We introduce the notion of a "configurationally-resolved planar fault" (CRPF) energy and extend the cluster expansion method from alloy theory to express the CRPF as a function of chemical occupation variables of sites surrounding the fault. We apply the approach to explore the composition and temperature dependence of the unstable stacking fault e…
In high-entropy alloys (HEAs), the local chemical fluctuations from disordered solute solution state into segregation, precipitation and ordering configurations are complex due to the large number of elements. In this work, the cluster expansion (CE) Hamiltonian for multi-component alloy systems is developed in order to investigate the dependence of chemical ordering of HEAs as a function of temperature dependence due to derivation of configuration entropy from the ideal solute solution. Analytic expressions for Warren-Cowley short-range order (SRO) parameters are derived for a five component …
The electronic and magnetic bulk properties of half-metallic Heusler alloys such as Co$_{2}$FeSi, Co$_{2}$FeAl, Co$_{2}$MnSi and Co$_{2}$MnAl are investigated by means of {\em ab initio} calculations in combination with Monte Carlo simulations. The electronic structure is analyzed using the plane wave code Quantum Espresso and magnetic exchange interactions are determined using the KKR method. From the magnetic exchange interactions the Curie temperature is obtained via Monte Carlo simulations. In addition, electronic transport properties of the trilayer systems consisting of two semi-infinite…
The superior properties of high-entropy multi-functional materials are strongly connected with their atomic heterogeneity through many different local atomic interactions. The detailed element-specific studies on a local scale can provide insight into the primary arrangements of atoms in multicomponent systems and benefit to unravel the role of individual components in certain macroscopic properties of complex compounds. Herein, multi-edge X-ray absorption spectroscopy combined with reverse Monte Carlo simulations was used to explore a homogeneity of the local crystallographic ordering and spe…
While it is known that alloy components can segregate to grain boundaries (GBs), and that the atomic mobility in GBs greatly exceeds the atomic mobility in the lattice, little is known about the effect of GB segregation on GB diffusion. Atomistic computer simulations offer a means of gaining insights into the segregation-diffusion relationship by computing the GB diffusion coefficients of the alloy components as a function of their segregated amounts. In such simulations, thermodynamically equilibrium GB segregation is prepared by a semi-grand canonical Monte Carlo method, followed by calculat…
In alloys cluster expansions (CE) are increasingly used to combine first-principles electronic-structure and Monte Carlo methods to predict thermodynamic properties. As a basis-set expansion in terms of lattice geometrical clusters and effective cluster interactions, the CE is exact if infinite, but is tractable only if truncated. Yet until now a truncation procedure was not well-defined and did not guarantee a reliable truncated CE. We present an optimal truncation procedure for CE basis sets that provides reliable thermodynamics. We then exemplify its importance in Ni$_3$V, where the CE has …
Grain boundaries have been shown to dramatically influence the behavior of relatively simple materials such as monatomic metals and binary alloys. The increased chemical complexity associated with multi-principal element alloys is hypothesized to lead to new grain boundary phenomena. To explore the relationship between grain boundary structure and chemistry in these materials, hybrid molecular dynamics/Monte Carlo simulations of a faceted Σ11 <110> tilt boundary, chosen to sample both high- and low-energy boundary configurations, are performed in face-centered cubic CrFeCoNiCu and CrFeCoNi equ…
The local atomic structure of an amorphous NiZr2 alloy was investigated using the anomalous wide-angle x-ray scattering (AWAXS), differential anomalous scattering (DAS) and reverse Monte Carlo (RMC) simulations techniques. The AWAXS measurements were performed at eight different incident photon energies, including some close to the Ni and Zr K edges. From the measurements eight total structure factor S(K,E) were derived. Using the AWAXS data four differential structure factors DSFi(K,Em,En) were derived, two about the Ni and Zr edges. The partial structure factors SNi-Ni(K), SNi-Zr(K) and SZr-…
