Warren-Cowley Parameters Research Articles

Composition-dependent diffusion and viscosity behavior in liquid Ti–Al–Ni ternary alloys

We conducted ab initio molecular dynamics simulations to investigate the dynamic properties of the liquid Ti–Al–Ni ternary alloy system at 2033 K. Through simulations across the entire composition range, we revealed the complex compositional dependence of self-diffusion coefficients and viscosity. The self-diffusion coefficients of Ti, Al, and Ni exhibit nonlinear distribution characteristics, while viscosity shows non-monotonic compositional dependence, with lower viscosity in Al-rich regions and higher viscosity in Ni-rich regions. To understand the structural origins of these behaviors, we analyzed chemical short-range order and local fivefold symmetry structures using Warren-Cowley parameters and fivefold symmetry parameters, uncovering a close correlation between atomic-scale structural features and dynamic properties. Evaluation of the Stokes-Einstein relation revealed varying degrees of deviation from its predicted viscosity values across composition regions. We observed a negative correlation between free volume fraction and viscosity, with varying strengths in different regions. These findings provide new perspectives for understanding the complex dynamic properties of Ti–Al–Ni liquid alloys.

Effect of local chemical order on monovacancy diffusion in CoNiCrFe high-entropy alloy

High-entropy alloys (HEAs) are promising materials for nuclear applications. Understanding the influence of local chemical order (LCO) on defect diffusion and evolution in these alloys is crucial for enhancing their resistance to radiation damage. In this study, we used molecular dynamics simulation to investigate the effect of LCO on monovacancy diffusion in CoNiCrFe HEA. Alongside the Warren-Cowley parameter, which quantifies the degree of local elemental ordering, we propose a new parameter to characterize the spatial scale of LCOs. Based on their degree, LCO structures have been classified as either chemical medium-range order (CMRO) or chemical short-range order (CSRO). Our study reveals a non-monotonic variation in vacancy diffusion coefficients, transitioning from random solid solution to CSRO and then to CMRO structures. Moreover, we observe a preference for vacancy diffusion in low-energy Fe, Co-rich regions, with their spatial distribution and spatial connectivity significantly influencing the vacancy diffusion. Due to the spatial scale of the inhomogeneity introduced by LCO, both global average diffusion parameters and single migration barriers cannot fully reflect the actual diffusion dynamics. Therefore, our study emphasizes the importance of understanding the preferred diffusion pathways and the associated energy landscapes to fully assess the defect diffusion dynamics in HEAs. This deeper investigation into localized diffusion behaviors influenced by LCO is crucial for evaluating and enhancing the radiation damage tolerance of HEAs.

Atomistic simulations reveal strength reductions due to short-range order in alloys

A theory for strengthening for multicomponent non-dilute alloys possessing short-range order (SRO) has recently been developed. The theory predicts that, in addition to a well-known athermal strengthening, there is a notable effect of SRO on the solute–dislocation interactions that can decrease or increase the strength relative to a random alloy. Here, carefully designed atomistic simulations in a model binary NbW alloy are used to demonstrate that alloy strength due to solute–dislocation interactions can be increased or decreased, depending on the SRO and consistent with theoretical predictions. Specifically, SRO is introduced using fictitious solute–solute interactions in an alloy system with very small true solute–solute interactions, and the Nudged Elastic Band (NEB) method is then used to compute the energy barriers for edge dislocation motion for various levels of SRO. Energy barriers, and hence alloy strengths, can be decreased when the Warren-Cowley SRO parameters are negative (attraction of unlike solutes). The theoretical predictions for the same system are in reasonable quantitative agreement with the simulation results. These findings demonstrate the unexpected possibility of reduced strength due to SRO and also further validate the analytical theory as a tool to guide alloy design.

Theoretical study on the element distribution characteristics and the effects of oxygen in TiZrHfNb high entropy alloys

Short range order and oxygen both have great effects on the mechanical properties like yield strength and ductility of refractory high entropy alloys. In this work, we studied the element distribution characteristics and oxygen occupation properties in TiZrHfNb high-entropy alloy based on first principles, molecular dynamics and Monte Carlo calculations. Two thousands of TiZrHfNb crystal models were firstly calculated based on first principles calculations to analyze the element distribution characteristics. The Warren-Cowley parameters were then evaluated, the Nb-Nb and Ti-Zr atomic pairs tend to form in TiZrHfNb. Hybrid of molecular dynamics and Monte Carlo calculations at 300 K and 1000 K are further carried out to study the possible short range order and phase transition in TiZrHfNb. The element distributions are not uniform, and the transition from body-centered cubic to hexagonal close packed structures are observed. The oxygen atoms are then placed into the enriched regions of Ti, Zr, Hf, and Nb in high-entropy alloy, respectively. The ab initio molecular dynamics calculations of these four configurations are carried out and the diffusion coefficients are evaluated. The oxygen owns the largest diffusion coefficient in the Nb-rich zone. Furthermore, the tensile simulations reveal the great effects of element distributions and oxygen occupations on the mechanical properties of TiZrHfNb. These findings will help us to understand the short range order characteristic and oxygen occupation effects on the phase stability and to regulate the mechanical properties of TiZrHfNb high-entropy alloy.

Accurate prediction of chemical short-range order and its effect on thermodynamic, structural, and electronic properties of disordered alloys: Exemplified in Cu3Au

Electronic-structure methods based on density-functional theory (DFT) were used to directly quantify the effect of chemical short-range order (SRO) on thermodynamic, structural, and electronic properties of archetypal face-centered-cubic (fcc) Cu3Au alloy. We show that SRO can be tuned to alter bonding and lattice dynamics (i.e., phonons) and detail how these properties are changed with SRO. Thermodynamically favorable SRO improves phase stability of Cu3Au from − 0.0343 eV-atom−1 to −0.0682 eV-atom−1. We use DFT-based linear-response theory to predict SRO and its electronic origin, and accurately estimate the transition temperature, ordering instability (L12), and Warren-Cowley SRO parameters, observed in experiments. The accurate prediction of real-space SRO gives an edge over computationally and resource intensive approches such as Monte-Carlo methods or experiments, which will enable large-scale molecular dynamic simulations by providing supercells with optimized SRO. We also analyze phonon dispersion and estimate the vibrational entropy changes in Cu3Au (from 9kB at 300–6kB at 100 K). We establish from SRO analysis that exclusion of chemical interactions may lead to a skewed view of true properties in chemically complex alloys. The first-principles methods described here are applicable to any arbitrary complex solid-solution alloys, including multi-principal-element alloys, so hold promise for designing technologically useful materials.

Giant Influence of Clustering and Anti-Clustering of Disordered Surface Roughness on Electronic Tunneling

This work reveals the giant influence of spatial distribution of disordered surface roughness on electron tunneling, which is of immediate relevance to the magneto tunnel device and imaging technologies. We calculate the spin-dependent tunneling in Fe/vacuum/Fe junction with disordered surface roughness with the first-principles non-equilibrium dynamical cluster theory. It is found that, at high concentration of surface roughness, different spatial distributions, including the clustered, anti-clustered and completely random roughness characterized by Warren–Cowley parameters, present large deviations from each other in all spin channels. By changing from clustered to anti-clustered roughness, it is surprising that spin polarization of tunneling in parallel configuration (PC) can be drastically reversed from –0.52 to 0.93, while complete randomness almost eliminates the polarization. It is found that the anti-clustered roughness can dramatically quench the tunneling of minority spin in both PC and anti-PC by orders of magnitude, but significantly enhance the transmission of majority spin in PC (by as large as 40%) compared to the results of clustered roughness, presenting distinct influences of differently correlated surface roughness. The spatial correlation of disordered surface roughness can significantly modify the surface resonance of Fe minority spin.

Local atomic structure of liquid Al87Mg13 alloy

The structure of the liquid Al87Mg13 alloy was investigated by high-temperature X-ray diffraction, reverse Monte Carlo (RMC) simulations, and the Voronoi diagram method. The quantitative characteristics of the short-range order: the number of the nearest neighboring atoms, the radius of the first coordination sphere, the distribution of valence angles were calculated by the experimental and simulated data. The calculated Warren-Cowley parameter α1 points out the existence of the chemical short-range order in the liquid Al87Mg13 alloy that dissimilar atoms prefer to be the nearest neighbors (i.e., Al-Mg). The peculiarities inherited to an icosahedral structure were found in the bond-angle distribution (Al-Al-Al) simulated by the RMC method. This result is in good consensus with the analysis of the topological indices of the Voronoi polyhedra built around Al atoms.

The structural evolution and abnormal bonding ways of the Zr80Pt20 metallic liquid during rapid solidification under high pressure

The structural evolutions and abnormal bonding ways of the Zr80Pt20 binary alloy during rapid solidification under different pressures from 0 to 120 GPa have been investigated by classical molecular dynamics simulations in conjunction with the embedding atom method. The pair distribution function, the coordination number, the Warren-Cowley parameter, the bond length and the pair analysis technique are used to reveal the structural evolution of the Zr80Pt20 solidified under normal and high pressures. Persuasive evidence indicates that the applied pressure strongly affects the vitrification (for 0 ≤ P ≤ 20 and 90 ≤ P ≤ 120 GPa) and crystallization (for 30 ≤ P ≤ 80 GPa) processes of the metallic liquid and causes significant changes in the microstructure of the system. Interestingly, we have observed that the crystallization for the Zr80Pt20 system is associated with volume expansion between 50 and 80 GPa, in contrast to the volume contraction observed under 30 and 40 GPa. The results of the atomic structure analysis show that there is an unexpected shortening of Zr-Zr bonds under high pressures, which is related to the change of the atomic packing in the Zr80Pt20 alloy from loose to dense with increasing pressure. The results of the analysis show that the bonds between Zr-Zr and Pt-Pt pairs can be shortened more easily than the bonds between Zr-Pt pairs at high pressures and also the clustering behaviors of Zr-Zr or Pt-Pt bonds reveals the presence of composition segregation. This study presents encouraging findings for the experimental investigation of glass transition and crystallization processes in Zr-Pt metallic liquids during rapid cooling and under high pressure.

Correlation between the chemical short-range order and binding energy of Cu-centred CunZr13−n(n = 6,7,8,9) icosahedral clusters in metallic glass

The correlation between shell atomic arrangement and binding energy of Cu-centred CunZr13−n (n = 6,7,8,9) icosahedral clusters is systematically investigated by chemical short-range order parameters (Spaepen–Cargill parameters δCuZr and Warren–Cowley parameters ) and first principles calculations. It is found that the shell homogeneous atoms prefer to bond each other and heterogeneous atoms tend to segregation in stable Cu-centred Cu–Zr icosahedral cluster. And analysis show that the shell atomic arrangement and energy stability of Cu-centred CunZr13−n (n = 6,7,8,9) icosahedral clusters are non-linearly related. Moreover, for , we found that the smaller the δCuZr value is, the more the number of homogeneous atomic bond pairs is. Whereas, for , the bigger the value of δCuZr is, the more the number of heterogeneous atomic bond pairs is. For , we also found an identical rule only the description of physical significance of positive and negative of parameter are different. That is to say when , the bigger the value of is, the larger the number of bond pairs of homogeneous atoms is. Whereas, for , the more negative the value of is, the larger the number of bond pairs of heterogeneous atoms is. This is a deeper development for the physical significance of Spaepen–Cargill and Warren–Cowley parameter.

<i>Ab Initio</i> Based Modelling of Diffusion and Phase Stability of Alloys

In this chapter, we present the basic principles and methods for modelling of diffusion and phase stability of alloys using ab-initio methods. We review briefly first-principles methods and their most important approximations. The direct and approximated methods of prediction of migration energies are shown both for pure metals and for alloys. The cluster expansion method is described in more detail. We show that it can be applied to understand interactions in the alloys, to generate the representative structures of alloys and to predict migration barriers in alloys. We describe the methods to compute the effective cluster interactions and to assess the accuracy of the model. Finally, we present the examples of Monte Carlo simulations with parameters obtained from cluster expansion method. We show that the ordering in alloys can be predicted by the calculations of Warren-Cowley parameters. We investigate also the role of entropy in the stability of alloys at elevated temperatures.

A new approach to the analysis of short-range order in alloys using total scattering

In spite of its influence on a number of physical properties, short-range order in crystalline alloys has received little recent attention, largely due to the complexity of the experimental methods involved. In this work, a novel approach that could be used for the analysis of ordering transitions and short-range order in crystalline alloys using total scattering and reverse Monte Carlo (RMC) refinements is presented. Calculated pair distribution functions representative of different types of short-range order are used to illustrate the level of information contained within these experimentally accessible functions and the insight into ordering which may be obtained using this new method. Key considerations in the acquisition of data of sufficient quality for successful analysis are also discussed. It is shown that the atomistic models obtained from RMC refinements may be analysed to identify directly the Clapp configurations that are present. It is further shown how these configurations can be enhanced compared with a random structure, and how their degradation pathways and the distribution of Warren-Cowley parameters, can then be used to obtain a detailed, quantitative structural description of the short-range order occurring in crystalline alloys.

Formation of chemical short range order and its influences on the dynamic/mechanical heterogeneity in amorphous Zr–Cu–Ag alloys: A molecular dynamics study

The chemical short range order of metallic glasses is expected to be correlated with their mechanical properties. In this article, classic molecular dynamics simulations of amorphous Zr45Cu45Ag10 alloys were carried out to reveal such links in metallic glasses. Our calculations of Warren–Cowley parameter indicate the growth of chemical short range order during supercooling process, which also depends on the effective cooling rates. The chemical short range ordering is related to the energetic stability of the system. Based on the chemical preference or avoidance for different bonds, the model is separated into Cu-rich regions and Ag-rich regions. Simulated structural relaxation and shear loading process were performed to study how chemical bonds affect the distribution of dynamic and mechanical heterogeneity in our systems. The Cu-rich regions exhibit slower dynamics and higher shear resistance, whereas Ag-rich regions have faster dynamics and prefer to be plastically deformed.

Structure of liquid Cu–Sb alloys by ab initio molecular dynamics simulations, high temperature X-ray diffraction, and resistivity

Structure of Cu–Sb melts has been studied by ab initio molecular dynamics simulations, high-temperature X-ray diffraction and resistivity measurements. Over the whole concentration range, heterogeneous coordination numbers are larger than that of homogeneous atoms. This indicates preferential Cu–Sb coordination in Cu–Sb melts. A drop is observed in maximum position of simulated Sb–Sb partial distribution functions around Cu75Sb25, which reveals the rapid increase of Sb–Sb coordination. Around eutectic melts, main peak splitting is observed in both structure factor and simulated total pair distribution functions, which reveals the co-existence of Cu–Sb heterogeneous and Sb–Sb clusters. Abnormal changes in temperature coefficient of resistivity are observed around pure Sb and in compound-forming range, which are well interpreted as reinforcement of Peierls distortion and Cu3Sb compound clusters, respectively. Structural inhomogeneity that results from atomic size effect also has been discussed by analyzing concentration dependence of Warren–Cowley parameters and concentration correlation functions.

Medium‐range order and physical properties of Cu–20at.% Sb melts

Local structure of Cu–20at.%Sb melts has been studied by X‐ray diffraction and ab initio molecular dynamics simulation. Pre‐peaks in relation with medium‐range order are observed in structure factor. Negative Warren–Cowley parameters reflect the existence of chemical order. With an obvious pre‐peak, broadening intensities of Cu3Sb are in good agreement with experimental results, indicating structure similarity of Cu3Sb to ordered clusters in the melts. These imply that origin of pre‐peaks is in relation with Cu3Sb‐like clusters. Abnormally large activation energy of viscous flow and negative temperature coefficient of resistivity are well interpreted as the existence of medium‐range order clusters.

Ordering in ternary nitride semiconducting alloys

We present a thorough theoretical study of ordering phenomena in nitride ternary alloys GaInN, AlInN, and AlGaN. Using the Monte Carlo approach and energetics based on the Keating model we analyze the influence of various factors on ordering in bulk crystals and epitaxial layers. We characterize the degree of both short range order (SRO) and long ranger order (LRO) for different compositions, temperatures and for substrates associated with different epitaxial strain. For the description of the SRO the Warren-Cowley parameters related to the first four coordination shells are used. The LRO is detected by means of the introduced sim-LRO parameter, based on the Bragg-Williams approach. The description of the observed long-range ordering patterns and conditions for their occurrence follows.

A three-dimensional Markov field approach for the analysis of atomic clustering in atom probe data

Solute clustering is increasingly recognised as a significant characteristic within certain material systems that can be tailored to the optimization of bulk properties and performance. Atom probe tomography (APT) is emerging as a powerful tool for the detection of these nanoscale features; however, complementary to experiment, precise and efficient characterization algorithms are required to identify and characterise these nanoclusters within the potentially massive three-dimensional atomistic APT datasets. In this study, a new three-dimensional Markov field (3DMF) cluster identification algorithm is proposed. The algorithm is based upon an analysis of the direct atomic neighbourhood surrounding each atom, and the only input parameter required utilises known crystallographic properties of the system. Further, an array of statistical approaches has been developed and applied with respect to the results generated by the 3DMF algorithm including: an S N statistic, a two-tailed z-test, a difference measure, the χ2 test, and a direct evaluation of the Warren–Cowley parameter for short-range ordering. Finally, the methodologies have been applied to the characterization of the nanostructural evolution of an Al-1.1Cu-0.5Mg (at.%) alloy subjected to a variety of heat treatments.

Influence of structural short-range order on the phase diagram of diluted anisotropic Heisenberg ferromagnet

The diluted anisotropic Heisenberg ferromagnet is considered in the pair approximation. The structural short-range-order, described by the Warren-Cowley parameter, is taken into account. In the presence of interaction anisotropy, the influence of dilution and structural correlations on the phase diagrams is studied. In particular, for the model in question the critical concentrations and Curie temperatures are calculated for exemplary two-dimensional and three-dimensional lattices.

Phase diagrams of a model diluted fcc magnet with arbitrary spin and modified RKKY interaction: Influence of external magnetic field and structural short-range order

A diluted FCC magnet with modified long-range RKKY interaction and arbitrary Ising spin S is considered within two-sublattice model. In the molecular field approximation the Gibbs free-energy is derived, from which all magnetic thermodynamic properties can be self-consistently obtained. In particular, the phase diagrams are studied for different magnetic ion and free-charge concentration, the atomic short-range-order (Warren-Cowley) parameter being taken into account.

Structural study of amorphous Te 2X (X = Br, I): X-ray diffraction, neutron diffraction and reverse Monte Carlo simulations

Reverse Monte Carlo simulations of the Te 2Br 0.75I 0.25 chalcohalide glass structure using high-energy X-ray and thermal neutron diffraction data show that the glass structure consists of finite –Te–Te–Te– and –Te–Br–Te– chain fragments interconnected by 3-coordinated I atoms. The average Te–Te nearest-neighbor coordination is equal to 2.2 ± 1.4, the Te–Te next nearest-neighbor coordination is equal 7.3 ± 2.6 and the Br–Br coordination is equal to 5.6 ± 0.6. Detailed analysis of the coordination numbers, bond-angle distributions, ring statistics and Warren–Cowley parameters of the different models demonstrates that the short-range order of the glass differs from that of crystalline Te 2X (X = Br, I). The presence of long Te–Te bonds (>3.0 Å) typical for liquid Te and crystalline tellurium-rich polytellurides is also established.

Local atomic order in nanocrystalline Fe-based alloys obtained by mechanical alloying

Using the 57Fe Mössbauer spectroscopy, a local atomic order in nanocrystalline alloys of iron with Al, Ni, W and Mo has been determined. Alloys were prepared by mechanical alloying method. Analysis of Mössbauer spectra was performed on the basis of the local environment model in terms of Warren–Cowley parameters. It was shown that impurity atoms are not randomly distributed in the volume of the first and the second co-ordination spheres of 57Fe nuclei and they form clusters.