Short-range Order Parameters Research Articles

Random Generation of Lattice Structures with Short-Range Order

Thermodynamically driven short-range order (SRO) is known to exist in multi-component alloys and can influence their mechanical properties. Atomistic and mesoscale simulations are frequently used to study the effects of SRO, but introducing SRO into the lattice usually requires costly Monte Carlo simulations. Here, we develop a novel method and open-source code to create lattices with specified SRO parameters that can be used as inputs to simulations to study the interaction of SRO with dislocations or other deformation mechanisms. The method, order through informed swapping (OTIS), uses a statistical smart swapping procedure to create lattices with known SRO parameters from an initially random lattice. We illustrate the use of OTIS on ternary and quinary equimolar alloys to create both BCC and FCC lattices with hundreds of thousands of atoms. The computation time and size scaling are discussed. As an example application of the method, the generated SRO lattices are incorporated into a phase-field dislocation dynamics to study dislocation loop growth.

First-principles calculations and thermodynamic assessment of the Nb–V system using CE-CVM

A thermodynamic assessment of the Nb–V system has been carried out based on first-principles calculations and all the available experimental thermodynamic and phase equilibria data. Mixed-parametric ab initio calculations were performed to calculate the enthalpy of mixing data with Special quasirandom structures (SQS) and cluster expansion (CE) method. The Gibbs energy of the bcc solid phase was described using tetrahedron approximation of the Cluster Expansion and Cluster Variation Methods (CE-CVM). A sub-regular solution model was used for describing Gibbs energy of the liquid phase. An optimal set of parameters has been obtained for describing the Gibbs energies of the liquid and solid phases in the Nb–V binary system. The calculated phase diagram and thermodynamic properties agree with experimental data. The relevance of CE-CVM has been demonstrated in the present case by calculating the solid phase's short-range order (sro) parameters as a function of composition and temperature.

3D Nanoscale Mapping of Short-Range Order in GeSn Alloys.

GeSn on Si has attracted much research interest due to its tunable direct bandgap for mid-infrared applications. Recently, short-range order (SRO) in GeSn alloys has been theoretically predicted, which profoundly impacts the band structure. However, characterizing SRO in GeSn is challenging. Guided by physics-informed Poisson statistical analyses of k-nearest neighbors (KNN) in atom probe tomography (APT), a new approach is demonstrated here for 3D nanoscale SRO mapping and semi-quantitative strain mapping in GeSn. For GeSn with ≈14 at. % Sn, the SRO parameters of Sn-Sn 1NN in 10 × 10 × 10 nm3 nanocubes can deviate from that of the random alloys by ±15 %. The relatively large fluctuation of the SRO parameters contributes to band-edge softening observed optically. Sn-Sn 1NN also tends to be more favored toward the surface, less favored under strain relaxation or tensile strain, while almost independent of local Sn composition. An algorithm based on least square fit of atomic positions further verifies this Poisson-KNN statistical method. Compared to existing macroscopic spectroscopy or electron microscopy techniques, this new APT statistical analysis uniquely offers 3D SRO mapping at nanoscale resolution in a relatively large volume with millions of atoms. It can also be extended to investigate SRO in other alloysystems.

Thermophysical behavior of mercury-lead liquid alloy

Thermophysical properties of compound forming binary liquid mercury-lead alloy at temperature 600 K have been reported as a function of concentration by considering HgPb2 complex using different modelling equations. The thermodynamic properties such as the Gibbs free energy, enthalpy of mixing, chemical activity of each component, and microscopic properties such as concentration fluctuation in long-wavelength limit and Warren-Cowley short range order parameter of the alloy are studied by quasi-chemical approximation. This research paper places additional emphasis on the interaction energy parameters between the atoms of the alloy. The theoretical and experimental data are compared to determine the model’s validity. Compound formation model, statistical mechanical technique, and improved derivation of the Butler equation have all been used to investigate surface tension. The alloy’s viscosity is investigated using the Kozlov-Ronanov-Petrov equation, the Kaptay equation, and the Budai-Benko-Kaptay model. The study depicts a weak interaction of the alloy, and the theoretical thermodynamic data derived at 600 K are in good agreement with the experimental results. The surface tension is slightly different in the compound formation model than in the statistical mechanical approach and the Butler equation at greater bulk concentrations of lead. The estimated viscosities in each of the three models are substantially identical.

Atomistic prediction on the composition- and configuration-dependent bandgap of Ga(As,Sb) using cluster expansion and ab initio thermodynamics

The composition- and configuration-dependent bandgaps of pseudobinary Ga(As,Sb) are examined by the cluster expansion method and statistical thermodynamics based on density functional theory. The bandgaps and energetic stability of 330,000 configurations in the entire composition range show a consistent inverse relationship, in that a configuration with lower energy has a higher bandgap for a given composition. This inverse relation can be deduced from the opposite signs of effective cluster interaction coefficients for bandgap and energy, and can be quantified by the correlations of properties with short-range order parameters. The bandgap of GaAs0.5Sb0.5 varies from 0.02 to 0.93 eV depending on the atomic configuration, which suggests another tremendous chance to tune the bandgap by the configuration control. The average bandgap of a certain composition, calculated by the ab initio thermodynamics, decreases with increasing temperature. The calculated average bandgap shows feasible agreement with the experimental bandgap, reproducing the bandgap bowing.

Thermodynamics and surface properties of Fe–V and Fe–Ti liquid alloys

Abstract A simple statistical mechanical model, based on a quasi-lattice approximation in which one assumes the formation of complexes, has been used to study bulk properties, such as free energy of mixing, the thermodynamic activity and enthalpy of mixing, in liquid Fe –Vand Fe –Ti alloys. The energetics and its effect on the alloying behavior of the liquid alloys has been investigated with the aim of correlating bulk phenomena with surface effects. The analysis shows that, assuming the formation of intermetallic complexes of the form Fe2V and FeTi in the liquid alloys, one can explain the energetics of the bulk alloys. Our results for the bulk calculations indicate that Fe –V and Fe –Ti both exhibit a significant tendency for compound formation. From a perusal of the diffusion coefficient D, we observe the same trend towards compound formation, as demonstrated by the chemical short-range order parameter (CSRO) close to the assumed stoichiometric composition. Furthermore, using the model calculations in the bulk, we study some surface properties. Our calculations indicate that Fe segregates to the surface at all bulk compositions in Fe –Vand Fe –Ti liquid, though the segregation effect is more pronounced in the former alloy. The reason for this is that Fe –Ti is a more ordered system than Fe –V and, thus, the driving force for surface segregation in these alloys is their energetics.

Bulk and surface properties of liquid Ga–Tl and Zn–Cd alloys

Abstract A simple thermodynamic model, based on the formation of self-associates, has been used to correlate the bulk and surface properties of mixing of liquid Ga–Tl and Zn–Cd alloys at temperatures of 973 K and 900 K, respectively. The model enables us to explain the positive deviation of the properties of mixing of the two liquid alloys from the ideal solution behavior. Our calculations indicate that the degree of phase separation in Zn–Cd, as measured using the Warren –Cowley short-range order parameter, is less than that in Ga–Tl.With regards to the surface, we show that the surface decomposition in Zn–Cd liquid alloys is greater than in Ga–Tl. We explain the contrast in the bulk and surface properties in terms of the possible roles of the entropic and enthalpic effects on the properties of mixing.

Analytical models of short-range order in FCC and BCC alloys

A statistical-mechanics analysis is used to create analytic estimates for the short-range order (SRO) parameters in FCC and BCC solid solution alloys as a function of composition and temperature. As in the classic quasi-chemical method, the analysis assumes pair interactions among atoms at different distances and partitions the entire crystal into a set of identical independent clusters that are then treated like molecules in a gas. This enables analytic development of the probabilities that govern SRO. For binary and ternary alloys, increasingly complex clusters are considered that systematically extend the range of accuracy of the analytic model relative to reference Monte Carlo simulations. The results enable fast assessment of likely SRO using estimated or computed inputs for atom-atom interaction energies.

Composition and temperature dependence of concentration fluctuations of liquid AlSn alloys

The composition dependence of the properties like excess free energy of mixing, free energy of mixing, activity coefficients, activity, heat of mixing, entropy of mixing and concentration fluctuations in the long wavelength limit of liquid AlSn alloys at 973 K have been computed using four-parameter model. The theoretical data have been compared with the corresponding experimental data available in the literature. An excellent agreement has been found. Again the excess free energy of mixing and concentration fluctuations of liquid AlSn alloys as a function of concentration have been computed at 1073 K, 1123 K and 1173 K. The theoretical values of excess free energy of mixing and concentration fluctuations have been compared with the data available in the literature. A reasonable agreement has been achieved with some discrepancies at the temperature 1173 K. The results indicate the decrease in the values of the concentration fluctuations of liquid AlSn alloys as the temperature increases. Further the short-range order parameter has been computed for AlSn liquid at 973 K, 1073 K, 1123 K and 1173 K which have been compared with the data available in the literature. A reasonable agreement has been observed. The values of short-range order parameter decrease on increasing the temperature of AlSn liquid alloys. The present study reveals that the segregating nature of AlSn liquid alloys deceases on increasing the temperature.11corresponding author : J mandal email id: jmandal1284@gmail.com

Concentration dependence of the bulk and surface properties of liquid AlZn alloys at 1000 K

The properties of mixing of the segregating liquid AlZn alloys at 1000 K have been investigated using the joint effect of size ratio and enthalpic contribution as well as entropic effect. The theoretical values of the bulk properties i.e. thermodynamic properties such as excess free energy of mixing, free energy of mixing, entropy of mixing, heat of mixing as well as the structural properties like concentration-concentration partial structure factor (or concentration fluctuations in the long wavelength limit) and short-range order parameter have been compared with the corresponding experimental data available in the literature. Again Butler model has been applied to study the surface properties such as the surface concentration, surface tension and surface concentration-concentration partial structure factor (or surface concentration fluctuations) of liquid AlZn alloys at 1000 K. The theoretical data of the surface tension have been compared with the experimental data available in the literature which show a qualitative agreement.

Atomic structure of liquid refractory Nb5Si3 intermetallic compound alloy based upon deep neural network potential

The knowledge of atomic structure for liquids, especially for liquid alloys with complex crystal structure and high liquidus temperatures, remains poorly understood. In this work, we have extended the development of deep neural network (DNN) potential for liquid Nb5Si3. The DNN potential captures the structural features of liquid alloys compared with ab initio results. The chemical short-range order parameter suggests that there exists strong affinity between Nb and Si atoms. The dynamic property was investigated, and the diffusion coefficient obeys the Arrhenius relationship. The atomic structure has been subsequently explored for normal and undercooled liquid Nb5Si3. Large amounts of fivefold symmetry Honeycutt–Andersen pairs have been identified in liquid Nb5Si3. However, due to the violent thermal motion in a high-temperature Nb5Si3 melt, icosahedral symmetry and distorted icosahedrons (ICOs) account for little proportion according to Voronoi polyhedron (VP) analysis. The effect of thermal motion on VPs has been discussed. Except from the well documented ⟨0,2,8,2⟩ and ⟨0,1,10,2⟩ distorted ICOs, six more quasi-ICOs (⟨0,1,9,3⟩, ⟨0,2,8,1⟩, ⟨0,2,8,4⟩, ⟨0,2,8,5⟩, ⟨0,1,10,3⟩, and ⟨0,1,10,4⟩) have been proven to deform from ICOs at high temperatures. The local environment motif obtained by the atomic cluster alignment method demonstrates the existence of dominant distorted ICOs. At last, the atomic structure during melting process is discussed by VP analysis. It is found that ⟨0,2,8,1⟩, ⟨0,2,8,2⟩, ⟨0,2,8,5⟩, and ⟨0,1,10,4⟩ prefer to form at the beginning of the melting but rapidly reduce when it is fully melted.

Theoretical assessment for the mixing properties of AlMg liquid alloys at 1073K

The alloying behavior of AlMg alloy in the liquid form at 1073 K has been theoretically investigated in the framework of four-parameter model which is based on Maclaurin series. The analytical expressions for thermodynamic functions such as excess free mixing energy, free mixing energy, enthalpy of mixing and entropy of mixing and microscopic functions such as concentration fluctuations at the long wavelength limit and Warren-Cowley chemical short range order parameter have been derived. These expressions have been used to compute the excess Gibbs free energy of mixing, Gibbs free energy of mixing, activity, enthalpy(heat) of mixing, excess entropy of mixing, entropy of mixing, concentration fluctuations in long wavelength limit and Warren-Cowley short range order parameters of AlMg liquid alloys at 1073 K. The investigation shows the excellent concurrence between the experimental and theoretical measurements of the mixing properties of AlMg liquid alloys at 1073 K. Interaction parameters of energy depends on temperature.

Effect of temperature on mixing behavior and stability of liquid Al-Fe alloys

A theoretical model based on the assumption of compound formation in binary liquid alloy has been used to investigate the thermodynamic properties (free energy of mixing, enthalpy of mixing and entropy of mixing), microscopic properties (concentration fluctuation in long wavelength limit and chemical short range order parameter), surface properties (surface tension and surface composition) and dynamic properties ( viscosity and diffusion coefficient). All the properties of Al2Fe binary melt have been measured using the same energy parameters configured for experimental values of free energy of mixing. The energy parameters are detected as independent of concentration, but depend on temperature. The findings are well consistent with the experimental standards.

Four-parameter model for the thermodynamic and microscopic properties of AlCu liquid alloys at 1373 K

The four-parameter model has been applied to study the thermodynamic properties like excess free energy of mixing, free energy of mixing, activity coefficients, activity, excess entropy of mixing, entropy of mixing, heat of mixing and microscopic function like concentration fluctuations in the long wavelength limit, SCC(0) of compound forming AlCu liquid alloys at 1373 K. The theoretical data have been compared with the experimental data available in the literature. There is an excellent agreement between the theoretical and experimental data. For the validation of experimental data, the available CALPHAD data have been used to compare the excess free energy of mixing, free energy of mixing, activity of AlCu liquid alloys at 1373 K. For the understanding of the atomic order of liquid alloy, the short-range order parameter has been computed for AlCu liquid alloys at 1373 K. The negative value of short-range order parameter indicates that AlCu liquid alloy at 1373 K is ordering in nature. Again the model parameters are temperature dependent.

Chemical short-range order strengthening mechanism in CoCrNi medium-entropy alloy under nanoindentation

The strengthening effect of chemical short-range order (SRO) structure in CoCrNi medium-entropy alloy (MEA) was investigated using molecular dynamics (MD) simulations of nanoindentation. The quantitative correlation between SRO parameters and mechanical properties was established. Results show that the strength and hardness of CoCrNi MEA increase with increasing chemical SRO parameters and reach a stable value with steady SRO structure. Compared with random solid solution (RSS) state model, the average hardness increases 8.1% in an intermediate SRO model and 13.7% in a stable SRO model. The dislocation nucleation force of SRO model is 55% larger than RSS model. Moreover, dislocation pinning induced by local Ni SRO structure, as well as the promoted unique dislocation interaction were observed during the nanoindentation process. Finally, results also show that as the temperature rises, the enhancement of hardness becomes more significant (11.4% at 70K, 17.24% at 300K, and 23.8% at 800K).

CO2 Electroreduction on Unsupported Pdpt Aerogels: Effects of Alloying and Surface Composition

The prospect of valorizing anthropogenic CO2 emissions by converting this greenhouse gas into added-value products (e.g., CO, formate) through electrochemical conversion in near-neutral aqueous media holds great research interest. While palladium-based catalysts have been repeatedly shown to display a switchable selectivity between CO and formate at high vs. low overpotentials, respectively, a large fraction of the total current is used to convert water into hydrogen as a parasitic byproduct. This is especially true for carbon-supported materials at high overpotentials (i.e., ≤ − 0.7 V vs. the reversible hydrogen electrode), in which the conversion of water to H2 on carbon and of CO2 to CO on Pd occur at comparable rates. Therefore, the removal of this carbon concomitant to the use of unsupported structures that can maintain a high surface area (e.g., as in aerogels) holds the promise of leading to higher selectivities towards CO2 reduction products. Additionally, alloying of metals is a well-researched approach to modify the adsorption kinetics of intermediate species enabling improvement in activity and the tuning of the selectivity towards a certain product. Specifically, alloys of palladium and platinum have been shown to possess high activities for formate generation from CO2 over a wide potential range [1].With this motivation, in this work, unsupported PdPt-aerogels were synthesized in five alloy compositions (from Pd50Pd50 to Pd90Pt10) and as pure metals (Pd100 and Pt100) at a constant web thickness of 6 ± 1 nm using a novel ethanolic synthesis approach [2]. The aerogels’ structure was studied using high-resolution transmission and scanning electron microscopies (HR-TEM, SEM) confirming the homogeneity of the materials. The alloying-degree of the PdPt aerogels was thereafter investigated using ex-situ X-ray absorption spectroscopy (XAS) measurements from which we derived the Cowley short-range order parameter [3], finding all compositions to be random alloys of Pd and Pt with a stoichiometry in good agreement with the Pt:Pd ratios aimed in the synthesis. Furthermore, energy dispersive X-ray spectroscopy (EDX) measurements in line-scan mode were used to investigate the elemental distribution within the structure of the gel (see Fig. 1A-1F), unveiling a slight enrichment of Pt on the surface of the bimetallic PdPt aerogels.These spectroscopic measurements were complemented by electrochemical characterization using CO-stripping as a means to infer the aerogels’ electrochemical surface area (ECSA) and surface composition. While the inferred ECSA values were all ≥70% of what is the expected value based on the aerogels’ web thickness, we observed significant changes in the shape of the hydrogen underpotential deposition (Hupd) that indicate alloy formation on the surface of the aerogels. Additionally, clear trends in the potential position of the CO-oxidation peak as a function of the alloy composition, and in the CO-oxidation charge depending on the CO-adsorption potential (i.e., 0.1 vs. 0.4 V vs. the reversible hydrogen electrode) were found.Lastly, the CO2-reduction activity of these bimetallic PdPt aerogels was tested in our custom, online gas chromatography setup for CO2-electroreduction. Using this approach, the pure palladium aerogel (Pd100) was shown to display Faradaic efficiencies towards CO and formate exceeding 90% at high or low overpotentials, respectively, proving the beneficial effect of the removal of the carbon support on palladium’s CO2 electroreduction selectivity. Meanwhile, the PdPt aerogel alloys featured formate and CO Faradaic efficiencies much lower than those previously reported in Ref. 1, with hydrogen making up the majority of the Faradaic efficiency (see Fig. 1G). Here, the activity towards CO2 electroreduction products was found to decrease with increasing Pt-content, so that on the pure Pt-aerogel (Pt100) hydrogen was the only product. These results are in line with the above-described Pt-enrichment of the alloys’ surfaces, which explains their high activity for the HER reaction and reduced activity for CO2 electroreduction. Figure 1

Symmetries in the properties of mixing of AgCu liquid alloys at 1423 K

The quasi-lattice theory based on the joint effect of size ratio and the energetic (or enthalpic) contribution as well as entropic effect has been applied to study the concentration dependence of the thermodynamic and structural properties of AgCu liquid alloys at 1423 K. The analytical expressions for the thermodynamic properties such as excess free energy of mixing, free energy of mixing, entropy of mixing, heat of mixing and the structural properties like the concentration fluctuations in the long wavelength limit and short range order parameter for a binary liquid alloy have been derived in the framework of quasi-lattice theory. The analytical expressions have been used to compute the various thermodynamic and structural properties of liquid AgCu alloys at 1423 K. The theoretical data of thermodynamic and structural properties have been compared with the available experimental data. The present theoretical investigation successfully explains the observed symmetries in the properties of mixing of liquid AgCu alloys at 1423 K.Further the energy parameter is found to be temperature dependent.

Composition analysis of AU–AG and AU–CU solid solution alloys by Friedel’s periodic spherical oscillation model

In this work, a two-nearest-neighbor structure model, named the 3-1 model, of the face-centered cubic (FCC) solid solution alloy is found based on the Cowley short-range order parameter and the Friedel’s periodic spherical oscillated (FPSO) model. The proposed 3-1 model has high symmetry, high density, and large separation. The model error between the 3-1 model and the standard spherical periodic model is only 0.004 nm. Besides, the chemical composition formula of the present model is applied to analyze the common grade compositions of various alloys. This work shows that the 3-1 model has universality in mature industrial grades of Au–Ag and Au–Cu alloys, and provides a simplified method to design the composition of alloys.

Calculation of Pairwise Effective Potentials in the Disordered Ni-22.5at.%Fe Alloy Using Model Potential Method with Account of Size Effect

Pairwise effective potentials in first seventeen shells of the Ni-22.5at.%Fe alloy are calculated using model potential method with account of the linear size effect. Using obtained values of pairwise effective potentials, the short range order parameters on the first seventeen shells of alloy are calculated by Krivoglaz-Clapp-Moss method. The calculated values ​​of the short-range order parameters were fitted to the experimental values ​​by varying the parameters of static atomic displacements. Reliable value of critical temperature of order-disorder phase transition in Ni-22.5at.%Fe alloy was calculated using obtained meanings of pairwise effective potentials.

Static Displacements and Short-Range Order in Ni-14 at. % Ir Alloy

In this paper, we are proposing a novel method to estimate static displacements of atoms caused by size effects in fcc substitutional binary polycrystalline solid solutions. Fourier transforms of static displacements of the atoms on every considered shell were calculated using the equations that include dynamical matrix and Fourier transform of interatomic forces. Short-range order parameters on the first seven shells of Ni-14 at. % Ir alloy have been identified from X-ray diffuse scattering intensity by accounting microscopic static displacements of atoms on a particular shell. Pairwise interatomic potentials on the considered shells and critical temperature of disorder-order phase transition were calculated using values of short-range order parameters.