Short-range Order Parameters Research Articles

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.

Effect of 0.25 and 2.0\xa0MeV He-Ion Irradiation on Short-Range Ordering in Model (EFDA) Fe-Cr Alloys

The effects of He+ irradiation on a distribution of Cr atoms in Fe100−xCrx (x = 5.8, 10.75, 15.15) alloys were studied by 57Fe Conversion Electron Mössbauer Spectroscopy (CEMS). The alloys were irradiated with doses up to 12 × 1016 ions/cm2 with 0.25 and 2.0 MeV He+ ions. The distribution of Cr atoms within the first two coordination shells around Fe atoms was expressed with short-range order parameters α1 (first-neighbor shell, 1NN), α2 (second-neighbor shell, 2NN), and α12 (1NN + 2NN). In non-irradiated alloys, α1 >0 and α2 <0 was revealed for all three samples. The value of α12 ≈0, i.e., the distribution of Cr atoms averaged over 1NN and 2NN, was random. The effect of the irradiation of the Fe94.2Cr5.8 alloy was similar for the two energies of He+, viz., increase of number of Cr atoms in 1NN and decrease in 2NN. Consequently, the degree of ordering increased. For the other two samples, the effect of the irradiation depends on the composition, and is stronger for the less energetic ions where, for Fe89.25Cr10.75 alloy, the disordering disappeared and some traces of Cr clustering appeared. In Fe84.85Cr15.15 alloy, the clustering was clear. In the samples irradiated with 2. 0 MeV He+ ions, the ordering also survived in the samples with x = 10.75 and 15.15, yet its degree became smaller than in the Fe94.2Cr5.8 alloy.

Simulation of Correlation Effects in Ordering Binary Alloys

.

A comparative study of primary damage state in Ni and NiCr/NiFe with a model grain boundary structure

The interaction of displacement cascades with atomic interfaces, specifically grain boundaries (GBs) is of great importance in design and development of radical advanced Ni-based super alloys with self-healing capabilities for future fission reactors. In this work, pure Ni and NiCr (with 5, 10, 15 and 20 at.% Cr content) and NiFe (with 5, 10 and 15 at.% Fe content) alloys with symmetric tilt Σ5[1 0 0](0 1¯ 3)θ = 37° GBs are used as model structures to study the influence of Cr and Fe on the primary and long-term radiation response of Ni-based alloys with microstructures. Molecular dynamics is used in simulating the primary damage event and the continuous ion bombardments in NiCr/NiFe structures to qualitatively represent the severe irradiation condition expected in next-generation fission reactors. In general, we observe that the GBs in “pristine” and “damaged” (∼after being continuously bombarded) forms preferentially absorb radiation-produced interstitials both Ni and Cr/Fe, over vacancies which results in accumulation and clustering of immobile vacancies in the grain interiors. The presence of Cr and Fe does not significantly affect the sink properties of our model GB and therefore, does not change the clustering behavior of excess vacancies in the bulk grains on picosecond (ps) timescale. The only evident phenomenon is a notable variation in the energetics and probably kinetics of point defects that slightly changes the evolution pattern of displacement cascades in the damage regions on ps timescale. The GB roughening incident is also observed in both Ni and NiFe/NiCr alloys during irradiation. In alloys with GBs, we also analyzed changes in the short range order parameter of irradiated structures. Our results indicate that in the primary event of radiation damage, a single bombardment is not enough to induce any trend in ordering or disordering of Cr and Fe solutes; in a prolonged irradiation, on the other hand, MD results reveal a very weak tendency of solutes to diffuse toward each other, although we did not observe any obvious Cr or Fe clustering in any of the performed displacement cascade simulations. Eventually, on ps timescale, we conclude that the Cr and Fe solutes contribute in enhancement of radiation tolerance of binary alloys in similar ways as Ni atoms do; but further details about the diffusion mechanisms of solutes on a longer timescale is essentially required to have more accurate predictions from a radiation damage perspective.

Chemical Ordering of Ag-Au Alloys in the Molten State

Simple statistical model has been used to report the thermodynamic, structural, transport and surface properties of liquid Ag-Au alloys at 1350K. In thermodynamic properties we have studied the free energy of mixing, heat of mixing, entropy of mixing and the chemical activity of both components of the alloys. For the structural investigation, our study includes concentration fluctuation in long wave length limit and Warren-Cowley short range order parameter. Viscosity and diffusivity of the alloys have been studied to understand transport properties. The surface behavior has been analyzed by computing surface concentration and surface tension of the alloys. The structural behaviors of the alloys are found to be symmetric with respect to concentrations of the species. The computed results are in good agreement with experimental data. Positive deviation of viscosity isotherms from linear law is observed. Surface tension of the alloys is found to be smaller than ideal values throughout bulk concentration of silver. For all theoretical analysis, concentration independent energy parameter takes important role, which is found to be temperature dependent and finally analysis confirms that presented alloy is hetero-coordinated.Journal of Institute of Science and Technology Volume 22, Issue 2, January 2018, Page: 191-201

Ordering effects in 2D hexagonal systems of binary and ternary C-B-N alloys

We present theoretical study of ordering phenomena in binary C1-xBx,C1-xNx, and ternary C1-2xBxNx alloys forming two-dimensional, graphene-like systems. In order to find equilibrium distribution of different species corresponding to minima of the energy, we use Monte Carlo approach in Metropolis regime. We employ empirical Tersoff potential to account for the interactions between atoms and to calculate the total energy. We model alloys considering large systems containing up to 20 000 atoms with various N and B concentrations. For quantitative description of ordering phenomena in the studied alloys, we determine Warren-Cowley Short Range Order (SRO) parameters for the first coordination shell. Our studies clearly demonstrate the presence of the SRO in the studied alloys. Binary alloys are neither random nor the clustering of N (or B) dopants takes place. In the ternary alloys, the h-BN domains are formed within the carbon areas.

Local configurations and atomic intermixing in as-quenched and annealed Fe1−xCrx and Fe1−xMox ribbons

Local atomic configuration, phase composition and atomic intermixing in Fe-rich Fe1−xCrx and Fe1−xMox ribbons (x = 0.05, 0.10, 0.15), of potential interest for high-temperature applications and nuclear devices, are investigated in this study in relation to specific processing and annealing routes. The Fe-based thin ribbons have been prepared by induction melting, followed by melt spinning and further annealed in He at temperatures up to 1250 °C. The complex structural, compositional and atomic configuration characterisation has been performed by means of X-ray diffraction (XRD), transmission Mössbauer spectroscopy and differential scanning calorimetry (TG-DSC). The XRD analysis indicates the formation of the desired solid solutions with body-centred cubic (bcc) structure in the as-quenched state. The Mössbauer spectroscopy results have been analysed in terms of the two-shell model. The distribution of Cr/Mo atoms in the first two coordination spheres is not homogeneous, especially after annealing, as supported by the short-range order parameters. In addition, high-temperature annealing treatments give rise to oxidation of Fe (to haematite, maghemite and magnetite) at the surface of the ribbons. Fe1−xCrx alloys are structurally more stable than the Mo counterpart under annealing at 700 °C. Annealing at 1250 °C in He enhances drastically the Cr clustering around Fe nuclei.

Local atomic structure of Co[sbnd]B-based glassy alloys: Ab initio molecular dynamics simulations

The first principle molecular dynamics simulations based on the density functional theory were performed to study the local structure of CoB-based glassy alloys. It was evidenced that the B-centered non-distorted (regular) Kasper polyhedra with a coordination number (CN) of 9–10, i.e. <0, 3, 6, 0> and <0, 2, 8, 0>, are primary structure-forming clusters in CoB-based glassy alloys. The formation of these regular clusters can be attributed to the efficient dense packing as well as the strong chemical interaction indicated by the results of chemical short range order parameter and electronic charge density. Compared with the Co65B35 glassy alloy, the Ta-bearing Co57B35Ta8 alloy has a higher fraction of Z9 and Z10 (Z = CN) Kasper polyhedra. A higher fraction of these regular Kasper polyhedra and their efficient and stable packing over medium range are likely to constitute the relatively stable regions which may compete with the corresponding crystals, and thus reduce atomic diffusivity and increase the viscosity of liquid/glassy structures. This result is in favor of higher thermal stability and better resistance to plastic flow. Therefore, the Co57B35Ta8 glassy alloy possesses a larger glass-forming ability and a higher mechanical strength than the Ta-free glassy alloy.

Investigation of the structure of CaO-Al2O3-SiO2 melts as a basis for the development of new agglomerated welding fluxes and industrial refractories

A significant number of welding fluxes and industrial ceramics are produced in the Ukraine. The production of these materials is sufficient for both domestic needs and significant export. It is assumed that the ternary CaO-Al2O3-SiO2 system may become the basis for the development of agglomerated welding fluxes and technical ceramics. Three samples of ternary CaO-Al2O3-SiO2 system were studied by means of high-temperature X-ray diffraction above the melting point: 23.3CaO- 14.7Al2O3-62.0SiO2 wt. % (sample 1, eutectic), 9.8CaO-19.8Al2O3-70.4SiO2 wt. % (sample 2, eutectic), 15.6 CaO- 36.5Al2O3-47.9SiO2 wt. % (sample 3). Experimental scattering intensity curves, structure factors and the radial distribution function of atoms were obtained. The structural parameters of short-range order were calculated using melt structure models obtained by Reverse Monte Carlo method. The existence of microparticle associates of the mullite or sillimanite type immersed in the slag matrix is assumed. It is assumed that the calcium ions coordinated aroundthese associates are surrounded by oxygen melt anions. Such a structure can be considered as a colloidal solution. The microparticle of mullite is the core of the aggregate that is surrounded by calcium and oxygen ions from the molten medium.

Thermo-Physical Properties of Al-Mg Alloy in Liquid State at Different Temperatures

Thermo-physical properties of Al-Mg alloys in molten state at 1073 K have been studied using thermodynamic modeling. Thermodynamic properties, such as free energy of mixing, heat of mixing, entropy of mixing, activities and structural properties, such as concentration fluctuation in long wavelength limit, Warren-Cowely short range order parameter have been studied at 1073 K, 1173 K, 1273 K and 1373 K on the basis of regular associated solution model. The surface properties such as surface concentrations and surface tension of the liquid alloys have been studied by using Butler’s model. A consistent set of model parameters have also been obtained by using optimization procedure based on statistical thermodynamics. Our analysis reveals that Al-Mg alloy is moderately interacting and it shows ordering nature at 1073 K. The nature of the alloys changes from ordering to segregating as the temperature increases.

Theoretical investigation of mixing properties of Sb-Sn binary liquid alloy at 905K

The thermodynamic, microscopic, surface and transport properties of Sb-Sn liquid alloy at 905K have been studied using regular solution model. In thermodynamic properties, free energy of mixing(GM) , activity(a), entropy of mixing(SM), heat of mixing (HM) have been studied. To understand structural behavior of the liquid alloys concentration fluctuations in the long wavelength limit i.e. (Scc(0)) and short range order parameter (α1) have been computed. Surface property is studied with the help of Butler’s model while transport property is computed from Moelwyn-Hughes equation. The theoretical and experimental values of thermodynamic and microscopic properties of Sb-Sn liquid alloy at 905K have been compared. In present work the value of interchange energy (w) is found to be negative suggesting that there is a tendency of unlike atoms pairing (i.e. Sb-Sn) as the nearest neighbor indicating the ordering behavior in Sb-Sn liquid alloy. The symmetric behavior of concentration fluctuations of the liquid alloy has been well explained by the model. The temperature dependence of interchange energy (w) has been found during the computation of entropy of mixing (SM) and heat of mixing (HM) of the liquid alloy.BIBECHANA 15 (2018) 1-10

Theoretical investigations on temperature dependence of thermodynamic properties and concentration fluctuations of In-Tl binary liquid alloys by optimization method

The thermodynamic properties, i.e. free energy of mixing (GM), heat of mixing (HM), entropy of mixing (SM) and activity (ai) of the component i (i , and structural property i.e. concentration fluctuations in long wave-length limit [Scc(0)] of In-Tl binary liquid alloy at a specified temperature have been investigated in the framework of quasi-lattice model on assuming the coupled effect of size ratio and entropic (or energetic) as well as enthalpic effect. These properties of In-Tl liquid alloy at 723 K have been computed theoretically by estimating the best fit value of order energy parameter (W) and size ratio () over the entire range of concentration in order to match their experimental values. The best fit value of W at 723 K has been used to determine the values of W at different temperatures with the help of temperature derivative of W which are then used for the optimization procedure in order to calculate the corresponding values of excess free energy of mixing, partial excess free energy of mixing and activity of the components involved in the alloy at different temperatures. These parameters have been used to investigate the concentration fluctuations in long wavelength limit {Scc(0)} of In-Tl binary liquid alloy at different temperatures over the entire range of concentration which have been used to predict the various other structural properties like excess stability function (EXS), diffusion coefficient ratio (Dm/Did), short range order parameter (α1) at different temperatures.BIBECHANA 15 (2018) 11-23

Modeling equations to predict the mixing behaviours of Al−Fe liquid alloy at different temperatures

Redlich−Kister (R−K) polynomials have been associated with the extended regular associated solution model to predict and explain the thermodynamic properties and structural properties of Al−Fe liquid alloy at 1873 K, 1973 K, 2073 K and 2173 K; 1873 K being its melting temperature. The thermodynamic properties, such as free energy of mixing and activities of free monomers ( and ) and structural properties, such as concentration fluctuation in long wave length limit, chemical short range order parameter and ratio of diffusion coefficients ( have been predicted at above stated temperatures. Renovated Butler model has been employed to predict the surface tension and surface segregation of the alloy at stated temperatures with the help of thermodynamic properties. Theoretical findings prevail that the tendency towards compound formation of the liquid alloy decreases with increase in its temperature beyond melting temperature. Eventually, its surface tension decreases and there is gradual exchange of atoms between the surface and bulk regions to maintain equilibrium at elevated temperatures. The liquid alloy under investigation thus shows ideal behaviours at higher temperatures. BIBECHANA 15 (2018) 60-69

Thermodynamic description of the Ge-Li liquid alloys

This paper presents the calorimetric results of the integral molar mixing enthalpy of liquid Ge-Li alloys, measured at two temperatures: at 1076K and 1176K for the mole fractions of Ge: XGe=0.02–0.69, and XGe=0.71–0.81, respectively. The obtained calorimetric results indicate that the integral molar enthalpy of liquid alloys from this binary system is independent of temperature. The available experimental data of partial or molar Gibbs free energies, together with the enthalpy of mixing, were used for the elaboration of the equation in the form proposed by Redlich and Kister, which describes the dependence of the excess Gibbs energy on the concentration and temperature. The experimental thermodynamic values of the excess free energy, mixing enthalpy change and activity were compared with those calculated with the use of the elaborated Redlich-Kister equation. Moreover, the partial structure factors and the short-range order parameter were calculated and discussed in relation to the thermodynamic properties and the phase diagram of the Ge-Li system.

Effects of Short-Range Order on the Magnetic and Mechanical Properties of FeCoNi(AlSi)x High Entropy Alloys

The properties of a material are sensitive to chemically-ordered structure in multi-element alloys. Understanding the effects of chemical short-range order (SRO) on magnetic and mechanical properties is important. In this work, we use the Monte Carlo method in combination with density functional theory to investigate atomic nearest neighbor distribution, magnetic moment and elastic modulus in FeCoNi (AlSi)x alloys. It is found that the prominent feature of the FeCoNi (AlSi)x alloys is the change of SRO parameters: the SRO parameters are positive between Al-Al, Al-Si, Si-Si pairs and negative between Ni-Al, Co-Si, Fe-Co, Ni-Si and Fe-Si pairs. The Al and Si elements tend to bond with Fe, Co, Ni elements to form an SRO structure. The change of the atomic nearest neighbor environment leads to a reduction in the atomic magnetic moments of magnetic elements. The calculated saturation magnetizations by considering the effect of SRO are in good accord with the experimental values. We further show that SRO leads to an increase of the elastic modulus, by sacrificing ductility and isotropy. In the study of the structure and properties of high entropy alloys, the effect of SRO should not be ignored.

Thermodynamic properties of Li-Pb system

The integral mixing enthalpy of liquid Li-Pb alloys was measured with the use of the calorimetric technique. The experimental studies involved measurements at different temperatures: 817, 923, 1021 and 1023K in the entire concentration range. The thermodynamic optimization was performed basing on the obtained results and the available literature data. The description of the excess Gibbs energy of temperature and composition was proposed with the use of a new model, which connects the polynomial and associated modelling. The obtained molar mixing enthalpy changes, excess Gibbs energy, and the molar excess entropy values are negative in the entire concentration range. Moreover, the existence of Li4Pb and LiPb associates in the liquid solutions was found, according to the analysis of the partial concentration structure factors (Scc(0)) and short range order (SRO) parameters.

Thermodynamic and Transport Properties of Molten Bi-In Alloys

We have used simple statistical theory to describe the mixing behavior of liquid Bi-In alloys in terms of energetic and structure through the study of their thermodynamic and transport properties. The structural characteristics of Bi-In melts are described by the two microscopic functions, i.e. the concentration fluctuation in long wavelength limit and the Warren-Cowley short range order parameter. The transport properties are analyzed through the diffusion coefficient ratio and viscosity. The Gibb’s free energy of mixing, enthalpy of mixing and entropy of mixing are the thermodynamic functions which are used to describe the thermodynamic behaviors. In whole analysis thermodynamic input parameter, i.e. interchange energy take important role which is temperature dependent. The computed results are in good agreement with experimental data and support a weak ordering tendency in molten Bi-In system.The Himalayan Physics Vol. 6 &amp; 7, April 2017 (5-9)

Distribution of Cr atoms in a strained and strain-relaxed Fe89.15Cr10.75 alloy: a Mössbauer effect study

An Fe89.15Cr10.75 alloy in a heavily strained (by cold rolling) state and in strain-relaxed states was studied by means of conversion electrons Mössbauer spectroscopy. Analysis of the spectra in terms of a two-shell model revealed significant differences between the studied samples, particularly in values of the hyperfine field and the distribution of Cr atoms within the first two neighbour shells. The latter is quantified in terms of short-range order parameters.

Calorimetric study and thermodynamic description of liquid In-Li alloys

This paper presents the results of the integral molar mixing enthalpy of liquid In-Li alloys, measured calorimetrically at three temperatures: at 653K for the concentration range of In lower than 0.12at.%, at 940K for the concentration range of In lower than 0.27at.%, and at 994K in the entire concentration range. The obtained experimental values in these ranges of temperatures indicate that the integral molar enthalpy of liquid alloys from this binary system is independent of temperature. The available experimental data of partial or molar Gibbs free energies, together with the enthalpy of mixing, were used for the elaboration of the equation in the form proposed by Redlich and Kister, which describes the dependence of the excess Gibbs energy on the concentration and temperature. The experimental thermodynamic values of the excess free energy, mixing enthalpy change and activity were compared with those calculated with the use of the elaborated Redlich-Kister equation. Moreover, the partial structure factors and short-range order parameter were calculated and discussed in relation to the thermodynamic properties and the phase diagram of the In-Li system.

Short-Range Order in High Entropy Alloys: Theoretical Formulation and Application to Mo-Nb-Ta-V-W System

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 alloy system. The theoretical formulation is used to investigate the evolution of the ten different SRO parameters in the MoNbTaVW and the sub-quaternary systems obtained by Monte-Carlo simulations within the combined CE and first-principles formalism. The strongest chemical SRO parameter is predicted for the first nearest-neighbor Mo-Ta pair that is in consistent agreement with high value of enthalpy of mixing in the B2 structure for this binary system. The prediction of B2 phase presence for Mo-Ta pairs in the considered bcc HEAs is reinforced by the positive contribution to the average SRO from the second nearest-neighbor shell. Interestingly, it is found that the average SRO parameter for the first and second nearest-neighbor shells of V-W pairs is also strongly negative in a comparison with the Mo-Ta pairs. This finding in the HEAs can be rationalized and discussed by the presence of the ordered-like B32 phase which has been predicted as the ground-state structure in binary bcc V-W system at the equimolar composition.