Short-range Order Parameters Research Articles

Molecular Interactions in [Hmim][NO3] Ionic Liquid and 2-Alkanol Mixtures: Kirkwood–Buff Integrals and Structure Factor

In this paper, the investigation on thermophysical properties, structure, and dominant interactions in the binary systems containing 1-hexyl-3-methylimidazolium nitrate ([Hmim][NO3]) and 2-alkanol (2-propanol, 2-butanol, and 2-pentanol) were carried out through the Kirkwood–Buff (KB) integrals, structural factor, and excess molar volumes. Binary i and j parameters are positive and indicate that unlike molecules tend to form the strong interactions via forming hydrogen bonds and stay alongside while an increase in the carbon atom of 2-alkanols reduces the strength of bonds and tendency of the unlike molecules to be together. Also, the structure of mixtures was studied using the concentration–concentration structure factor, $${{S}_{{CC}}}(0)$$. Results from the application of this parameter show that in all binary mixtures, heterocoordination is predominant, ordering occurs in solutions and fluctuations are less than random orientation. Moreover the chemical short-range order parameter α′, which is an important function to understand the complex formation and phase segregation in the liquid mixtures, was calculated and discussed for mentioned mixtures. For current binary mixtures, experimental data and theoretical investigations are novel and reported for the first time.

New Method for Calculating Pairwise Effective Potential in Binary Solid Solutions

A new method for calculating the pairwise effective potential on arbitrary shells of the binary disordered solid solutions is proposed with account for the linear size effect. The method is based on the fitting of the order–disorder temperature calculated by the model potential method to its known experimental value. In disordered Cu $${}_{3}$$ Au alloy, the pairwise effective potential is calculated and the short-range order parameters on the first fourteen shells are estimated using the Krivoglaz–Clapp–Moss method. A satisfactory coincidence with the experimental data is obtained.

Theoretical and experimental study of valeric acid and 1-alkanol: COSMO-RS method and structure factors

Abstract This paper attempts to describe the types and nature of interactions present in binary mixtures containing valeric acid and 1-alkanols (1-pentanol up to 1-decanol) using theoretical and experimental methods. The density and viscosity of the mixtures above were measured at temperatures of 293.15 K to 323.15 K. Values of excess molar volumes (VmE) and viscosity deviations(Δη) were calculated. The findings indicate that strong interactions occur in binary solutions containing short-range 1-alkanol, and increasing the length of the alcohol chain causes a weakening of intermolecular interactions. To confirm the experimental results, the conductor-like screening model for real solutions (COSMO-RS) method was used to calculate the activity coefficients of the compounds in the liquid mixtures and the contact probability (CP) of alcohols with the valeric acid. Then, the D parameter, the concentration-concentration structure factor (SCC(0)), and the chemical short-range order parameter (α') were obtained and used to describe the existing interactions for binary mixtures. For binary systems, viscosity and density data are novel and have not previously been reported.

Ab initio molecular dynamics and high-dimensional neural network potential study of VZrNbHfTa melt

The structural and dynamics properties of melts are directly related to their solidification processes, and consequently to the properties of as-cast solid alloys. Ab initio molecular dynamics (AIMD) is a powerful tool that can study both of these factors. However, the main disadvantage of this method is its low performance which is critical for simulation of the multicomponent liquids. At the same time the atomistic simulation of multicomponent liquids has found its application for prediction of the formation of high-entropy alloys—a novel class of materials with enhanced mechanical properties. An effective method to solve the problem of AIMD low performance may be the design of pair or many-body potentials for classical molecular dynamics. One of the promising approaches is high-dimensional neural networks—the method of constructing many-body potentials for classical molecular dynamics from ab initio data. Thus, in this work, the high-dimensional neural network potential for multicomponent liquid VZrNbHfTa melt was constructed. The structure of this melt obtained by AIMD and high-dimensional neural network potential was compared by analyzing partial radial distribution functions. Dynamics of the melt obtained by both methods was also compared analyzing velocity autocorrelation functions and mean-square displacement for each type of atom in multicomponent VZrNbHfTa melt. It was shown that structure and dynamics are reproduced well by high-dimensional neural network potential (HDNNP). Some differences between HDNNP- and AIMD-obtained structure and dynamics are explained by finite-size effect and lack of statistics in AIMD simulation along with inherent errors in energy and force estimations made by high-dimensional neural network potentials. Analysis of melt structure via partial radial distribution functions and chemical short range order parameters led to the conclusion that vanadium atoms are repulsed from all the atoms of another type in liquid VZrNbHfTa system, which lowers the probability of single phase disordered solid solution formation. Diffusivity in multicomponent melt was found to decrease with increasing mass and size of an atom.

Speed-up of Monte Carlo simulations by preparing starting off-lattice structures that are close to equilibrium.

The Monte Carlo (MC) technique is an important tool for studying equilibrium properties of materials. When the starting configuration provided as an input to a MC calculation is far from equilibrium, an inordinate amount of computational effort may be required to bring the system closer to equilibrium in the pre-equilibration step of the MC calculation. In order to alleviate this cost, a new computational strategy is presented with the aim of rapidly generating starting off-lattice atomic structures that are already close to equilibrium. The method involves preparing a collection of on-lattice configurations using fast reverse MC calculations. Each configuration corresponds to a different value of short-range order parameter(s). Next, by performing short MC calculations with each starting structure, one measures the extent to which the distribution of local atomic arrangements has changed. The optimal configuration exhibits the smallest change in the distribution. While the optimal configuration can serve as an input to longer MC calculations, in many situations, the resulting structure may be directly used for the estimation of thermodynamic properties. Application of our approach to several off-lattice binary and ternary metal alloy systems with phase separation, good mixing, ordering, and surface segregation is demonstrated. A speed-up of >100-1000 times over the standard MC approach is achieved even with small systems containing a few thousand particles, and close-to-equilibrium structures containing million atoms can be rapidly prepared using our method within a day on a standard desktop computer.

Statistical mechanical studies of Al rich Al–Cu melts

We evaluate the microscopic correlation functions in Al1−xCux melts (x= 0.10, 0.17, 0.25, 0.33 and 0.40) in the attractive and repulsive region of the square well (SW) potential under the mean spherical model (MSM) principle. We derive the temperature and concentration dependent transport coefficients through the computed structural functions and verify the Dzugutov’s scaling law in Al1−xCuxliquid alloys. The liquid Al-Cu alloys follow the Stokes–Einstein relation especially in Al-rich melts. The concentration–concentration fluctuations in the long-wavelength limit, i.e. SCC(0) and the Warren–Cowley short-range order parameters, α1 have been computed which explains the compound forming behavior in this melts. SCC(0) is also employed to determine the thermodynamic factor for calculating inter-diffusion coefficients from Darken’s approach in liquid alloys. The temperature variation of diffusion coefficients are being applied for the computation of activation energy in liquid Al-Cu alloys by following Arrhenius equation. The theoretically evaluated activation energies of the alloys are in fair agreement with reported values. The composition dependent surface tension is determined and compared with the available experimental results which are in satisfactory agreement. Thus we establish a closer relationship between structure, transport and surface properties in Al1−xCuxmelts without using any adjusting parameters.

Study of interactions in binary mixtures containing normal alkanols; KB integrals and structure factor

ABSTRACT In this paper, the investigation on the structure and molecular interactions in the binary systems containing aniline and 1-alkanol (1-pentanol up to 1-decanol) was performed in the framework of Kirkwood-Buff (KB) integrals and experimental techniques. The interpretation of obtained parameters shows that in binary mixtures with shorter chain alcohols, unlike molecules tend to form strong interactions, while increasing in the carbon atom of 1-alkanols reduces the strength of bonds and tendency of the heterogeneous molecules to stay along side. Mixtures structure was studied using the concentration-concentration structure factor, . Results from the application of this parameter show that the heterocoordination occurs in solutions involving 1-pentanol up to 1-heptanol, while for mixtures containing 1-octanol to 1-decanol, homocoordination is predominant. Also, the chemical short-range order parameter, α′which is an important function to understand the complex formation and phase segregation in the liquid mixtures was obtained and discussed for mentioned mixtures.

Atomic Redistribution in a Fe-Cr System in the Course of Mechanical Alloying and Subsequent Annealing

Evolution of the structure and atomic distribution in Fe1−xCrx (x = 0.2, 0.3, 0.4 and 0.48) samples in the course of Fe and Cr elemental powder mechanical alloying (MA), as well as during the subsequent isochronous (4 hours) annealing in the 400 °C to 700 °C temperature range, has been studied using 57Fe Mossbauer spectrometry and X-ray diffraction with a focus on the short-range order (SRO). It was established that MA proceeds in one stage for x ≤ 0.3 or three consecutive stages for x > 0.3. The single-stage process is characterized by preferential penetration of Cr into the Fe matrix, while the three-stage process comprises diffusion of Cr into Fe as in the previous case, formation of Cr- and Fe-rich areas, and formation of homogeneous α-Fe(Cr) solid solution. The change in the MA mechanism occurs as Fe is saturated with Cr and is caused by the inversion of the mixing energy sign from negative to positive. For all samples with x ≤ 0.3 annealed at all temperatures and for x > 0.3 annealed at 400 °C, only a small trend toward SRO was observed (SRO parameter 0.3 annealed at temperatures > 400 °C are subjected to thermally induced decomposition, which is accompanied by chromium segregations to the grain boundaries.

Kirkwood-Buff integrals and structure factor for binary mixtures of ionic liquid with 1-alkanol

In this paper, we have tried to describe the factors affecting molecular interactions and structure of binary systems including 1-Hexyl-3-methylimidazolium Nitrate ([Hmim][NO3]) and 1-alkanol (1-hexanol, up to 1-decanol) using Kirkwood-Buff (KB) integrals and structure factor. Obtained results indicate that unlike molecules tend to form favorable interactions via forming hydrogen bonds or dipolar interactions and stay alongside, while an increase in the carbon chain of 1-alkanols reduces the strength of bonds and tendency of the unlike molecules to stay together. Moreover, the structure of mixtures was studied using the concentration-concentration structure factor, SCC(0). Results from the application of this parameter show that in all binary mixtures, heterocoordination is predominant, ordering occurs in solutions and fluctuations are less than random orientation. In addition, the chemical short-range order parameter α′, which is an important function to understand the complex formation and phase segregation in the liquid mixtures, was calculated and discussed for mentioned mixtures. For current binary mixtures, experimental data and theoretical investigations are novel and reported for the first time.

An optimized random structures generator governed by chemical short-range order for multi-component solid solutions

Multi-component random solid solutions have caused much interest for research because they often exhibit excellent mechanical properties. Many computational efforts have been made through various length scales, by first principles, molecular dynamics or finite elements. Here, a quasi-simulated-annealing (Markov Chain Monte Carlo algorithm) with prior burn-in procedure using chemical short-range order parameters as input values is developed for searching the global optimal distribution of species with regard to the phase stability of face-centered cubic CoCrNi alloys. The results show that this new approach could effectively generate the stable structures with a desired concentration and moreover, the stacking fault energies of these configurations have less uncertainties statistically.

The Influence of Variations in Atomic Composition on Low-Stability Pretransitional Structural-Phase States of a NiAl Intermetallic Compound

An analysis of the influence of a deviation of atomic composition from stoichiometry performed by the Monte Carlo method using a NiAl intermetallide as an example in the course of its cooling demonstrates that such deviation is an important factor in the region of pretransitional low-stability structural-phase states preceding transformation. The short-range order parameter values in non-stoichiometric alloys in their absolute values are essentially lower than those of a stoichiometric intermetallide; hence the tendency towards atomic ordering in non-stoichiometric intermetallics is noticeably lower than that in the stoichiometric alloys. The behavior of the temperature plots of the long-range order parameter in non-stoichiometric alloys during their cooling is considerably different from that of a stoichiometric intermetallide. In the case of cooling of non-stoichiometric alloys, a considerable degree of overcooling is required for the long-range order to set, and the formation of ordered phases occurs at much lower temperatures. Moreover, the temperature plot of long-range parameter of the Ni45Al55 alloy lies somewhat lower than that of the Ni55Al45 alloy, which implies that setting of the longrange order in these non-stoichiometric alloys occurs in different ways. It is underlined that a deviation of the system’s composition from stoichiometry gives rise to an essential refinement of the ordered and disordered regions.

Bhatia–Thornton fluctuations, transport and ordering in partially ordered Al–Cu alloys

The Bhatia–Thornton (BT) correlation functions namely the number–number, concentration–concentration and number-concentration correlation functions in liquid binary melts are important parameters for understanding the complexities in binary liquids. In this paper, the microscopic BT correlation functions of liquid Al–Cu alloys are investigated using square well (SW) potential under mean spherical model approximation. These correlation functions are linearly related to the Ashcroft–Langreth type partial structure factors. Thermodynamically important microscopic function i.e. concentration–concentration correlation function in the long-wavelength limit, SCC(0) is analytically calculated, which is well-known in BT formalism and is often used to characterized the mixing behavior in binary melts. The Warren–Cowley chemical short range order parameters, as function of Cu concentration is also computed in the liquid Al–Cu alloys through structural studies in the long wavelength limit, which gives valuable information regarding ordering in melts. The compound forming behavior in Al–Cu alloys is evidenced by the results obtained for the value of SCC(0) and . Further, transport properties in binary mixture have been determined by using BT-correlation functions and its long wavelength limit values. Kinetic as well as thermodynamic factors were taken care in the computation of dynamic properties of alloys.

The Influence of Vacancy Concentration of Low-Stability Pre-Transitional Structural-Phase States and Energy Characteristics of NiAl Intermetallide

Using the Monte Carlo method, the influence of vacancy concentration on the structural-phase states and energy characteristics is investigated by the example of an intermetallic compound NiAl in the course of its heating and cooling. According to the analysis, the availability and concentration of vacancies are important factors in the pre-transitional low-stability structural-phase states prior to transformation. On the one hand, neither the vacancies nor their concentration affect the temperature ranges of structural-phase transformations, on the other hand, they essentially influence both the pre-transitional low-stability structural-phase states and the rate of diffusion processes. The temperature behavior of the short-range order parameter suggests that the higher the vacancy concentration (i.e., system’s defectiveness), the higher the temperatures at which the tendencies for increasing atomic ordering would be manifested due to intensified diffusion. This, in turn, evidences of a higher starting structural transformation temperature with an increase in the number of defects in the alloy during cooling. An analysis of the temperature curves of the long-range order parameter of the NiAl intermetallide allows making a conclusion that an increased vacancy concentration (i.e., the alloy’s defectiveness) gives rise to a logical result – decreased long-range ordering in the system in the region of low-stability pre-transitional states and increased starting transformation temperature.

Estimation of the Critical Temperatures of Order-Disorder Phase Transitions in Cu-Au Alloys Using Short-Range Order Parameters

An expression for calculating the critical temperature of order-disorder transition in face-centered cubic alloys is developed with accounting of pairwise interatomic potential in the first eleven shells. Obtained expression was applied for the estimation of critical temperatures at Cu3Au, CuAu, and CuAu3 alloys in comparison with experimental data from phase diagram of Cu-Au system. Magnitudes of the pairwise interatomic potential in considered alloys was computed using values of the short-range order parameters which were experimentally obtained from X-ray diffuse scattering intensity. In this computation, the Krivoglaz-Clapp-Moss approximation and Cowley equations were applied.

БЛИЖНИЙ ПОРЯДОК В СПЛАВАХ Fe–Cr: МОДЕЛИРОВАНИЕ

Short-range order in Fe–Cr alloys was studied by the Monte Carlo method. The simulation was carried out in the framework of the Metropolis algorithm in LAMMPS software package. Simulation data analysis was carried out using Ovito data visualization and analysis software. The alloy model assumes that the lattice structure is fixed and that interactions exist between the first neighbors and the second neighbors. The FeCr interaction was determined using the Abell–Brenner–Tersoff interatomic interaction potential (ABOP). Various admixture concentrations of chromium interstitial in iron have been studied, namely, 5–50 at. %. The mixing energy of the Fe–Cr system was calculated for various concentrations of interstitial impurities. Calculations showed that the chosen interaction potential correctly simulates changes in the sign of the mixing energy as a function of Cr concentration. When used in Monte Carlo kinetic modeling, the potential correctly predicts decomposition of initially random Fe–Cr alloys, depending on Cr concentration. The Cowley short-range order parameter, which is used for quantitative assessment of the degree of order, has been determined. According to experiments, there is a strong tendency of ordering in distribution of Cr at low concentrations, which becomes evident in negative values of the short-range order parameters.

The structure of near stoichiometric Ge-Ga-Sb-S glasses: A reverse Monte Carlo study

The structure of Ge22Ga3Sb10S65 and Ge15Ga10Sb10S65 glasses was investigated by neutron diffraction (ND), X-ray diffraction (XRD), and extended X-ray absorption fine structure (EXAFS) measurements at the Ge, Ga and Sb K-edges. Experimental data sets were fitted simultaneously in the framework of the reverse Monte Carlo (RMC) simulation technique. Short range order parameters were determined from the obtained large-scale configurations. It was found that the coordination numbers of Ge, Sb and S are around the values predicted by the Mott-rule (4, 3 and 2, respectively). The Ga atoms have on average 4 nearest neighbors. The structure of these stoichiometric glasses can be described by the chemically ordered network model: Ge-S, Ga-S and Sb-S bonds are the most important. Long Sb-S distances (0.3–0.4 Å higher than the usual covalent bond lengths) are observed, suggesting that Sb atoms can be found in various local environments.

Riemannian Geometry of Ising Model in the Bethe Approximation

A method combining statistical equilibrium theory and metric geometry is used to study thermodynamic scalar curvature in the neighborhood of the Curie critical temperature for an Ising model of ferromagnetism. Using a Bethe type free energy expression, a non-diagonal metric is introduced on the two-dimensional phase space of long-range and short-range order parameters. Based on the metric elements Christoffel symbols, curvature tensor and Ricci tensor are found. An expression (containing equilibrium order parameters) is derived for Riemann scalar curvature (R). Its behavior near the critical temperature is examined analytically. We find that R tends toward plus infinity while approaching the critical point. This result fits well with those in the exact one-dimensional chain and mean-field Ising model in the lowest order approximation.

Effects of Mn and Al addition on structural and magnetic properties of FeCoNi-based high entropy alloys

The effects of Mn and Al additions on the structural stability and magnetic properties of FeCoNi-based alloys were investigated by density functional theory. The simulation results show that adding Al into FeCoNi alloy leads to the transformation of alloy structure from FCC to BCC with B2 structure. The doping of non-magnetic Al reduces the saturation magnetization, regardless alloy structure is FCC, BCC or B2 phase. The FeCoNiMn alloy prefers to form L12 structure to diminish the magnetic frustration. In the L12 structure, Mn minority spin peak moves from above to below Fermi level, further increasing Mn magnetic moment. For FeCoNi(MnAl)x alloys, the alloy structures change from FCC to BCC with the increase of Mn and Al content. The Mn atoms are transformed from anti-ferromagnetic to ferromagnetic order and the saturation magnetizations are significantly enhanced due to phase transition. It is found that there is obvious short-range order (SRO) in FeCoNi(MnAl)2 alloy. The SRO parameters are positive between Al–Al, Co-Co, Co-Ni pairs and negative between Ni-Al, Co-Al, Co-Mn, and Mn-Ni pairs. The electronic structure near the Fermi level shows significant difference from random solid structure, which will affect magnetic and electrical properties of FeCoNi(MnAl)2 alloy.

Surface and transport properties of liquid Ag–Sn alloys and a case study of Ag–Sn eutectic solder

This review represents the state of the art in the thermophysical properties of liquid Ag–Sn alloys highlighting the surface and wetting properties of Ag–Sn eutectic solder. It includes an atomistic approach developed within the framework of statistical mechanical theory in conjunction with a Quasi Lattice Theory that, through a rigorous mathematical formalism, provides exact relationships between the properties in terms of classical thermodynamics. The model predicted property values are substantiated by available experimental data. Based on the phase diagram evidence about the existence of e-Ag3Sn intermetallic compound, the surface (surface tension and surface composition), transport (viscosity and diffusivity) properties and microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) have been studied using the Compound Formation Model in a weak interaction approximation and Quasi Chemical Approximation for regular solutions. A case study of Ag–Sn eutectic alloy is presented. Taking into account its importance for design and development of lead free solder alternatives, the literature data on the wettability and the phases formed at the interface between Ag–Sn eutectic alloy and different substrates (Cu, Ni, Au, Pd) have also been analysed.

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.