Short-range Order Model Research Articles

Short-Range Order Modeling in Alloys

The short and long-range orders in alloys can be assessed based on a new expression for the combinatorial factor, which is more convenient and intuitive than the traditionally used form. This novel expression can be directly applied to reproduce the results of several well-known statistical-thermodynamic models that are typically considered independent or even inconsistent. The short list of models includes Quasichemical Theory, Associated Solution Model, Surrounded Atom Model, and Cluster Site Approximation. As a result, the formalism and interpretation of these models are significantly clarified, allowing us to identify and fix several long-standing errors that might otherwise have gone unnoticed. Multicomponent generalization of these models is also greatly simplified. For systems undergoing a phase transition, an extended version of the theory provides a mechanism that allows the correct critical temperature of phase transition to be reproduced, as well as a significant increase in the accuracy of thermodynamic functions. In the case of order–disorder transformations, the new theory ensures an integrated description of short and long-range orders, which has long been considered an important and difficult problem.

A thermodynamic model for high temperature corrosion applications: The (Na2SO4 + K2SO4 + ZnSO4 + PbSO4) system

The (Na2SO4 + K2SO4 + ZnSO4 + PbSO4) salt system is important for deposit buildup, fouling and associated corrosion of metallic structural and heat exchanger materials of municipal solid waste incinerators, low-grade fuel firing boilers, as well as metallurgical heat recovery boilers. In this study, a complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (Na2SO4 + K2SO4 + ZnSO4 + PbSO4) system, and optimized model parameters have been found. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase while most of the relevant solid solutions were modeled using the Compound Energy Formalism. The (Na2SO4 + K2SO4) sub-system has been critically evaluated in a previous article. A (60 mol% PbSO4 + 40 mol% ZnSO4) binary mixture was investigated by DTA-TGA since no thermodynamic data were available in the literature for this particular sub-system. The model parameters obtained for the binary and ternary sub-systems of the (Na2SO4 + K2SO4 + ZnSO4 + PbSO4) system can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. In particular, ternary and quaternary eutectics (corresponding to the formation of a liquid phase at low temperatures) may be predicted, thus permitting to avoid “catastrophic” corrosion. This work is part of a large thermodynamic model for the Na+, K+, Zn2+, Pb2+ // Cl−, SO42− system.

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.

The Debye Method is Used to Create 3D Structure Models of Electroactively Transformed Microcrystalline Cellulose

In this paper, we carried out the XRD results and 3D structural models of short-range order of amorphous cellulose obtained by ball milling of microcrystalline cellulose. The amorphous cellulose has the well-reproducible effect of influence of ozone treatment on its proton conductivity, which allows to use this material as a gas sensor. Calculation of the quantitative characteristics of the short-range order (radii of coordination spheres and their dispersions, coordination numbers) of amorphous cellulose was carried out from distribution pair functions curve by using the Finback-Warren method. The space atoms configurations was carried out by Debye method. After that, the models were distorted by converting into packages disoriented relative to each other layers. The X-Ray diffraction patterns were calculated for 3D models and compared with experimental curves.

Thermodynamic evaluation and optimization of the (LiCl + NaCl + KCl + MgCl2 + CaCl2 + CeCl3) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (LiCl + NaCl + KCl + MgCl2 + CaCl2 + CeCl3) system, and optimized model parameters have been found. The (LiCl + NaCl + KCl + MgCl2 + CaCl2) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase, and the Compound Energy Formalism was used for the various solid solutions.

3D model of short-range order of one-hour milled cellulose

The main purpose of this work was to investigate the structure of short-range order of microcrystalline cellulose (MCC) milled for one hour. Usually mechanical milling produces amorphous segments of crystalline cellulose. Investigation of short-range order was conducted by Debay’s method to get X-ray diffraction (XRD) pattern when the coordinates of atoms in a cluster are known. The samples were studied by XRD. Crystallinity degree was measured using Segal’s method. Cellulose Iα and Iβ were used as the initial structures to form clusters. The profile factor (Rp) was used, as the evaluation factor. The results showed that the cluster based on cellulose Iβ insufficiently characterized the short-range order of crystalline-amorphous cellulose (Rp>18%). Consequently, we examined a unit cell consisting of one cellobiose fragment. The final modeling cluster had the size of 35Å×22Å×29Å. The cluster consisted of 3 layers orientated randomly in relation to one another. The result of comparison of theoretical and experimental XRD patterns revealed that Rp was 11.4%. Therefore, the structure of short-range order of one-hour ground cellulose can be characterized by disordered cellulose chains with the length of 21 Å.

Short-range order and nonstoichiometry in titanium monoxide TiO y from DFT calculations

Structural models of short-range order in the arrangement of structural vacancies have been proposed for stoichiometric and nonstoichiometric compositions of titanium monoxide TiO y . A combined effect of the short-range order and nonstoichiometry on the ground-state energy and the electronic structure of the compound has been investigated using the first-principles methods. The energetically favorable models of short-range order reproduce the local distribution of atoms and vacancies, which is characteristic of the Ti5O5(mon) and Ti5O5(cub) superstructures. In these models, the correlations between the vacancies of the metal sublattice and the vacancies of the nonmetal sublattice make a more significant contribution to the decrease in the energy of the compound as compared with the correlations between the vacancies in only one of the sublattices.

The properties and structure of Ge[sbnd]Se[sbnd]Te glasses and thin films

Ge30Se70−xTex bulk glasses and thin films for x=0, 10 and 20 were prepared. The properties and structure were characterized by differential scanning calorimetry (DSC), Raman spectroscopy and also by 77Se and 125Te MAS NMR spectroscopy. The optical properties were also measured. The absence of crystalline phases was verified by XRD, while DSC indicated that the glasses were not phase separated. Although the glass transition temperature of both Ge30Se70 glass and thin film is the same, different ΔCp reveal a higher disorder of the thin film. Both the glass transition temperature and ΔCp of Te glasses as well as crystallization temperatures decrease when Te increases due to increasing GeTe2/2 instead of GeSe4/2 structural units thereby reducing 3D interconnection of the glassy network. Based on the 77Se MAS NMR results, the short-range order model was determined as a suitable structural model for Ge30Se70 glass. 77Se and 125Te MAS NMR confirmed that Ge in alloys with Te only reaches oxidation state +II in agreement with GeTe phase diagram and therefore no GeTe4/2 tetrahedra can be present in these glasses and/or films. Raman spectroscopy confirmed that the short-range order of glasses and films is basically the same. The refractive index of thin films increases with tellurium content. The optical band gap of the thin films strongly decreases from 2.02eV to 1.36eV with increasing Te content and simultaneously the increasing structural disorder and width of the band tails increase. Reduction of the oxidation state of germanium to GeII caused by a reaction with tellurium ultimately leads to a reduction in 3D connectivity of the non-crystalline matrix and the loss of the glass-forming ability of the GeSeTe system.

Cationic ordering in tysonite type structures: II: Crystal structure of α-, β- and γ-baryum hexafluoridouranates (IV)

Three polymorphic varieties of BaUF6 have been synthesized and their crystal structure determined by X-ray diffraction on single crystals.The high temperature α- BaUF6 belongs to the disordered tysonite type and its structure is compared to BaThF6 using the same defect models: ideal structure, split-model structure and introduction of anharmonic thermal vibration factor for cations. Both structures are similar.β-BaUF6 is stable in a narrow temperature range (962–992K) below the disordered variety. It crystallizes in the triclinic P-1 space group and contains 3 Ba and 3U independent cationic sites. The structure derives from tysonite type with BaF10 and BaF11 Edshammar polyhedra, similar to those described in tysonite, forming complex sheets alternating with homologous sheets of UF8 and UF9 polyhedra.The low-temperature γ-BaUF6 (T<962K) is a monoclinic P21/c ordered superstructure of the tysonite type, much simpler than β-BaUF6, with BaF11 Edshammar polyhedra and UF8 dodecahedra forming alternate zigzag layers.The structural features of both ordered superstructures allow to propose a model of short range order for all the disordered tysonite M(II)M’(IV)F6 phases. This model involves a decrease of the coordination number of M’(IV) cations and of the connectivity of M(II) and M’(IV) polyhedra from face-sharing to edge-sharing and from edge-sharing to corner-sharing, locally distorting the hexagonal sublattice.

Models for the thermodynamic properties of molten salt systems: Perspectives for ionic liquids

Over the past several years, the Modified Quasichemical Model for short-range ordering has been used successfully to obtain a quantitative thermodynamic description of various multicomponent high temperature inorganic molten salt systems. In the present paper, it was applied to the (LiN(FSO2)2 + KN(FSO2)2 + CsN(FSO2)2) ternary system and the ([C2mim]Cl + AlCl3) binary system (where [C2mim]Cl refers to 1-ethyl-3-methyl-imidazolium chloride), which both involve some ionic liquid compounds. Those two systems were selected as prototypes since experimental data were available for them in the literature. The (LiN(FSO2)2 + KN(FSO2)2 + CsN(FSO2)2) liquid displays relatively little short-range ordering, and the experimental ternary eutectic at T = 309 K or 312 K was satisfactorily reproduced by using solely the optimized binary parameters along with a standard symmetric interpolation method. The ([C2mim]Cl + AlCl3) liquid displays strong negative deviations from ideality, and two different compositions of maximum short-range ordering (near the [C2mim]AlCl4 and [C2mim]Al2Cl7 compositions) were introduced. All available experimental data (phase diagram, emf measurements, partial enthalpies of mixing) were satisfactorily reproduced by the model. The Volume-based Thermodynamics (VBT) from Glasser and Jenkins was used to assess the missing thermodynamic data for [C2mim]Cl, and it was also tested on several ionic liquid compounds of the methyl-imidazolium type.

Growth kinetics of [formula omitted] particles in [formula omitted]-Ti matrix studied by in situ small-angle X-ray scattering

Nucleation and growth kinetics of nanoparticles of hexagonal ω phase in a body-centered cubic β titanium matrix in single crystals of β-Ti alloys were investigated by small-angle X-ray scattering measured in situ during ageing at various temperatures up to 450°C. The experimental data were compared with numerical simulations based on a three-dimensional short-range order model of nanoparticle self-ordering. The X-ray contrast of the particles is caused by an inhomogeneous distribution of impurity atoms (Mo, Fe and Al), whose density profile around growing nanoparticles was simulated by solving the corresponding diffusion equation with moving boundary conditions. From the analysis of the experimental data we determined the mean distance and size of the nanoparticles and confirmed the validity of the ∝t1/3 growth law following from the Lifshitz–Slyozov–Wagner theory. From a detailed comparison of the experimental data with simulations we also assessed the diffusion coefficient of the impurity atoms and its activation energy.

Thermodynamic evaluation and optimization of the CH3COOLi–CH3COOK–CH3COOCs system using the Modified Quasichemical Model

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the CH3COOLi–CH3COOK–CH3COOCs system, and optimized model parameters have been found which best reproduce all available experimental data simultaneously. The CH3COOLi–CH3COOK–CH3COOCs system may be used in supported molten salt catalysis. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase. No ternary model parameters were required for the liquid phase; the optimized binary parameters suffice to reproduce satisfactorily the available experimental data for the ternary system using a standard symmetric interpolation method. The calculated (predicted) minimum liquidus temperature corresponds to a ternary eutectic at T=368K, with a liquid composition of (22.4mol% CH3COOLi+32.3mol% CH3COOK+45.3mol% CH3COOCs). This relatively low liquidus temperature makes the ternary mixture an interesting alternative to ionic liquids.

A Thermodynamic Model for the NH4+, K+ // H2PO4-, H2P2O72-, NO3-, Cl- - H2O System

We have developed a quantitative thermodynamic description of the NH4H2PO4-(NH4)2H2P2O7-KH2PO4-K2H2P2O7-NH4NO3-KNO3-NH4Cl-KCl-H2O system, which is of great importance for fertilizers applications. The liquid phase and all solid solutions were modeled using the Modified Quasichemical Model for short-range ordering. The liquid model includes the reaction of dimerization of AH2PO4 (where A = NH4+ or K+) according to: 2 AH2PO4(liquid) ↔ A2H2P2O7(liquid) + H2O(liquid or gas). The model parameters are mainly obtained by the critical evaluation and optimization of available thermodynamic and phase equilibrium data for the lower-order subsystems. The model is then used to estimate the properties of multicomponent salts from these assessed parameters for the lower-order subsystems, using interpolation methods along with Gibbs energy minimization software. When used in conjunction with thermodynamic databases for solids, solid solutions, and gases, these databases permit the calculation of complex multiphase equilibria in multicomponent systems, using the FactSage thermochemical software. In particular, calculations of interest for the production and storage of fertilizers may be performed.

Bipolar charge transport property of N,N′-dicarbazolyl-1,4-dimethene-benzene: A study of the short range order model

Short range order model is commonly used to explain the charge transport property of disordered organic semiconductors. However, its validity is not yet studied. In this paper, the hole and electron mobilities of a bipolar material, N,N′-dicarbazolyl-1,4-dimethene-benzene (DCB), were measured through time of flight method. The hole and electron mobilities of DCB based on the crystalline structure were calculated. In order to investigate the short range order model, the ratios of charge mobilities at zero electric field of holes to electrons were calculated. The results showed that this model cannot fully explain our case. The reason was discussed in detail, and a correction method was proposed. We showed that using the short range order model without preconditions to explain the charge transport property of amorphous materials may lead to deviations, which is often neglected in the past.

Model of short-range order in 5,6-dichloroquinolino-5,8-dione organic compound

Model of short-range order in 5,6-dichloroquinolino-5,8-dione organic compound

Ab initio molecular dynamics model for density, elastic properties and short range order of Co–Fe–Ta–B metallic glass thin films

Density, elastic modulus and the pair distribution function of Co–Fe–Ta–B metallic glasses were obtained by ab initio molecular dynamics simulations and measured for sputtered thin films using x-ray reflectivity, nanoindentation and x-ray diffraction using high energy photons. The computationally obtained density of 8.19 g cm−3 for Co43Fe20Ta5.5B31.5 and 8.42 g cm−3 for Co45.5Fe24Ta6B24.5, as well as the Young’s moduli of 273 and 251 GPa, respectively, are consistent with our experiments and literature data. These data, together with the good agreement between the theoretical and the experimental pair distribution functions, indicate that the model established here is useful to describe the density, elasticity and short range order of Co–Fe–Ta–B metallic glass thin films. Irrespective of the investigated variation in chemical composition, (Co, Fe)–B cluster formation and Co–Fe interactions are identified by density-of-states analysis. Strong bonds within the structural units and between the metallic species may give rise to the comparatively large stiffness.

Scattering properties and structure functions of Boolean models

The Boolean model is a successful short-range order model for ensembles of overlapping grains possessing many applications. Convex grains, randomly distributed in space with a certain density, are characterized by their SAS correlation function γ 0( r). Characteristics, such as volume fraction c (porosity 1 − c) and sample correlation function γ( r) result. The function γ 0( r) of unknown grains can be re-constructed from γ( r). Information on size and shape of the grains results. The chord length distributions of grain phase and matrix phase are analyzed. The latter distribution is an exponential distribution. The distribution law of the grain phase is determined explicitly, incorporating formulas for the moments.

New Route to Local Order Models for Disordered Crystalline Materials: Diffuse Scattering and Computational Modeling of Phloroglucinol Dihydrate

A new, readily tractable route to determining short-range order models for materials exhibiting occupational disorder and diffuse scattering using first-principles solid-state quantum mechanical calculations is presented and illustrated with application to the disordered, layered molecular material phloroglucinol dihydrate.

Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl 2 + CaCl 2 + ZnCl 2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases and relevant gaseous species of the (NaCl + KCl + MgCl 2 + CaCl 2 + ZnCl 2) system, and optimized model parameters have been found. The (NaCl + KCl + MgCl 2 + CaCl 2) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase.

Microscopic mechanism of martensitic stabilization in shape-memory alloys: Atomic-level processes

Aging in martensite, which is accompanied by a gradual change in physical properties, has been observed in most shape-memory alloys for more than half a century. However, its microscopic mechanism has remained controversial due to a lack of experiments that can probe the atomic-level processes. By using a method which combines molecular-dynamics and Monte Carlo simulations, we clarify the atomic mechanism for one of the well-observed martensitic aging effects, martensitic stabilization. We successfully reproduce the observed effects using our method. Quantitative analysis of the atomic configurations during aging reveals that martensite stabilization is not associated with a change in the average martensite structure. It involves instead a gradual change in the short-range order of point defects so that the defect short-range order tends to adopt the same ``symmetry'' as the crystal symmetry of the host martensite lattice. Our simulation results are consistent with the symmetry-conforming short-range order model [X. Ren and K. Otsuka, Nature (London) 389, 579 (1997)].