Binary Substitutional Alloys Research Articles

STUDY ON ELASTIC PROPERTY OF STAINLESS STEEL UNDER PRESSURE

The paper presents analytic expressions of the Helmholtz free energy and characteristic elastic deformation quantities such as the elastic moduli E, K, G and the elastic constants C11, C12, C44 for BCC interstitial and substitutional alloy with four components are determined by the statistical moment method. The obtained elastic quantities depend on temperature, pressure, the concentration of interstitial atoms, and the concentration of substitutional atoms. This is the elastic deformation theory of BCC interstitial and substitutional alloy with four components published for the first time. The elastic deformation theories of BCC metal, BCC binary interstitial alloy, BCC binary substitutional alloy, and BCC ternary interstitial and substitutional alloy are limit cases of the elastic deformation theory of BCC substitutional and interstitial alloy with four components. Our numerical calculations of the obtained theoretical results for metal Fe and alloy FeSi are in good agreement with other calculations and experiments. Other numerical calculations for alloys FeCr, FeNi, FeCrSi, FeNiSi, FeCrNiSi (some atoms Fe are substituted by atoms Cr and some other atoms Fe are substituted by atoms Ni) called stainless steels predict and orient experimental results in the future. Our numerical calculations for alloy FeCrNiSi are published for the first time.

Determining the Interphase Boundary Parameters in Heterogeneous Binary Alloys on the Basis of the Hypothesis of Weak Nonlocality

Based on our earlier hypothesis of weak nonlocality, we developed a method for calculating the temperature dependences of the width and specific energy of the interphase boundary for binary substitutional alloys, using the concentration dependence of the internal energy or the equilibrium phase diagram of the alloy. Numerically calculated temperature dependences of the solubility limits, specific energy, and thickness of the interphase boundary are presented for three thermodynamic models: the regular solution model (Nb–Cu alloy), the quasi-regular solution model, and the general case (Fe–Cu alloy and A–B alloy that differs from Fe–Cu in the sign of excess entropy).

On the deviation from the Vegard's law for the solid solutions

A method is proposed for calculating the lattice parameter (l) for the solid solution (i.e. disordered binary substitutional alloy), which takes into account the pressure (P) in the alloy. An analytical expression is obtained for calculating the dependence of the function l on the alloy concentration at different values of P. It is shown that for P = 0 the deviation from the Vegard's law (Δl) is due to the difference in compressibility and in specific volumes of the pure crystals. The method is approved on SiGe, CuAu and AuFe alloys, and it was showed the good agreement with the experimental data. With an isothermal increase in pressure, the value Δl increases both for alloys with a negative and for alloys with a positive deviation from the dependence obtained by the Vegard's law. Calculations showed that for the SiGe alloy, the function Δl(P) passes over to the positive region at P0 = 0.685 GPa. It was shown the thermal expansion coefficient of a solid SiGe substitution solution at P = 0 deviates in the negative direction from the dependence that follows from the Vegard's law.

Incorporating density jumps and species-conserving dynamics in XPFC binary alloys

This work presents a consistent formulation of the structural phase-field-crystal model of substitutional binary alloys that allows for the description phases of unequal densities, a key feature in solidification. We further develop the dynamics of the model to be consistent with conserved Langevine dynamics in the true governing species densities. Additionally, this work expands on the ability to control pressure, so far only implemented in pure materials, to binary alloys by improving the control system that controls pressure from previous work. We study the equilibrium properties of the new model, and demonstrate that control of pressure can drive various kinematic microscopic processes in materials such as grain boundary pre-melting, phase instability, and grain or inter-phase boundary motion.

Modeling solute segregation in grain boundaries of binary substitutional alloys: Effect of excess volume

The effect of excess volume in grain boundary (GB) on GB solute segregation was quantitatively evaluated by means of thermodynamic modeling. Helmholtz free energies of bulk (grain interior) and GBs in binary substitutional systems with fcc (face centered cubic) and bcc (body centered cubic) crystal structures were derived as functions of composition, temperature and atomic volume by applying Embedded-atom-method (EAM) to standard thermodynamic relations under random site occupation assumption. The equilibrium solute distribution between GBs and bulk was then obtained in terms of the parallel tangent construction between bulk and GB phases’ Helmholtz free energy curves. By modeling the CuAg (fcc) and WNb (bcc) systems, an enhanced GB segregation with increased GB excess volume was predicted. The segregation enthalpy and the solute enrichment ratio were further calculated, showing good agreements with the experimental and simulated results.

Phase field crystal study on the grain boundary porosity induced by the Kirkendall effect

Grain boundary (GB) porosity strongly degrades the bonding quality of interfaces and affects the physical and mechanical properties of solid polycrystalline materials. In this paper, the formation and evolution mechanisms of porosity at the grain boundary were investigated using the binary phase field crystal simulation method. Simulated results indicate that the Kirkendall effect existing in the interdiffusion of substitutional binary alloys can result in GB porosity. For the low-angle grain boundary interdiffusion system, the porosity initially forms at the isolated dislocation core, evolving from circle to irregular polygon. For the large-angle GB interdiffusion system, the porosity initially forms at the dislocation core close to the diffusion plane, and then evolves toward the dislocation cores away from the diffusion plane. The porosities finally connect as a continuous slit that splits up the GB. The results also show that the diffusion of fast diffusers along the GB is obviously enhanced with the mobility ratio of species A and B increasing. Our simulation results agree well with theoretical and experimental results.

NGHIÊN CỨU BIẾN DẠNG ĐÀN HỒI CỦA HỢP KIM THAY THẾ AB VỚI CẤU TRÚC LẬP PHƯƠNG TÂM DIỆN Ở ÁP SUẤT KHÔNG

NGHIÊN CỨU BIẾN DẠNG ĐÀN HỒI CỦA HỢP KIM THAY THẾ AB VỚI CẤU TRÚC LẬP PHƯƠNG TÂM DIỆN Ở ÁP SUẤT KHÔNG

Effects of Alloying on Nanoscale Grain Growth in Substitutional Binary Alloy System: Thermodynamics and Kinetics

Applying the regular solution model, the Gibbs free energy of mixing for substitutional binary alloy system was constructed. Then, thermodynamic and kinetic parameters, e.g., driving force and solute drag force, controlling nanoscale grain growth of substitutional binary alloy systems were derived and compared to their generally accepted definitions and interpretations. It is suggested that for an actual grain growth process, the classical driving force P = γ/D (γ the grain boundary (GB) energy, D the grain size) should be replaced by a new expression, i.e., $$ P^{\prime} = \gamma /D - \Delta P $$ . ΔP represents the energy required to adjust nonequilibrium solute distribution to equilibrium solute distribution, which is equivalent to the generally accepted solute drag force impeding GB migration. By incorporating the derived new driving force for grain growth into the classical grain growth model, the reported grain growth behaviors of nanocrystalline Fe-4at. pct Zr and Pd-19at. pct Zr alloys were analyzed. On this basis, the effect of thermodynamic and kinetic parameters (i.e., P, ΔP and the GB mobility (M GB)) on nanoscale grain growth, were investigated. Upon grain growth, the decrease of P is caused by the reduction of γ as a result of solute segregation in GBs; the decrease of ΔP is, however, due to the decrease of grain growth velocity; whereas the decrease of M GB is attributed to the enhanced difference of solute molar fractions between the bulk and the GBs as well as the increased activation energy for GB diffusion.

First-principles investigations on the phase stability, elastic and thermodynamic properties of Zr–Al alloys

In this paper, we employ first-principles methods based on electronic density functional theory (DFT) to investigate the phase stability, elastic and thermodynamic properties of Zr – Al binary substitutional alloys which are Zr 3 Al , Zr 2 Al , ZrAl , ZrAl 2 and ZrAl 3. By analyzing the elastic constants and enthalpy of formation, those phases both satisfy the generalized stability criteria and the results show that ZrAl 2 is the most stable. Due to high bulk modulus B, shear modulus G and Youngs modulus Y, ZrAl 2 also possesses excellent mechanical properties. Moreover, it is expected that there will be covalent bonding between Zr and Al atom in ZrAl 2 compound, which is confirmed by the electronic structure and the differences of charge density discussions. In the end, based on the calculated elastic modulus, the elastic wave velocity, Debye temperature ΘD and specific heat CV are discussed. As a result, ZrAl 3 possesses the highest Debye temperature and sound velocity, meaning a larger associated thermal conductivity and higher melting temperature.

Modeling grain growth kinetics of binary substitutional alloys by the thermodynamic extremal principle

The thermodynamics and kinetics fundaments of grain growth in binary substitutional alloys were analyzed using the thermodynamic extremal principle. Applying the regular solution approximation, a new equation for solute segregation at steady-state diffusion is proposed, which suggests reduced solute segregation as the grain boundary (GB) solute concentration increases, differently from previous models [Acta Mater 2009;57(5):1466, Acta Mater 2012;60:4833, Scripta Mater 2010;63:989] that adopt constant segregation enthalpy. Furthermore, a self-consistent consideration has been carried out to account for the coupled changes in GB energy and GB mobility as a result of solute segregation. On this basis, the quantitative relation is evaluated between the thermodynamic and kinetic effects of solute segregation to determine the dominant role in retarding and even suppressing grain growth, by comparison of the dimensionless GB energy (i.e., the GB energy of alloy over that of pure solvent) and the dimensionless effective GB mobility (i.e., the effective GB mobility over that of pure solvent): the kinetic effect prevails if the dimensionless effective GB mobility is smaller than the dimensionless GB energy, and vice versa. The present model is adopted to describe well the experimental results for Fe–P alloys, and nanocrystalline Ni–P and Pd–Zr alloys.

Solid-state phase transformation kinetics in the near-equilibrium regime

Solid-state phase transformation kinetics in the near-equilibrium regime behaves differently from that in extremely non-equilibrium regime since their thermodynamic states are different. Incorporating temperature- and transformed fraction-dependent thermodynamic terms, a thermo-kinetic model is derived to describe the transformation kinetics in the near-equilibrium regime. The model predicts a sluggish stage in isothermally conducted transformation and a temperature-dependent stage in non-isothermally conducted transformation. Then, the kinetics of γ/α transformations in two binary substitutional Fe-based alloys (i.e. Fe-3.28 at.% Mn and Fe-1.73 at.% Co), measured by isothermal and non-isothermal dilatometry, is investigated by the newly proposed model. The model quantitatively describes the retarded isothermal kinetics in Fe-3.28 at.% Mn alloy and the abnormal non-isothermal kinetics in Fe-1.73 at.% Co alloy.

Complex nanoprecipitate structures induced by irradiation in immiscible alloy systems

We investigate the fundamentals of compositional patterning induced by energetic particle irradiation in model $A\ensuremath{-}B$ substitutional binary alloys using kinetic Monte Carlo simulations. The study focuses on a type of nanostructure that was recently observed in dilute Cu-Fe and Cu-V alloys, where precipitates form within precipitates, a morphology that we term ``cherry-pit'' structures. The simulations show that the domain of stability of these cherry-pit structures depends on the thermodynamic and kinetic asymmetry between the $A$ and $B$ elements. In particular, both lower solubilities and diffusivities of $A$ in $B$ compared to those of $B$ in $A$ favor the stabilization of these cherry-pit structures for $A$-rich average compositions. The simulation results are rationalized by extending the analytic model introduced by Frost and Russell for irradiation-induced compositional patterning so as to include the possible formation of pits within precipitates. The simulations indicate also that the pits are dynamical structures that undergo nearly periodic cycles of nucleation, growth, and absorption by the matrix.

An extended analytical model for solid-state phase transformation upon continuous heating and cooling processes: Application in γ/α transformation

An extended analytical model is derived for non-isothermal solid-state phase transformation assuming interface-controlled growth mode, e.g. polymorphic or allotropic transformation. In the modeling, incorporation of thermodynamic factor into kinetics of nucleation and growth is performed, so that the model can be used to describe the transformation occurring either near or far from the equilibrium state. Furthermore, the effect of the initial transformation temperature is included through a special treatment for the “temperature integral”, so that the model can be used to depict the transformation during either continuous heating or continuous cooling. Numerical calculations demonstrate that the extended analytical model is accurate enough for practical use. On this basis, a general rate equation for non-isothermal (isochronal heating and cooling) transformation is derived. Applying the present model, the overall kinetic behavior of γ/α transformation in binary substitutional Fe-based alloys (e.g. Fe–Mn and Fe–Cu) upon cooling, measured by dilatometry, is described successfully. Compared with previous work, where a site saturation assumption is generally made, the prevalence of continuous nucleation deduced using the present model prediction seems more reasonable.

ELECTRONIC TRANSPORT IN METALLIC SYSTEMS AND GENERALIZED KINETIC EQUATIONS

This paper reviews some selected approaches to the description of transport properties, mainly electroconductivity, in crystalline and disordered metallic systems. A detailed qualitative theoretical formulation of the electron transport processes in metallic systems within a model approach is given. Generalized kinetic equations which were derived by the method of the nonequilibrium statistical operator are used. Tight-binding picture and modified tight-binding approximation (MTBA) were used for describing the electron subsystem and the electron-lattice interaction correspondingly. The low- and high-temperature behavior of the resistivity was discussed in detail. The main objects of discussion are nonmagnetic (or paramagnetic) transition metals and their disordered alloys. The choice of topics and the emphasis on concepts and model approach makes it a good method for a better understanding of the electrical conductivity of the transition metals and their disordered binary substitutional alloys, but the formalism developed can be applied (with suitable modification), in principle, to other systems. The approach we used and the results obtained complements the existent theories of the electrical conductivity in metallic systems. The present study extends the standard theoretical format and calculation procedures in the theories of electron transport in solids.

Pressure-induced phase transition of Bi2Te3to a bcc structure

The pressure-induced phase transition of bismuth telluride, Bi2Te3, has been studied by synchrotron x-ray diffraction measurements at room temperature using a diamond-anvil cell (DAC) with loading pressures up to 29.8 GPa. We found a high-pressure body-centered cubic (bcc) phase in Bi2Te3 at 25.2 GPa, which is denoted as phase IV, and this phase apperars above 14.5 GPa. Upon releasing the pressure from 29.8 GPa, the diffraction pattern changes with pressure hysteresis. The original rhombohedral phase is recovered at 2.43 GPa. The bcc structure can explain the phase IV peaks. We assumed that the structural model of phase IV is analogous to a substitutional binary alloy; the Bi and Te atoms are distributed in the bcc-lattice sites with space group Im-3m. The results of Rietveld analysis based on this model agree well with both the experimental data and calculated results. Therefore, the structure of phase IV in Bi2Te3 can be explained by a solid solution with a bcc lattice in the Bi-Te (60 atomic% tellurium) binary system.

Continuum simulations of the formation of Kirkendall-effect-induced hollow cylinders in a binary substitutional alloy

We examine binary substitutional diffusion in cylindrical diffusion couples in which free surfaces are considered explicit vacancy sources and sinks. The central region of the cylinder is initially occupied by an atomic species with a larger hop frequency, while the outer region is occupied by another atomic species with a smaller hop frequency. Equilibrium vacancy concentration is maintained at free surfaces that serve as vacancy sources and sinks. In the crystal, diffusion is governed by the standard diffusion equations with analytically evaluated diffusion coefficients. The void growth dynamics and hollow cylinder formation stemming from the Kirkendall effect are simulated. Our results show that the Kirkendall void growth involves two competing factors. One is the net inward vacancy flux that favors void growth. The other is the Gibbs–Thomson effect that favors void shrinkage. We compute the critical initial radius for void growth above which the Kirkendall effect dominates over the Gibbs–Thomson effect. The fully grown void radius and the elapsed time to the fully grown size are also predicted for different fast-diffuser volume fractions and fast-to-slow diffuser atomic hop frequency ratios.

Substitutional diffusion and Kirkendall effect in binary crystalline solids containing discrete vacancy sources and sinks

We investigate vacancy-mediated diffusion in a binary substitutional alloy by explicitly accounting for discrete vacancy sources and sinks. The regions between sources and sinks are treated as binary crystals with a perfect lattice structure containing a dilute concentration of vacancies. The sources and sinks are assumed ideal, maintaining an equilibrium vacancy concentration in their immediate vicinity. Diffusion within the perfect lattice is described with a diffusion-coefficient matrix determined by kinetic Monte Carlo simulations for a binary, thermodynamically ideal alloy in which the components have different vacancy-exchange frequencies. Continuum simulations are performed for diffusion couples with discrete grain boundaries acting as vacancy sources and sinks. Effective grain coarsening due to the Kirkendall effect is observed even in the absence of Gibbs-Thomson driving forces. As in standard ternary systems, uphill diffusion is observed. We also find that the drift of the lattice frame of reference as a result of the Kirkendall effect increases with the source/sink density. Upon increasing the density of vacancy sources and sinks, we recover the conventional treatment of substitutional diffusion, which assumes a dense and uniform distribution of vacancy sources and sinks that maintain an equilibrium vacancy concentration throughout the solid. The inverse Kirkendall effect, where the slower component segregates at grain boundaries acting as vacancy sinks, is also observed in the simulations.

Effect of stress on the diffusion-controlled dissolution of a spherical particle

The diffusion-controlled dissolution of a spherical particle consisting in two epitaxially stressed solid phases of a substitutional binary alloy in contact with an undersaturated solution is investigated. A linear stability analysis of the solid-liquid interface demonstrates that a morphological instability of the particle may occur due to the epitaxial stress generated by the spherical precipitate embedded in the solid matrix, the liquid pressure being neglected. The critical radius of the particle below which the interface is unstable is determined and the conditions for the roughness development are discussed.

Order-disorder effects on the equation of state for fccNi−Alalloys

Order-disorder effects on equation of state (EOS) properties of substitutional binary alloys are investigated with the cluster variation method (CVM) based on ab initio effective cluster interactions (ECI). Calculations are applied to the fcc based $$system. Various related quantities are shown to vary with concentration around stoichiometry with a surprising ``W shape,'' such as the thermal expansion coefficient, the heat capacity, and the Gr\"uneisen parameter, due to configurational ordering effects. Analysis shows that this feature originates from the dominated behavior of some elements of the inverse of Hessian matrix, and relates to antisite defects occurring around stoichiometric compositions. This kind of strong compositional effects on EOS properties highlights the importance of subtle thermodynamic behavior of order-disorder systems.

Construction of radiation-modified phase diagrams under cascade-producing irradiation: application to Zr–Nb alloy

A general theoretical formalism developed for the description of phase stability alteration in substitutional binary alloys under irradiation is applied to Zr–Nb alloys. We examine the stability of β-Nb precipitates in Zr–Nb alloy subjected to the cascade-producing irradiation. The results of phase stability studies are presented in the form of radiation-modified phase diagram. Evolution of large precipitates (as compared to the size of cascade region) differs from that of small precipitates. In the radiation-modified phase diagram there exists a low temperature boundary for stability of large precipitates, the location of which depends on interface type and displacement rate. Above this boundary large precipitates coarsen with radiation-enhanced rate. Below it the alloy is maintained in a quasi-steady-state of supersaturated solid solution with a population of fine-grained precipitates. The competition between processes of cascade destruction; nucleation and growth of coherent precipitates; and coherency loss can lead to the formation of the distribution of fine-grained precipitates with slowly varying parameters. In particular, such a distribution may form in Zr–Nb alloys under thermal reactor conditions.