Spinodal Gaps Research Articles

Oxygen-assisted spinodal structure achieves 1.5 GPa yield strength in a ductile refractory high-entropy alloy

Refractory high-entropy alloys (RHEAs) with room-temperature ductility are drawing growing attention for potential high-temperature applications. However, the most widely used metallurgical mechanisms appear weak in optimizing their strength and ductility. Here, we report that the nanoscale spinodal structure in Ti41V27Hf15Nb15O2 leads to the highest tensile yield strength (∼1.5 GPa) among the existing RHEAs and good elongation of ∼12%. With the aid of thermodynamic calculations, we show that oxygen plays a dominant role in controlling the formation of the spinodal structure by influencing the spinodal gap of the Ti-V-Hf-Nb system. Exploring the atomic structure of the spinodal structure (β + β*), we showed that the large lattice misfit of the spinodal phases is mainly responsible for the excellent strengthening effect while the planar to wavy dislocation glide mode transition accounts for the retained ductility. This work provides a novel strategy to improve the mechanical properties of the RHEAs and deepens the understanding of their phase stabilities.

Analysis of the dependence of spinodal decomposition in nanoparticles on boundary reaction rate and free energy of mixing

The mathematical model for intercalation dynamics in phase-separating materials (Singh et al., 2008) is a powerful tool for the investigation of the spinodal decomposition in nanoparticles. By means of this model, we conduct a careful mathematical analysis of the intercalation dynamics in nanoparticles to study the dependence of spinodal gap on the boundary reaction rate and the particle size, which can be used for LiFePO4 battery material application. Consistent with previous investigations, we found that for some range of the boundary reaction rate and the particle size the concentration spinodal gap is not continuous, but it has stable “islands” where no spinodal decomposition is expected. The new important observation is that the presence of an infinitesimally small boundary reaction rate will destabilize nanoparticles even for infinitesimal length. In particular for nanoparticles having the size of order or less than interphase width λ, the spontaneous charge or discharge will occur at the reaction rate of order 0.1 D/λ. The further raise of the intercalation rate will stabilize the system until some size limit of order two diffusion length. The intercalation effects are proven by means of numerical simulations. We also show that the increasing enthalpy of the spinodal mixture as well as increasing elastic energy due to the lattice misfit can destabilize the particles and increase the spinodal gap.

Erratum to: Thermodynamic coupling between gradient elasticity and a Cahn–Hilliard type of diffusion: size-dependent spinodal gaps

Erratum to: Thermodynamic coupling between gradient elasticity and a Cahn–Hilliard type of diffusion: size-dependent spinodal gaps

Thermodynamic coupling between gradient elasticity and a Cahn–Hilliard type of diffusion: size-dependent spinodal gaps

In the electrode materials of lithium ion batteries, the large variations of Li concentration during the charge and discharge processes are often accompanied by phase separations to lithium-rich and lithium-poor states. In particular, when the composition of the material moves into the spinodal region (linearly unstable uniform compositions) or into the miscibility gap (metastable uniform compositions), it tends to decompose spontaneously under composition fluctuations. If the lattice mismatch of the two phases is not negligible, coherency strains arise affecting the decomposition process. Furthermore, when the dimensions of a specimen or a grain reduce down to the nanometer level, the phase transition mechanisms are also substantially influenced by the domain size. This size effect is interpreted in the present article by developing a thermodynamically consistent model of gradient elastodiffusion. The proposed formulation is based on the coupling of the standard Cahn–Hilliard type of diffusion and a simple gradient elasticity model that includes the gradient of volumetric strain in the expression of the Helmholtz free energy density. An initial boundary value problem is derived in terms of concentration and displacement fields, and linear stability analysis is employed to determine the contribution of concentration and strain gradient terms on the instability leading to spinodal decomposition. It is shown that the theoretical predictions are in accordance with the experimental trends, i.e., the spinodal concentration range shrinks (i.e., the tendency for phase separation is reduced) as the crystal size decreases. Moreover, depending on the interplay between the strain and the concentration gradient coefficients, the spinodal region can be completely suppressed below a critical crystal size. Spinodal characteristic length and time are also evaluated by considering the dominant instability mode during the primary stages of the decomposition process, and it is found that they are increasing functions of the strain gradient coefficient.

Heat Treatment of Duplex Stainless Steel 2205 by Inserting Nano Nd2FeB14 in HIP Manifolds Under the Scope of Category Theory

In this paper, improving mechanical properties of duplex stainless steel by spinodal reaction inhibitors has been discussed. Spinodal gaps can be minimized when the host particles are minimized to the nanoscale. The Cahn-Hilliard Equation and the Allen-Cahn Equation on Manifolds with Conical Singularities can be related to manifolds produced by hot isostatic pressing (PM HIP) are used to improve mechanical strength. Spinodal reactions will be Inhibited by magnetic treatment and Nd-Fe-B Magnets. Grain refiners will be used to retard spinodal reactions. Mathematically, category theory is used to establish links between these different concepts.

Determination of the phase diagram from interatomic potentials: The iron–chromium case

Prior to applying any interatomic potential, it is important to know the stability of the different phases it describes. In the literature many methods to determine the phase diagram from an interatomic potential are described. Although for pure elements the procedure to obtain the thermodynamic functions is well established, for alloys it is not. In this work a method is developed to determine the phase diagram, i.e., solubility limits and spinodal gap, for the case of miscibility gaps. The method combines Monte Carlo simulations in the isobaric semi-grand canonical ensemble, full thermodynamic integration and Redlich–Kister expansions to parameterize the Gibbs free energy. Besides numerical inaccuracies, this method does not rely on any physical approximations to determine the phase diagram of a given interatomic potential. The method is applied to two different Fe–Cr potentials that are widely used in the literature. The resulting phase diagrams are discussed by comparing them to the experimental one and ones obtained in other works from the same potentials.

MBSSAS: A code for the computation of margules parameters and equilibrium relations in binary solid-solution aqueous-solution systems

The computer code MBSSAS uses two-parameter Margules-type excess-free-energy of mixing equations to calculate thermodynamic equilibrium, pure-phase saturation, and stoichiometric saturation states in binary solid-solution aqueous-solution (SSAS) systems. Lippmann phase diagrams, Roozeboom diagrams, and distribution-coefficient diagrams can be constructed from the output data files, and also can be displayed by MBSSAS (on IBM-PC compatible computers). MBSSAS also will calculate accessory information, such as the location of miscibility gaps, spinodal gaps, critical-mixing points, alyotropic extrema, Henry's law solid-phase activity coefficients, and limiting distribution coefficients. Alternatively, MBSSAS can use such information (instead of the Margules, Guggenheim, or Thompson and Waldbaum excess-free-energy parameters) to calculate the appropriate excess-free-energy of mixing equation for any given SSAS system.