Combining phase field crystal methods with a Cahn-Hilliard model for binary alloys

During phase transitions certain properties of a material change, such as composition field and lattice-symmetry distortions. These changes are typically coupled, and affect the microstructures that form in materials. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model describing the composition field of a material system, with a phase field crystal (PFC) model describing its underlying microscopic configurations. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method, to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square lattice symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse composition phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process.Comment: 9 pages, 5 figure

Quantified Uncertainty in Thermodynamic Modeling for Materials Design

Phase fractions, compositions and energies of the stable phases as a function of macroscopic composition, temperature, and pressure (X-T-P) are the principle correlations needed for the design of new materials and improvement of existing materials. They are the outcomes of thermodynamic modeling based on the CALculation of PHAse Diagrams (CALPHAD) approach. The accuracy of CALPHAD predictions vary widely in X-T-P space due to experimental error, model inadequacy and unequal data coverage. In response, researchers have developed frameworks to quantify the uncertainty of thermodynamic property model parameters and propagate it to phase diagram predictions. In previous studies, uncertainty was represented as intervals on phase boundaries (with respect to composition) or invariant reactions (with respect to temperature) and was unable to represent the uncertainty in eutectoid reactions or in the stability of phase regions. In this work, we propose a suite of tools that leverages samples from the multivariate model parameter distribution to represent uncertainty in forms that surpass previous limitations and are well suited to materials design. These representations include the distribution of phase diagrams and their features, as well as the dependence of phase stability and the distributions of phase fraction, composition activity and Gibbs energy on X-T-P location - irrespective of the total number of components. Most critically, the new methodology allows the material designer to interrogate a certain composition and temperature domain and get in return the probability of different phases to be stable, which can positively impact materials design

Identifying the Onset of Phase Separation in Quaternary Lipid Bilayer Systems from Coarse-Grained Simulations

Understanding the (de)mixing behavior of multicomponent lipid bilayers is an important step towards unraveling the nature of spatial composition heterogeneities in cellular membranes and their role in biological function. We use coarse-grained molecular dynamics simulations to study the composition phase diagram of a quaternary mixture of phospholipids and cholesterol. This mixture is known to exhibit both uniform and coexisting phases. We compare and combine different statistical measures of membrane structure to identify the onset of phase coexistence in composition space. An important element in our approach is the dependence of composition heterogeneities on the size of the system. While homogeneous phases can be structured and display long correlation lengths, the hallmark behavior of phase coexistence is the scaling of the apparent correlation length with system size. Because the latter cannot be easily varied in simulations, our method instead uses information obtained from observation windows of different sizes to accurately distinguish phase coexistence from structured homogeneous phases. This approach is built on very general physical principles, and will be beneficial to future studies of the phase behavior of multicomponent lipid bilayers

Comparison of the Magnetic properties of Mn3Fe2Si3O12 as a crystalline garnet and as a glass

The crystalline garnet Mn3Fe2Si3O12 and an amorphous phase of the same nominal composition are synthesized at high pressure. The magnetic properties of the two forms are reported. Both phases order antiferromagnetically. The crystalline phase exhibits a Curie-Weiss theta of -47.2 K, with a sharp ordering transition at 12 K. The glassy phase exhibits a larger antiferromagnetic Curie-Weiss theta, of -83.0 K, with a broad ordering transition observed at 2.5 K. Both phases can be classified as magnetically frustrated, although the amorphous phase shows a much higher degree of frustration. The amorphous phase exhibits spin-glass behavior and is determined to have an actual composition of Mn3Fe2Si3O13.Comment: 14 pages, 7 figures, 2 table

The thermodynamic properties of the wustite phase are studied

Study of the precise location of the wustite phase boundaries and the dependence of the partial pressure of oxygen on the temperature and composition of the solid phase was made. From the pressure of oxygen, the temperature and the composition thermodynamic quantities can be determined

Inclusions induced phase separation in mixed lipid film

The effect of rigid inclusions on the phase behavior of a film containing a mixture of lipid molecules is investigated. In the proposed model, the inclusion-induced deformation of the film, and the resulting energy cost are strongly dependent upon the spontaneous curvature of the mixed film. The spontaneous curvature is in turn strongly influenced by the composition of film. This coupling between the film composition and the energy per inclusion leads to a lateral modulation of the composition, which follows the local curvature of the membrane. In particular, it is shown that the inclusion may induce a global phase separation in a film which would otherwise be homogeneously mixed. The mixed film is then composed of patches of different average composition, separated by the inclusions. This process may be of relevance to explain some aspects of lipid-protein association in biological membranes.Comment: 19 pages, 5 figure

An Effective Method to Estimate Composition Amplitude of Spinodal Decomposition for Atom Probe Tomography Validated by Phase Field Simulations

Reasonable evaluation of composition amplitude in spinodal decomposition is a challenge to microanalysis of atom probe tomography, especially at early stages when phase separation is not prominent. This impedes quantitative analysis of spinodal structure in atom probe tomography as well as comparison with simulated results from phase field simulations. We hereby report an effective method to estimate the composition amplitude by constructing an amplitude density spectrum. This method can sensitively determine the composition amplitude at early stages. In particular, it substantially bridges experimental and simulation techniques comprising both discrete and continuum data in the study of spinodal decomposition. Moreover, it was found that the commonly adopted Langer-Bar-on-Miller method for atom probe analysis underestimates the composition amplitude of spinodal decomposition. Case studies have been performed on the Fe-Cr binary alloys.Comment: 5 pages, 4 figure

Exploration of the High Entropy Alloy Space as a Constraint Satisfaction Problem

High Entropy Alloys (HEAs), Multi-principal Component Alloys (MCA), or Compositionally Complex Alloys (CCAs) are alloys that contain multiple principal alloying elements. While many HEAs have been shown to have unique properties, their discovery has been largely done through costly and time-consuming trial-and-error approaches, with only an infinitesimally small fraction of the entire possible composition space having been explored. In this work, the exploration of the HEA composition space is framed as a Continuous Constraint Satisfaction Problem (CCSP) and solved using a novel Constraint Satisfaction Algorithm (CSA) for the rapid and robust exploration of alloy thermodynamic spaces. The algorithm is used to discover regions in the HEA Composition-Temperature space that satisfy desired phase constitution requirements. The algorithm is demonstrated against a new (TCHEA1) CALPHAD HEA thermodynamic database. The database is first validated by comparing phase stability predictions against experiments and then the CSA is deployed and tested against design tasks consisting of identifying not only single phase solid solution regions in ternary, quaternary and quinary composition spaces but also the identification of regions that are likely to yield precipitation-strengthened HEAs.Comment: 14 pages, 13 figure

Composition-tuned smeared phase transitions

Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. In this paper, we study such smeared phase transitions (both classical and quantum) in substitutional alloys A$_{1-x}$B$_x$ that can be tuned from an ordered phase at composition $x=0$ to a disordered phase at $x=1$. We show that the ordered phase develops a pronounced tail that extends over all compositions $x<1$. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also compare our results to computer simulations of a toy model, and we discuss experiments.Comment: 6 pages, 4 eps figures included, final version as publishe