Helena Zapolsky

Atom probe analyses and numerical calculation of ternary phase diagram in Ni-Al-V system

Abstract The ternary phase diagram in the Ni-Al-V system is studied using three dimensional atom probe (3DAP) analyses and numerical calculations using a mean-field model. Our focus is on the Ni-rich corner of the isothermal section at 800°C of the ternary phase diagram, where disordered f.c.c. matrix coexists with the L12 and DO22 ordered phases. Both the experimental measurements and numerical calculations showed that the equilibrium compositions of the coexisting phases are quite different from those predicted by published phase diagrams. It is demonstrated that the aluminium and vanadium compositions in the L12 phase are approximately the same, and there is more aluminium in the disordered matrix than that indicated in the existing phase diagram. A possible explanation of this disagreement is discussed.

A phase field model for snow crystal growth in three dimensions

Snowflake growth provides a fascinating example of spontaneous pattern formation in nature. Attempts to understand this phenomenon have led to important insights in non-equilibrium dynamics observed in various active scientific fields, ranging from pattern formation in physical and chemical systems, to self-assembly problems in biology. Yet, very few models currently succeed in reproducing the diversity of snowflake forms in three dimensions, and the link between model parameters and thermodynamic quantities is not established. Here, we report a modified phase field model that describes the subtlety of the ice vapour phase transition, through anisotropic water molecules attachment and condensation, surface diffusion, and strong anisotropic surface tension, that guarantee the anisotropy, faceting and dendritic growth of snowflakes. We demonstrate that this model reproduces the growth dynamics of the most challenging morphologies of snowflakes from the Nakaya diagram. We find that the growth dynamics of snow crystals matches the selection theory, consistently with previous experimental observations.Spontaneous patterns: Simulating snowflakes with a softer touchA model that reproduces complex 3D snowflake growth using versatile interface descriptors may benefit other dendritic materials. Snow crystals solidify by expanding outward from an initial seed, capturing water molecules as they travel through the atmosphere. While most simulation methods treat this growing interface as a sharp boundary, Gilles Demange and colleagues from the University of Rouen in France report that a less rigid approach yields highly realistic results. Their technique uses a phase field model to represents the snowflake’s surface as a thin moveable layer where ice and vapour mix, and a new surface tension function to explain the anisotropic crystallisation. Including a special algorithm to simulate 3D crystal faceting enabled the model to duplicate essential snowflake morphologies and potentially predict ice water content in clouds under various weather conditions.

Statistical Thermodynamics and Ordering Kinetics of D019-Type Phase: Application of the Models for H.C.P.-Ti–Al Alloy

Using the self-consistent field approximation, the static concentration waves approach and the Onsager-type kinetics equations, the descriptions of both the statistical thermodynamics and the kinetics of an atomic ordering of D019 phase are developed and applied for h.c.p.-Ti–Al alloy. The model of order–disorder phase transformation describes the phase transformation of h.c.p. solid solution into the D019 phase. Interatomic-interaction parameters are estimated for both approximations: one supposes temperature-independent interatomic-interaction parameters, while the other one includes the temperature dependence of interchange energies for Ti–Al alloy. The partial Ti–Al phase diagrams (equilibrium compositions of the coexistent ordered α2-phase and disordered α-phase) are evaluated for both cases. The equation for the time dependence of D019- type long-range order (LRO) parameter is analyzed. The curves (showing the LRO parameter evolution) are obtained numerically for both temperature-independent interaction energies and temperature-dependent ones. Temperature dependence of the interatomic-interaction energies accelerates the LRO relaxation and diminishes a spread of the values of instantaneous and equilibrium LRO parameters versus the temperature. Both statistical-thermodynamics and kinetics results show that equilibrium LRO parameter for a non-stoichiometry (where an atomic fraction of alloying component is more than 0.25) can be higher than for a stoichiometry at high temperatures. The experimental phase diagram confirms the predicted (ordered or disordered) states for h.c.p.-Ti– Al.

Kinetics of cubic-to-tetragonal transformation in Ni–V–X alloys

Computer simulations based on the Khachaturyans Onsager diffusion equation have been performed to model microstructure evolution during the cubic-to-tetragonal transformation in Ni-based alloys. A 2D model was employed. The fcc-DO22 ordering has been studied as a model case of this type of transformation. Particular emphasis is placed on the formation mechanism of DO22 monovariant structures. Computer simulations demonstrate that strain-induced interactions between coherent DO22 precipitates lead to the formation of intermediate two-variant chessboard-like structures, which are found to be unstable and coalesce into subsequent single-variant maze structures. It is shown that the stability of the chessboard-like structures is very sensitive to lattice misfits. These simulation results are in good agreement with TEM observations.

Atomic Density Function Simulations of Crystal Growth Kinetics of FCC Crystal and BCC-FCC Transition

Spontaneous self-assembling of interacting atoms prototyping crystallization and reconstructive phase transitions in crystalline state is discussed in terms of Atomic Density Function (ADF) theory. It is demonstrated that a multi-mode potential can reproduce any crystal structure. 3D computer modeling of formation of the FCC crystal and crystal lattice rearrangement in the FCCàBCC transformation is presented.