Abstract
To design tailored materials, it is highly desirable to predict microstructures of alloys without empirical parameter. Phase field models (PFMs) rely on parameters adjusted to match experimental information, while first-principles methods cannot directly treat the typical length scale of 10 μm. Combining density functional theory, cluster expansion theory and potential renormalization theory, we derive the free energy as a function of compositions and construct a parameter-free PFM, which can predict microstructures in high-temperature regions of alloy phase diagrams. Applying this method to Ni-Al alloys at 1027 °C, we succeed in reproducing evolution of microstructures as a function of only compositions without thermodynamic empirical parameter. The resulting patterns including cuboidal shaped precipitations are in excellent agreement with the experimental microstructures in each region of the Ni-Al phase diagram. Our method is in principle applicable to any kind of alloys as a reliable theoretical tool to predict microstructures of new materials.
Highlights
To design tailored materials, it is highly desirable to predict microstructures of alloys without empirical parameter
Phase field models (PFMs)[2,3,4] offer a promising computational tool to study such phenomena, where microstructures are described by order parameters
Our method is in principle applicable to any kind of alloys, we demonstrate its ability by treating Ni–Al binary alloys as an example, which have attracted considerable attention for their excellent mechanical properties; very hard and good oxidation- and heat-resistances suitable for turbine disks and blades[12,13]
Summary
The first-principles free energy and the diffusion equation. The resulting local free energies F(φNi, φAl) are shown in Figs. 2 and 3, and are plotted in 1D and 2D in Fig. 4a, b. The particle size decreases with increasing Ni concentration and the microstructure becomes almost homogeneous for Ni 35.5% (Fig. 5f) as we enter region II. In region VII, rectangular Ni particles are formed in the Ni3Al matrix from the Ni-rich seeds of the input structure. For higher Ni concentrations, the particle size reduces and the microstructure disappears forming a uniform phase in the region; see Figs. Disscussion To understand the growth mechanism of the microstructures from the initial pattern, we plot the change in local concentration and the local free energy at various time steps, as shown in Supplementary Fig. 1a, b for Ni 60%. We plot the magnitude of the free energy gradient (|∇F|), which corresponds to the local stress of the system at each grid point in Supplementary Fig. 1c. >Ni 80%: Ni3Al precipitates in pure Ni4 matrix containing small Ni3Al particles VIII Single-phase region
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