Search

The phase separation behaviors from the single B2 ordered phase into the two separate B2 and L2$_1$ ordered phases in the X-Al-Ti (X: Fe, Co, and Ni) alloys are analyzed using the cluster variation method (CVM) with the interaction energies evaluated from the electronic band structure calculations. The cubic approximation of the CVM is employed for the X$_2$Al$_{2-x}$Ti$_x$ ($0 \leq x \leq 2$) alloys limiting an interchange between Al and Ti atoms on the $\alpha$- and $\beta$-sublattices of the L2$_1$ ordered structure with the X atoms fixed on the $\gamma$-sublattice. The phase stabilities of the B2 and L2$_1$ structures are examined, and the phase diagrams at the pseudo-binary section, XAl-XTi, are determined. The two-phase regions of B2 and L2$_1$ phases, i.e., phase separation behavior, are successfully produced in both Co- and Ni-Al-Ti alloy systems, whereas no phase separation is predicted in the Fe-Al-Ti alloy. The origin of the phase separation in the Co- and Ni-Al-Ti alloys is, respectively, attributed to the mechanical instability and the combination of mechanical instability and chemical repulsions of unlike pairs., Comment: 8 pages, 5 figures

Cluster variation method (CVM) and path probability method (PPM) have generally been employed to study replacive phase transitions in alloy systems. Recently, displacive phase transitions have been explored within the realm of replacive phase transition in the CVM theoretical framework by viewing displaced atoms as different atomic species, i.e., by converting a freedom of atomic displacement to a configurational freedom. The same methodology is applied to the PPM calculations in this work, and the kinetics of displacive phase transition from tetragonal to cubic phases in ZrO2 are investigated as well as their equilibrium states., Comment: 5 pages, 4 figures

The path probability method (PPM), which is a natural extension of the cluster variation method (CVM) to a time domain, has been employed in a relaxation process of atomic configurations in alloy systems. Although the vacancy mechanism is the main atomic migration process in an alloy system, most studies of PPM have used the spin flipping mechanism (or the direct exchange mechanism) because of the huge computational burden imposed by the vacancy mechanism. In this paper the computational problem is circumvented by treating various path variables in the PPM as cluster probabilities in the CVM, and the vacancy mechanism is explicitly taken into account in the theoretical framework. The method is employed to explore the relaxation process in a Ni3Al ordered phase within the tetrahedron approximation, and the effect of vacancy concentration is investigated., Comment: 6 pages, 4 figures

The continuous displacement cluster variation method (CDCVM) has introduced local atomic displacements into the theoretical framework of the cluster variation method (CVM) by viewing an atom displaced from a Bravais lattice point as a particular atomic species located at the lattice point. This idea of conversion from a freedom of local displacements into configurational freedom is extended in this paper to magnetic freedoms. Various magnitudes of local magnetic moments are considered, as well as two spin directions, on up-spins and down-spins. The approach is applied to pure Ni and its Curie temperature is explored with the entropy formula of the tetrahedron approximation in the CVM, using the first-nearest-neighbor pair interaction energies extracted from the total energies of various spin configurations, which are estimated from electronic-structure calculations., Comment: 18 pages, 10 figures

Extending previous work [T. Pusztai, L. R\'atkai, A. Sz\'all\'as, and L. Gr\'an\'asy, Phys. Rev. E {\bf 87}, 032402 (2013)], we have studied the formation of eutectic dendrites in a model ternary system within the framework of the phase-field theory. We have mapped out the domain in which two-phase dendritic structures grow. With increasing pulling velocity, the following sequence of growth morphologies is observed: flat front lamellae $\rightarrow$ eutectic colonies $\rightarrow$ eutectic dendrites $\rightarrow$ dendrites with target pattern $\rightarrow$ partitionless dendrites $\rightarrow$ partitionless flat front. We confirm that the two-phase and one-phase dendrites have similar forms, and display a similar scaling of the dendrite tip radius with the interface free energy. It is also found that the possible eutectic patterns include the target pattern, and single- and multiarm spirals, of which the thermal fluctuations choose. The most probable number of spiral arms increases with increasing tip radius and with decreasing kinetic anisotropy. Our numerical simulations confirm that in agreement with the assumptions of a recent analysis of two-phase dendrites [S. Akamatsu, S. Bottin-Rousseau, G. Faivre, and E. A. Brener, Phys. Rev. Lett. {\bf 112}, 105502 (2014)], the Jackson-Hunt scaling of the eutectic wavelength with pulling velocity is obeyed in the parameter domain explored, and that the natural eutectic wavelength is proportional to the tip radius of the two-phase dendrites. Finally, we find that it is very difficult/virtually impossible to form spiraling two-phase dendrites without anisotropy, an observation that seems to contradict the expectations of Akamatsu {\it et al.}. Yet, it cannot be excluded, that in isotropic systems two-phase dendrites are rare events difficult to observe in simulations., Comment: For more informations and videos, please visit our website: http://phasefield.hu/spiral_eutectic_dendrites Previous paper: arXiv:1302.4884