All-proportional solid solution versus two-phase coexistence in the Ti–V alloy by first-principles phase field and SQS methods

Abstract

The microstructures of the Ti–V alloy are studied by purely first-principles calculations without relying on any empirical or experimental parameter. The special quasirandom structure model is employed to treat the all-proportional solid solution $$\beta$$ β phase, while the first-principles phase field method or its variant is employed to treat the coexistence phases. The linearity of the calculated local free energy against the integer Ti$$_n$$ n V$$_m$$ m composition in the cluster expansion method manifests a clear evidence of the solid solution behavior. From a detailed energy comparison, our results are consistent with the experimental fact that the Ti–V alloy is an all-proportional solid solution of the $$\beta$$ β phase at high temperatures and exhibits an $$\alpha +\beta$$ α + β coexistence at low temperatures. Moreover, it is found that mosaic-type microstructures may appear as a metastable phase, as observed by many experiments. The first-principles criterion for the all-proportional solid solution behavior presented in this paper is very general and can be applied to any other binary or multi-component alloys.

Microstructures in Iron-rich FeSi Alloys by First-principles Phase Field and Special Quasirandom Structure Methods

“…As well as the total energy, the resulting local free energy becomes a stepwise function of the concentration, i.e., the number of atoms of each element inside one tetrahedron. The renormalization procedure is the same as our previous papers on the FPPF method, [10][11][12][13][14] which can be done automatically by using the Pipeline Pilot protocol. 11) Denoting the concentration, the chemical potential, the mobility, and the random force, respectively, as ϕ X , μ X , M X , and η for element X, we derive the Cahn-Hilliard equation from ∂ϕ…”

“…For more details, please refer to our previous papers. [10][11][12][13][14] The simulation code is available on the website. 36) It is for the TiV alloy 14) but applicable to the FeSi alloy also.…”

“…[10][11][12][13][14] The simulation code is available on the website. 36) It is for the TiV alloy 14) but applicable to the FeSi alloy also. Data for "in_para" file used in the present FPPF simulation of iron-rich FeSi alloys at 1 050 K is given in Table S1 of Supporting Information.…”

“…In the present paper, we apply two first-principles methods to the iron-rich region of the bcc FeSi alloy to clarify the origin of the zero magnetostriction and low magnetic anisotropy of Fe-6.5 wt% Si. One is the first-principles phase field (FPPF) method [10][11][12][13][14] and the other is the special quasirandom structure (SQS) method. [15][16][17] Both of them have distinct ability of predicting the free energy and microstructure of alloys without relying on any experimental or empirical information.…”

“…[19][20][21] Coincidentally, in the same region, the magnetostriction becomes almost zero, 22,23) which should be compared with the behavior of other compositions. [24][25][26] Recently, we proposed a first-principles criterion 14) whether the alloy behaves as a solid solution using both the FPPF method and the supercell calculations for the purely random configurations generated by the SQS method. Here, we apply the same methods to the FeSi alloy with less than 33 at% Si, focusing mainly on microstructures.…”