Investigating gas-phase defect formation in late-stage solidification using a novel phase-field crystal alloy model

Nan Wang, Nathan Smith, and Nikolas Provatas

Phys. Rev. Materials 1, 043405 – Published 28 September 2017

Abstract

We study late-stage solidification and the associated formation of defects in alloy materials using a novel model based on the phase-field-crystal technique. It is shown that our model successfully captures several important physical phenomena that occur in the late stages of solidification, including solidification shrinkage, liquid cavitation and microsegregation, all in a single framework. By examining the interplay of solidification shrinkage and solute segregation, this model reveals that the formation of gas pore defects at the late stage of solidification can lead to nucleation of second phase solid particles due to solute enrichment in the eutectic liquid driven by gas-phase nucleation and growth. We also predict a modification of the Gulliver-Scheil equation in the presence of gas pockets in confined liquid pools.

Received 11 May 2017

DOI:https://doi.org/10.1103/PhysRevMaterials.1.043405

Physics Subject Headings (PhySH)

Defects

Alloys

Phase-field modeling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Nan Wang, Nathan Smith, and Nikolas Provatas

Department of Physics, McGill University, Montreal, Québec, Canada H3A 2T8

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Issue

Vol. 1, Iss. 4 — September 2017

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Images

Figure 1
Basic thermodynamic properties of PFC model. Here $c$ and $n_{o}$ refer to mean concentration and mean density, respectively. (a) Numerical phase diagram showing two solid phases $α$ and $β$ and a liquid phase $L$ . (b) Demonstration of liquid $\to$ liquid-vapour transition in eutectic liquid $(c = 0.5)$ with temperature $(ε)$ . This transition in a liquid is a path to cavitation of the liquid. (c) and (d) Demonstration of $α$ -liquid (c) and $β$ -liquid (d) coexistence region at a given concentration, where solid and liquid state free energies are shown with dashed and solid lines, respectively. Model parameters used in this work are $W_{1} = 1.3, W_{2} = 0.6, α = 8.0, B_{x 1} = 0.3, B_{x 2} = 0.9, q_{1} = \sqrt{2}, q_{2} = 1, u_{1} = 6.0, v_{1} = 3.0, c_{0} = 0.5, a_{1} = 43, b_{1} = - 30, c_{1} = 90$ , and $λ = λ_{c} = 0.04$ .
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Figure 2
Pressure drop in liquid due to solidification shrinkage. Pressure change is plotted along the horizontal line shown in the inset as a function of position $(x)$ in the liquid. $x / a$ measures the distance from reference liquid reservoir. The green vertical dashed line indicates the position where $f_{l} = 0$ . In the inset, $S$ refers to solid and $L$ to liquid. Numerical dimensions are given in the text. Other model parameters are given in Fig. 1.
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Figure 3
(a) Peak pressure drop ahead of the interface as a function of solidification velocity. (b) Pressure drop as a function of shrinkage factor $\bar{β}$ . $P_{0}$ is the liquid pressure far from the solid. The green dashed lines are to guide the eye. Model parameters are given in Fig. 2.
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Figure 4
Solute segregation in eutectic liquid channel with (red curve) and without (green curve) gas-phase formation in late-stage solidification. The top left inset figure corresponds to the top (green) data. The bottom right inset figure corresponds to the bottom (red) data. The color fields in the inset figures show the density configuration of the system corresponding to the highest concentration of of each curve. Solid phase has the highest density and is colored as bright yellow. Gas phase has the lowest density and is colored as dark blue. Liquid is colored as dark yellow. Solid, liquid, and gas phases are labeled using letters S, L, G, respectively. The simulations start with $f_{L} = 0.06, c_{L} = 0.15$ and liquid density $ρ_{L} / ρ_{S} = 1.0$ for the bottom line, $ρ_{L} / ρ_{S} = 0.85$ for the top line. Cooling rate $ε / t = 10^{- 6}$ . Solute concentration is averaged over the liquid.
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Figure 5
Liquid cavitation promoting the nucleation and growth of the high concentration solid phase. (a)–(d) are average density maps. (a) Liquid pool confined in a low concentration solid $α$ phase. The solid and the liquid regions are marked by S and L, respectively. (b) Cavitation of the liquid triggers the nucleation of the high concentration solid $β$ phase. (c) Subsequent growth of the high concentration $β$ solid and associated deformation of the remaining gas pocket. (d) A second nucleation event occurs to the left of the gas pocket toward the end of the simulation sequence. (e) Solute concentration map of (d). The color bar to the right shows the concentration scale. (f) Microscopic PFC order parameter (density) field showing different solid structures for the triple-phase region in the inset box of frame (d). Small dark dots in the solid seen in (b)–(d) are dislocations formed during solidification. The starting configuration is a separate liquid pool of size $R = 30 a$ with $ρ_{L} / ρ_{S} = 0.85, c_{L} = 0.3$ , and $c_{S} = 0.07$ . The system is quenched below eutectic point $(ε = 0.2)$
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