Microstructure Formation in Directionally Solidified Pb-Al Alloy

doi:10.11900/0412.1961.2021.00492

Acta Metall Sin

2022, Vol. 58

Issue (8): 1072-1082 DOI: 10.11900/0412.1961.2021.00492

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Microstructure Formation in Directionally Solidified Pb-Al Alloy

LI Yanqiang¹^,², ZHAO Jiuzhou¹^,²(

), JIANG Hongxiang¹^,², HE Jie¹^,²

^1.Shi -changxu Innovation Center for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
^2.School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China

Cite this article:

LI Yanqiang, ZHAO Jiuzhou, JIANG Hongxiang, HE Jie. Microstructure Formation in Directionally Solidified Pb-Al Alloy. Acta Metall Sin, 2022, 58(8): 1072-1082.

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Abstract

Pb is widely used as grid material for lead-acid batteries, an electrowinning electrode and a nuclear radiation shield. To improve the performance of these materials, alloying elements such as Ag, Sb, and Ca are commonly added. Pb's conductivity and strength can be improved using Al as an alloying element. However, the phase diagram of the Pb-Al alloy is characterized by the large liquid-liquid and liquid-solid miscibility gaps. When a homogeneous single-phase Pb-Al liquid is cooled into the miscibility gaps, Al-rich droplets/particles precipitate first from the melt, causing the Pb-Al alloy to form a microstructure with coarse Al-rich particles or serious phase segregation. Understanding the evolution of microstructure in the liquid-solid phase separation has remained a scientific challenge thus far. The solidification of the Pb-Al alloy is investigated using directional solidification experiments in this work. A numerical model is developed to describe the microstructure formation in a directionally solidified liquid-solid phase separation alloy using the population dynamics method. The evolution of the microstructure is simulated. The simulation results agree well with the experimental results. They show that a supercooling zone appears in front of the solidification interface, where the liquid-solid phase separation of the Pb-Al alloy occurs. In this zone, Al-rich particles (dispersed phase) form and grow by solute diffusing as they move toward the solidification interface. The nucleation rate and the number density of Al-rich particles increase as the solidification rate increases, whereas the average radius of the particles decreases. The Al-rich particles' Stokes movement velocity has the same direction as the melt's solidification velocity, resulting in an enrichment of Al-rich particles in front of the solidification interface. Because of the convective flow of the melt in front of the solidification interface, the cooling rate of the melt is unevenly distributed along the radial direction, resulting in an uneven distribution of nucleation rate, number density, and average radius of Al-rich particles. The formation of a solidification microstructure with the dispersive distribution of Al-rich particles is dependent on the solidification rate being fast enough to ensure that all size particles in the liquid-solid phase separation region move toward the solidification interface under the effect of the Stokes movement of Al-rich particles and the convective flow of melt.

Key words: liquid-solid phase separation Pb-Al alloy directional solidification microstructure simulation

Received: 15 November 2021

ZTFLH:

TG111.4

Fund: National Natural Science Foundation of China(51971227);National Natural Science Foundation of China(51771210);China Manned Space Engineering Project

About author: ZHAO Jiuzhou, professor, Tel: (024)23971918, E-mail: jzzhao@imr.ac.cn

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https://www.ams.org.cn/EN/10.11900/0412.1961.2021.00492 OR https://www.ams.org.cn/EN/Y2022/V58/I8/1072

Fig.1 Pb-rich part of the Pb-Al phase diagram (a) and the liquid-solid phase separation process in a directionally solidifying Pb-Al alloy (b) (T—temperature, L_Al—Al-rich liquid phase, S_Al—Al-rich solid phase, L_Pb—Pb-rich liquid phase, S_Pb—Pb-rich solid phase, C₀—initial composition of the alloy, T_s(C₀)—solubility line temperature of initial composition alloy, T_e—eutectic reaction temperature of Al-Pb alloy, rOz—coordinate system, V₀—pulling velocity of samples, g —acceleration of gravity, L—liquid, S—solid)

Fig.2 Experimental (symbols) and calculated (lines) results of the temperature profile in front of the solidification interface along the central z-axes for the Pb-0.15Al alloy solidified at different solidification rates (V₀)

Fig.3 Microstructures of the Pb-0.15Al alloy direction-ally solidified at V₀ = 4 mm/s (a), 7 mm/s (b), and 10 mm/s (c)

Fig.4 2D radius distributions of the Al-rich particles in the Pb-0.15Al alloy directionally solidified at V₀ = 4 mm/s (a), 7 mm/s (b), and 10 mm/s (c)

Fig.5 Average 2D radius (<R>_2D) of the Al-rich particles in the Pb-0.15Al alloys directionally solidified at different V₀

Parameter	Value	Unit
Dynamic viscosity of Pb, $η m$	0.0004636 × exp(1036.7 / T)	Pa·s
Thermal conductivity of liquid Pb, $k m$	15.88	W·m^-1·K^-1
Thermal conductivity of Al₂O₃ crucible, $k c r u$	10	W·m^-1·K^-1
Density of liquid Pb, $ρ m$	10678	kg·m^-3
Density of solid Al, $ρ β$	2700	kg·m^-3
Specific heat of liquid Pb, $c p m$	127.61	J·kg^-1·K^-1
Latent heat of solidification of Pb, $L$	24700	J·kg^-1

Table 1 Thermophysical property parameters of Pb-Al system^[24]

Fig.6 T, solubility line temperature (T_s) of the matrix melt, and nucleation rate (I) of the Al-rich particles in front of the solidification interface along the central z-axes for the Pb-0.15Al alloy solidified at V₀ = 4 mm/s

Fig.7 I, number density (N), average radius (<R>), and volume fraction (ϕ) of the Al-rich particles, and supersaturation (s) of the matrix melt in front of the solidification interface along the central z-axes for the Pb-0.15Al alloys solidified at V₀ = 4 mm/s

Fig.8 T, T_s of the matrix melt, and I of the Al-rich particles in front of the solidification interface along the central z-axes for the Pb-0.15Al alloys solidified at V₀ = 4 mm/s (blue lines), 7 mm/s (red lines), and 10 mm/s (black lines) (The inset shows the shape of the solidification interface at different V₀)

Fig.9 I, N, and <R> of the Al-rich particles in front of the solidification interface along the central z-axes for the Pb-0.15Al alloys solidified at V₀ = 4 mm/s (blue lines) and 10 mm/s (black lines)

Fig.10 Stokes movement rate of the average size Al-rich particles (u_S(<R>, z)) in front of the solidification interface along the central z-axes for the Pb-0.15Al alloy solidified at V₀ = 4 mm/s (z_nuc—the axial position where Al-rich particles have just finished nucleation)

Fig.11 N (a) and ϕ (b) of the Al-rich particles in front of the solidification interface along the central z-axes for Pb-0.15Al alloys solidified at V₀ = 4 mm/s ( u_S—Stokes movement of Al-rich particles, V_c—convective flow of melt. Insets show the high magnified curves)

Fig.12 Temperature field and flow field of the melt in front of the solidification interface when solidifying the alloy at V₀ = 4 mm/s (a), z component of the melt convection velocity at the position of r = 0 (V_c_z (r = 0)), and r component of the melt convection velocity at the position of r = 1 mm (V_c_r (r = 1 mm)) along the axial position z (b)

Fig.13 Maximum nucleation rate (I_max) of the Al-rich particles and the V_c_z at the corresponding position (V $c z, I m a x$ ) along the r direction for the sample solidified at V₀ = 4 mm/s

Fig.14 N and ϕ of the Al-rich particles in front of the solidification interface along the r direction for the sample solidified at V₀ = 4 mm/s (The subscript “nuc”, “z = 5 mm”, and “s/l” refer to the axial position of z = z_nuc, z = 5 mm, and the solidification interface, respectively)

Fig.15 Maximum of the z component of Stokes movement velocity of Al-rich particles ( $u S z m a x$ ), maximum of the z component of melt convection velocity ( $V c z m a x$ ) and maximum of the z component of the resultant velocity ( $u S z m a x$ + $V c z m a x$ + $V 0 z$ ) versus V₀ when directionally solidifying Pb-0.15Al alloys ( $V 0 c$ —the critical value of solidification rate. Inset shows the high magnified curves)

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