Supplementary Material for a Full View of the Segregation Evolution in Al-Bi Immiscible Alloy

Supplementary Material for “A full view of the segregation evolution in Al-Bi immiscible alloy”

Wenquan Lu a,b, Shuguang Zhang a, †, Wei Zhang a, Qiaodan Hu a, *, Jianding Yu,c Yanan Fud and Jianguo Lia, *

aSchool of Materials Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Rd., Shanghai 200240, China

bSchool of Environmental Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Rd., Shanghai 200240, China

cShanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China

dShanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201204, China.

*Corresponding author. Tel & Fax: +86 21 54744246. E-mail: (Q.D. Hu); (J.G. Li)

† Deceased.

Part 1: Pseudo-color images of segregation evolution in solidifying Al-10 wt.% Bi immiscible alloy

Figure S1 Pseudo-color images of segregation evolution corresponding to Fig. 2b-e. The lighter contrast represents the parent liquid, while the darker contrast represents Bi.

From Figure S1b-c, it is easy to distinguish that Bi sinks to and accumulates in the bottom part of the liquid alloy sphere. And it is clear that the lower half of the sample has higher atomic concentration of Bi than the rest in Figure S1c. At that time, the liquid was still miscible and the surface segregation just started to develop and formed a thin layer at the left corner of the sample (see Figure S1c). Such a broad distribution of the inhomogeneity of Bi does not represent the surface segregation. After surface segregation, Bi droplets were precipitated from the matrix melt because of the occurrence of the liquid phase separation (Figure S1e). It directly confirms that surface segregation occurs in the bulk liquid before the liquid decomposition.

Part 2: The calculation of the upward temperature gradient

Figure S2 Schematic representation of the Al-10 wt.% Bi alloy sphere with a diameter of 1.94 mm placed centrally on the Cu nozzle (unit: ?m) and the two types of movement of Bi droplets. Vm is the Marangoni velocity and Vs is the Stokes velocity.

For the upper part of the Al-10 wt.% Bi alloy sphere, the total heat loss (Q1) includes the loss of thermal radiation (Qr),[1] thermal convection (Qc)[2] and the heat input from laser (Qlaser):

(1)

While, only the convection process was taken into account for calculating the heat loss at the lower part of the sample (Q2):

(2)

Thus, the cooling rate of the alloy sphere is determined as:[1]

(3)

where, A1 and A2 are the surface area of the upper part and lower part of the sample, respectively, and h1, h2 are their heat transfer coefficients, respectively; Tg is the ambient temperature; is the surface emissivity; is the Stefan-Boltzmann constant; Ri (i=1, 2) is the cooling rate of the upper part (R1) and lower part (R2); mi (i=1, 2) is the mass of the upper part (m1) and lower part (m2); CPL is the specific heat of the Al-10 wt.% Bi alloy.

As the Al-10 wt.% Bi alloy particle was placed centrally on the Cu nozzle, and it was heated by a CO2 laser with the focused beam hitting the sample from the top. This produces an upward temperature gradient across the sample. Suppose the top layer does not get the heat input from laser, the temperature difference between top and bottom will be minimized, giving a minimum temperature gradient. Therefore, by neglecting the heat input from laser, the maximum cooling rate of the upper part and further the minimum temperature gradient can be estimated. Thus, according to the parameters listed in Table S1, the maximum cooling rate of the upper part is:

(4)

with the abbreviation,

(5)

The cooling rate of the lower part is:

(6)

Thus, the minimum temperature gradient upward is about 148 K/mm, which can be used to calculate the velocities of Bi droplets.

The velocities of Bi droplets due to Marangoni motion (Vm) and Stokes (Vs) are described as:[2,3]

(7)

(8)

where, ?d and ?m are the viscosities of the Bi droplets and matrix, respectively; r the radius of the Bi droplets; g the gravity coefficient; Δρ the difference of density between the Bi droplets and matrix; the temperature gradient; σ the interfacial energy, which can be described as:[4]

(9)

where, Nv the atom numbers of unit volume; λa the interface atom distance; k the Boltzmann constant; Tc the critical temperature.

Figure S3 shows the calculated Vm and Vs with the parameters presented in Table S1.

Figure S3 Vm and Vs as a function of radius inside Al-10 wt. % Bi alloy sphere at 1000 K.

Table S1. The parameters used in the calculation

References

1. B.C. Luo, X.R. Liu, and B. Wei: J. Appl. Phys., 2009, vol. 106, pp. 053523.

2. N.O. Young, J.S. Goldstein, and M.J. Block: J. Fluid Mech., 1959, vol. 6, pp. 350-6.

3. L. Ratke and P.W. Voorhees: Growth and Coarsening, New York: Springer-Verlag; 2002.

4. J.W. Cahn and J.H. Hilliard: J. Chem. Phys., 1958, vol. 28, pp. 258-67.

5. W.Q. Lu, S.G. Zhang, and J.G. Li: Mater. Lett., 2013, vol. 107, pp. 340-3.

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