P19
シアーセル法と分子動力学計算による液体 Pb 中の自己および不純物拡散係数
Self and impurity diffusion coefficient in liquid Pb
measured by using shear cell techniqueand molecular dynamics〇川嶋啓太 1, 山中亜里紗 1, 小林由央 1, 椎木政人 1, 2, 鈴木進補 1〇Keita KAWASHIMA1, Arisa YAMANAKA1, Yoshihiro Kobayashi1, Masato SHIINOKI1, 2,Shinsuke SUZUKI1
1
2

早稲田大学，Waseda University
ドイツ航空宇宙センター，Deutsches Zentrum für Luft- und Raumfahrt

1. Introduction
Diffusion coefficient in liquid metal is an important physical property for solidification simulation incasting. Molecular dynamics simulation (MD) is a useful method for simulating microscopic behavior of atom
in liquid metal. It is necessary to obtain the diffusion coefficient experimentally as the benchmark for MD
simulation. The objective of this study is to clarify how accurate impurity diffusion coefficient can be obtainedin liquid Pb by comparing the diffusion coefficients obtained by using shear-cell technique and MD.
2. Experimental and analytical methods
The impurity diffusion coefficient of Sn in Pb was measured using the shear cell technique. Diffusion
couples of pure Pb and Pb-5 at.%Sn alloy were placed in four capillaries (labeled Cap. A, B, C and D). Eachsample was set in each capillary, as shown in Fig. 1(a), so as to provide the stable density layering1). Diffusion
experiments were performed at 773 K for a diffusion time of 18000 s. After the diffusion time, each capillary
was separated into 20 cells (labeled No.1-20). Each solidified sample was dissolved in a mixed acid solution
and then the Sn concentration in the solution was analyzed by ICP-OES.
The MD simulation of self-diffusion of Pb and impurity diffusion of Sn in Pb-5 at.%Sn were performed.
13500 Pb atoms were arranged in a cubic simulation box which had an fcc structure. 675 atoms were replacedwith Sn atoms only in impurity diffusion simulation. Calculations were carried out with PFP2) version 4.0.0 on
Matlantis3). Simulations of self-diffusion and impurity diffusion were performed under the NVT ensemble at
773 K with the time of 1 fs × 5000 steps and 10000 steps, respectively, after the equilibration with the time of 1
fs × 2000 steps. The simulations of impurity diffusion were performed four times under the same conditions.
Diffusion coefficients were calculated from the mean square displacement in MD results. In the simulations ofself-diffusion, the number density was 27.2 nm-3. The number density for the simulation of impurity diffusion
was obtained by linearly interpolating the number density4) with the concentration of Sn.
3. Results
Figure 1(b) shows the Sn concentration profiles obtained by using the shear cell technique. Floatingobjects appeared when the samples are dissolved in a mixed acid. The self-diffusion coefficient of Pb was 3.02
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× 10-9 m2s-1 when number density was 27.2 nm-3. The diffusion coefficients calculated by using MD were (3.61± 0.09) × 10-9 m2s-1 for Sn and (3.09 ± 0.02) × 10-9 m2s-1 for Pb.

Figure 1.

Shear cell technique and experimental results. (a) Schematics of the experimental procedure. (b) Snconcentration profiles for four capillaries. Each curve was calculated by the thick layer solution.

4. Discussion
According to Fig. 1(b), some plots in Cap. B deviated from the thick layer solution. It is considered thatthe measured concentration dropped due to the floating object. The values of No.1 and No.2 were considered
to be outliers. When the fitting was performed with excluding cells No. 1 and No. 2, the diffusion coefficientin Cap. B was corrected to be 3.02×10-9 m2s-1. The obtained diffusion coefficient was (3.16±0.03)×10-9 m2s-1 after
the correction. The self-diffusion coefficient of Pb calculated by using MD increased with decreasing numberdensity. The diffusion coefficient calculated by using MD was 13.9 % larger than that of shear cell technique.
The density4) in MD (9.26 × 103 kgm-3) was smaller than the actual density (1.044 × 104 kgm-3)5). Therefore, thecalculated diffusion coefficient become larger with decreasing the number density.
5. Conclusion
By eliminating plots on concentration profile which dropped due to the floating object, the relative
standard deviation of the obtained diffusion coefficient decreased. Diffusion coefficient calculated by using
MD increased with decreasing number density.
Acknowledgement
This study was supported by financial support from ENEOS Corporation, Grant-in-Aid for Kimura Foundry Co.,Ltd.,
Grant-in-Aid for Scientific Research(C) Grant Number JP23K04364, Grant-in-Aid for JSPS Research Grant Number
JP20J14950, and Grant-in-Aid for JST SPRING, Grant Number JPMJSP2128.

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© 2023 by the authors. Submitted for possible open access publication under theterms and conditions of the Creative Commons Attribution (CC BY) license(http://creativecommons.org/li censes/by/4.0/).
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