Simulation of lutetium metal evaporation with considering atomic metastable state

Lai Gan-Ping; Zhang Xiao-Wei

doi:10.7498/aps.72.20230602

Abstract

Lutetium-177, one of the current global research hotspots for medical isotopes, can be produced by reactor irradiation of lutetium-176, which can be produced and processed with the assistance of the electron beam physical vapor deposition (EB-PVD). The metal evaporation process is an important part of EB-PVD, which aims to convert solid metal into metal atomic vapor. The distribution of each macroscopic characteristic quantity, such as thermal population distribution, density distribution, velocity distribution, and temperature distribution of metal atomic vapor, will directly affect the utilization of metal vapor atoms, the subsequent deposition process, and coating process. In this paper, two-dimensional model and three-dimensional model of the metal evaporation process are established based on the direct simulation Monte Carlo method, and atomic metastable state is introduced into the collision assumption. The macroscopic characteristic quantities, such as the number density of metal atomic vapor, the motion velocity and the discrete degree of the total motion velocity in the evaporation process with or without considering the lutetium atomic metastable state, are analyzed and compared. The spatial distribution characteristics of each energy level of metal atomic vapor are observed, and the variation characteristics of the macroscopic characteristic quantities in the center with the slit opening size and the evaporation source surface temperature are discussed. The study results show that the number density of metal vapor passing through the beam flow device decreases, the average velocity in the x-direction and z-direction and the discrete degree of the total motion velocity increase, with the atomic metastable state taken into consideration. The beam flow device intensifies the transformation of the atomic energy level of the metal vapor and changes the physical parameters of the metal atomic vapor. At the same time, the slit opening size and the evaporation source surface temperature trigger off the change of the macroscopic characteristic quantity distribution of the metal vapor, including the degree of anomalous protrusion of each macroscopic characteristic quantity above the slit. The results of the three-dimensional simulation based on the two-dimensional model are consistent with the changes in the order of magnitude of data distribution and spatial distribution pattern, which can serve as a reference and guidance for the experimental study of the electron beam metal evaporation process.

Keywords:

Authors and contacts

1.
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
2.
Science and Technology on Particle Transport and Separation Laboratory, Tianjin 300180, China

Corresponding author: Zhang Xiao-Wei, 2809024720@qq.com

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References

[1]	卓连刚, 杨宇川, 岳海东, 熊晓玲, 王关全, 王海麟, 杨林, 林青川, 陈琪萍, 涂俊, 魏洪源 2022 同位素 35 217 Google Scholar Zhuo L G, Yang Y C, Yue H D, Xiong X L, Wang G Q, Wang H L, Yang L, Lin Q C, Chen Q P, Tu J, Wei H Y 2022 J. Isot. 35 217 Google Scholar
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Cited By

图 1 镥前5个能级的热布居分布比例

Figure 1. Thermal population distribution proportion of lutetium’s first five energy levels.

DownLoad: Full-Size Img PowerPoint

图 2 二维非弹性碰撞的能量变化示意图

Figure 2. Schematic diagram of the energy change in a two-dimensional inelastic collision.

DownLoad: Full-Size Img PowerPoint

图 3 二维和三维模型示意图　(a) 二维模型; (b) 三维模型

Figure 3. Schematic diagram of two-dimensional and three-dimensional models: (a) Two-dimensional model; (b) three-dimensional model.

DownLoad: Full-Size Img PowerPoint

图 4 金属原子蒸气各宏观特征量的二维空间分布(左为不考虑原子亚稳态, 右为考虑原子亚稳态)　(a) 数密度$n$; (b) 总运动速度的离散程度$T$; (c) $x$方向平均速度${u_x}$; (d) $z$方向平均速度${u_z}$

Figure 4. Two-dimensional spatial distribution of macroscopic characteristic quantities of metal atomic vapor (left is not considering atomic metastable states, right is considering atomic metastable states): (a) Number density $n$; (b) the discrete degree of total motion velocity $T$; (c) average velocity ${u_x}$ in the $x$-direction; (d) average velocity ${u_z}$ in the $z$-direction.

DownLoad: Full-Size Img PowerPoint

图 5 各能级占比分布图　(a) 能级1; (b) 能级2; (c) 能级3; (d) 能级4

Figure 5. Layout of the proportion of each energy level: (a) Energy level 1; (b) energy level 2; (c) energy level 3; (d) energy level 4.

DownLoad: Full-Size Img PowerPoint

图 6 金属原子蒸气在蒸发源中心位置处的宏观特征量变化曲线(不同狭缝开口大小)　(a) 数密度$n$; (b) 总运动速度的离散程度$T$; (c) $z$方向平均速度${u_z}$

Figure 6. Variation curves of macroscopic characteristic quantities of metal atomic vapor at the center of the evaporation source (different slit opening sizes): (a) Number density $n$; (b) the discrete degree of total motion velocity $T$; (c) average velocity ${u_z}$ in the $z$-direction.

DownLoad: Full-Size Img PowerPoint

图 7 金属原子蒸气在蒸发源中心位置处的宏观特征量变化曲线(不同蒸发源表面温度)　(a) 数密度$n$; (b) 总运动速度的离散程度$T$; (c) $z$方向平均速度${u_z}$

Figure 7. Variation curves of macroscopic characteristic quantities of metal atomic vapor at the center of the evaporation source (different surface temperatures of evaporation source): (a) Number density $n$; (b) the discrete degree of total motion velocity $T$; (c) average velocity ${u_z}$ in the $z$-direction.

DownLoad: Full-Size Img PowerPoint

图 8 金属原子蒸气各宏观特征量的三维空间分布　(a) 数密度$n$; (b) 总运动速度的离散程度$T$; (c) $x$方向平均速度${u_x}$; (d) $y$方向平均速度${u_y}$; (e) $z$方向平均速度${u_z}$

Figure 8. Three-dimensional spatial distribution of macroscopic characteristic quantities of metal atomic vapor: (a) Number density $n$; (b) the discrete degree of total motion velocity $T$; (c) average velocity ${u_x}$ in the $x$-direction; (d) average velocity ${u_y}$ in the $y$-direction; (e) average velocity ${u_z}$ in the $z$-direction.

DownLoad: Full-Size Img PowerPoint

[1]	卓连刚, 杨宇川, 岳海东, 熊晓玲, 王关全, 王海麟, 杨林, 林青川, 陈琪萍, 涂俊, 魏洪源 2022 同位素 35 217 Google Scholar Zhuo L G, Yang Y C, Yue H D, Xiong X L, Wang G Q, Wang H L, Yang L, Lin Q C, Chen Q P, Tu J, Wei H Y 2022 J. Isot. 35 217 Google Scholar
[2]	Bournaud C, Kelly A, Hindié E, Tenenbaum F, Faivre-Chauvet A, Courbon F, Taïeb D, Dierickx L O, Coriat R, Ansquer C 2017 Med. Nucl. 41 42 Google Scholar
[3]	Strosberg J, El-Haddad G, Wolin E, Hendifar A, Yao J, Chasen B, Mittra E, Kunz P L, Kulke M H, Jacene H, Bushnell D, O’Dorisio T M, Baum R P, Kulkarni H R, Caplin M, Lebtahi R, Hobday T, Delpassand E, Van Cutsem E, Benson A, Srirajaskanthan R, Pavel M, Mora J, Berlin J, Grande E, Reed N, Seregni E, Öberg K, Lopera Sierra M, Santoro P, Thevenet T, Erion J L, Ruszniewski P, Kwekkeboom D, Krenning E, NETTER-1 Trial Investigators 2017 N. Engl. J. Med. 376 125 Google Scholar
[4]	彭述明, 杨宇川, 谢翔, 钱达志 2020 科学通报 65 3526 Google Scholar Peng S M, Yang Y C, Xie X, Qian D Z 2020 Chin Sci Bull 65 3526 Google Scholar
[5]	胡映江, 王磊, 吴建荣, 李波, 罗宁, 陈云明, 曾俊杰, 孙志中, 贾致军, 张劲松 2023 同位素 36 83 Google Scholar Hu Y J, Wang L, Wu J R, Li B, Luo N, Chen Y M, Zeng J J, Sun Z Z, Jia Z J, Zhang J S 2023 J. Isot. 36 83 Google Scholar
[6]	张世宏, 王启民, 郑军 2020 气相沉积技术原理及应用 (北京: 冶金工业出版社) 第36, 37页 Zhang S H, Wang Q M, Zheng J 2020 Principle and Application of Vapor Deposition Technology (Beijing: Metallurgical Industry Press) pp36, 37
[7]	赖奇, 李俊翰, 吴恩辉, 崔晏, 李亮, 廖先杰 2020 钢铁钒钛 41 76 Google Scholar Lai Q, Li J H, Wu E H, Cui Y, Li L, Liao X J 2020 Iron, Steel, Vanadium, Titanium 41 76 Google Scholar
[8]	杨光, 刘欢, 王丁丁, 罗立平, 吕绪明, 祁阳 2021 真空 58 81 Google Scholar Yang G, Liu H, Wang D D, Luo L P, Lv X M, Qi Y 2021 Vacuum (Shenyang, China) 58 81 Google Scholar
[9]	滕晓丹, 彭徽, 李刘合, 郭洪波, 宫声凯 2023 航空制造技术 66 40 Google Scholar Teng X D, Peng H, Li L H, Guo H B, Gong S K 2023 Aeronautical Manufacturing Technology 66 40 Google Scholar
[10]	王德武 1999 激光分离同位素理论及其应用 (北京: 原子能出版社) 第338—340页 Wang D W 1999 Theory and Application of Laser Isotope Separation (Beijing: Atomic Energy Press) pp338–340
[11]	谢国锋, 王德武, 应纯同 2002 物理学报 51 584 Google Scholar Xie G F, Wang D W, Ying C T 2002 Acta Phys. Sin. 51 584 Google Scholar
[12]	谢国锋, 王德武, 应纯同 2002 物理学报 51 2286 Google Scholar Xie G F, Wang D W, Ying C T 2002 Acta Phys. Sin. 51 2286 Google Scholar
[13]	翟蕊 2019 硕士学位论文 (北京: 清华大学) Zhai R 2019 M. S. Dissertation (Beijing: Tsinghua University
[14]	卢肖勇, 张小章 2018 物理学报 67 154701 Google Scholar Lu X Y, Zhang X Z 2018 Acta Phys. Sin. 67 154701 Google Scholar
[15]	Lu X Y, Zhang X Z, Zhang Z Z 2018 Chin. Phys. B 27 124702 Google Scholar
[16]	Lu X Y, Chai J J 2019 Chin. Phys. B 28 074702 Google Scholar
[17]	卢肖勇 2020 博士学位论文 (北京: 清华大学) Lu X Y 2020 Ph. D. Dissertation (Beijing: Tsinghua University
[18]	Fan J, Boyd I D, Shelton C 2000 J. Vac. Sci. Technol. A 18 2937 Google Scholar
[19]	Balakrishnan J, Boyd I D, Braun D G 2000 J. Vac. Sci. Technol. A 18 907 Google Scholar
[20]	谢国锋, 王德武, 应纯同 2002 原子能科学技术 36 147 Google Scholar Xie G F, Wang D W, Ying C T 2002 Atom. Energ. Sci. Tech. 36 147 Google Scholar
[21]	Bird G A 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows (New York: Oxford University Press) pp218–220
[22]	沃尔夫冈·戴姆特瑞德著 (姬扬译) 2012 激光光谱学 (第1卷: 基础理论) (北京: 科学出版社) 第10—13页 Demtröder W (translated by Ji Y) 2012 Laser Spectroscopy (Vol. 1: Basic Principles) (Beijing: Science Press) pp10–13
[23]	李阳 2015 硕士学位论文 (天津: 天津大学) Li Y 2015 M. S. Dissertation (Tianjin: Tianjin University
[24]	沈青 2003 稀薄气体动力学 (北京: 国防工业出版社) 第122—127页 Shen Q 2003 Rarefied Gas Dynamics (Beijing: National Defense Industry Press) pp122–127
[25]	王权, 李小江, 陈勇, 陈英 2019 化学反应工程与工艺 35 129 Google Scholar Wang Q, Li X J, Chen Y, Chen Y 2019 Chem. React. Eng. Technol. 35 129 Google Scholar

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