Molecular dynamics simulation of the aggregation and diffusion of iron in liquid lead-bismuth

doi:10.7523/j.ucas.2025.028

Abstract

Abstract:

Liquid lead-bismuth is considered as the core coolant of the fourth-generation lead-cooled fast reactors， and its compatibility with structural steels is one of the focuses of current research. In this paper， the aggregation process of iron atoms in liquid lead-bismuth and the diffusion behavior of iron clusters were simulated by using the molecular dynamics method. The influence laws and microscopic mechanisms of the temperature of the system， the size and mass concentration of iron clusters on the coalescence process between iron clusters and the diffusion behavior of iron clusters were analyzed. The results show that iron atoms tend to form clusters in liquid lead-bismuth and that high temperatures can accelerate the aggregation process. In addition， it is found that the coalescence between iron clusters in liquid lead-bismuth needs to overcome energy barriers， the energy barrier to be overcome for the coalescence of two iron clusters of radii 10 Å at 473 K is about 2.14 eV， and the increase of system temperature and the increase of iron clusters size are favorable for the occurrence of coalescence between iron clusters. Furthermore， the diffusion coefficients of iron clusters were calculated， and found to increase with the decrease of their mass concentration， decrease with the increase of their size， and increase with the increase of the temperature of the system. The effect of iron clusters size on the diffusion activation energies was not significant， and the diffusion activation energies of iron clusters with radii of 10， 12.5， and 15 Å were 0.128， 0.140， and 0.134 eV， respectively.

Key words: molecular dynamics, iron clusters, liquid lead-bismuth, diffusion coefficient

CLC Number:

O551.3

Xuefeng HAN, Xingang YU. Molecular dynamics simulation of the aggregation and diffusion of iron in liquid lead-bismuth[J]. Journal of University of Chinese Academy of Sciences, 2026, 43(5): 614-622.

Figures/Tables 10

Fig.1 Dynamic evolution of Fe atoms in liquid Pb-Bi at 473 K

Fig.2 Time-dependent Fe cluster number and isolated Fe atom number at different temperatures

Fig.3 Dynamic evolution of Fe atoms in liquid Pb-Bi at 873 K

Fig.4 Central distance dependent average potential energy of Fe atoms in Fe clusters with radius of 10 Å at 473 K

Fig.5 Dynamic evolution of Fe clusters with radius of 12 Å in liquid Pb-Bi at different temperatures

Fig.6 Dynamic evolution of Fe clusters with different radii in liquid Pb-Bi at 973 K

Fig.7 Fe cluster mass concentration dependent diffusion coefficient of Fe cluster at 823 K

Fig.8 Fe cluster mass concentration dependent viscosity of liquid Pb-Bi at 823 K

Table 1 Number of atoms in the system

铁团簇半径/Å	铁原子数	铅铋原子数
10	339	42 391
12.5	701	42 223
15	1 243	41 989

Fig.9 Temperature-dependent diffusion coefficient of Fe cluster at different sizes and single Fe atom

References 32

[1]	Zhang J S， Li N. Review of the studies on fundamental issues in LBE corrosion［J］. Journal of Nuclear Materials， 2008， 373（1/2/3）： 351-377. DOI： 10.1016/j.jnucmat.2007.06.019 .
[2]	Zhang J S. A review of steel corrosion by liquid lead and lead-bismuth［J］. Corrosion Science， 2009， 51（6）： 1207-1227. DOI： 10.1016/j.corsci.2009.03.013 .
[3]	Ballinger R G， Lim J. An overview of corrosion issues for the design and operation of high-temperature lead- and lead-bismuth-cooled reactor systems［J］. Nuclear Technology， 2004， 147（3）： 418-435. DOI： 10.13182/NT04-A3540 .
[4]	Wang W T， Yang C X， You Y H， et al. A review of corrosion behavior of structural steel in liquid lead-bismuth eutectic［J］. Crystals， 2023， 13（6）： 968. DOI： 10.3390/cryst13060968 .
[5]	Zhang J S. Lead-bismuth eutectic （LBE）： a coolant candidate for gen. IV advanced nuclear reactor concepts［J］. Advanced Engineering Materials， 2014， 16（4）： 349-356. DOI： 10.1002/adem.201300296 .
[6]	Gorynin I V， Karzov G P， Markov V G， et al. Structural materials for atomic reactors with liquid metal heat-transfer agents in the form of lead or lead： Bismuth alloy［J］. Metal Science and Heat Treatment， 1999， 41（9）： 384-388. DOI： 10.1007/BF02469876 .
[7]	Barbier F， Rusanov A. Corrosion behavior of steels in flowing lead-bismuth［J］. Journal of Nuclear Materials， 2001， 296（1/2/3）： 231-236. DOI： 10.1016/S0022-3115（01）00521-9 .
[8]	Hosemann P， Dickerson R， Dickerson P， et al. Transmission electron microscopy （TEM） on oxide layers formed on D9 stainless steel in lead bismuth eutectic （LBE）［J］. Corrosion Science， 2013， 66： 196-202. DOI： 10.1016/j.corsci.2012.09.019 .
[9]	Zhu Z G， Zhang Q， Tan J B， et al. Corrosion behavior of T91 steel in liquid lead-bismuth eutectic at 550 °C： effects of exposure time and dissolved oxygen concentration［J］. Corrosion Science， 2022， 204： 110405. DOI： 10.1016/j.corsci.2022.110405 .
[10]	Song C， Li D D， Xu Y C， et al. Corrosion related properties of iron （100） surface in liquid lead and bismuth environments： A first-principles study［J］. Chinese Physics B， 2014， 23（5）： 056801. DOI： 10.1088/1674-1056/23/5/056801 .
[11]	Xu Y C， Song C， Zhang Y G， et al. An energetic evaluation of dissolution corrosion capabilities of liquid metals on iron surface［J］. Physical Chemistry Chemical Physics， 2014， 16（31）： 16837-16845. DOI： 10.1039/c4cp01224k .
[12]	Long X L， Shi J L， Zhu J， et al. First-principles calculation of the resistance to lead-bismuth eutectic corrosion on Fe （111） surface of austenitic stainless steel［J］. Surface Science， 2022， 725： 122132. DOI： 10.1016/j.susc.2022.122132 .
[13]	Zhou T， Gao X， Ma Z W， et al. Atomistic simulation of α-Fe（100）-lead-bismuth eutectic （LBE） solid-liquid interface［J］. Journal of Nuclear Materials， 2021， 555： 153107. DOI： 10.1016/j.jnucmat.2021.153107 .
[14]	Chen L M， Xu S， He X X， et al. Molecular dynamics study of corrosion behavior of iron with vacancies exposed to lead-bismuth eutectic［J］. Materials and Corrosion， 2023， 74（5）： 793-802. DOI： 10.1002/maco.202213375 .
[15]	Gao Y， Takahashi M， Cavallotti C， et al. Molecular dynamics simulation of metallic impurity diffusion in liquid lead-bismuth eutectic （LBE）［J］. Journal of Nuclear Materials， 2018， 501： 253-260. DOI： 10.1016/j.jnucmat.2018.01.044 .
[16]	Daw M S， Baskes M I. Embedded-atom method： derivation and application to impurities， surfaces， and other defects in metals［J］. Physical Review B， 1984， 29（12）： 6443-6453. DOI： 10.1103/physrevb.29.6443 .
[17]	Belashchenko D K. Computer simulation of the properties of liquid metals： gallium， lead， and bismuth［J］. Russian Journal of Physical Chemistry A， 2012， 86（5）： 779-790. DOI： 10.1134/S0036024412050056 .
[18]	Zhou X W， Johnson R A， Wadley H N G. Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers［J］. Physical Review B， 2004， 69（14）： 144113. DOI： 10.1103/physrevb.69.144113 .
[19]	Gao Y， Raos G， Cavallotti C， et al. Molecular dynamics simulation on physical properties of liquid lead， bismuth and lead-bismuth eutectic （LBE）［J］. Procedia Engineering， 2016， 157： 214-221. DOI： 10.1016/j.proeng.2016.08.359 .
[20]	Nosé S. A unified formulation of the constant temperature molecular dynamics methods［J］. The Journal of Chemical Physics， 1984， 81（1）： 511-519. DOI： 10.1063/1.447334 .
[21]	Hoover W G. Canonical dynamics： equilibrium phase-space distributions［J］. Physical Review. A， General Physics， 1985， 31（3）： 1695-1697. DOI： 10.1103/physreva.31.1695 .
[22]	Parrinello M， Rahman A. Crystal structure and pair potentials： A molecular-dynamics study［J］. Physical Review Letters， 1980， 45（14）： 1196-1199. DOI： 10.1103/physrevlett.45.1196 .
[23]	Müller-Plathe F. Reversing the perturbation in nonequilibrium molecular dynamics： an easy way to calculate the shear viscosity of fluids［J］. Physical Review. E， Statistical Physics， Plasmas， Fluids， and Related Interdisciplinary Topics， 1999， 59（5 Pt A）： 4894-4898. DOI： 10.1103/physreve.59.4894 .
[24]	Xu B， Liu S， Yu X. Molecular simulation study of the effect of iron clusters on the viscosity of liquid lithium［J］. Journal of University of Chinese Academy of Sciences， 2023， 40（2）： 165-172. DOI： 10.7523/j.ucas.2021.0062 .
[25]	Thompson A P， Aktulga H M， Berger R， et al. LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic， meso， and continuum scales［J］. Computer Physics Communications， 2022， 271： 108171. DOI： 10.1016/j.cpc.2021.108171 .
[26]	Stukowski A. Visualization and analysis of atomistic simulation data with OVITO-the open visualization tool［J］. Modelling and Simulation in Materials Science and Engineering， 2010， 18（1）： 015012. DOI： 10.1088/0965-0393/18/1/015012 .
[27]	Weeks J R， Romano A J. Liquidus curves and corrosion of Fe， Ti， Zr， and Cu in liquid Bi-Pb alloys［J］. Corrosion， 1969， 25（3）： 131-136. DOI： 10.5006/0010-9312-25.3.131 .
[28]	Xu C， Li Z Y， Chen L G， et al. Atomic-scale insights into the precipitation behaviors of copper atoms in liquid lithium［J］. Fusion Engineering and Design， 2023， 194： 113901. DOI： 10.1016/j.fusengdes.2023.113901 .
[29]	Cui W Z， Shen Z J， Yang J G， et al. Effect of chaotic movements of nanoparticles for nanofluid heat transfer augmentation by molecular dynamics simulation［J］. Applied Thermal Engineering， 2015， 76： 261-271. DOI： 10.1016/j.applthermaleng.2014.11.030 .
[30]	Gan X L， Xiao S F， Deng H Q， et al. Clustering of Fe atoms in liquid Li and its effect on the viscosity of liquid Li［J］. Nuclear Fusion， 2016， 56（4）： 046004. DOI： 10.1088/0029-5515/56/4/046004 .
[31]	He Y R， Jin Y， Chen H S， et al. Heat transfer and flow behaviour of aqueous suspensions of TiO₂ nanoparticles （nanofluids） flowing upward through a vertical pipe［J］. International Journal of Heat and Mass Transfer， 2007， 50（11/12）： 2272-2281. DOI： 10.1016/j.ijheatmasstransfer.2006.10.024 .
[32]	Zwanzig R. On the relation between self-diffusion and viscosity of liquids［J］. The Journal of Chemical Physics， 1983， 79（9）： 4507-4508. DOI： 10.1063/1.446338 .