Molecular Dynamics Simulation To Studying The Effect Of Molybdenum In Stainless Steel On The Corrosion Resistance By Lead-Bismuth M. Susmikanti a, D. Andiwayakusuma a, Ghofir a and A. Maulana b a) Nuclear Information Development Center, National Nuclear Energy Agency, Kawasan PUSPIPTEK, Tangerang, Indonesia b) Nuclear Industry Material Technology Center, National Nuclear Energy Agency Kawasan PUSPIPTEK, Tangerang, Indonesia Abstract. The study of characteristic material structure is the important issue to understand the phenomena of corrosion. Molecular dynamic simulation has been carried out for studying the surface interaction between stainless steel and coolant material Lead-Bismuth (Pb-Bi) in several temperatures. The material with complex molecular interactions has a long simulation process that needs parallel processing in cluster system. MOLDY is an open source program which can be used to mono atomic or polyatomic in cluster computer. This paper will discuss the effect of Molybdenum (Mo) on the corrosion with Mo 2%-3% and Mo 3%-4% in several temperatures. The simulation is done between crystals steel Fe 71%, Ni 10% and Cr 16% with Mo 2%-3% and Fe 70%, Ni 10%, Cr 16% with Mo 3%-4%. The effect of increasing Mo content in crystal steel for resistance corrosion will be presented in this paper. The results of this simulation show that the phenomena of Mo with difference content on the corrosion in several temperatures. That can be used to identify whether the system has resistance corrosion or not. This simulation obtain that the surface of stainless steel by lead-bismuth Pb-Bi with Mo 3%-4% content has less corrosion than the surface of stainless steel with Mo 2%-3% content. This phenomenon has the same with the statement from experiment that the stainless steel with Mo 3%-4% content has corrosion resistance than the stainless steel with Mo 2%-3% content. Keywords: Molecular Dynamics, Corrosion Resistance, Coolant Material, Crystal Steel PACS: http://www.aip.org/pacs/index.html INTRODUCTION In development of nuclear power plant especially for safety reactor, the characteristic of material utilized is the important thing to know the condition of material. Corrosion is important in temperature are endured such as nuclear power plants and heat exchangers. In many cases the materials with experiencing corrosion can not be obviated, but there are many ways to control it. Many investigations of corrosion phenomena of stainless steel in liquid leadbismuth (Pb-Bi) have been carried out macroscopically by experiments [1, 2, 3]. Stainless steel has many content of alloy such as Fe, Ni, Cr, Mo, Mn etc. 317L (S31703) stainless steel with composition of Molybdenum (Mo) 3%-4% increase for resistance of corrosion. That has been analyzed. 317L (S31703) stainless steel is considerably more resistance corrosive than alloy 316L (S31603) with composition of Molybdenum (Mo) 2%-3% [4].
This paper will discuss the interaction beetwen crystal steel Fe 71,5%, Ni 10%, Cr 16% by added Mo 2%-3% [4]. This interaction was simulated with Pb-Bi 55%-45%. in several temperatures. This stainless steel including Mo 2%-3% is analog with composition in alloy type 316L with assumption that another element included in iron Fe. The phenomena of the effect corrosion will be presented in this paper. This paper also discusses the phenomena of interaction beetwen crystal steel Fe 70,5%, Ni 10%, Cr 16% by added Mo 3%-4% [4]. This interaction was simulated too with Pb-Bi 55%- 45%. The molecular dynamic simulation has been carried out for surface interaction between crystal steel Fe 71%, Ni 10%, Cr 16%, Mo 2%-3% and coolant material Pb- Bi 55%-45% in several temperature. That phenomena was investigated. The phenomena with Mo 3%-4% content was investigated too in crystal steel. The effect of increasing Mo content for resistance corrosion was investigated. This simulation is done in molecular dynamic cluster computer for efficiency a long process. The results of this simulation are the phenomena of Mo with difference content on the corrosion in several temperatures. METHODOLOGY Molecular Dynamics (MD) is a computer simulation technique which is represented by the interaction of a number of atoms in a certain period of time. With the rapid developments of computer power, it is becoming more feasible to calculate the macroscopic properties of experimental interest from the details, such as the masses of the atoms, the interactions between them through molecular dynamics method. In molecular dynamics method, the model system is composed of a large number of atoms with well-defined interatomic interaction potentials. The atoms are assumed to be the following the Newton s equations of motion for atom i in equation (1) [2]. 2 v r i Fi mi m, ( i = 1,, N) (1) 2 t t where F i is the force exerted on atom i of mass mi, vi are the velocity and r position vectors, respectively. The force F is determined from the interatomic pair potential in equation (2), where (r) is the effective pair-wise potential. ( r ) F F (i,j=1,..., N) (2) i j ji r is the sum of forces F on atom i due to atom j (j i) in the system. In principle, it is possible to construct an exact picture of a liquid using the molecular dynamics, provided that the pair potentials are accurately known. The accuracy of the potentials used to determine the forces between the atoms is essential to the success of a computer experiment. Some nuclear materials that become candidates for the reactor coolant are corrosive to stainless steel constituent materials, because the diffusion process between the cooling of atoms with the atoms make up stainless steel. Simulations using molecular dynamics method basically start with determining the configuration of the atoms of a material reviewed and then the atoms are randomly given initial velocity. Initial configurations of the material Fe, Ni, Cr, Mo, Pb and Bi have lattice parameter by experiment in Table 1 [3, 4, 5, 6],
TABLE 1. Lattice Parameter of Fe, Cr, Ni, Mo, Pb and Bi. Laticce Parameter No Atom Structure (Angstrom) Angle 1 Fe BCC 2.87 2.87 2.87 α = β = γ =90 2 Pb FCC 4.95 4.95 4.95 α = β= γ = 90 3 Bi Monoclinic 6.67 6.12 3.31 α = 90, β = 110.33, γ = 90 4 Mo BCC 3.15 3.15 3.15 α = β = γ = 90 5 Cr FCC 2.88 2.88 2.88 α = β = γ = 90 6 Ni FCC 3.52 3.52 3.52 α = β = γ= 90 From the above data it is determined atomic coordinates for the position of each element in a single unit cell. After the unit cell reproduced in the XYZ directions, so that the number of unit cells are to be increased as shown in Fig 1. FIGURE 1. Unit cell reproduced in XYZ directions This simulation has explore in crystal steel are Fe, Ni, Cr and Mo. The interation done with coolant material Pb and Bi. Initial positions of atoms Pb (black), Bi (violete), Fe (orange), Ni (green), Cr (grey), Mo (blue) and their interaction in this simulation set occupy a cube lattice repeatedly in the direction of three dimensions. The total number of atom in crystal steel structure is 2000. Each number of atom for iron 1438 (71,5%), nickel 192 (10%), chrom 320 (16%) and molybdenum 50 (2%- 3%). The total number of atom in coolant material is 864. The number of atom for lead 477 (55%) and bismuth 387 (45%). The simulation for molybdenum 3%-4%, the number of atom for iron1438 (70,5%), nickel 192 (10%), chrom 320 (16%) and molybdenum 50 (3%-4%). The initial velocity of each atom gives a random value between 0 and 1, through a random generator. So the point of intersection of the horizontal axis and the depth of potential wells is considered as Lennard-Jones parameters [7]. Those data are fitting using Lennard-Jones potential in equation (3),
12 6 ( r ) 4 (3) r r where ( r ) : potential function,, : parameters for the Lennard-Jones interaction potential function. r : distance beetwen atom i and j. : features the distance at which the potential function has its minimum value of - (energy potential beetwen atom i and j). i and j which has its minimum value of - i and - j (energy potential for atom i and j). The Lennard Jones parameters for atom pairs are determined from the arithmethic combining rules use equation (4) and (5) [8], 1 ( i j ) (4) 2 (5) The parameter of each atoms interacts to each other in this case is assumed from the Lennard-Jones potential or experiment. The atoms move at many times in high temperature with the number of steps. The potential energy and nearest distance that can be obtained from inter-atomic forces are expressed in equations (5) and (6). The energy potential of Mo atom can be get from literature based on experiment [9] as shown in Fig. 2. The Lennard-Jones potential and their interaction between each atom Fe, BP, Bi, Cr, Mo and Ni were taken from the literature [1, 5, 8, 9] are describe in Table 2. i j FIGURE 2. Energy potential of Mo based on experiment Moldy is an open source program used for performing molecular dynamics simulations of condensed matter. The results of this simulation are radial distribution function, mean square displacement, diffusi constan, stress and pressure which reflect characteristic of the material. Moldy is free from such arbitrary constraints. The system may contain a mixture of an arbitrary number of molecular species, each with an arbitrary number of atoms and an arbitrary number of molecules of each. Molecules or ions may be monoatomic or polyatomic, linear or three dimensional in any combination. The potential functions may be the other of the Lennard-Jones, Buckingham (including Born-Mayer) or Matsuoka Clementi Yoshimine (MCY) types may be easily added.
TABLE 2. Lennard-Jones Parameter interaction of Fe, Pb, Bi, Ni, Cr and Mo No Atom ε (ev) ( Å ) 1 Fe-Fe 0.62 2.26 2 Pb-Pb 0.125 2.75 3 Fe-Pb 0.278 2.505 4 Ni-Ni 0.60 1.90 5 Fe-Ni 0.601 2.08 6 Pb-Ni 0.276 2.325 7 Cr-Cr 0.20 2.50 8 Fe-Cr 0.352 2.38 9 Pb-Cr 0.158 2.625 10 Ni-Cr 0.346 2.20 11 Bi-Bi 0.075 3.20 12 Fe-Bi 0.216 2.78 13 Pb-Bi 0.097 2.975 14 Ni-Bi 0.212 2.55 15 Cr-Bi 0.162 2.85 16 Mo-Mo 0.03 1.00 17 Fe-Mo 0.136 1.63 18 Pb-Mo 0.061 1.875 19 Ni-Mo 0.134 1.45 20 Cr-Mo 0.077 1.75 21 Bi-Mo 0.0474 2.10 There are many visualisation open source software for moleculer dynamics, such as Pymol, Jmol, Rasmol etc. The visualisation can be shown and create from.pdb file in Moldy. Moldy has been used to simulate the material properties for performing molecular dynamics simulations [10]. Simulation can be done from initial configuration of the atoms. Initial configurations of the material Fe, Ni, Cr, Mo, Pb and Bi have a lattice parameter by experiment that depends on each crystal structure. Interactions between the combination of atoms Fe, Ni, Cr, Mo, Pb and Bi are assumed to follow Lenard-Jones potential parameter or by experiment. The results of this simulation are Radial Distribution Function (RDF) calculated. RDF is a function of position which can be used to see the state of phase of the system as well as a function of temperature. The phenomena of staintless steal corrosion can be considered as function of temperature. RESULT AND DISCUSSION MD simulation is done for interaction crystal steel Fe 71%, Ni 10%, Cr 16% and Pb 55%, Bi 45% with Mo 2%-3% content in crystal steel. The left side is atoms of crystal steel and the right side is atoms of coolant material Pb-Bi. The interaction between crystal steel Fe, Ni, Cr, Mo and Pb-Bi at temperature 573K, 773K, 973K, 1173K and 1373K were investigated. The simulation takes 20000 number of steps. The content of each atom in crystal steel are Fe 70%, Ni 10%, Cr 16%, Mo 2%-3%, Pb 50% and Bi 50%. The phenomena for the increasing content of Mo 3%-4% are investegated too at temperature 573K, 773K, 973K, 1173K and 1373K. The analyses have two proceses. The first proses made the input file for generating the atom position through control file. The second process is a molecular dynamic simulation.
This visualisation used Jmol open source program. The results of this simulation are the value of RDF calculated. The phenomena of corrosion can be create from.pdb file. The output of MD simulation with Mo 2%-3% content are shown only at temperature 773K, 973K and 1373K in Fig. 4, Fig. 5 and Fig. 6. Mo25-773K FIGURE 4. Mo 2%-3% content in crystal steel at temperature 773K Mo25-973K FIGURE 5. Mo 2%-3% content at Temperature 973K Mo25-1373K FIGURE 6. Mo 2%-3% content at Temperature 1373K
The surface of stainless steel in temperature 973K with Mo 2%-3% has been seen has more corrosion than at temperature 773K. In temperature 1373K the surface of stainless steel has more corrosion than at temperature 973K. The output of MD simulation with Mo 3%-4% content at temperature 773K, 973K and 1373K shown in Fig.7, Fig. 8 and Fig. 9. Mo35-773K FIGURE 7. Mo 3%-4% content at Temperature 773K Mo35-973K FIGURE 8. Mo 3%-4% content at Temperature 973K Mo35-1373K FIGURE 9. Mo 3%-4% content at Temperature 1373K
In temperature 973K with Mo 3%-4% content, the surface of stainless steel has seen more corrosion than the surface at temperature 773K and in temperature 1373K has seen more corrosion than the surface at temperature 973K. These phenomena in temperature 773K, 973K and 1373K with Mo 3%-4% content, have less corosion than in Mo 2%-3% content. This phenomenom has the same with the statement from experiment that the stainless steel with Mo 3%-4% content has more resistance to corrosion than the stainless steel with Mo 2%-3% content CONCLUSIONS The phenomena beetwen crystal steel Fe 71%, Ni 10%, Cr 16% with Mo 2%-3% content and Pb 55%, Bi 45% in several temperature have been investigated with MD simulation. The phenomena with Mo 3%-4% content have been investigated too. The effect of increasing Mo content for resistance corrosion has been investigated. The results of this simulation are the phenomena of Mo with difference content on the corrosion in several temperatures. The surface of stainless steel with Mo 3%-4% content by lead-bismuth Pb-Bi at the temperature 773K, 973K and 1373K has less corrosion than the surface of stainless steel with Mo 2%-3% content by lead-bismuth Pb-Bi. This phenomenom has the same with the statement from experiment that the stainless steel with Mo 3%-4% content has corrosion resistance than the stainless steel with Mo 2%-3% content. ACKNOWLEDGMENT I would like to thank to the Ministry of Research and Technology of the Republic of Indonesia that has funded this research through funding incentive program in 2011. REFERENCES [1] Yingxia Qi, Minoru Takahashi (2002), Computer Simulation of Diffusion of Pb-Bi Eutectic in Liquid Sodium by Molecular Dynamics Method, Proceedings of ICONE 10-22236, The10TH International Conference on Nuclear Engineering, Arlington, VA, USA [2] Yingxia Qi, Minoru Takahashi (2003), Study on Corrosion phenomena of Steels in Pb-Bi Flow, Proceedings of ICONE11-36376 [3] Alan Maulana, Zaki Suud, Hermawan K.Dipoyono and Khairural (2007), Preliminary Study of Steels Corrosion Phenomena in Liquid Lead-Bismuth using Molecular Dynamics Methods, Indonesian Journal of Physics, Vol 18 No 1 [4] www.sandmeyersteel.com/types 316 (S31600), 316L (S31603), 317 (S31700), 317L (S31703) [5] Donald R. Askeland, Phule, P. Pradeep (2006), "The Science and Engineering of materials, Nelson, a division of Thomson Canada [6] Keonwook Kang and Wei Cai (2005), Vacancy Formation Energy, http://micro.stanford.edu/~caiwei/forum/ [7] Allen, Michael P. (2004), Introduction to Molecupar Dynamics Simulation, John Von Neumann Institute for computing, Volume 23 [8] Yajun Liu and Xianming Shi (2010), Molecular Dynamics Study of Interaction Between Corrosion Inhibitors, nanoparticles, and Other Minerals in Hydrated Cement, Transportation Research Record 2142 [9] Michael J. Mehl and Dimitrios A. P (1996), Application of tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surface of monoatomic metals, Physical Review B [10] James Adler (2003), "Molecular Dynamic of Simulations of Copper using Moldy, Research Experience for Undergraduates, National High Magnetic Field Laboratory