DFT study of the fouling deposition process in the steam generator by simulating the absorption of Fe2+ on Fe3O4 (001) 


 In this paper, the interaction between free Fe2+ and Fe3O4 corrosion products on the pipe surface in the secondary circuit of PWR nuclear power plant was studied, and the reason of agglomeration formation was analyzed. The complex physical and chemical interaction was simplified by describing the electron interaction. Based on the first principles, CASTEP was used to simulate seven kinds of highly symmetric adsorption structure models of Fetet1 and Feoct1 on Fe3O4 (001) surface, and their adsorption energies and stable adsorption conformations were calculated. The results show that the most stable adsorption structures of the Fe2+/Fe3O4 (001) configurations are Feoct1-b and Fetet1-Oh. During the adsorption, the Fe-Fe, Fe-O bond length and Fe-Fe-O bond angle of (001) surface changed, and the atomic positions parallel and perpendicular to (001) surface changed correspondingly, the surface layer changes the most. The results prove that the adsorption has great effect on the physical structure of Fe2+ and Fe3O4 (001). The calculation of charge population, the density of states and electron local function of Fe2+/Fe3O4 (001) optimal adsorption configuration also shows that there is electron transfer between Fe2+ and Fe3O4 (001), and the adsorption type is chemisorption. Among them, Fe (Fe2+)-Fe (Fe3O4) forms a metal bond, and Fe (Fe2+)-O (Fe3O4) forms the ionic bond.


Introduction
The secondary heat exchange surface of steam generator (SG) in pressurized water reactor (PWR) of nuclear power plant (NPP) is easy to fouling, making the wing hole being gradually blocked by corrosion products [1]. The fouling phenomenon in SG secondary circuit was first found in Chalk River [2,3]. The blocking phenomenon reduces the flow rate of the fluid passing through the supporting plate, and also increases the pressure drop, hinders the liquid passing through the secondary circuit, and reduces the heat exchange efficiency of SG [4]. When the blockage phenomenon becomes serious, the SG heat exchange tube and support plate will have strong vibration, and lead to fatigue fracture of the steam generator pipe. At present, several works proved that the majority of the fouling is in form of magnetite (Fe 3 O 4 ) [1,5,6] Fe 3 O 4 has strong sub-magnetism and high electrical conductivity at room temperature, and widely used as a metal oxide catalyst. The fouling magnetite is composed of particle deposition and soluble ions in the medium. The soluble ions mainly come from the surface of materials dissolved in the secondary circuit. Moreover, the existence of Fe 3 O 4 on the surface of SG heat exchange tube also has a certain adsorption effect on Fe 2+ in the secondary circuit [7,8].
In order to analyze the interaction between Fe 2+ and Fe 3 O 4 surface in the agglomeration process, the density functional theory (DFT) was used for theoretical calculation [9][10][11][12]. At the same time, some studies involved the corresponding nanoscale model of corrosion fouling were carried out to find the most stable adsorption configuration of corrosion fouling in the protective layer and verified by molecular simulation [13,14]. Fe 3 O 4 is a kind of widely used oxide in industry, which has important catalytic performance [15][16][17]. The related research about the adsorption and dissociation of gas molecules on Fe 3 O 4 surface provides a reference method for the interaction and agglomeration of Fe 3 O 3 surface in the secondary circuit [18][19][20]. Yang et.al. [21] studied the surface structures of Fe 3 O 4 (111), (110) and (001) by DFT method, and reasonably explained the diversity and complexity of the adsorption and catalytic properties of Fe 3 O 4 . Yin et.al. [22] used DFT method to analyze the behaviour of adding singlewalled carbon nanotubes (SWNTs) to Fe 3 O 4 nanoparticle electrodes, which can significantly improve the conductivity and performance of lithium-ion batteries. They believe that transition metal (Fe, Ni) atoms or clusters are helpful to form strong chemical bonds between SWNTs and Fe 3 O 4 (001) surfaces, which provides a good channel for electrons and improve the conductivity. Xue et.al. [23] studied the adsorption characteristics of CO on the non-defect and defect (oxygen-containing vacancy) B-layer Fe 3 O 4 (001) surface (octahedral environment) by using spin polarization DFT and Hubbard u parameter (DFT + U).
They confirmed that both two types of B-layer Fe 3 O 4 (001) surfaces had great CO oxidation ability. Yu et.al. [24] systematically analyzed the adsorption behaviour of CO on Fe 3 O 4 (111), (110) and (001) surfaces, and analyzed the adsorption mechanism according to the projected density of states. Zhou et.al. [25] used DFT method to calculate the oxidation mechanism of Hg0 on Fe 3 O 4 (001) surface by heterogeneous H 2 O 2 . The results show that the oxidation process may go through three different ways at the same time, and the mechanism may become an attractive method for mercury control in the flue gas. Therefore, the adsorption behaviour of particles on Fe 3 O 4 (001) surface is affected by many factors, such as the structural electrification and surface integrity. At present, we can only find out that Fe 2+ released by secondary side surface can adsorb on Fe 3 O 4 surface, and lead to the continuous increase of Fe 3 O 4 fouling in SG secondary circuit, but the relevant mechanism is still unclear.
In this paper, we simulate the deposition behaviour of Fe 2+ on different terminals of (001) surface based on the first principles and find out the most stable adsorption configuration. We also analyze the adsorption structure characteristics and physical parameters and the adsorption behaviour characteristic.
The adsorption behaviour can be considered as the basis of the Fe 3 O 4 deposition and agglomeration on the heat exchange tube secondary surface of the steam generator. In addition, by studying the geometry structure and adsorption energy of Fe 2+ on Fe 3 O 4 (001) surface, we can better understand the active electron properties, track the transfer direction of active electrons, and analyze the charge to describe the electronic properties of the most favourable adsorption configuration of Fe 2+ on Fe 3 O 4 (001) surface.

Methods
All the DFT calculations are performed using the Cambridge sequential total energy program package (CASTEP) module in the Materials Studio software package. The interaction between nucleus and electron is treated by ultra-soft pseudopotential. The generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerh (PBE) is used to describe the exchange correlation energy, and the plane wave basis set is used to expand the wave function [26][27][28], and the truncation energy is 450eV.
In the SG secondary circuit of PWR, fouling deposit Fe 3 O 4 have a low index surface (001) with higher symmetry, which has stable surface free energy in thermodynamics. Six nonequivalent ideal terminals can be obtained by cutting the Fe 3 O 4 (001) stacking sequence. The terminals with fewer dangling bonds have higher stability. Therefore, the Fe 3 O 4 (001) surfaces terminated by fetet1 and feoct1 can be regarded as the most stable terminals. The main content of this experiment is to explore the specific behaviour of fe tet1 and fe oct1 terminal configurations on Fe 3 O 4 (001) surface in the secondary circuit [23].
By cutting (001), there are four terminals of stacking sequence, which are Fe tet1 and Fe tet2 with tetrahedral coordination Fe atoms exposed, Fe oct1 with exposed octahedral coordination Fe atoms and close packing O oct1 layer. The atomic plane stacking sequence perpendicular to (001) direction can be written as Fe oct1 -Fe tet1 -O oct1 -Fe tet2 . The (001) surface low index crystal surface of Fe 3 O 4 , with low Bragg index and high symmetry. In thermodynamics, the surface free energy of (001) surface is more favourable than that of natural growth surface (111), and its catalytic activity is consistent with (111) [32]. There will be different terminal faces after cleaving (001) surface, and the terminal surfaces with fewer dangling bonds are relatively stable. That is, the Fe tet1 and Fe oct1 -terminal surface with the least dangling bonds are stable. Fe tet1 -terminal surface has one exposed tetrahedral Fe atom, and Fe oct1 -terminal surface two exposed octahedral Fe atoms and four exposed O atoms. Among these two kinds of terminal surfaces, the Fe oct1 -terminal surface is more likely to be the most active surface, because the exposed octahedral Fe atoms on this terminal surface have two valence states, which electrons can transition between them [21].
To analyze the stability of different adsorption configurations, we use the adsorption energy E AD to compare the energy difference before and after adsorption. The formula is as follows: where 2+ / 3 4 is the total energy of adsorbate and surface, 3 4 is the total energy of Fe 3 O 4 (001) surface, and 2+ is the total energy of isolated Fe 2+ . When the adsorption energy is negative, it can be adsorbed, and the greater the absolute value, the easier the adsorption.

Models
Although Fe tet1 , O oct1 , Fe oct1 , and Fe tet2 can obtain nonequivalent ideal body termination by cutting Fe3O4 (001) stacking sequence, Fe tet1 and Fe oct1 terminals (as shown in Fig. 1) have only 6 bond breaks, and other terminations are more than this, so Fe tet1 and Fe oct1 terminals are stable. The Fe oct1 -terminal surface with exposed octahedral Fe atoms, as shown in Fig. 2, is selected as the model to study the secondary circuit reaction. Choosing the atomic model as the research object can achieve a good balance in precision and calculation time. The thickness of the vacuum layer is set at 15 Å to eliminate the periodic interaction. In the calculation process, the atoms at the bottom are fixed, and the atoms at the top two layers and adsorbate are allowed to relax.  In previous research, it had been concluded that the spin-down Fermi surface in PDOS diagram is mainly occupied by the electrons of Fe oct atom and has a certain bandwidth, which leads to the semimetallicity of Fe 3 O 4 bulk structure [33,34]. In the energy band diagram of Fe tet1 , we can find the 0.11eV spin-down bandgap, but no bandgap in the total density of states diagram. The bandgap indicates that the semi-metallicity of Fe tet1 surface exists, but it is not as strong as the original structure.  Figure 3 shows the front and top views of the corresponding configurations.

Adsorption structures and energy
The possible stable adsorption configuration of Fe 2+ on Fe 3 O 4 (001) surface is shown in Fig. 4. The corresponding geometric structure parameters and adsorption energy can be seen in

Fig. 6 Simulation outcome of Fe3O4 (001) tet -Oh (a) 1ps (b) 16ps (c) 33ps (d) 37ps (e) 50ps
Fig . 6 oct -b is the most stable adsorption site of (001) surface. In the relaxation process, electron interaction can be found between Fe 2+ and the surface, meaning that Fe 2+ adsorption is chemisorption. This configuration has the most of chemical bonds and the highest adsorption energy.    It can be seen from Table 4 that the newly formed bond O2-Fe10 population is 0.39e and the bond length

Electronic density of states
To analyze the electronic density of states of different bonding formed at adsorption sites, the PDOS of Fe 3 O 4 oct -b configuration after adsorption is made, as shown in Fig. 7, so the comprehensive changes of bonding conditions, adsorption energy and electronic density of states can be studied. oct -b configuration, the 2s orbital of O atom will participate in the orbital hybridization of Fe 2+ and affect the bonding, but the effect is not as great as that of 3d orbital of Fe atom. The energy band diagram of Fe 3 O 4 (001) oct -b configuration is shown in Fig. 8. Compared with Fig. 8 and Fig. 3c  For further analysis about the electron localized behaviour of Fe 2+ on the Fe 3 O 4 oct -b site, as shown in Fig.9, the differential electron density diagram is used to directly describe the redistribution of surface

Conclusion
Fe 2+ adsorption on the surface of the nuclear power plant steam generator secondary circuit heat transfer tube will agglomerate the fouling and accelerate the scaling process through the electron interaction. Through the first-principles calculation, we simulated the changes of