Thermodynamic Assessment and Solubility of Ni in LBE Coolants

Abstract

Lead–Bismuth Eutectic (LBE) is a heavy metal liquid alloy used as a coolant for compact high temperature reactors (CHTRs), fast breeder reactor (FBRs) and as a spallation target for ADS. In spite of many advantages due to its thermophysical properties, corrosion towards structural materials remains one of the major issues of LBE. In absence of any oxygen impurity, corrosion in LBE is driven by dissolution processes and the solubility of the main elements of the structural material alloys. Using the CALPHAD method, Thermo-Calc software, a thermodynamic database was developed to assess the interaction between Ni and LBE coolant. The solubilities of Ni in LBE, Bi and Pb liquids have been calculated at different temperatures.

1. Introduction

In the framework of the Generation-IV Nuclear Energy Systems [1] initiative, Pb/LBE is being explored as a coolant for compact high temperature reactors (CHTRs) and fast breeder reactors (FBRs) due to its favourable physical, chemical and nuclear properties. High temperature nuclear reactors have a large potential for sustainably supplying energy for these hydrogen production processes at required high temperature conditions [2]. In Accelerator-driven sub-critical reactor systems (ADS) [3,4,5,6,7,8], LBE is also considered for coolant and spallation targets [9], with the aim of producing low-cost energy and burning/transmuting the minor actinides and the long-lived radioactive fission product. Other than being inherently safe as they generate power in a subcritical condition, the main advantage of ADS is their application to decrease the radio toxicity load on nature by disposing long-lived radioactive wastes produced in other nuclear reactors. The concept of ADS (frequently called hybrid systems) combines a particle accelerator with a sub-critical core (see Figure 1) [3].

The choice of LBE, as a coolant for fast reactor and as a candidate for spallation target and coolant for ADS, has a number of positive aspects, especially with regard to safety and the strong implications on design simplifications, which provide obvious financial advantages.

However, LBE corrosion of structural materials (clad) is a critical limitation for their use as coolants for nuclear applications; stainless steels are severely damaged when exposed to this heavy liquid at high temperatures. The corrosion behavior of austenitic or martensitic steels in LBE was studied by several authors [10,11,12]. Most of these studies focused on the oxidation phenomena, directly linked to the oxygen potential imposed during the static or flowing experiments. Compared to corrosion by aqueous media which has been found to be primarily an electro-chemical process, corrosion by liquid metal such as liquid lead and lead–bismuth alloy is a physical or physico-chemical process involving dissolution of material constituents, transportation in the two phases (liquid and solid) and reactions between corrosion products and impurities [13,14,15]. It has been reported that the corrosion by liquid metals/alloys can change the microstructure, composition, and surface morphology of the structural materials, which in turn affects the mechanical and physical properties of the structural materials, leading to system failure [15,16,17,18,19,20,21,22,23,24,25,26,27]. The rate of dissolution of the structural materials remains of major importance too when considering the resistance of the alloys because it drives the LBE chemistry [10,11]. To understand the clad–coolant interaction, i.e., the interaction of stainless-steel structural materials with Bi-Pb, it is important to know the thermo-physical properties of alloys/compounds formed by interaction of Pb and Bi with all major elemental component of steel, i.e., Fe, Cr and Ni. Among Fe, Cr and Ni, the former two elements, Fe and Cr, have very slight solubilities in Pb/Bi, whereas the solubility of Ni in Pb/Bi is maximum. Nickel also makes two intermetallic compounds with Bi. However, the lack of reliable thermodynamic data (solubility limit and chemical activity) in such complex systems makes it difficult to explain the non-equilibrium behavior and the interactions observed in experimental studies on LBE [10,11,12,13,14]. Unfortunately, computation based on the CALPHAD approach is not available in the literature for the interactions between the Bi-Pb heavy metal coolant and the major constituting elements of the alloys: Fe-Cr-Ni. Nickel is the main component of stainless-steel structural material that shows strong interactions with lead, bismuth or LBE coolants. Therefore, in this study, assessment of the Bi-Ni-Pb ternary system using only binary interaction parameters was carried out and solubility limits of nickel in Bi, Pb and LBE coolants at different temperatures was calculated.

2. Thermodynamic Modeling

The temperature dependencies of the molar free energies for the pure elements are described in the following form according to ref [28]:

$$G_i^0(T)-H_i^{SER}=A_i+B_{i}T+C_{i}TlnT+D_i{T}^2+E_i/T+F_i{T}^3+I_i{T}^4+J_i{T}^7+K_i{T}^9+\Delta G_{mag}(T)$$

(1)

where, $G_i^0$(T) is the Gibbs energy of a pure element ‘i’ at temperature T, H_i^SER represents the enthalpy of the pure element ‘i’ in its stable state at the standard temperature 298.15 K and pressure 1 bar; T is temperature and ΔG_mag(T) is the magnetic term. Values of coefficients A, B, C and K for the lattice stabilities of the pure elements were taken from Pure4 database in Thermocalc [29]. The molar Gibbs energy for a binary phase is expressed by the following equation:

$${}^{o}G_m^{\phi }-{\displaystyle \sum _{i=A,B}{x}_i^{\phi }}{}^{o}H_i^{SER}(298.15 \mathrm{K})={\displaystyle \sum _{i=A,B}{x}_i^{\phi }}\{{}^{o}G_i^{\phi }-{}^{o}H_i^{SER}(298.15 \mathrm{K})\}+RT{\displaystyle \sum _{i=A,B}{x}_i^{\phi }}\ln (x_i^{\phi })+G^{\phi ,xs}$$

(2)

where, x_i denotes the atomic fraction of the ‘i’ element. ‘R’ is the universal gas constant. The excess Gibbs energy, G^φ,xs, of a binary solution is expressed by the Redlich–Kister polynomial equation [30].

$$G^{\phi ,xs}=x_i^{\phi }{x}_i^{\phi }{\displaystyle \sum _{\nu =1}^n{}^{\nu }L_{i,j}}{(x_i^{\phi }-x_j^{\phi })}^{\begin{array}{l}\nu \\ \end{array}}$$

(3)

where, the interaction parameters, L^ϕ_i,j (with υ = 0,1) can be temperature dependent in the Redlich–Kister power series, are expressed by:

^υL^ϕ_i,j = α + βT

(4)

where, α and β are the adjustable interaction parameters refined to replicate the experimental data. The ternary Ni-Bi-Pb assessment is based on extrapolations of the most important binary sub systems: the Bi-Pb, Bi-Ni and Ni-Pb systems. The thermodynamic assessments of the Bi-Pb and Bi-Ni binary systems were performed in this study. The third binary Ni-Pb system was taken from the literature.

2.1. Thermodynamic Assessment of Bi-Pb System

The use of LBE as a coolant in nuclear systems makes it necessary to improve interpretation of the origin of the low temperature liquid phase. In this binary system, the liquid comes from the eutectic reaction (Liquid ↔ Bi-Rhombo + BiPb_3±x), calculated at 399 K. At this temperature, rhombohedral Bi (Bi-Rhombo), liquid and hexagonal close-packed intermetallic phase (BiPb_3±x) are in equilibrium. Therefore, the Bi-Pb system has only one non-stoichiometric compound, BiPb_3±x. The maximum solubility of Bi in Pb-FCC is ~78 at% Pb at 457 K [31,32]. The solubility of Pb in Bi-Rhombo is negligible [31]. The phase boundary of BiPb_3±x was based on the studies carried out by Wolt et al. [33] (resistivity measurement), Predel et al. [34] (thermal analysis, microscopy, resistivity and X-ray) and Hoff et al. [35] (X-ray and resistivity measurement). The emphasis is given on the Predel et al. [34] and present thermodynamic calculations. The data of obtained by resistivity measurements sometimes appeared to be overestimated. The solubility limit of the Bi in Pb-FCC phase is a combination of X-ray data of Hay et al. [36], the results of Predel et al. [34] and the data of Wolt et al. [33] and Hoff et al. [35], and the phase diagram of Yoon et al. [32]. It is evident from Figure 2, that the result of resistivity measurement is too high as compared to other data. The reason behind this is the poor resolution in the measurement and systematic error associated with non-ideal nature of measurement. However, the time of equilibration of BiPb_3±x phase is also important when below a temperature of 200 °C. Complete homogenization of alloys into that BiPb_3±x phase may not have accomplished due to low diffusion rate. It can take a long time to determine the phase boundary at a lower temperature. The phase diagram was optimized by Boa et al. [31] and Yoon et al. [32]. It was found that the optimized parameters of Boa et al. and Yoon et al. did not have any excess heat capacity coefficients for BiPb_3±x. The heat capacity, enthalpy of formation of BiPb₃ and the enthalpy of mixing of liquid solution were measured by the authors [37,38]. Using these important thermodynamic data along with phase-diagram and Gibbs energy data available in the literature [32,33,34,35,36,39,40], the optimization of interaction parameters of the system was performed with the help of Thermocalc software based on CALPHAD approach. The calculated phase diagram of the Bi-Pb system and all experimental phase diagram data [32,33,34,35,36,39,40], which are used in the present optimization, are shown in the Figure 2. The phase boundaries calculated from previous optimizations reported in the literature are also drawn in the Figure 2 [30,31]. It is seen that the present assessment is in reasonable agreement with previously reported assessments and experimental data. All invariant reactions in the Bi-Pb system are summarized in

Table 1. Comparison of invariants in Bi-Pb system between previous assessment and this study.

Reaction	Type	T/K	Composition, x(Pb)			References
L + Pb-FCC = BiPb3	Peritectic	457.5	0.62	0.78	0.719	[31]
		457	0.64	0.769	0.72	[32]
		457	0.63	0.819	0.719	This Study
L = BiPb3 + (Bi-Rhomb)	Eutectic	398.5	0.446	0.58	0.005	[31]
		398.5	0.446	0.58	0.005	[32]
		399	0.446	0.58	0.005	This Study

, with the calculated data from previous assessment. A complete set of the present assessed thermodynamic descriptions of this system is given in

Table 2. Assessed parameters for the Bi-Ni-Pb ternary system.

Phase and Model	Thermodynamic Parameters
LIQUID [Bi,Ni,Pb]1	${}^{0}L_{Bi,Ni}^{Liq}$ = −19992.628 + 99.11350 × T − 10.0574 × T × ln(T) ${}^{1}L_{Bi,Ni}^{Liq}$ = 1.2944 − 191.9533 × T + 25.5048 × T × ln(T) ${}^{2}L_{Bi,Ni}^{Liq}$ = 12521.6048 − 1.5602 × T ${}^{0}L_{Bi,Pb}^{Liq}$ = −5050.202 + 1.85 × T ${}^{1}L_{Bi,Pb}^{Liq}$ = −1050.01 + 1.18 × T ${}^{0}L_{Ni,Pb}^{Liq}$ = +31532.257 − 2.42 × T ${}^{1}L_{Ni,Pb}^{Liq}$ = +10459.949 − 2.49 × T ${}^{2}L_{Ni,Pb}^{Liq}$ = −10927.18 + 7.952 × T ${}^{3}L_{Ni,Pb}^{Liq}$ = −3732.467 − 0.109 × T
BiPb3 [Bi, Pb]1	${}^{0}L_{Bi,Pb}^{BiPb3}$ = −3450.04 + 9.781 × T − 2.5001 × T × ln(T) − 496987.08/T ${}^{1}L_{Bi,Pb}^{BiPb3}$ = −1.801 × T
Pb-FCC [Bi, Pb]1	${}^{0}L_{Bi,Pb}^{Pb-FCC}$ = −3550.05 + 1.11 × T
Bi-Rhomb [Bi, Pb]1	${}^{0}L_{Bi:PB}^{Bi-R\mathrm{hom}b}$ = 3461.56
Bi3Ni [Bi]3 [Ni]1	${}^{0}G_{Bi:Ni}^{Bi3Ni}$ = −2450.002 + 9.1195 × T − 1.9 × T × ln(T) + 0.75GBi-rhombo + 0.25GNi-FCC
BiNi[Bi]0.3334 [Ni]0.3333[Bi,Va]0.3333	${}^{0}G_{Bi:Ni:Bi}^{BiNi}$ = 0.667GBi-rhombo + 0.333GNi-FCC ${}^{0}G_{Bi:Ni:Va}^{BiNi}$ = −4250 + 13.37 × T − 1.8 × T × ln(T) + 0.333GBi-rhombo + 0.333GNi-FCC ${}^{0}L_{Bi:Ni:Bi,Va}^{BiNi}$ = −1647 + 1.434 × T
Ni-FCC [Bi,Ni,Pb]1	${}^{0}L_{Bi,Ni}^{Ni-FCC}$ = −20000 + 12.5 × T ${}^{0}L_{Ni,Pb}^{Ni-FCC}$ = +29980 + 0.59 × T ${}^{1}L_{Ni,Pb}^{Ni-FCC}$ = −20000 + 25 × T

.

2.2. Thermodynamic Assessment of Bi-Ni System

There are two intermetallic compounds, Bi₃Ni and BiNi, in the Bi-Ni system. The solubility of Bi in Ni-FCC is very limited. No Ni solubility is considered in the rhombohedral structure of Bi. The Bi₃Ni phase is stoichiometric while BiNi exhibits a narrow composition range towards the Bi-rich domain. Some publications indicate a narrow non-stoichiometric region for both compounds. However, due to lack of experimental data on non-stoichiometric range of stability of Bi₃Ni, only BiNi is assumed to be non-stoichiometric in the present assessment calculations. In light of new calorimetric data of the system; acquired by authors [41,42], the Bi-Ni system was re-optimized. The thermodynamic assessment was carried out by optimizing experimental phase diagram and thermodynamic data available in the literature [43,44,45,46,47] and our experimental data of (i) heat capacity, (ii) enthalpy increment, (iii) enthalpy of formation of compounds and (iv) enthalpy of mixing of liquid phase [41,42]. The calculated phase diagram of the Bi-Ni is shown in Figure 3. It is seen that the calculated results are in reasonable agreement with previous assessments [43,48] as well as experimental phase diagram data [43,44,45,46,47]. A complete set of the present assessed thermodynamic descriptions of this system is given in Table 2.

All invariant reactions in the Bi-Ni system are summarized in

Table 3. Comparisons of invariants in Bi-Ni system.

Reaction	Type	T/K	Composition, x(Ni)			References
BiNi = (Ni-FCC) + Liq	Peritectic	920.7	0.759	0.515	0.00485	[43]
		919.0	0.762	0.510	0.022	[48]
		921.0	0.76	0.517	0.005	This work
Bi3Ni = BiNi + Liq	Peritectic	737.2	0.881	0.75	0.52	[43]
		738.0	0.877	0.75	0.515	[48]
		737.5	0.878	0.75	0.52	This work
Liq = Bi3Ni + (Bi-Rhomb)	Eutectic	542.8	0.75	0.993	1.0	[43]
		543.0	0.75	0.993	1.0	[48]
		543	0.75	0.991	1.0	This work

, along with the calculated data from previous assessments for comparison.

3. Interaction of Pb/Bi with Ni

As discussed earlier, nickel is one of the main components of stainless-steel structural material that will show strong interactions with lead, bismuth or LBE coolants. Therefore, it is important to assess this ternary system and find out solubility limits of nickel in these coolants at different temperatures. It is also of great significance to know what solid phases may precipitate out at different temperatures. Precipitation of a compound in a coolant can be detrimental to its performance as it can be carried to different parts and accumulate in certain sensitive areas, which can obstruct the smooth flow of coolant, thus causing local heating and swelling. In addition to this, these interactions thin the clad due to chemical abrasion. In extreme conditions, this can cause a burst of coolant channels and an accidental loss of coolant. In addition, thermodynamic properties such as heat capacities, enthalpies of formations and enthalpies of transitions of these precipitating phases at different temperature can affect the thermal performance of the coolant, which goes through different thermal conditions during the heating and cooling of the reactor. Depending on its location, even in an operating nuclear reactor, coolant can be exposed to very different temperatures.

➣

Therefore, to understand different phases formed by the interaction of Pb/Bi and Ni, the Bi-Ni-Pb ternary was computed. As discussed in Section 2.1 and Section 2.2, respectively, Bi-Pb and Bi-Ni binaries of this ternary were re-optimized using the experimental data acquired during this work. The third binary required for computing the Bi-Ni-Pb ternary is Ni-Pb. This binary system does not have any intermetallic compound and its thermodynamic assessment can be reliably obtained from a thermodynamic description of unary elements and the binary phase diagram data available in the literature. Therefore, no new experimental data was acquired for this system. The phase description for Ni-Pb system was taken from Ghosh et al. [49]. The modeling by Ghosh et al. considers numerous sets of phase diagram data and thermodynamic information from the literature [44,46,50,51,52,53]. For the sake of clarity, the Ni-Pb system is shown in the Figure 4. The Ni-Pb binary has a liquid phase miscibility gap, does not have any intermetallic compound and the FCC-Ni phase dissolves a small amount of Pb. In the absence of experimental thermodynamic or phase diagram data for the Bi-Ni-Pb ternary, computation of this system was based on the following assumptions:

➣

As crystal structures of all the intermetallic compounds, Bi₃Ni, BiNi and BiPb₃, are quite different, they were assumed to be present as pure binary compounds in the ternary system.

➣

The liquid phase and end member solubilities were modeled by using only binary interaction parameters

➣

In absence of any experimental data to indicate the presence of stable ternary compounds, no new ternary phase was considered.

➣

To understand Ni interaction with LBE at different temperatures, a pseudo binary diagram along the isopleth LBE-Ni was computed (Figure 5). As there was no available experimental data in the literature on this ternary system, it was decided to study transition temperatures of this pseudo-binary system, using DTA. For this purpose, alloys with different compositions of Ni in LBE (0.38 < x(Ni) < 0.46) were prepared. The alloys were prepared by melting desired ratios of lead, bismuth and a fine powder of nickel metal. The liquid mixture was slowly cooled in a furnace to ambient temperature. DTA analysis of these alloys was carried out using an indigenously fabricated DTA instrument. The temperatures of phase transitions were obtained from the extrapolated peak onset temperature during heating of alloys at 5K/min. The present DTA results of selected compositions are plotted in Figure 5 of pseudo-binary phase diagram of LBE-Ni system. Our experimental data shows reasonable agreement with the computed pseudo binary diagram. It proves that the above listed assumptions used for the computation of the ternary system were acceptable. Hence, inferences based on the ternary database, generated using binary interactions, should be reliable.

The pseudo binary phase diagram of LBE-Ni given in Figure 5 has generic similarity to Bi-Ni phase diagram. This is mainly due to the presence of high melting nickel metal in both the diagrams and low temperature decomposition of BiPb₃ compound. However, the prominent difference in these two diagrams is that the solubility limit of nickel in bismuth liquid is much higher than in LBE, as the liquid of Bi-Ni is richer in nickel than of LBE-Ni system. For example, solubility of Ni in bismuth liquid at 600 K is 2 at.% Ni and in LBE is 0.6 at.%, whereas at 770 K, 14 at.% Ni dissolve in Bi(l) and 2.6 at.% Ni in LBE and at 1273 K, 35 at.% Ni dissolve in Bi(l) and 16 at.% Ni in LBE. The latter temperature (1273 K) is seen by the coolant of High Temperature Compact Reactor (CHTR) [54]. At temperatures below 770 K, longer erosion of Ni by LBE will result in formation of BiNi/Bi₃Ni compound. At room temperature, LBE has the BiPb₃ compound in equilibrium with ‘Bi-Rhomb’. Due to the interaction of LBE with ‘Ni’ at high temperatures, the Bi₃Ni compound may also become precipitated. At ambient temperature, the Pb-FCC phase will not be observed as it interacts with bismuth to form BiPb₃. Therefore, bismuth metal will react with both Ni and lead and form compounds, BiPb₃ and Bi₃Ni. During the cooling of liquid coolant, significant heat will be generated due to enthalpy of fusion of Pb/Bi and formation of intermetallic compounds, BiPb₃, Bi₃Ni and BiNi. Heat capacity of these intermetallic compounds is slightly higher than that of pure elements [38,41]. Therefore, coolant temperature will decrease at a slower rate in presence of intermetallic compounds. A similar effect will be seen when heating coolant to liquid phase, as coolant that contains these compounds will need more heat to melt completely.

A complete set of the presently assessed thermodynamic descriptions of this ternary system is given in Table 2.

4. Solubility of Nickel in LBE/Bi/Pb

As discussed earlier, due to the relatively high solubility of the major alloying components of steel, LBE is severely corrosive to steel, especially at high temperatures (>1000 K). As previously mentioned, precipitation at cold walls is catastrophic because severe precipitation may lead to the clogging of piping and degradation of heat transfer. During a long period of operation, especially at high temperature, corrosion of structural material can change its composition, microstructure and strength, which can be detrimental to its safe operation. Hence, it is important to know the solubility of components of steel in pure liquid Pb, Bi and LBE. Solubility limits of Ni were calculated in Pb(l), Bi(l) and LBE(l). The calculations were carried out using the interaction parameters given in Table 2. Calculated and experimentally determined solubilities of Ni in Pb, Bi and LBE are compared in Figure 6.

As can be seen in Figure 6, there is an excellent agreement between experimental data reported in the literature [50,55,56] and values calculated from the present thermodynamic assessment of this ternary system. Solubility of Ni in LBE is more than that in Lead. Among major steel components, solubility of Ni is highest in Bi, LBE or Pb. At most of the reactor operation temperatures, Bi is not a suitable coolant as it is more corrosive than Pb and LBE. The corrosion process is mainly driven by dissolution of the alloying element in the coolant [57]. The key parameters to model such a process is the solubility and chemical activity of the main elements of the alloy. According to Figure 6, the solubility of Ni in Bi(l) is the highest as compared to Pb and LBE. At the same time, pure Bi has highest chemical activity to react with Ni in steel and it has more potential to penetrate through grain boundaries/pores of the structural materials as compared to LBE, which results in more corrosiveness. In the absence of Ni, LBE is a better coolant than Bi, as it dissolves a lowest amount of Fe/Cr. Solubility of Fe, Cr and Ni in Pb(l), LBE(l) and Bi(l) is tabulated in the

Table 4. Solubility {log₁₀ S (wt%)} of Fe and Cr in liquid Pb, LBE and Bi.

Temp.	Fe Solubility			Cr Solubility			Ni Solubility
T(K)	Pb(l)	LBE(l)	Bi(l)	Pb(l)	LBE(l)	Bi(l)	Pb(l)	LBE(l)	Bi(l)
600	−8.03	−6.76	−5.78	−8.86	−5.36	−5.07	−1.08	−0.6	−0.24
700	−6.78	−5.71	−4.84	−7.27	−4.64	−4.20	−0.69	0.30	0.41
800	−5.85	−4.93	−4.14	−6.09	−4.09	−3.57	−0.39	0.48	0.69
900	−5.13	−4.32	−3.59	−5.16	−3.67	−3.06	−0.16	0.62	0.90
1000	−4.54	−3.83	−3.16	−4.42	−3.33	−2.66	0.03	0.73	0.87
1100	−4.07	−3.43	−2.80	−3.81	−3.05	−2.33	0.18	0.82	0.91
1200	−3.67	−3.09	−2.50	−3.32	−2.82	−2.06	0.31	0.90	0.95

. This indicates that the solubility of Fe and Cr is approximately 2–3 order of magnitude less than that of Ni in the temperature range 700–1100 K. Pb(l) has lowest power to dissolve Fe and Cr.

The solid solubility of Ni in Pb is negligible at 598 K. The solubility of nickel is 0.53 at.% at 645 K and 18.63 at.% at 1473 K [50]. The solubility of Ni in liquid Bi has three domains due to formation of an intermetallic. The first domain of temperature range where liquid and Bi₃Ni are in equilibrium is 543–742 K and the second is 742–917 K. Beyond 918 K, the liquid and Ni-FCC are in equilibrium. The Ni solubility given in Table 4 are in accordance with these three domains and are in in excellent agreement with Gosse et al. [58]. The solubility of Ni in LBE is much higher than that of Fe and Cr, indicating that Ni content in steels used as a container of LBE needs to be reduced or the steel needs to be protected to increase the corrosion resistance. The solubility of Fe, Cr and Ni in LBE is always greater than that in liquid lead, as is shown in Table 4. However, the pure lead melting point is higher than that of LBE and a higher operation temperature is needed if liquid lead is to be used as a nuclear coolant.

5. Mechanisms of Liquid Metal/Alloy Corrosion

Degradation of steels in liquid Bi, Pb or LBE occurs mainly through dissolution of steel components into the liquid under static flow. The key driving force for liquid metal corrosion is the chemical potential and activity of the element for dissolution in contact with the liquids [58]. The rate of dissolution is governed by the composition of solid metal and liquid media, the area of the solid surface exposed, the flow rate as well as the surface morphology and impurity content. The local corrosion occurs mainly due to intergranular penetration of liquid through the solid meeting, due to the presence of pore defects. During non-static condition of liquid coolant, the flow assisted or erosion corrosion are found to occur. Factors affecting the corrosion rate are distributed into three groups in terms of chemical, metallurgical, and technological factors. We will discuss chemical factor in this paper. The chemical factors include the chemical composition of the liquid metal and its impurity contents, the flowing conditions (the pressure and the flow velocity), the temperature and its profile, the exposure time, etc.

The chemical composition of liquid is changed due to dissolution and formation of compound. Therefore, the dissolution plays a significant role in corrosion phenomena. In this study, we have seen that among Fe, Cr and Ni, the solubility/dissolution of Fe and Cr is less as compared to Ni, as shown in Table 4. In LBE coolant, it also forms an intermetallic compound.

To tackle corrosion problems of lead based liquid coolants, nickel-free steel alloys are being investigated. In addition, some corrosion inhibitors, e.g., oxygen, Zr or Ti, and alloying elements, e.g., aluminium and molybdenum, are being tested.

6. Conclusions

Analysis by CALPHAD method and experimental DTA techniques of Bi-Ni-Pb system were carried out. Using the CALPHAD method, a thermodynamic database was developed to assess the interaction between Ni alloys and LBE. Bi-Pb and Bi-Ni systems were reassessed, based on our experimental data. LBE-Ni pseudo-binary phase diagram was calculated from a ternary database. DTA analysis of LBE-Ni in the present work was carried out to experimentally confirm the invariant temperature computed from the ternary database. This work shows that the solubility of Ni is higher in Bi than in Pb or LBE. The experimental solubility results from the literature and the thermodynamic calculations. These calculations may provide a better thermodynamic description of the dissolution phenomena in the Bi-Ni-Pb system when corrosion mechanisms are mostly assisted by dissolution or precipitation processes.