14.2.1 Simple Dissolution

The solubility of metals in molten metals and its variation have not been explained properly up to the present days. Stratchan and Harris (1956) and Kerridge (1961) noted that plotting the solubilities of metals (at.%) in a number of solvent metals showed a periodic variation with the solute and not the solvent, i.e. a given metal such as manganese showed a consistently high solubility in molten magnesium, tin, bismuth, and copper, compared with iron or chromium, and this variation was correlated with the solute lattice energy and hence the latent heat of fusion.

In the more practical sense, dissolution may be uniform or localized. Preferential solution can take two forms:

1. Leaching: One component of an alloy is preferentially dissolved, an example being nickel, which is leached from stainless steels by molten lithium or bismuth, sometimes to such an extent that voids are left in the steel.
   
2. Intergranular attack: The liquid penetrates along the grain boundaries, owing either to the accumulation of soluble impurities in the boundaries or to the development at the junction of a grain boundary with the metal surface of a low dihedral angle to satisfy surface‐energy relationships.

When this process is accompanied by stress, catastrophic failure can occur, a classical example being the action of mercury on brass.

The situation may be described in terms of the surface‐energy changes when a crack propagates through a solid metal as shown in Figure 14.2 where γ_S is the solid–gas interfacial energy, γ_SL is the solid–liquid interfacial energy, and γ_B is the grain boundary energy.

Tabulated below are the energy changes involved for different cracking modes, with numerical values for the case of copper in contact with liquid lead with a dihedral angle at a copper grain boundary of 90° and γ_S = 1.8 J m⁻², γ_B = 0.6 J m⁻², and γ_SL = 0.4 J m⁻²:

14.1

It is seen that the presence of the liquid metal greatly lowers the surface‐energy change for grain boundary cracking (Rostoker et al. 1960).

A good example of the even removal of metal from the surface to saturate the liquid metal can be that of a titanium specimen after being exposed to lead at 1000 °C for 40 hours. In the case of a complex alloy, the attack can also be a simple dissolution type as it can be shown by the corrosion of Type 304 low carbon stainless steel in sodium after 40 hours at 1000 °C. Another attack that might be termed simple dissolution is the decarburizing action of lithium and sodium, as it happens with Type 430 stainless steel after 40 hours at 1000 °C in lithium.

If all the phase diagrams of liquid metal–solid metal systems were available, an ascertainment could be made of the depth of attack that would occur in a static system as a result of simple solution by examining the solubility limit of the solid metal in the liquid metal at the operating temperature. However, there would be no conception of the rate at which the solubility limit was achieved. Thus, upon looking at the Fe–Li phase diagram in Figure 14.3, it can be seen that the amount of attack of iron by lithium should be quite small in a static isothermal system, and corrosion tests have proved this. Therefore, in simple solution‐type attack, the amount of damage that the solid metal will receive depends on the ratio of surface area to volume of the system, but the rate at which the attack occurs can be greatly influenced by other variables, such as impurities in the system.

It is well established that the dissolution of a solid metal in a liquid metal can be described by Eq. 14.2 (Dybkov 1990):

14.2

where c is the concentration of the solute element in the melt, c_s the saturation concentration, c₀ the initial concentration of the solute, k the dissolution rate constant, S the solid metal surface, V the melt volume, and t the time. For a fixed volume of melt, when the dissolution proceeds, the concentrations of the elements rise, resulting in a decrease in the rate of further dissolution.

When stirring is present in the melt, the dissolution rate constant, k, can be calculated by the equations below (Dybkov 1990):

14.3

and

14.4

Here ω is the angular rotating speed of the solid metal, ν the kinematic viscosity of melt, D the diffusion coefficient of the solute across the interfacial zone, and I = f (Sc).

From the above equations it can be seen that the presence and intensity of agitation affect the dissolution rate of solids in liquid. Another important loss mechanism from agitation is that it may damage the protective layer or accelerate the wear by the detachment of the reaction product, such as protuberances. The effect of melt agitation is much more drastic for those materials that form thick reaction layers that do not adhere well to substrate and are not hard enough.

Temperature is one of the most important variables affecting liquid metal corrosion, because the higher the temperature, the higher the solubility of the solid metal in the liquid phase. Also, as the temperature increases, diffusion rates increase, which is quite important in certain types of liquid metal corrosion, namely, simple dissolution. In general, the solubility, S, of a metal in molten metal varies with the temperature according to

14.5

where A and B are constants for a given system. It is therefore possible for more material to dissolve from a container at its highest temperature end than at the low temperature end, and if the melt flows around the container by natural or forced convection, the liquid arriving at the cold region will be supersaturated and will precipitate solute until equilibrium is attained. If it is then recycled to the hot end, it dissolves more metal until saturated and then returns to the cold end to precipitate this excess. This thermal‐gradient mass transfer is illustrated in Figure 14.4, which shows a convection loop being circulated by a corrosive metal such as bismuth. Ward and Taylor (1957–1958) analyzed this process in some detail as shown in Figure 14.5. They found that the solution of solid copper in liquid lead and bismuth obeyed the following equations.

Under static conditions, at temperature T

14.6

where c_t = concentration of solute after time t, c₀ =  saturation concentration of solute, S =  surface area of solid exposed to liquid of volume V, K = k₀ exp. (−ΔE^≠/RT) (ΔE^≠ = activation energy for solution).

Under flowing conditions

14.7

If, therefore, the solute atoms can be prevented from entering the boundary film from the solid, the process will be halted. A method for doing this was discovered by workers at the US General Electric Company 60 years ago (Frost 1958).

They found that small quantities of dissolved titanium, zirconium, chromium, nickel, and aluminum were effective as inhibitors of the corrosion of steels by hot mercury, the first two being particularly so. Later interest in the use of liquid bismuth as a carrier of uranium in a liquid metal‐fueled reactor led to the extension of the use of zirconium inhibitor to bismuth in steel circuits and to an elucidation of the inhibiting mechanism. The zirconium reacts with the nitrogen, which is always present in steel to the extent of about 100 ppm, to form a surface layer of ZrN, which is thermodynamically a very stable compound and is an effective diffusion barrier. Furthermore, as long as there is residual zirconium in solution in the bismuth (or mercury) and dissolved nitrogen in the steel, the film is self‐healing. Mercury boilers have operated successfully for thousands of hours relying on this principle.

The cyclic temperature fluctuation is helpful in explaining erroneous static corrosion results since under a supposedly isothermal condition in a poorly controlled furnace, the liquid metal–solid metal interface temperature can fluctuate quite appreciably around a mean temperature. Thus, at the high temperature, material goes into solution and subsequently at the lower temperature comes out of solution and precipitates in the bulk liquid or forms dendrites or a uniform layer on the container wall. The Cu–Bi system is an example of this, at 500 ± 0.5 °C.

Purity of the liquid metal can also have quite an effect on the rate at which the solubility limit is reached and can markedly affect the wetting tendency of the liquid metal on the solid metal.

14.2.2 Alloying Between Liquid Metal and Solid Metal

The next type of corrosion to be discussed is the alloying that occurs between liquid metals and solid metals. For this to result, there must be some solubility of the liquid metal in the solid metal. The Ag–Pb phase diagram (Figure 14.6) is an example of a system in which the liquid metal is soluble in the solid metal. In some experiments, the liquid metal dissolves considerably in the solid metal with the formation of an intermetallic compound. When vanadium is tested for 400 hours in lead at 1000 °C, an intermetallic compound is formed between the vanadium and lead.

When Type 446 stainless steel is tested in lead at 1000 °C, it is found that after 400 hours, lead has diffused into the alloy predominantly at the grain boundaries and has formed a compound. Sodium will penetrate solid copper at the grain boundaries and will form an intermetallic compound, which is considerably harder than the base metal, copper.

14.2.3 Intergranular Penetration

One of the most serious types of corrosion that can occur is the deep intergranular penetration brought about by the removal of one constituent from an alloy. The best example of this is the selective removal of nickel from austenitic stainless steels, for example, a Type 347 stainless steel after 400 hours of testing in lead at 800 °C. Other examples of this type of corrosion are the attack on Type 304 low carbon stainless steel after 400 hours in lead and in lithium at 1000 °C. A considerable portion of the attack is attributed to the removal of nickel caused by the alloying of the nickel with the iron container wall, and it is assumed that the attack would have been less if the specimens and containers had been of the same material. The selective removal of nickel from a 75% Ni–25% Mo alloy also occurred in a sample from the hot leg of a thermal‐convection loop (TCL), which operated for 200 hours with lead at 800 °C and with a 300 °C temperature gradient. In this case, the nickel was preferentially removed from the hot zone and deposited in the cold zone of the loop.

14.2.4 Impurity Reactions

In liquid metals, impurities such as oxygen, nitrogen, and carbon can have an appreciable effect upon the rate of attack, and, in some cases, the whole mode of attack can be changed because of the effect of the impurity on the surface tension or because of the reactivity of the impurity. An example is the attack of stainless steels by lithium when nitrogen is the principal contaminant. However, the lithium is contaminated with a small quantity of nitrogen, the complete tube wall, comprising 0.89 mm, will be penetrated by the lithium during the same type of test (Casteels 1984). This is due to the nitrogen‐contaminated lithium reacting with the carbides that form the grain boundary network, since a test in Type 316 stainless steel with lithium that was contaminated with nitrogen resulted in shallow attack when the testing temperature was above the solution temperature of the carbides. The true effect of nitrogen on corrosion by lithium is not understood. High temperature alloys can be severely carburized by liquid metals, especially sodium and lithium, if the liquid metals have been stored under kerosene or have acquired carbonaceous material from some other source.

In corrosion by sodium, oxygen impurities can have an appreciable effect on the rate at which the solubility limit is attained (Thorley and Tyzack 1967). In lead, the oxygen contamination, if any, decreases the rate of corrosion since most of the constituents of high temperature alloys can reduce the lead oxide and form a film that will act as a diffusion barrier between the solid metal and the liquid.

The solubility of carbon in sodium has been measured; it is considered lower than the corresponding value for oxygen (2 ppm of carbon at 520 °C) but is sufficiently high to give rise to undesirable effects. Carburization of refractory metals and of austenitic stainless steels has been observed in sodium contaminated with carbon, e.g. oil, grease, or a low‐alloy ferritic steel, the source of which can be either decomposed organic material, e.g. oil or a ferritic steel of low‐ or zero‐alloy content. The latter is an example of chemical‐gradient transfer against the temperature gradient since the activity of carbon in Fe–18Cr–12Ni, possibly stabilized with titanium or niobium, is clearly lower than that in a plain carbon steel and there is, therefore, a driving force for carbon transfer. A deterioration in properties of both steels occurs, the austenitic becoming embrittlement and the ferritic softened. The effect can be minimized if the carbon activity in the ferritic steel is reduced to that in the stainless steel by the incorporation in the steel of a “carbon stabilizer” such as titanium. Hot trapping with zirconium removes carbon as well as residual oxygen, but generally carbon sources should be kept from liquid metal circuits containing materials sensitive to carburization effects.

In summary, for the transfer of a nonmetal along an activity gradient (chemical gradient), chemical thermodynamics is a useful guide to probable behavior. The transfer of a nonmetal, X, dissolved in a molten metal, M′, to another metal, M″, will depend on the relative free energies of formation of M′X and M″X. Thus, sodium will give up oxygen to Zr, Nb, Ti, and U, as the free energy of oxide formation of these metals is greater than that for sodium; on the other hand, sodium will remove oxygen from oxides of Fe, Mo, and Cu unless double oxides are formed.

Impurity reactions can be controlled or eliminated by adequate purification of the liquid metals, and in pumped loop systems, this can be achieved by using techniques known as cold trapping or hot trapping. Cold trapping involves taking a small percentage of the main loop flow and bypassing it through a container that is cooled to the required temperature to precipitate out the impurities. Hot trapping, on the other hand, involves removal of impurities by chemical reaction between the soluble species and a material that has a higher thermodynamic affinity for the impurity than the liquid metal or its containment.

In certain systems where metal solubilities are relatively high (e.g. Ni in liquid lithium), the use of cold traps can encourage thermal‐gradient mass transfer; consequently, under these circumstances, other methods of purification may be required.

14.2.5 Temperature‐Gradient Mass Transfer

The most damaging type of liquid metal corrosion is temperature‐gradient mass transfer. The even removal of a slight amount of a container wall will not adversely affect its load‐carrying abilities; however, the collection of this material in the colder regions of heat exchanger tubes as dendritic crystals would cause a cessation of flow. An example of mass‐transferred material is seen in Figure 14.7, which is a plug from a Type 446 stainless steel TCL that operated 200 hours at 800 °C with a temperature gradient of 200 °C. These crystals were primarily alpha iron. Note that a plug is a precipitate that eventually blocks the pipe to liquid flow. Another example is the massive matte of mass transfer material that can be observed as a plug from an Inconel‐lead TCL that operated for 125 hours at 800 °C. In some loop experiments the crystals do not grow from nuclei in the bulk liquid, but mass‐transferred material nucleates on the wall, and the crystals grow out into the stream as revealed by iron crystals formed on a Type 410 stainless steel TCL after 40 hours at 1000 °C with lithium. The driving force for temperature‐gradient mass transfer is the difference in the solubility of the dissolved metal in the liquid metal at the temperature extremes of the heat transfer system. In examining the Cu–Pb phase diagram (Figure 14.8), it can be seen that there is considerable solubility of copper in lead at 900 °C, whereas at 500 °C it is much lower. Thus, by examining the phase diagram, the driving force for this phenomenon can be determined, but no information concerning the rate of the process can be determined.

If there is selective removal of one element from an alloy, these atoms must diffuse to the surface and then go into solution. The atoms must then diffuse through the lamellar layer into the bulk liquid stream and are finally carried to the cold portion of the system where supersaturation will occur. A collection of such atoms can accumulate and form a nucleus that will grow to a stable size and then drop from the liquid. On the other hand, the atom may supersaturate close to the wall, diffuse through the lamellar layer, and then nucleate on the metallic wall and form a dendritic crystal, or it may diffuse into the wall. As yet, the rate‐controlling step in temperature‐gradient mass transfer has not been found.

To obtain more data on mass transfer in liquid lead, a series of quartz TCL were operated at Oak Ridge National Laboratory (ORNL) with various alloys and the elements comprising the alloys. Results of these tests have indicated that the rate‐controlling step for mass transfer by lead at the velocities used in the TCL takes place in the hot leg and is probably a solution step. For example, it was found that the formation of an intermetallic compound, or other type of diffusion barrier, in the hot zone greatly increases the time that elapses before a plug occurs in the loop.

In diffusion‐controlled mass transfer situations involving turbulent fluids, Epstein (1957) has suggested that mass transfer equations can be derived from heat transfer analogies and expressions relating corrosion rate to the dimensionless groups. Reynolds number (Re) and Schmidt number (Sc) have been found to have some application where corrosion rates are sensitive to changes in flow velocity or diffusivity in the liquid phase. The equation suggested by Epstein to meet this situation is of the form

14.8