Active gas corrosion

In the previous section, we considered one of the most basic gas-solid kinetic processes the simple adsorption or desorption of atoms to/from a surface under the assumption that the rate is limited by the impingement of atoms from the gas phase to the surface. In this section, we consider a more complex situation in which a gas species actively etches or corrodes a solid surface via a chemical reaction process, thereby continuously removing material from the surface over time. Consider, for example, the corrosion of a Ti metal surface with HCl acid vapor  

Transport of the TiCl4(g) and H2(g) products away from the surface 

The slowest of the three steps will control the overall rate of the process. At low temperatures, the surface reaction (step 2) may be the slowest. However, since reaction 

Surface Reaction Control We will first examine the behavior of this system under the assumption that the surface reaction step (step 2) is the slowest step and hence controls the overall corrosion rate. To start, we must write the rate law for this surface reaction. We assume that the reaction is first order with respect to the HCl reactant. Recalling Chapter 3, we can write the rate law for this first-order reaction as 

During an active gas corrosion process, one often wants to know how quickly the solid surface is being etched away. Based on the rate at which the HCl(g) is consumed, we can determine the rate at which the Ti(s) is consumed using the reaction 

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Problem 2.5. Iron is undergoing active gas corrosion at atmospheric pressure and T = 1027 °C by the following reaction ... 

This expression indicates that the Ti etching rate is constant thus we would expect the thickness of a Ti plate undergoing active gas corrosion to decrease linearly with time. The expression also indicates that the etching rate will increase linearly with increasing HCl(g) pressure. Since HCl is the etchant, this makes sense The effect of temperature is less obvious. While temperature appears directly in the denominator of this expression, recall that the rate constant A is an exponentially temperature-activated quantity. Thus, the exponential increase in k with increasing temperature dominates over the T term in this expression the overall effect is that the etching rate will increase rapidly with increasing temperature. 

Question (a) Calculate the etching rate of a Ti surface undergoing active gas corrosion in HCl(g) assuming that the surface reaction is rate controlling, (b) Under these conditions, how much time would be required to etch 1 mm deep into a Ti plate The following information is provided ... 

FIGURE 5.4 Schematic illustration of the active gas corrosion of Ti by HCl(g) when controlled by the diffusion of HCl(g) to the surface. Under diffusion control, the reaction rate is limited by the rate at which the HCl(g) reactant can diffuse across the diffusion zone (of thickness 5) to the surface. At steady state, the concentration profile across the diffusion zone is typically approximated as linear, enabling the diffusion flux to be calculated using a straightforward solution of Pick s first law. 

Mixed Control In the previous two sections we have examined the kinetics of active gas corrosion from the standpoint of two limiting scenarios (1) surface reaction control and (2) diffusion control. Under many conditions, it is quite likely that one of these two processes will limit the overall rate of corrosion, and hence one of these two limiting models can be used to calculate the corrosion rate. Under certain conditions, however, the surface reaction and diffusion rates may be comparable, in which case both will influence the overall rate of corrosion. When two series processes both affect the overall rate, they essentially act as two series resistances. Like electronic resistors, these two kinetic resistances will add in series. However, it is important to keep in mind one key point the resistance of each process is effectively given by the inverse of its rate thus. 

FIGURE 5.5 Summary of the key kinetic concepts associated with active gas corrosion under the surface reaction, diffusion, and mixed-control regimes, (a) Schematic iUusIration and corrosion rate equation for active gas corrosion under surface reaction control, (b) Schematic illustration and corrosion rate equation for active gas corrosion under reactant diffusion control. (c) Schematic illustration and corrosion rate equation for active gas corrosion under mixed control, (d) Illustration of the crossover from surface-reaction-conlrolled behavior to diffusion-controlled behavior with increasing temperature. The surface reaction rate constant (k ) is exponentially temperature activated, and hence the surface reaction rate tends to increase rapidly with temperature. On the other hand, the diffusion rate inereases only weakly with temperature. The slowest process determines the overall rate. 

Question As we learned from Examples 5.2 and 5.3, for the active gas corrosion of Ti by HCl at T = 1500 K the surface reaction rate and diffusion rate are approximately equal. Considering both processes operating in series, calculate the actual overall etching rate for Ti under this situation. 

Question Calculate the crossover temperature between the surface-reaction-controlled regime and the diffusion-controlled regime for the active gas corrosion of Ti(s) by HCl(g). In other words, calculate the temperature at which the rates of these two processes are equal. Use the same values provided in Examples 5.2 and 5.3 and assume that Z>hci is independent of temperature. 

Our kinetic treatment of CVD will be very similar to our treatment of active gas corrosion (except, of course, material is being deposited rather than removed). There will be one key difference, however. In our treatment of active gas corrosion, we made the implicit assumption that the reaction process went to completion. In the Ti corrosion example, as long as ANY HCl(g) was available to react, we assumed that it would do so completely. As you may recall from Chapter 3, the assumption that a reaction goes all the way to completion is valid in many cases. However, there are many other reactions that do not go all the way to completion. This is particularly tme for many CVD reactions, whose thermodynamics are purposely tuned so that the driving forces for reaction are relatively small (and thus homogeneous nucleation is avoided). 

Based on this understanding of the incomplete nature of the CVD reaction, the kinetic behavior of this system under surface reaction, diffusion, and mixed control can now be developed. The results will be very similar to the active gas corrosion example with only minor changes due to the incomplete nature of the reaction and the different reaction stoichiometry of this example. 

As in the active gas corrosion example, the flux of Si can be transformed into a deposition rate (i.e., the increase in the thickness of the Si film per unit time, dx/dt) via some simple algebraic transformations using the density and molecular weight of... 

Mixed Control In the mixed-control regime, the surface reaction and diffusion rates are comparable, and thus both influence the overall rate of deposition. Analogous to the active gas corrosion example, the growth rate under mixed control for this... 

Did you know that the kinetic principles of active gas corrosion and CVD processes can be used to understand some of the factors leading to dangerous avalanche conditions in mountain areas From 1950 to 2012, avalanches have killed nearly 1000 people in the United States. Intriguingly, Colorado has had far and away the most avalanche deaths over this period (> 250). In comparison, California has sustained only about 60 avalanche deaths during this same period. This may come as a surprise, since the California Sierra Nevada mountains typically receive more than twice as much snow as the Colorado Rocky Mountains and California has 7x more people than Colorado Can kinetic factors be contributing to this startling discrepancy The answer is yes. ... 

This expression should look vaguely familiar In fact, it is quite similar to the mixed-control equations we developed for active gas corrosion and for chemical vapor deposition (Equations 5.18 and 5.32). 

This chapter examined gas-solid kinetic processes. We saw how to apply the basic tools we learned in calculating thermodynamic driving forces (Chapter 2), reaction rates (Chapter 3), and mass diffusion (Chapter 4) to understand and model a number of important gas-solid kinetic processes including adsorption/desorption, active gas corrosion, chemical vapor deposition, and passive oxidation. The main points introduced in this chapter include ... 

Active gas corrosion is a gas-solid kinetic process involving etching (removal) of a solid surface by a corrosive gas species. The rate of this corrosion process depends on both the rate of transport of gases to/from the solid surface and the rate of the corrosion reaction on the solid surface. Depending on the temperature and pressure conditions, either the gas diffusion or the surface reaction process can limit the overall corrosion rate. An overall corrosion rate can be derived which takes into account both processes according to... 

Problem 5.7. Titanium undergoes active gas corrosion in HCl according to the reaction... 

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