Formation and Breakdown of Oxide Films in High-Rate Anodic Dissolution of Chromium–Nickel Steels in Electrolytes for Electrochemical Machining

It is shown that, in high-rate pulsed galvanostatic anodic dissolution of type CSN17335 and AISI 304 chromium–nickel steels in electrolytes for electrochemical machining (ECM) (chloride, nitrate, and mixed chloride–nitrate solutions with a conductivity of 0.15 S/cm) using microsecond pulses with a duration of 20–2000 μs and current densities in the range of 1–100 A/cm2, a substantial fraction of charge (up to ~40%) is spent on the formation of a passivating oxide film with a semiconducting behavior. The electrochemical treatment therefore directly involves the oxide film, not the alloy. As a consequence, the current efficiency of ECM of these materials is ~60–70%, depending on the alloy composition. When using direct current, the rate of machining increases as a result of the oxide film breakdown due to its thermokinetic instability (“thermal explosion”) caused by a rise in the surface temperature.


INTRODUCTION
Anodic dissolution of metals and alloys is a basis of a number of processes aimed at both imparting specific properties to metal surfaces and metal shaping, i.e., the processes which render them the required shape and size and involving also the micro-and nanoscale levels [1][2][3][4][5][6][7][8]. This work concentrates on high-rate anodic dissolution processes that occur at high anodic current densities and high anodic potentials and are considerably far away from thermodynamic equilibrium. Mostly, these processes are observed in different types of electrochemical machining (ECM) [1][2][3][4][5].
The rate of an ECM process is known to be determined by the Faraday law: where v i is the machining rate (i.e., the anodic dissolution rate; mm/min), ρ is the density of material subjected to machining, i avg is the average current density, C is the electrochemical equivalent of the material, and η is the current efficiency. Typically, current efficiency η is determined experimentally provided that a calculated value for electrochemical equivalent is available. Since a value for C, which depends on the oxidation states assumed for dissolvable alloy components, is typically not known, it is reasonable to take ηC (mg/C or g/Ah) as a parameter amenable to experimental determination. This parameter can be considered as the rate of faradaic dissolution (RFD), i.e., the mass of metal removed per unit charge passed during machining. As will be shown below, this is a perfectly reasonable approach, especially when applied to pulsed ECM.
Knowing the factors determining the RFD behavior and its distribution pattern across the processed surface is crucial, especially, in pulsed ECM. Pulsed machining enables control over (i) the distribution of local rates of machining by influencing the conductivity of a gas-liquid mixture within the interelectrode avg , i Ci = η ρ v gap and (ii) the accuracy of shaping, because RFD depends on local current density [2,3,5].
Several studies [10,17,20] suggest that the RFD observed in pulsed machining can be lower-sometimes substantially-than in machining using direct current (DC). And in this case, the dissolution rate decreases not because of a decrease in the average current density as a result of current-off periods during machining but the dissolution rate decreases per unit of passed charge (mg/C, g/Ah). This phenomenon is caused by several of factors, e.g., involvement of double-layer effects. In pulsed machining with short and ultrashort pulses, a fraction of charge may be consumed in charging the double layer, which will result in lower RFD. Study [16] concentrated, in particular, on estimation of pulse durations at which this effect may be substantial. The conditions and equipment required to make use of this effect in micro-ECM (μ-ECM) were described in studies [7,18,19]. In the case considered in this work, however, the double-layer effects can be neglected, as was experimentally shown earlier [20].
The presence of thermokinetic effects can be another factor. In the conditions considerably far away from thermodynamic equilibrium, the surface temperature rises due to the positive feedback loop "electrochemical reaction rate (current density) -surface heat liberation-electrochemical reaction rate;" therefore, a critical temperature drop that leads to thermokinetic instability (TKI) of surface layers and to activation of anodic dissolution can be achieved [21][22][23][24]. The critical surface temperature of transition to TKI may not be achieved under conditions of pulsed machining.
The third factor is related to so-called passivating electrolytes, which are used in ECM to improve localization of anodic dissolution. In this case, as the current density (or potential) increases, the anodic dissolution reaction takes over the water oxidation reaction, which is accompanied by oxygen evolution, and for sufficiently short pulse durations, a fraction of charge is consumed in a side process, thereby decreasing the RFD [1-3, 5, 7]. However, as was shown in [20], the use of passivating electrolytes did not necessarily lead to lower RFD values. A decrease in RFD, in particular, was observed in the pulsed current mode in nonpassivating (chloride) solutions [20].
Similarly, in a study of anodic dissolution of chromium-nickel steels in ECM electrolytes using pulsed DC and current densities up to 100 A/cm 2 [20], noticeable difference in RFD values were observed between machining using DC and pulsed current, despite the identical amount of charge passed. The causes of this difference, however, remained unidentified.
One specific feature of study [20] was in situ measurements of the surface temperature during the treatment. However, the impact of thermokinetic effects on the dissolution rate (and the current efficiency) was ambiguous. In a broad range of values for parameters of pulsed current (duty cycle D below 50%, i.e., the mark-space ratio less than 2), the rise in surface temperature to values as high as the boiling point did not have an effect on the dissolution rate and the current efficiency. However, as the parameters of processing conditions approached DC-based machining, it was the established values of surface temperature that determined the dissolution rate and current efficiency.
The cited study [20] was purely experimental, it did not concern itself with the nature of observed effect. Meanwhile, establishing the underlying mechanism is crucial from the perspective of both the theory of electrochemical processes that occur under conditions far away from thermodynamic equilibrium and the development of new methods for controlling pulsed ECM processes.

EXPERIMENTAL
Anodic dissolution of the two types of chromiumnickel steels-corrosion-resistant AISI 304 and heatresistant CSN17335 steels-was performed in an electrochemical cell the electrode assembly of which is shown in Fig. 1. A rotating disc electrode (RDE) made of the considered steel types was connected as the anode, and in some experiments a stationary disk electrode (SDE) with diameter d = 3 mm was used (Fig. 1). A copper cathode with a bore with diameter d 0 = 1.5 mm was placed at distance Δ = 0.2 mm away from the anode. The bore in cathode served to create a flow of electrolyte around the anode with a volumetric flow rate of 0.5 L/min. Linear ambient flow rate v of electrolyte around the bore in the cathode was ~6 m/s. It was shown [20] that the heat flux at the interface was an order of magnitude higher in the direction of the electrolyte than in the direction of the metal as a result of thermal conductivity. For this reason, temperature T m monitored during experiments can be identified, within the experimental error, with surface temperature T s (Fig. 1).
The elemental composition of steel types under study, as measured by X-ray fluorescence spectroscopy, is given in Table 1. Anodic treatment was performed in three different electrolytes: a so-called activating electrolyte (sodium chloride), passivating electrolyte (sodium nitrate), and a mixed chloride-nitrate electrolyte. The electrolyte concentrations were chosen to ensure the same electrical conductivity for each electrolyte, which was 0.15 S/cm. Specifically, the concentrations were 117 g/L of sodium chloride in the chloride electrolyte, 230 g/L of sodium nitrate in the nitrate electrolyte, and the mixed electrolyte contained 100 and 80 g/L of sodium chloride and sodium nitrate, respectively. We note that the actual current distribution in ECM typically follows the primary current distribution, i.e., it is determined primarily by the electrolyte conductivity.
Processing of steel samples (i.e., anodic dissolution) was carried out in the pulsed DC mode at current densities in the range of 1 to 100 A/cm 2 . The pulse duration (pulse on-time) was varied from 20 μs to 2 ms. Several variants of pulsed DC dissolution were used: for duty cycle D in the range of 10-50%, D was held constant at 10% (mark-space ratio s = 10) while varying the pulse duration from 20 μs to 2 ms; or D was varied between 10 and 50%, while the pulse duration was held constant at 20 μs. For D > 50% and up to the DC mode (i.e., D = 100%), the pulse off-time was maintained constant at 20 μs while increasing the ontime to 2 ms. The electrolyte temperature in the cell (i.e., the temperature of incoming flow) was maintained at 21 ± 2°С. In some experiments, the electrolyte temperature was varied from 25 to 75°C while holding the surface temperature at a constant level. A more detailed description of the experiments can be found elsewhere [17,20].
The RFD (mg/C) was determined experimentally by a weight loss method (a loss of ~10-30 mg was measured with a precision of 0.05 mg) in which the amount of charge passed was determined as the product of period-averaged current density and electrolysis duration. Current efficiency η was calculated by taking into account the electrochemical equivalents of the considered steels, assuming the lowest degree of oxidation for Fe and Cr species (i.e., 2 and 3, respectively), the other degrees of oxidation being 2 for Ni, 4 for Ti, and 6 for W. As a result, the values calculated for electrochemical equivalents were 0.274 mg/C for AISI steel and 0.266 mg/C for CSN17335 steel. Figure 2 shows experimentally measured dependences of RFD (ηС) on the density of pulsed (and DC) current for dissolution of AISI 304 steel in different electrolytes (Fig. 2a) and, as an example, for dissolution at different D in the nitrate electrolyte (Fig. 2b). These dependences have a number of important features to highlight. First, for the identical amounts of charge passed and current density values, RFD in the pulsed mode was around half as much as that observed in the DC mode (in this case, the pulse off-time constituted ~1% of the on-time). Second, unlike the case with the activating chloride-containing electrolyte, we observed an increasing dependence of the dissolution rate (and the current efficiency) on the current density in the nitrate electrolyte, but only at particular D values (Fig. 2b). A interesting feature of this dependence is that it is observed at low D values and disappears at D = 30%, but it is also observed in the DC mode (Fig. 2b).

RESULTS AND DISCUSSION
We note that ηС reaches a limiting value of ~0.16 mg/C in the pulsed current mode in all of the considered electrolytes (Fig. 2). The fact that RFD can reach a plateau (but slightly higher, 0.18 mg/C) in the pulsed mode was also observed in work [20]. This is related to lower surface temperatures. The data shown in Fig. 2 were obtained using the RDE, whereas a value of 0.18 mg/C was found for the SDE (see also Fig. 3). The calculations of the surface temperature carried out in [20] showed that when the RDE was set into rotation the surface temperature decreased by ~10-15%, and the dissolution rate fell by the same value.
It is also important to note that the influence of anion type on RFD is observed only within a certain range of current densities (in both the DC and pulsed current modes). At high i (in both the pulsed current and DC modes), the process becomes independent   not only of the current density and the type of anion but also the nature of processed material (Figs. 2, 3). Results presented in Fig. 3 are for a density of pulsed current of 50 A/cm 2 and D = 10%. It is also evident that the limiting value for ηС (~0.18 mg/C for SDE) is observed not only at fairly small pulse durations (20 μs) but also in the entire range of pulse durations considered in this work (Figs. 2, 3). The measured RFD values (0.16-0.18 mg/C) correspond to the current efficiency of 60%, if the latter value is calculated assuming the lowest degree of oxidation of the alloy components, while for the highest degree of oxidation the calculated current efficiency is close to 100%.
Taken together, all of the findings reported above strongly suggest that it is the film forming on the surface being processed-not the steel itself-that undergoes dissolution during anodic treatment. At the same time, the data in Fig. 3 suggest that the effects due to nonfaradaic processes (i.e., the period of double layer charging) can be neglected, else RFD would have exhibited a dependence on the pulse duration, which was not the observed.  The dependences described above can be explained within the modern passivation theory (i.e., transpassive dissolution), which was developed in a number of studies [25][26][27]. It is based on a point-defect model (PDM). The underlying concept of this theory is that passivation develops as a result of the formation of a surface oxide film containing point defects (a perfect oxide film would be insulating). Importantly, the PDM was developed in the context of the phenomenon of passivation and, strictly speaking, so far it has not been directly relevant to the processes of high-rate dissolution and ECM. However, as early as in the 1980s, several studies [28][29][30][31][32] pointed to the implications of passivating semiconducting films for ECM. In fact, the interrelation between the nature of these films and ECM identifiers, such as the rate of machining and current efficiency, was illustrated.
Referring to the PDM in the context of steel passivation (so-called PDM-II [25,26]), the film growth kinetics is determined by the expression: where L is the film thickness; a and b are factors; V is the dissolution rate, which does not depend on potential [25,26]; and V ≠ f(E), i.e., V is the rate of chemical dissolution. Evidently, for V = const, ∂L/∂t → 0 as L increases, and for certain L, a steady state is established: L = L ss (i.e., the film thickness becomes constant).
Considering the semiconducting behavior of the film, the latter can exhibit different types of conductivity, depending on the defect type. In particular, it was repeatedly shown that passivating oxide films on chromium-nickel steels exhibit mostly n-type con- ductivity [33][34][35]. The possibility of formation of mixed-type films during ECM was suggested in earlier works [29][30][31][32].
As can be observed from the results presented in Fig. 4, the increase in reaction rate (i.e., current density) at relatively low current densities (upon scanning the potential to 1.5 V) contributes to the growth of a passivating film, because the potential increases on scanning in the reverse direction (the hysteresis associated with more extensive passivation occurs; Figs. 4a, 4b)). It seems that the observed increase in current is related to the progress of reaction (I), because the formed film displays electronic conductivity. However, when the potential increases, and the current density rises as a result, depassivation occurs due to the breakdown and dissolution of the film (Figs. 4c, 4d) and involves the substitution of anodic dissolution reaction for reaction (I).
Reaction (I) is the reaction of solvent (water) oxidation to form oxygen, if an n-type film is formed: (I) On the other hand, in the context of the processes of film formation and dissolution, we may write [7, p. 21]: (II) (III) These reactions must truly be complemented by the anodic dissolution reaction: (IV) the validity of which in this context will be discussed below.
According to reaction (II), the charge is consumed in the oxide formation process. However, the film is conductive due to the presence of point defects in it, and the charge carriers can be either electrons or holes (or both), depending on the type of conductivity.
The kinetics of this reaction is determined by the first term in Eq. (1), where V is the rate of reaction (III), i.e., the dissolution rate, and f is the fraction of total charge consumed in the oxide formation, which essentially is the current efficiency of oxide formation.
Importantly, according to (II) and (III), the loss of the mass of sample, i.e., its anodic dissolution, is due only to chemical reaction (III), while electrochemical reaction (II) leads to mass gain. Since the two reactions are coupled, the anodic dissolution at V = const will occur through the passivating film with a constant thickness.
In consideration of the semiconducting behavior of the formed film, when currents applied exceed the passivation current (Fig. 4), especially in the pulsed 2  = + current mode, the passed charge is distributed between three faradaic processes: oxide formation, oxide dissolution, and oxidation reaction (I); and in terms of current density we may write: (2) where i e is the density of electronic current, i.e., the one due to reaction (I), and i d is the current density due to faradaic dissolution. Since the charge is consumed in reactions (I) and (II) ((III) is a chemical reaction), the charge, provided the current efficiency f of oxide formation is constant (without involvement of reaction (III)), will be distributed between the current due to dissolution and the electronic current, and RFD is determined by Eq. (3): Reaction (I) will be dominant at relatively low current densities, especially in passivating electrolytes, and RFD will be minimal (Fig. 2). However, as the current density increases, the type of conduction in the film may change as a result of a surface temperature rise. As was shown by way of example for anodic dissolution of Ni in nitrate solutions [23, pp. 86-91], it is the rise in surface temperature that led to the transition from reaction (I) to the increase in dissolution rate, i.e., the increase in i d . Clearly, a similar situation is observed in this work as well (Fig. 2).
However, according to Eq. (3), RFD has a limit imposed by fraction f of the total charge consumed in the formation of oxide film. This is precisely why RFD plateaus at ~0.16 mg/C in the pulsed mode (Fig. 2). Evidently, the presence of limiting value for RFD is due to the fact that a fraction of charge in the pulsed mode is always consumed in the oxide formation, and if f = const, ηC must reach a limiting value.
In contrast, for dissolution in the chloride electrolyte, the formed surface film displays ionic conductivity, but, as with the dissolution in the nitrate electrolyte, RFD reaches a plateau due to the fact that f = const (Fig. 2a). It is also clear that for the limiting situation described above, i e → 0.
The transition from electronic to ionic conduction that occurs upon increasing the current density in current pulses and is caused by the rise in surface temperature manifests not only when the pulsed current density is increased but on increasing D as well. Thus, in the case of electrodissolution of AISI 304 steel in the pulsed mode with a current density of 30 A/cm 2 during pulses and D = 10%, surface temperature T m was measured to be ~30°C in both the chloride and nitrate electrolytes for the same current density during pulses, whereas at τ = 30% the surface temperature reached ~50°C. Of course, this resulted in the higher dissolution rate, but within the limit imposed by the In view of the above, the condition for the increasing dependence of the current efficiency (i.e., RFD) on the current density, which leads to improved localization of anodic dissolution, may not be satisfied. The dependence of this kind must be observed only at specific τ values ( Fig. 2b; see also [17]).
Summing up the above, we can state that the observed features of pulsed current dissolution of considered steel types are determined by (i) the electrochemical formation of the passivating oxide film, with the presence of point defects in it ensuring a certain rate of anodic dissolution, and (ii) the change in surface temperature, with a temperature rise ensuring a transition from mostly electronic conduction to hole conduction. However, in all of the cases considered above, the current efficiency of film formation was constant, which led to the current efficiency of dissolution and ηC reaching their corresponding limiting values.
Importantly, for V > аe -bL , we have ∂L/∂t < 0 (see Eq. (1)), and the passivation film starts dissolving. This, in turn, results in lower f values (the current efficiency of the formation of passive oxide film diminishes) and consequently to an increase in RFD. And this is what was observed when the surface temperature reached ~100°C or higher (Fig. 5). In the meantime, we highlight that the rise in surface temperature to certain values did not cause RFD to increase, clearly because the thickness of forming oxide film was constant under these conditions and f = const as a result. The obvious reason is the fact that reactions (II) and (III) are coupled.
It is particularly important to note that the rise in surface temperature when occurred upon the transition to the DC mode (Fig. 5). Results presented in Fig. 5 were obtained for the amplitude of pulsed current density of 50 A/cm 2 . In the process, the increase in RFD observed during the temperature rise and the transition to the DC mode was due to longer pulse on-time while keeping the off-time unchanged (20 μs). This resulted in a decrease in mark-space ratio s and its value approaching unity (i.e., the DC mode), and the D value approached 100% (i.e., DC) or when D > 50%.
At the same time, the results presented in Fig. 5 is another evidence to confirm that it is the oxide film being formed during surface treatment-not the steel itself-that undergoes dissolution. The effect of surface temperature is two-fold: (i) it causes the transition from electronic to hole (ionic) conduction in the film, which is obviously related to the role that the temperature plays when the fraction of charge consumed in the film formation is constant (the case when f = const), and (ii) it increases the rate of film dissolution (breakdown), which results in that the fraction of charge consumed in its formation diminishes. According to [25,26], the second term in Eq. (1), i.e., V, which contributes to a decrease in the film thickness, does not depend on the potential, but this can be a consequence of not only chemical dissolution but also have a physical nature. The film, in particular, may also be destroyed as a result of thermal explosion (i.e., TKI). The disruption of the forming passivating film can occur via at least two pathways: chemical dissolution and TKI [21][22][23][24]. In both cases, the current efficiency of oxide formation diminishes and RFD increases.
The question of which mechanism, chemical or TKI (thermal explosion), is responsible for film disruption was solved based on experiments the results of which are shown in Fig. 6. The critical temperature of thermal explosion is known to be a function of only the activation energy of electrode process and the temperature in the bulk of electrolyte [21][22][23]. As the electrolyte temperature increases, the critical temperature drop grows and the probability of film breakdown falls as a consequence. As distinct from this, the increase in temperature must result in the thickness of the film decreasing, provided it undergoes chemical dissolution. The results presented in Fig. 6 provide unambiguous proof of the hypothesis that the film is disrupted as a result of TKI. Admittedly, RFD diminished as the electrolyte temperature was raised while the surface temperature was constant. This occurred as a consequence of the f value increasing (Eq. (2)). The presence of potential oscillations under galvanostatic conditions observed after TKI was established [21][22][23][24] also supports this conclusion. The presence of oscillations indicates that under the conditions of high-rate dissolution the film forms again after having been disrupted, but it is then destroyed again when the critical temperature is reached, and the process repeats. Persistent cycles of the film formation and breakdown, which result in a considerable increase in RFD, indicate that in this case reaction (IV) will be dominant upon the transition to the DC mode. In fact, it was shown [20] that no oxide film was formed on the sur-face subjected to processing at a high DC current density.
The analysis of presented results requires an answer to another question: Why does the increase in RFD that results from continuous breakdown of the surface film occur specifically when the solution boiling point is reached (Fig. 5)? Clearly, this occurs due to the transformation of film structure, with the resulting structure amenable to treatment within PDM-III [25,26]. As was remarked in [25], the film gets blocked at the film/solution interface as a result of electrolyte boiling inside pores of the passivating film (the structure treated within PDM-II has a compact barrier layer at the interface with the metal and a porous layer at the interface with electrolyte). This mechanism of the formation of passivating film is typical for Al, Ti, Zr, W, and other metals, but under certain conditions it may apply to steel as well [25]. The structural transformation of passivating film that occurs when the boiling point is reached is the cause of its persistent formation and breakdown as a result of the TKI of the film present at the interface with the solution when the surface temperature exceeds the boiling point.
In conclusion, it is important to note that the consumption of a substantial fraction of charge for the formation of oxide film (up to ~40% of the total charge passed during machining (Fig. 2)) is expected to be observed primarily in the pulsed current mode, but it tends to decrease when the machining conditions approach the DC mode. This also means that when the machining conditions change from DC to pulsed current the rate of machining diminishes due to the decreases in both the average current density and the current efficiency of dissolution process resulted from the fact that a large fraction of charge is now consumed in the oxide film formation.
The features of pulsed dissolution described above are illustrated, by way of example, for high-rate dissolution of chromium-nickel steels. Further research is needed to establish to what extent they occur in machining of other metals and alloys.

CONCLUSIONS
Using the example of high-rate anodic dissolution of two types of chromium-nickel steels (AISI 304 and CSN17335) in ECM electrolytes, it was shown that the process of their anodic treatment is determined by the electrochemical formation of anodic oxide film on the surface undergoing dissolution, and the amount of charge consumed in the oxide film formation can be as high as 40% of the total passed charge. It was shown that it is the oxide film-not the steel (alloy)-that is directly involved in the machining process.
The increase in rate of faradaic dissolution (RFD) observed in going from the pulsed current mode to the DC mode is a consequence of persistent periodic for- ηC, mg/C T electrolyte , °C mation and breakdown of a passivating surface film. At the same time, because the rate of film depassivation is higher than the rate of its formation, the average film thickness diminishes; therefore, the fraction of charge consumed in its formation decreases and RFD rises. The breakdown of passivating film is a consequence of its thermokinetic instability (i.e., thermal explosion). Using pulsed current with pulse durations in the microsecond range, which improves the accuracy of ECM of steels under study, results in the reduction in the rate of machining as a result of decreases in both the average current in the pulsed mode (the duty cycle is lower) and RFD, with the decrease in RFD being due to the consumption of a fraction of charge in the oxide film formation.