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Electrochemical dissolution and passivation of tin in citric acid solution using electron microscopy techniques
Elecfrochimica
Acta, Vol. 31, No.
1, pp. 143-148,
1992 0
Printed in Great Britain.
Km-46s6/92 $5.00+ 0.00 1991. Pergomon Pros pk.
ELECTROCHEMICAL DISSOLUTION AND PASSIVATION OF TIN IN CITRIC ACID SOLUTION USING ELECTRON MICROSCOPY TECHNIQUES B. F. GIANNETTI,* P. T. A. SUMODJO,* T. RABOCKAI,* A. M. Souwt and J. BARBOZA~ +Instituto de Quhnica da Universidade de Slo Paula, C.P. 20.780, 01498 SHoPaula, SP, Brazil; tGenera1 Motors do Brasil, C.P. 197, 09500 8&oCaetano do Sul, SP, Brazil (Received 4 October 1990; in revisedform 13 March 1991)
Abstract-The electrochemical behaviour of tin in 0.5 M citric acid solution was studied by electron microscopy techniques in addition to the potentioclynamic method. The observed electrochemical dissolution is quite similar to pure chemical dissolution when metallographic practices are used and takes place distinctly between the grains. The film growing process follows a dissolution/precipitation mechanism. The local reactivation process occurs primarily along the tin grain boundaries locations. Key woruk citric acid, electrochemical stability, potentiodynamic perturbation, scanning electron rnicroscopy, surface Bhn, tin electrodes.
INTRODUCTION
Numerous papers on the electrochemical behaviour of tin, a metal with many technological uses, have been reported. In a previous paper[l], we discussed the electrochemical behaviour of tin in deaerated 0.5 M citric acid by means of the potentiodynamic method. It was shown that, despite the simplicity of the E/Z profile, the anodic oxidation of the metal involves the formation of a soluble Sn(I1) species which is subsequently oxidized to Sn(Iv). The nature of the soluble species, which cannot be discussed from our results, is the object of investigation by different authors[2, 31. Passivation occurs via the hydrolysis of Sn(IV) to yield either Sn(OH), or SnO,. When applied to solid electrodes, potential perturbation programmes are able to cause structural and morphological modifications on their surfaces inducing changes in crystallographic orientation and composition. In the present paper we discuss the microstructural features of a tin surface subjected to an electrochemical perturbation program in 0.5 M citric acid. The surface was examined by means of scanning electron microscopy (SEM). EXPERIMENTAL
The working electrode, a disk with an apparent area of 0.8 mm2, was constructed following the procedure described by Sharpe and Meibhur[4]. A platinized platinum electrode was used as the counter electrode and a reversible hydrogen electrode, placed in the same solution, was used as reference electrode (rhe). All potentials quoted are referred to this electrode. The electrolyte was a 0.5 M citric acid solution, which corresponds to pH 1.8. It was prepared with analytical grade reagent and triply distilled water and stored at low temperature to avoid decomposition. EA 37/l-K
Prior to each experiment the working electrode was polished with 600 emery paper and suspensions of alumina powder (0.3 and 0.02 pm, respectively), following the usual metallographic procedure[q. The electrode was then rinsed with distilled water, dipped in the solution which had previously been deaerated with purified nitrogen. Immediately after the electrochemical experiment the electrode was dried with compressed air and taken for SEM examination, on a Phillips PSEM 500 scanning electron microscope. Some polished cross-sections were etched in Nital 2% (2ml HNO, + 98 ml ethanol)[5] to reveal the microstructure for metallographic examination. All volammetric experiments were performed at a sweep rate of 0.1 V s-r.
RESULTS AND DISCUSSION
The micrograph shown in Fig. 1 exhibits the electrode surface after mechanical polishing. There are observed parallel scratches, dark spots, incrustation (5-10 pm in diameter) and microvoids. The dark spots appearance is not altered even by an extensive cathodization at -0.9 V, at which hydrogen evolves vigorously. This fact and the size of the dark spots suggest that they arise from the emery paper used during the final grinding operation and were only partially removed during subsequent polishing. The micrographs obtained before and after a cathodization at -0.9 V for 5 min do not reveal significant changes on the surface features. However, this electrochemical pretreatment is essential for the acquisition of stable and reproducible Z/E profiles. Although not detected by SEM examination, a thin fllm of tin oxide is probably formed in air. The reduction of this film, during the cathodixation, produces a fresh metallic surface, allowing the aquisition of reproducible electrochemical data.
B. F.
GIANNETTI et al.
Fig. 1. SEM micrograph of tin surface after mechanical polishing. The distance between the left and right margins of the micrograph is about 310 pm. x 210.
The typical anodic I/E curve of tin in 0.5 M citric acid solution after the mechanical and electrochemical pretreatment is depicted in Fig. 2. Detailed analyses of the electrochemical experiments and the resulting data are found in Ref.[l]. Points A, B and C shown in Fig. 2 represent the anodic end potentials, EF, selected for SEM examination of the morphological changes of the electrode surface when submitted to a linear potential sweep. SEM examination of the electrode surface after the application of a linear potential sweep with EF = -0.15 V, corresponding to point A in Fig. 2, reveals the existence of different planes. The dark spots observed just after the mechanical polishing disappear completely with the electrochemical treatment. The observed planes were possibly formed either by the dissolution of the metal or formation of a new phase, or both. During the voltammetric experiment the electrode experiences an abrupt increase in current when the potential reaches a value related to point A (Fig. 2). This increase in current with potential is practically due to metal dissolution, evidenced by the complete removal of the dark spots during the electrochemical procedure. Anodic current peak a, in Fig. 2 is characteristic of a passivation process, ie the sharp decrease in current is due to the formation of a passive film[6]. When the electrode is submitted to the electrochemical perturbation with the values of EF equal to 0.0 and +0.12 V, related to points B and C, respectively, no significant differences in the surface morphology are observed. Figure 3, a micrograph related to point C, shows that the different planes on the electrode surface are better defined. In order to decide whether the observed planes are a consequence of the metal dissolution, film formation or both, SEM examin-
ations were performed on the electrode surface after the application of a triangular potential sweep with E, = EF = -0.9 V and E,,a = 1.5 V. The corresponding cyclic voltammogram, Fig. 2, shows a cathodic current peak, cI, at ca -0.42 V which is associated with the reduction of the anodically formed film[l]. SEM examinations reveal that the surface topography is exactly the same as that shown in Fig. 3. Since the surface morphology does not change in the two experiments, it can be concluded that the planes on the surface are formed by the dissolution of the metal. When a polished tin surface is etched in Nital 2%, the polycrystalline nature of the metal is apparent (Fig. 4). Figures 3 and 4 show that the resulting surface after an electrochemical treatment and after a chemical treatment are similar. Since the etching procedure reveals the grains, the similarity of the two micrographs clearly demonstrates that the electro-
a i \
- 1.2
-0.6 E/VO
I.2 (EFZ)
Fig. 2. Potentiodynamic I/E profile of tin in 0.5 M citric acid; v = 0.1 V SK’; geometric area = 0.8 mm2.
Tin in citric acid solution
Fig. 3. SEM micrograph of tin surface after mechanical polishing and potentiodynamic perturbation; final potential corresponding to point C in Fig. 2. The distance between the left and right margins of the micrograph is about 155 pm. x 480.
Fig. 4. SEM micrograph of tin surface after mechanical polishing and etching in reagent Nital 2%. The distance between the left and right margins of the micrograph is about 155 pm. x 480.
145
146
B. F. GIANNETTI ef al.
Fig. 5. Cyclic voltammogram obtained with the schematized perturbation programme: v = 0.1 v s-1; .I?,= -0.9 v, E+ = EF= 1.5 V, EC= -0.22 V; geometric area 0.8 mm*.
chemical dissolution occurs distinctly on the different crystallographic planes. In our previous paper[l] the potentiodynamic formation of a passivating film constituted by Sn(OH), which undergoes a further transformation to give SnOz was suggested. The experiments and observations discussed in this paper are unable to prove the existence on the surface of the passivating layer. This is probably because of the thickness of the film. However, its presence can be detected in an indirect way. All attempts to achieve a sharp and clear image of SEM examination of a tin electrode submitted to an anodic polarization in a potential region where doubtless a passivation occurred were unsuccessful. This difficulty can be explained by the higher electric resistivity of this phase in relation to the bare metal.
Naturally this obstacle could be overcome by the deposition of a thin conducting film technique; however, since the same electrode was used in all experiments, to avoid possible contaminations this procedure was not employed. When a triangular potential sweep with E, = -0.9 V, E,, = 1.5 V and EF = -0.22 V is applied, the electrode maintains its passivating condition because the passive layer is not allowed to be reduced under certain conditions (Fig. 5). Moreover, (0.2 V < E,,a < 0.7 V), a reactivation process takes place[ 11. SEM examination of a surface submitted to a voltammetric experiment with E, = -0.9 V, E,,a = EF = 2.0 V followed by a potential hold at EF for 10 min, reveals clearly the existence of the passivating layer (Fig. 6). This film seems to be developed as floes, suggesting that it could be formed by precipitation. The interaction between the electron beam and the
0
2
4
8
IO
t/InL
Fig. 7. Current-time curve for a tin electrode submitted to mechanical polishing followed by a voltammetric experiment with E,= -0.9V, Ei,=EF=0.24V,v =O.lVs-’ with a subsequent potential hold at EF for 10min. Geometric area 0.8 mm*.
Fig. 6. SEM micrograph of tin surface submitted to mechanical polishing followed by a voltammetric V, El,+ = EF = 2.0V, u = 0.1 V s-’ plus a potential hold at EF for 10 min. The experiment with E,= -0.9, distance between the left and right margins of the micrograph is about 155 pm. x480.
Tin in citric acid solution
Fig. 8. SEM micrograph of tin surface submitted to mechanical polishing followed by a voltanunetric experiment with E, = -0.9 V, E,,a = EF = 0.24V, u = 0.1 V s-r plus a potential hold at EF for (a) 10 min and (b) 30 min. The distance between the left and right margins of the micrograph is about 155pm. x 480.
film caused small bubbles which likely was a result of boiling water which might have been trapped in the tihn or could be an indication of a hydrated film. The application of a repetitive triangular potential sweep in the absence of film reduction and reactivation processes leads to the formation of the same film observable by SEM.
Surfaces on which the film was developed potentiostatically at two distinct times are compared. After a potential sweep from Et = -0.9 V to Er = 0.24 V, which corresponds to a value slightly higher than the potential of peak at, this potential was held for 10 and 30min and the surface examined. The current-time behaviour is shown in Fig. 7. The initial
B. F. GIANNETTI et al.
148
current decrease with time may be due to a thickening of the film and the subsequent increase can be explained by a reactivation process at which there is a breakdown of the film followed by redissolution of the metal[7j. The resulting micrographs reveal that the grain boundaries are attacked on distinct sites (Fig. 8b). The latter is not observed when the film is grown for 10 min (Fig. 8a), indicating that the reactivation process occurs more intensely on the grain boundaries.
SEM associated with electrochemical studies on the tin/citric acid electrode support the conclusions based on pure electrochemical measurements. When is submitted
to relatively
Acknowledgements-Financial support from Financiadora de Estudos e Projetos (FINEP), Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) and Conselho National de Desenvolvimento Cientifico e Tccnologico (CNPq) is gratefully recognized.
REFERENCES
CONCLUSIONS
the electrode
Under certain conditions the electrode can suffer a reactivation process which happens more intensively on the grain boundaries.
slow linear
potential sweeps the oxidation current is due essentiallv to metal dissolution. which occurs distinctly on the different crystallographic planes. Tin oxide film which is either formed naturally in air or by a potentiodynamic oxidation is very thin and is not observable by SEM. However, the film
grown under stationary conditions seems to be hydrated and shows characteristics of films formed by precipitation.
1. B. F. Giannetti, P. T. A. Sumodjo and T. Rabockai, J. appl. Electrochem. 20, 612 (1990).
2. R. G. P. Elboume and G. S. Buchanan, J. inorg. Nucl. Chem. 32, 493 (1970); 32, 3559 (1970). 3. J. C. Sherlock and S. C. Britton, Br. Corros. J. 7, 180 (1972). 4. T. _F.__.Sharpc and S. G. Meibhur, J. them. Educ. 46, 103 (lY6Y). 5. C. J. Tawaites and C. A. Mackay, Metals Handbook, Vol. 8 (Edited by T. Lyman), 8th Edn, p. 139. American Society for Metals, Ohio (1973). 6. D. D. MacDonald, Transient Techniques in Electrochemistry, p. 297. Plenum Press, New York (1977). 1. B. N. Stirrup and N. A. Hampson, J. appl. Electrochem. 6, 353 (1976).
Acta, Vol. 31, No.
1, pp. 143-148,
1992 0
Printed in Great Britain.
Km-46s6/92 $5.00+ 0.00 1991. Pergomon Pros pk.
ELECTROCHEMICAL DISSOLUTION AND PASSIVATION OF TIN IN CITRIC ACID SOLUTION USING ELECTRON MICROSCOPY TECHNIQUES B. F. GIANNETTI,* P. T. A. SUMODJO,* T. RABOCKAI,* A. M. Souwt and J. BARBOZA~ +Instituto de Quhnica da Universidade de Slo Paula, C.P. 20.780, 01498 SHoPaula, SP, Brazil; tGenera1 Motors do Brasil, C.P. 197, 09500 8&oCaetano do Sul, SP, Brazil (Received 4 October 1990; in revisedform 13 March 1991)
Abstract-The electrochemical behaviour of tin in 0.5 M citric acid solution was studied by electron microscopy techniques in addition to the potentioclynamic method. The observed electrochemical dissolution is quite similar to pure chemical dissolution when metallographic practices are used and takes place distinctly between the grains. The film growing process follows a dissolution/precipitation mechanism. The local reactivation process occurs primarily along the tin grain boundaries locations. Key woruk citric acid, electrochemical stability, potentiodynamic perturbation, scanning electron rnicroscopy, surface Bhn, tin electrodes.
INTRODUCTION
Numerous papers on the electrochemical behaviour of tin, a metal with many technological uses, have been reported. In a previous paper[l], we discussed the electrochemical behaviour of tin in deaerated 0.5 M citric acid by means of the potentiodynamic method. It was shown that, despite the simplicity of the E/Z profile, the anodic oxidation of the metal involves the formation of a soluble Sn(I1) species which is subsequently oxidized to Sn(Iv). The nature of the soluble species, which cannot be discussed from our results, is the object of investigation by different authors[2, 31. Passivation occurs via the hydrolysis of Sn(IV) to yield either Sn(OH), or SnO,. When applied to solid electrodes, potential perturbation programmes are able to cause structural and morphological modifications on their surfaces inducing changes in crystallographic orientation and composition. In the present paper we discuss the microstructural features of a tin surface subjected to an electrochemical perturbation program in 0.5 M citric acid. The surface was examined by means of scanning electron microscopy (SEM). EXPERIMENTAL
The working electrode, a disk with an apparent area of 0.8 mm2, was constructed following the procedure described by Sharpe and Meibhur[4]. A platinized platinum electrode was used as the counter electrode and a reversible hydrogen electrode, placed in the same solution, was used as reference electrode (rhe). All potentials quoted are referred to this electrode. The electrolyte was a 0.5 M citric acid solution, which corresponds to pH 1.8. It was prepared with analytical grade reagent and triply distilled water and stored at low temperature to avoid decomposition. EA 37/l-K
Prior to each experiment the working electrode was polished with 600 emery paper and suspensions of alumina powder (0.3 and 0.02 pm, respectively), following the usual metallographic procedure[q. The electrode was then rinsed with distilled water, dipped in the solution which had previously been deaerated with purified nitrogen. Immediately after the electrochemical experiment the electrode was dried with compressed air and taken for SEM examination, on a Phillips PSEM 500 scanning electron microscope. Some polished cross-sections were etched in Nital 2% (2ml HNO, + 98 ml ethanol)[5] to reveal the microstructure for metallographic examination. All volammetric experiments were performed at a sweep rate of 0.1 V s-r.
RESULTS AND DISCUSSION
The micrograph shown in Fig. 1 exhibits the electrode surface after mechanical polishing. There are observed parallel scratches, dark spots, incrustation (5-10 pm in diameter) and microvoids. The dark spots appearance is not altered even by an extensive cathodization at -0.9 V, at which hydrogen evolves vigorously. This fact and the size of the dark spots suggest that they arise from the emery paper used during the final grinding operation and were only partially removed during subsequent polishing. The micrographs obtained before and after a cathodization at -0.9 V for 5 min do not reveal significant changes on the surface features. However, this electrochemical pretreatment is essential for the acquisition of stable and reproducible Z/E profiles. Although not detected by SEM examination, a thin fllm of tin oxide is probably formed in air. The reduction of this film, during the cathodixation, produces a fresh metallic surface, allowing the aquisition of reproducible electrochemical data.
B. F.
GIANNETTI et al.
Fig. 1. SEM micrograph of tin surface after mechanical polishing. The distance between the left and right margins of the micrograph is about 310 pm. x 210.
The typical anodic I/E curve of tin in 0.5 M citric acid solution after the mechanical and electrochemical pretreatment is depicted in Fig. 2. Detailed analyses of the electrochemical experiments and the resulting data are found in Ref.[l]. Points A, B and C shown in Fig. 2 represent the anodic end potentials, EF, selected for SEM examination of the morphological changes of the electrode surface when submitted to a linear potential sweep. SEM examination of the electrode surface after the application of a linear potential sweep with EF = -0.15 V, corresponding to point A in Fig. 2, reveals the existence of different planes. The dark spots observed just after the mechanical polishing disappear completely with the electrochemical treatment. The observed planes were possibly formed either by the dissolution of the metal or formation of a new phase, or both. During the voltammetric experiment the electrode experiences an abrupt increase in current when the potential reaches a value related to point A (Fig. 2). This increase in current with potential is practically due to metal dissolution, evidenced by the complete removal of the dark spots during the electrochemical procedure. Anodic current peak a, in Fig. 2 is characteristic of a passivation process, ie the sharp decrease in current is due to the formation of a passive film[6]. When the electrode is submitted to the electrochemical perturbation with the values of EF equal to 0.0 and +0.12 V, related to points B and C, respectively, no significant differences in the surface morphology are observed. Figure 3, a micrograph related to point C, shows that the different planes on the electrode surface are better defined. In order to decide whether the observed planes are a consequence of the metal dissolution, film formation or both, SEM examin-
ations were performed on the electrode surface after the application of a triangular potential sweep with E, = EF = -0.9 V and E,,a = 1.5 V. The corresponding cyclic voltammogram, Fig. 2, shows a cathodic current peak, cI, at ca -0.42 V which is associated with the reduction of the anodically formed film[l]. SEM examinations reveal that the surface topography is exactly the same as that shown in Fig. 3. Since the surface morphology does not change in the two experiments, it can be concluded that the planes on the surface are formed by the dissolution of the metal. When a polished tin surface is etched in Nital 2%, the polycrystalline nature of the metal is apparent (Fig. 4). Figures 3 and 4 show that the resulting surface after an electrochemical treatment and after a chemical treatment are similar. Since the etching procedure reveals the grains, the similarity of the two micrographs clearly demonstrates that the electro-
a i \
- 1.2
-0.6 E/VO
I.2 (EFZ)
Fig. 2. Potentiodynamic I/E profile of tin in 0.5 M citric acid; v = 0.1 V SK’; geometric area = 0.8 mm2.
Tin in citric acid solution
Fig. 3. SEM micrograph of tin surface after mechanical polishing and potentiodynamic perturbation; final potential corresponding to point C in Fig. 2. The distance between the left and right margins of the micrograph is about 155 pm. x 480.
Fig. 4. SEM micrograph of tin surface after mechanical polishing and etching in reagent Nital 2%. The distance between the left and right margins of the micrograph is about 155 pm. x 480.
145
146
B. F. GIANNETTI ef al.
Fig. 5. Cyclic voltammogram obtained with the schematized perturbation programme: v = 0.1 v s-1; .I?,= -0.9 v, E+ = EF= 1.5 V, EC= -0.22 V; geometric area 0.8 mm*.
chemical dissolution occurs distinctly on the different crystallographic planes. In our previous paper[l] the potentiodynamic formation of a passivating film constituted by Sn(OH), which undergoes a further transformation to give SnOz was suggested. The experiments and observations discussed in this paper are unable to prove the existence on the surface of the passivating layer. This is probably because of the thickness of the film. However, its presence can be detected in an indirect way. All attempts to achieve a sharp and clear image of SEM examination of a tin electrode submitted to an anodic polarization in a potential region where doubtless a passivation occurred were unsuccessful. This difficulty can be explained by the higher electric resistivity of this phase in relation to the bare metal.
Naturally this obstacle could be overcome by the deposition of a thin conducting film technique; however, since the same electrode was used in all experiments, to avoid possible contaminations this procedure was not employed. When a triangular potential sweep with E, = -0.9 V, E,, = 1.5 V and EF = -0.22 V is applied, the electrode maintains its passivating condition because the passive layer is not allowed to be reduced under certain conditions (Fig. 5). Moreover, (0.2 V < E,,a < 0.7 V), a reactivation process takes place[ 11. SEM examination of a surface submitted to a voltammetric experiment with E, = -0.9 V, E,,a = EF = 2.0 V followed by a potential hold at EF for 10 min, reveals clearly the existence of the passivating layer (Fig. 6). This film seems to be developed as floes, suggesting that it could be formed by precipitation. The interaction between the electron beam and the
0
2
4
8
IO
t/InL
Fig. 7. Current-time curve for a tin electrode submitted to mechanical polishing followed by a voltammetric experiment with E,= -0.9V, Ei,=EF=0.24V,v =O.lVs-’ with a subsequent potential hold at EF for 10min. Geometric area 0.8 mm*.
Fig. 6. SEM micrograph of tin surface submitted to mechanical polishing followed by a voltammetric V, El,+ = EF = 2.0V, u = 0.1 V s-’ plus a potential hold at EF for 10 min. The experiment with E,= -0.9, distance between the left and right margins of the micrograph is about 155 pm. x480.
Tin in citric acid solution
Fig. 8. SEM micrograph of tin surface submitted to mechanical polishing followed by a voltanunetric experiment with E, = -0.9 V, E,,a = EF = 0.24V, u = 0.1 V s-r plus a potential hold at EF for (a) 10 min and (b) 30 min. The distance between the left and right margins of the micrograph is about 155pm. x 480.
film caused small bubbles which likely was a result of boiling water which might have been trapped in the tihn or could be an indication of a hydrated film. The application of a repetitive triangular potential sweep in the absence of film reduction and reactivation processes leads to the formation of the same film observable by SEM.
Surfaces on which the film was developed potentiostatically at two distinct times are compared. After a potential sweep from Et = -0.9 V to Er = 0.24 V, which corresponds to a value slightly higher than the potential of peak at, this potential was held for 10 and 30min and the surface examined. The current-time behaviour is shown in Fig. 7. The initial
B. F. GIANNETTI et al.
148
current decrease with time may be due to a thickening of the film and the subsequent increase can be explained by a reactivation process at which there is a breakdown of the film followed by redissolution of the metal[7j. The resulting micrographs reveal that the grain boundaries are attacked on distinct sites (Fig. 8b). The latter is not observed when the film is grown for 10 min (Fig. 8a), indicating that the reactivation process occurs more intensely on the grain boundaries.
SEM associated with electrochemical studies on the tin/citric acid electrode support the conclusions based on pure electrochemical measurements. When is submitted
to relatively
Acknowledgements-Financial support from Financiadora de Estudos e Projetos (FINEP), Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) and Conselho National de Desenvolvimento Cientifico e Tccnologico (CNPq) is gratefully recognized.
REFERENCES
CONCLUSIONS
the electrode
Under certain conditions the electrode can suffer a reactivation process which happens more intensively on the grain boundaries.
slow linear
potential sweeps the oxidation current is due essentiallv to metal dissolution. which occurs distinctly on the different crystallographic planes. Tin oxide film which is either formed naturally in air or by a potentiodynamic oxidation is very thin and is not observable by SEM. However, the film
grown under stationary conditions seems to be hydrated and shows characteristics of films formed by precipitation.
1. B. F. Giannetti, P. T. A. Sumodjo and T. Rabockai, J. appl. Electrochem. 20, 612 (1990).
2. R. G. P. Elboume and G. S. Buchanan, J. inorg. Nucl. Chem. 32, 493 (1970); 32, 3559 (1970). 3. J. C. Sherlock and S. C. Britton, Br. Corros. J. 7, 180 (1972). 4. T. _F.__.Sharpc and S. G. Meibhur, J. them. Educ. 46, 103 (lY6Y). 5. C. J. Tawaites and C. A. Mackay, Metals Handbook, Vol. 8 (Edited by T. Lyman), 8th Edn, p. 139. American Society for Metals, Ohio (1973). 6. D. D. MacDonald, Transient Techniques in Electrochemistry, p. 297. Plenum Press, New York (1977). 1. B. N. Stirrup and N. A. Hampson, J. appl. Electrochem. 6, 353 (1976).