\ PERGAMON Corrosion Science 30 "0888# 0446Ð0473 The stability of the passive state of ironÐ chromium alloys in sulphuric acid solution M[ Bojinova\ b\ I[ Betovac\ G[ Fabriciusb\ T[ Laitinena\ \ R[ Raiche} d\ T[ Saarioa a VTT Manufacturing Technology\ FIN!91933 VTT\ Espoo\ Finland Laboratory of Physical Chemistry and Electrochemistry\ Helsinki University of Technology\ FIN! 91904 HUT\ Espoo\ Finland c Central Laboratory of Electrochemical Power Sources\ Bulgarian Academy of Sciences\ 0002 So_a\ Bulgaria d Department of Electrochemistry and Corrosion\ University of Chemical Technology and Metallurgy\ 0645 So_a\ Bulgaria b Received 19 May 0887^ accepted 8 December 0887 Abstract The passivation and the transpassive dissolution of FeÐCr alloys "01) and 14) Cr# was studied with a combination of electrochemical techniques*conventional and rotating ringÐ disk voltammetry\ impedance spectroscopy and the contact electric resistance "CER# technique developed to measure the dc resistance of surface _lms[ Rotating ringÐdisk studies indicated that both soluble Cr"VI# and Fe"III# are released from the alloys in the transpassive region[ The electronic resistance of the transpassive anodic _lm was found to decrease as Cr"VI# is released from the outermost layers adjacent to the interface and to increase subsequently due to the formation of a Fe"III# rich secondary passive _lm[ Impedance spectra of the FeÐ 14) Cr alloy were found to include contributions from both the _lm growth and transpassive dissolution reactions\ whereas the corresponding spectra of the FeÐ01) Cr alloy re~ected mainly the contribution of the _lm[ On the basis of the experimental results\ a generalized model of the transpassivity of FeÐCr alloys is proposed[ The model represents the anodic _lm as a highly doped n!type semiconductorÐinsulatorÐp!type semiconductor "nÐiÐp# structure[ Injection of negative defects at the _lm:solution interface results in their accumulation as a negative surface charge[ It alters the non!stationary _lm growth rate controlled by the transport of positive defects "oxygen vacancies#[ The transpassive dissolution reaction is assumed to be a two!stage process featuring a Cr"IV# intermediate[ The relaxation of the Fe fraction in the outermost cation layer of the _lm is taken into account as well[ Fitting of the experimental data on the basis of equations derived for the steady state and impedance response enable the  Corresponding author[ Tel[] ¦99247!8!345!4751^ fax] ¦99247!8!345!4764 E!mail address] timo[laitinenÝvtt[_ "T[ Laitinen# 9909!827X:88:, ! see front matter Þ 0888 Elsevier Science Ltd[ All rights reserved[ PII] S 9 9 0 9 ! 8 2 7 X " 8 8 # 9 9 9 9 2 ! 6 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0447 determination of the kinetic parameters of transpassive dissolution[ Þ 0888 Elsevier Science Ltd[ All rights reserved[ Keywords] IronÐchromium alloy^ EIS^ RRDE^ Contact electric resistance^ Transpassivity Nomenclature a A B bi cO "dF# CF CM:F CF:S C9 dF dF:S DO E E i iM:F iF iF:S iS j ki m MM OO qn Rt Rel V 1¦ O 2− VM Vm S xFe xCr ZM:F ZF ZF:S a atomic jump distance\ cm constant in the high!_eld migration equation\ A cm−1 _eld coe.cient in the high!_eld equation V −0 cm Tafel coe.cients of the interfacial reactions "i0Ð5#\ V −0 concentration of oxygen vacancies at the metal:_lm interface\ mol cm−2 high!frequency capacitance of the _lm\ F cm−1 capacitance of the metal:_lm interface\ F cm−1 capacitance of the cation vacancy accumulation layer\ F cm−1 faradaic pseudocapacitance\ F cm−1 thickness of the anodic _lm\ cm thickness of the metal vacancy accumulation layer\ cm di}usivity of oxygen vacancies\ cm1 s−0 applied potential\ V electric _eld strength\ V cm−0 current density\ A cm−1 current density at the metal:_lm interface\ A cm−1 _lm formation current density\ A cm−1 current density at the _lm:solution interface\ A cm−1 steady state current density\ A cm−1 imaginary unit rate constants of the interfacial reactions "i0Ð5#\ mol=cm−1 s−0 metal atom in the metal phase metal position in the anodic _lm oxygen position in the anodic _lm negative surface charge at the _lm:solution interface\ C cm−1 charge transfer resistance\ V cm1 electrolyte resistance\ V cm1 oxygen vacancy in the anodic _lm metal vacancy in the anodic _lm molar volume of the phase in the barrier _lm\ cm2 mol−0 capture cross section for a positive defect\ cm1 C −0 iron position in the anodic _lm bulk chromium position in the anodic _lm bulk impedance of the metal:_lm interface\ V cm1 impedance of the anodic _lm\ V cm1 impedance of the _lm:solution interface\ V cm1 polarizability of the _lm:solution interface M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 b gFe gCr o o9 fM:F fF:S u v 0448 maximum surface excess\ mol cm−1 iron position in the outermost layer of the anodic _lm chromium position in the outermost layer of the anodic _lm dielectric constant of the _lm dielectric permittivity of vacuum local potential drop at the metal:_lm interface\ V local potential drop at the _lm:solution interface\ V surface coverage of Cr"IV# intermediate angular frequency\ rad s−0 0[ Introduction Transpassive dissolution of a range of alloys is closely related to passive _lm breakdown and localized corrosion phenomena[ It leads to a depletion of alloying elements such as Cr in the _rst atomic layers near the electrolyte\ which are the most susceptible to localized attack by aggressive anions[ Two approaches can serve as a basis for a theoretical treatment of the problem] the bipolar passive _lm model of Clayton et al[ ð0Ð3Ł and the Point Defect Model "PDM# for the growth and breakdown of passive _lms advanced by Macdonald et al[ ð4Ð01Ł[ In the bipolar _lm model\ it is assumed that due to the incorporation of Cr as CrO 31− \ the passive _lm behaves as an ionic ~ow recti_er which hampers the chloride ion adsorption:ingress and sup! presses the localized corrosion process[ The PDM assumes segregation of alloying elements such as Cr in the _lm as high!valency cations[ These cations are assumed to reduce the concentration and di}usivity of cation vacancies in the _lm by means of forming complexes with them[ Hence they retard passivity breakdown[ Both models imply that there is a separation of charges in the barrier layer[ According to Clayton et al[ ð0Ð3Ł\ injected metal ions "positive carriers# are accumulated at the metal:_lm interface and chromate ions "negative charges# at the _lm:solution interface[ On the other hand\ Macdonald et al[ ð8Ð00Ł assume that there is an accumulation of oxygen vacancies "positive charges# at the metal:_lm interface and a corresponding accumu! lation of cation vacancies "negative charges# at the _lm:solution interface[ Recently\ we proposed the so!called surface charge approach to the growth of anodic passive _lms on metals ð02Ð06Ł[ The passive _lm was represented as a doped n!type semiconductorÐinsulatorÐp!type semiconductor "nÐiÐp# structure with injec! tion of oxygen vacancies "donors# from the metal substrate during _lm growth and metal vacancies "acceptors# from the electrolyte during _lm dissolution[ Assuming that the transport of metal vacancies is slower than the rate of their annihilation at the metal:_lm interface\ they accumulate at the _lm:solution interface[ This accumu! lation of negative charge enhances the non!stationary transport of positively charged oxygen vacancies\ thus explaining the low!frequency inductive loop in the impedance response of a range of passive metals[ This paper comprises an extension of the surface charge approach to cover trans! passive dissolution phenomena\ as well as a generalized model for the transpassive dissolution process[ Experimental results on the transpassive dissolution of FeÐ 0459 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 01) Cr and FeÐ14) Cr alloys obtained using several electrochemical techniques* conventional and rotating ringÐdisk voltammetry\ impedance spectroscopy and the dc contact electric resistance "CER# technique*are presented and compared to the model predictions[ This work on FeÐCr alloys can be regarded as a next step in the study recently initiated in our group by modelling the transpassive dissolution of pure Mo ð07\ 08Ł and Cr ð19\ 11\ 12Ł[ Part of the experimental results on the behaviour of a FeÐ01) Cr alloy together with a preliminary version of the theoretical approach have already been published ð13Ł[ 1[ Experimental 1[0[ Electrodes and electrolyte Laboratory made high!purity FeÐ01) Cr and FeÐ14) Cr alloys\ as well as pure Fe "88[7)# and Cr "88[6)# were used[ To prepare working electrodes for the con! ventional voltammetric and impedance measurements\ the samples were sealed in PTFE holders with epoxy resin to expose a disk area of 9[1 cm1[ For the rotating ringÐdisk studies\ electrodes featuring a disk made of the material under investigation "area 9[05 cm1# and a ring made of Au "88[8)\ ring area 9[0 cm1# were employed[ The theoretical collection e.ciency\ 9[21\ of the ringÐdisk electrode arrangement was experimentally veri_ed using the ferricyanide:ferrocyanide couple[ For the contact electric resistance "CER# measurements\ electrode tips with a diameter of 1[4 mm made of the investigated materials were used[ The working electrode pretreatment consisted of mechanical polishing on a _ne grade emery paper\ degreasing and rinsing with water puri_ed in a Milli!ROþ 04 "Millipore# water puri_cation system[ A three electrode cell featuring a Pt counter electrode and a Hg:Hg1SO3:sat[ K1SO3 reference electrode "SSE[ ESSE9[55 V vs[ SHE# was employed[ All the potentials in the paper are given vs[ this reference electrode[ The electrolyte "0 M H1SO3# was prepared from analytical grade 86) H1SO3 "Merck# and Milli!ROþ water[ The experiments were carried out at 1920>C in naturally aerated solutions[ 1[1[ Apparatus and procedures Conventional voltammetry and impedance spectroscopy were carried out with a Solartron 0175:0149 system[ All the potential values were corrected for the IR!drop[ The current vs time curve was recorded at each potential until a steady state current was reached "criterion] variation during an experiment ¾1)#[ The impedance spectra were measured at this steady state in a frequency range 9[90Ð09\999 Hz at an ac amplitude of 09 mV "rms#[ The reproducibility of the impedance spectra was 20) by gain and 21> by phase shift[ The software for impedance data acquisition and the routines for impedance spectra simulation were elaborated by one of the authors "M[B[# In the rotating ringÐdisk experiments\ an Autolabþ PGSTAT 19 "Eco Chemie B[V[# potentiostat:galvanostat was used[ A Wenking LB 70M potentiostat "Bank Elektronik#\ combined with a PPR0 function generator "HITEK# was used for poten! M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0450 tial control in the contact electric resistance "CER# measurements[ The working principle of the contact electric resistance "CER# technique is based on the measure! ment of the electric resistance across a solidÐsolid contact surface using direct current ð14Ł[ During the measurement\ the surfaces are brought together and pulled apart at regular intervals[ When the probes are apart from each other\ their surfaces are exposed to the in~uence of the environment[ The potential of the probes is controlled by a potentiostat and the electrochemical current density is measured[ When the potentiostatically controlled probes are brought into contact\ a direct current is passed through the contact surface and the resulting voltage is measured in order to determine the resistance of the surface _lm[ The pressure applied during the contact situation is well below the typical compressive strength of metal oxide _lms[ The measurement system allows both the current vs[ potential and the resistance vs[ potential depen! dences to be recorded during one and the same experiment[ 2[ Results 2[0[ General electrochemical behaviour Figure 0 summarizes the conventional voltammetric behaviour of pure Fe\ Cr and both investigated alloys in 0 M H1SO3[ The regions of active dissolution\ passivation\ passivity\ transpassive dissolution\ secondary passivation and oxygen evolution can Fig[ 0[ Linear sweep voltammograms of pure Fe\ Cr and FeÐCr alloys "01) and 14) Cr# in 0 M H1SO3[ Sweep rate] 0 mV s−0[ 0451 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 be easily discerned[ As expected\ the addition of Cr greatly in~uences the active!to! passive transition of Fe and signi_cantly stabilizes the passive state of the alloys[ By contrast\ the addition of Cr has an opposite e}ect on the transpassive behaviour\ leading to pronounced transpassive dissolution[ This becomes predominant for the FeÐ14) Cr alloy in analogy to pure Cr\ whereas secondary passivation and oxygen evolution are observed for the FeÐ01) Cr alloy in analogy to pure Fe ð13Ł[ Voltammetric curves of the pure metal constituents and the two alloys studied in 0 M H1SO3 are presented in Fig[ 1"a# "pure Fe#\ Fig[ 1"b# "pure Cr# Fig[ 1"c# "FeÐ 01) Cr# and Fig[ 1"d# "FeÐ14) Cr#\ together with the simultaneously registered surface _lm resistance measured by the CER technique[ It can be seen that the passivation of all the materials due to the formation of an anodic _lm is associated with an abrupt increase of the electronic resistance by several orders of magnitude[ In the passive state\ relatively high and stable _lm resistance values are measured[ For pure Fe ðFig[ 1"a#Ł\ a _lm with lower resistance is found at −9[4Ð9[9 V\ while a strong increase in the resistance occurs at E×9 V[ The latter is associated with an abrupt drop in the current density of Fe[ It is worth mentioning that the potential at which this drop in the current is observed is more positive with higher sweep rates[ RRDE measurements performed at a sweep rate of 29 mV s−0 ðFig[ 2"a#Ł indicate that the drop in the anodic current also marks the end point of the release of soluble Fe"II# species\ which were found to enter the solution at relatively high concentrations at potentials above the rest potential[ Preceding the abrupt drop of the current on Fe\ the release of Fe"III# at lower concentrations was also observed ðFig[ 3"a#Ł[ At high positive potentials approaching the oxygen evolution region\ the resistance of Fe slowly decreases and _nally drops signi_cantly when intensive oxygen evolution starts[ Simultaneously\ the release of small amounts of Fe"III# can be detected[ For pure Cr\ the behaviour is similar to that reported earlier ð19\ 11\ 12Ł[ The quasilinear dependence of log R on E in the passive state is in agreement with the idea of an exponential increase of the blocking character of the _lm with increasing potential[ The slope of the log R vs[ E curve in the region −9[1Ð9[5 V is in accordance with an estimation of the potential dependence of the rate constant for electron transfer through the passive _lm on Cr\ based on the data reported by Mo}at et al[ ð10Ł[ After the formation of a high!resistive _lm\ the resistance starts to decrease already in the passive region\ most probably due to a solid state oxidation of Cr"III# in the _lm to Cr"VI# ð19\ 11\ 12Ł[ Finally\ the resistance reaches very low values in the region of intensive transpassive dissolution ðFig[ 1"b#Ł[ The resistanceÐvoltage curves for the FeÐ01) Cr and FeÐ14) Cr alloys ðFig[ 1"c\d#Ł show that the _lm resistance on the alloys starts to increase at potentials corresponding to the behaviour of pure Fe ðFig[ 1"a#Ł and not to that of Cr ðFig[ 1"b#Ł[ After this\ a gradual increase of the _lm resistance is observed up to E39[4 V[ The release of soluble Fe"II# species ðFig[ 2"b\c#Ł takes place in a much narrower potential range than in the case of pure Fe\ most likely because of the totally di}erent nature of the anodic _lm in the presence of Cr[ The maximum resistance values in the passive region of the alloys are signi_cantly smaller than those measured for pure Fe and Cr[ The transpassive dissolution of Cr from the outermost layers of the anodic _lm on the alloys leads to a decrease in _lm resistance at ca[ 9[4Ð9[6 V ðFig[ 1"c\d#Ł[ The M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0452 Fig[ 1[ Linear sweep voltammogram of "a# pure Fe\ "b# pure Cr\ "c# FeÐ01) Cr alloy and "d# FeÐ14) Cr alloy in 0 M H1SO3\ together with the simultaneously registered resistance vs[ potential curve using the CER technique[ Sweep rate] 0 mV s−0[ transpassive reaction is also observed on the basis of the RRDE results shown in Fig[ 3"b\c#[ The subsequent increase of the resistance at E×9[7 V can be ascribed to secondary passivation\ most probably due to the growth of a Fe"III#!based _lm[ These 0453 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 Fig[ 1[ "continued# changes are much more pronounced for the FeÐ14) Cr alloy\ in which case the onset of transpassive dissolution of Cr from the alloy leads to a decrease of the _lm resistance by more than three orders of magnitude ðFig[ 1"d#Ł[ Even if no clear secondary passivation features are observed in the voltammetric curve\ the subsequent slow M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0454 Fig[ 2[ Linear sweep voltammogram of "a# Fe\ "b# FeÐ01) Cr alloy and "c# FeÐ14) Cr alloy disk in 0 M H1SO3 "sweep rate] 29 mV s−0\ rotation rate] 0199 rpm# together with the detection of soluble Fe"II# by its oxidation to Fe"III# at the Au ring "ring potential] 9[4 V#[ increase of the _lm resistance shows that the growth of the Fe"III# based _lm proceeds in this case as well[ Summarizing\ the simultaneous measurement of currentÐpotential curves and _lm 0455 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 Fig[ 2[ "continued#[ resistance potential curves together with the RRDE results show that\ at high positive potentials\ transpassive dissolution of mainly Cr from FeÐCr alloys takes place[ The transpassive behaviour is associated with a gradual transformation of the anodic _lm which\ in turn\ is re~ected in its electronic properties[ 2[1[ Release of soluble products durin` transpassive dissolution of a prepassivated elec! trode Further investigations on the release of soluble products from Fe and FeÐCr alloys during transpassive dissolution were carried out using prepassivated electrodes[ Figure 4"a# shows the detection of Fe"III# dissolved from a Fe disk prepassivated at 9[04 V by means of reducing it at the Au ring to Fe"lI# "potential of the ring] −9[2 V# during a voltammetric scan of the Fe disk up to the oxygen evolution region[ The increase of the disk current at E×9[8 V is associated with the simultaneous release of Fe"III#[ The disk current plateau at 0[94Ð0[04 V corresponds to an almost potential!inde! pendent dissolution of Fe"III# in the same region[ Finally\ further potential!dependent Fe"III# release occurs simultaneously with current increase at the disk at higher positive potentials\ which must be associated with oxygen evolution[ In general\ the current due to Fe"III# is only a small fraction of the disk current in the whole potential region investigated[ In the curve for pure Cr prepassivated at 9 V ðFig[ 4"b#Ł\ the increase of the disk current at 9[5 V coincides with an increase of the current of the ring polarised at −9[2 V[ At this ring potential\ Cr"VI# is detected by its reduction to Cr"III#[ It can be seen that the current due to the production of soluble Cr"VI# must contribute the major part of the overall disk current[ M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0456 Fig[ 3[ Linear sweep voltammogram of "a# Fe\ "b# FeÐ01) Cr alloy and "c# FeÐ14) Cr alloy disk in 0 M H1SO3 "sweep rate] 29 mV s−0\ rotation rate] 0199 rpm# together with the detection of soluble Fe"III# by its reduction to Fe"II# and:or the detection of soluble Cr"VI# by its reduction to Cr"III# at the Au ring "ring potential] −9[5 V#[ 0457 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 Fig[ 3[ "continued#[ Figure 4"c# summarizes the results for the FeÐ01) Cr alloy prepassivated at 9 V[ In the _rst positive sweep following prepassivation\ a disk peak at 9[54 V is associated with a corresponding ring peak "potential of the ring] −9[2 V#[ This is most probably due to the release of soluble Cr"VI# formed via oxidation of Cr"III# in the outermost layers of the passive _lm ðcf[ Figure 4"b#Ł[ Subsequently\ both the disk and the ring currents remain almost constant at 9[7Ð0[04 V[ The subsequent increase of the disk current at ca[ 0[1 V\ mainly due to oxygen evolution\ is associated with an increase in the ring current\ most probably due to release of Fe"III# from the _lm in analogy to pure Fe ðcf[ Figure 4"a#Ł[ This interpretation can be made more comprehensive on the basis of the results obtained during the second positive!going sweep following an intermediate polarization at 9 V to a steady current density ðFig[ 4"c#Ł[ No peak is observed\ either in the disk or in the ring current curve at Edisk9[5 V during this second sweep[ Instead\ a gradual rise of the disk and ring currents at ca[ 9[6Ð9[8 V is detected\ in qualitative analogy to the curve for pure Fe ðFig[ 4"a#Ł[ Moreover\ the values of both the disk and ring currents for the two sequential sweeps coincide within the error limit at potentials higher than 0[9 V[ Thus it can be concluded that Cr"III# present in the outermost layers of the _lm was released as soluble Cr"VI# during the _rst sweep from the passive to the transpassive region and\ thus\ the _lm was modi_ed to behave in analogy to that formed on pure Fe[ This conclusion is in accordance with the suggestions of other authors ð29Ł[ The curves for the FeÐ14) Cr alloy following prepassivation at 9 V ðFig[ 4"d#Ł show essentially the same features[ However\ as the passive _lm contains mostly Cr"III# because of the higher Cr content of the alloy\ the transpassive dissolution of Cr during the _rst sweep does not cause such big changes in the composition of the M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0458 Fig[ 4[ Linear sweep voltammogram of "a# Fe disk prepassivated at 9[04 V and "b# Cr disk prepassivated at 9 V in 0 M H1SO3\ together with "a# the detection of soluble Fe"III# species by its reduction to Fe"II# and "b# the detection of soluble Cr"VI# by its reduction to Cr"III# at the Au ring[ The _rst and second positive!going linear sweep voltammograms of "c# FeÐ01) Cr disk and "d# FeÐ14) Cr disk prepassivated at 9[04 V in 0 M H1SO3\ together with the detection of soluble Fe"III#¦Cr"VI# by their reduction to Fe"II# and Cr"III# at the Au ring[ Sweep rate] 29 mV s−0\ ring potential] −9[2 V[ 0469 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 Fig[ 4[ "continued#[ outermost layer\ i[e[ no evidence of strong depletion in Cr is observed[ Nevertheless\ the di}erence found in the onset potential of the transpassive dissolution between the _rst and second voltammetric sweep clearly demonstrates that some modi_cation of the passive _lm toward more iron!like behaviour occurs in the case of the FeÐ14) Cr alloy as well[ M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0460 The steady state polarization curves of the transpassive dissolution of Fe and the FeÐCr alloys in 0 M H1SO3\ measured both with and without rotation\ are shown in Fig[ 5"aÐc# together with the steady state ring currents of the Cr"VI#¦Fe"III# detec! tion[ A similar curve for Cr has been given in Ref[ ð11Ł[ An important feature of the results is that the disk current for Fe and the alloys is almost independent on the rotation rate\ i[e[ the solution transport is not a rate determining step in the overall transpassive reaction[ The obtained disk and ring current curves for the alloys can be regarded as some kind of algebraic combination of the curves of the pure metals[ As also discussed above\ Cr is depleted from the outer layers of the passive _lm on the alloys due to the transpassive dissolution ð29\ 20Ł[ As a result of this\ a secondary passivation state is reached for the FeÐ01) Cr alloy at 9[54 V via the formation of an Fe!based secondary _lm ð17\ 29Ł[ No secondary passivation is reached for the FeÐ 14) Cr alloy\ at least for current densities ³099 mA cm−1[ This can be ascribed to the fact that the preferential dissolution of Cr from the outermost layers is readily compensated by a growth of a _lm strongly enriched in Cr underneath ð29Ł[ This provides a continuous supply of Cr species to be dissolved and thus prevents the formation of a Fe!based _lm[ An important point to mention is that\ in the region of the transpassive dissolution of the alloys\ the release of soluble Fe"III# was found to be potential!dependent for pure Fe as well\ inferring the electrochemical nature of the _lm dissolution process[ 2[2[ Impedance measurements in the transpassive re`ion Impedance spectra of pure Fe and pure Cr in 0 M H1SO3 in the potential region of transpassive dissolution of the alloys are presented in Fig[ 6"a\b#[ The spectrum for pure Fe at 9[74 V is similar to those published by Gabrielli et al[ ð21Ł[ According to them\ the high!frequency semicircle depicts the high!_eld migration of defects during _lm growth\ the inductive loop at intermediate frequencies is due to the relaxation of mobile FeIII and\ at the lowest frequencies\ the faradaic pseudocapacitance of the growing _lm is detected ð21Ł[ For higher potentials\ a multistep oxygen evolution reaction takes place\ as commented upon earlier in detail by Bojinov et al[ ð13Ł[ The impedance spectra for pure Cr are also similar to those published by several authors ð19\ 11\ 22\ 23Ł[ Recently\ a kinetic model for the transpassive process on Cr was developed\ including two parallel dissolution paths of Cr as Cr"VI# and a continuously changing valency state of Cr in the outermost layer in contact with the electrolyte[ The model was found to quantitatively reproduce the experimental impedance response ð19\ 11Ł[ Figure 6"c\d# shows impedance spectra for the FeÐ01) Cr and FeÐ14) Cr alloys in 0 M H1SO3 in the transpassive range[ For the FeÐ01) Cr alloy\ two time constants*a high!frequency capacitive and a low!frequency inductive*followed by a capacitive behaviour at the lowest frequencies are observed at E³0[9 V\ as also reported earlier ð13Ł[ Above 0[9 V\ the spectrum is similar to that measured for pure Fe due to the oxygen evolution reaction ðFig[ 6"a#Ł[ The behaviour of the lower!chromium alloy in the transpassive and secondary passive range is in full agreement with the predictions of the surface charge approach\ i[e[ the impedance response depicts mainly the growth 0461 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 Fig[ 5[ Steady state polarization curve for the transpassive dissolution of "a# Fe\ "b# FeÐ01) Cr alloy and "c# FeÐ14) Cr alloy in 0 M H1SO3 measured with a motionless "9 rpm# and a rotating "0199 rpm# disk electrode\ together with the steady state ring current due to detection of Fe"III# and:or Cr"VI# "ring potential] −9[2 V#[ M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0462 Fig[ 5[ "continued#[ Fig[ 6[ Impedance spectra of "a# pure Fe in the region of transpassive dissolution and oxygen evolution on FeÐCr alloys\ of the transpassive dissolution of "b# pure Cr\ "c# the FeÐ01) Cr alloy and "d# the FeÐ 14) Cr alloy in 0 M H1SO3[ Parameter is frequency in Hz[ 0463 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 Fig[ 6[ "continued# and dissolution of the anodic _lm ð13Ł[ Thus\ the high!frequency capacitive loop re~ects the high!_eld assisted migration of defects in the _lm bulk\ the inductive loop at intermediate frequencies is due to the relaxation of the negative surface charge formed by the accumulation of metal vacancies at the _lm:solution interface and\ at the lowest frequencies\ the faradaic pseudocapacitance is detected[ This explanation of the features of the impedance spectrum di}ers from that proposed by Gabrielli et al[ ð21Ł in the origin of the phenomenon responsible for the inductive behaviour[ However\ the concept of a _nite!rate accumulation of metal vacancies is electrically analogous to the relaxation of mobile FeIII suggested by Gabrielli et al[ ð21Ł[ M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0464 For the FeÐ14) Cr alloy\ a further low!frequency capacitive time constant is already detected at 9[6 V[ At higher transpassive current densities "at E×9[7 V#\ where the polarization curve deviates strongly from that of pure Cr ðFig[ 4"b\d#Ł\ two additional time constants*one capacitive and another inductive*are observed in the frequency range 9[4Ð09 Hz[ They may be ascribed to the contribution of the relaxation of the coverage by some intermediate in the transpassive dissolution reac! tion of Cr ð19Ð11Ł and of the fraction of the outermost cation layer occupied by Fe atoms\ respectively[ 3[ Discussion 3[0[ A physical model of the metal:transpassive _lm:electrolyte system In this section\ a theoretical approach to the transpassive process of FeÐCr alloys is brie~y described[ The processes that are taken into account are depicted in a simpli_ed reaction scheme shown in Fig[ 7"a\b# and also discussed earlier ð02Ð06Ł[ According to this approach\ annihilation of metal vacancies and injection of oxygen vacancies takes place at the metal:_lm interface as follows "a KroegerÐVink notation is used#] k0 2− : MM¦2e− m¦VM "I# k1 − m : MM¦0[4V 1¦ O ¦2e "II# 2− In the _lm\ high!_eld assisted transport of V 1¦ O and V M proceeds[ At the _lm:solution interface\ metal vacancies are produced via Fe cation dissolution from the Fe positions of the outermost layer\ whereas oxygen vacancies react with water\ resulting in _lm growth k2 2− 2¦ ¦Feaq FeFe "gFe # : VM "III# k3 ¦ H1 O¦V 1¦ O : OO¦1H "IV# At the steady state\ the growth of the anodic _lm is balanced by its dissolution at the _lm:solution interface "assuming that Fe dissolves selectively through the _lm in the passive state ð29Ł#] Fe1 O2 ¦5H ¦ : 1Fe2¦ aq ¦2H1 O[ The production of soluble Fe"III# during transpassive dissolution of FeÐCr alloys suggested in the above reaction scheme was demonstrated by the rotating ringÐdisk experiments in the present work[ Transpassive dissolution of Cr can be regarded as a M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0465 Fig[ 7[ "a# A schematic representation of the processes in the metal:transpassive anodic _lm:electrolyte system\ according to the surface charge approach[ "b# A more detailed representation of the electrochemical reactions at the anodic _lm:solution interface during transpassive dissolution of FeÐCr alloys in 0 M H1SO3[ two!step reaction with an adsorbed intermediate ð19\ 11\ 15\ 16Ł taking place at the Cr positions in the outermost cation layer k4 2− − CrCr "gCr # : Cr3¦ ad \u0 ¦V M ¦e "V# k5 1− ¦ − Cr3¦ ad ¦3H1 O : CrO 3 ¦7H ¦1e "VI# M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0466 The transpassive dissolution reaction implies electron transfer through the _lm\ i[e[ with the increase of the rate of this reaction\ the electronic conductivity of the _lm is expected to increase[ This was con_rmed in the present work by measuring the dc electronic resistance of the _lms by the CER technique[ For a given potential at steady state\ the continuity equation imposes] iM:F iF iF:S iS constant[ Based on the ideas of Macdonald et al[ ð4\ 00Ł\ the total applied potential\ E\ can be assumed to be distributed as follows] EfM:F ¦fF ¦fF:S \ 9 fF:S aE¦fF:S and 9 \ fM:F "0−a#E−EdF −fF:S where a is the polarizability of the _lm:solution interface\ dF is the _lm thickness and E the _eld strength[ The overall impedance is the sum of the impedances of the metal:_lm interface\ of the _lm and of the _lm:solution interface[ ZZM:F ¦ZF ¦ZF:S dfM:F :di¦dfF :di¦dfF:S :di¦Rel [ 3[0[0[ Steady state current and impedance response of the `rowin` _lm Assuming that the current density of _lm growth is due to oxygen vacancy motion in the _lm driven by the electric _eld at the metal:_lm interface ðFig[ 7"a#Ł ð05\ 06\ 13Ł\ the current for _lm growth can be written as iF A exp"Bð"0−a#E¦qn dF:S :oo9 Ł:dF #\ "0# where A1FDOcO "dF#:1a\ B1Fa:RT\ a is the atomic jump distance\ cO "dF# is the interfacial concentration of oxygen vacancies\ DO their di}usivity\ dF is the _lm thickness and dF:S the width of the accumulation layer[ The time dependence of the surface charge\ qn\ is treated in analogy to the surface charge approach ð02\ 06Ł\ dqn iF:S S"aEoo9 :dF:S −qn #\ dt "1# where S is the capture cross section for a defect[ The steady state growth current "dqn:dt9# reads as iF\SS A exp 6 7 BE [ dF "2# At the steady state\ the _lm thickness is constant for a given potential\ so the rate of _lm growth becomes equal to the rate of _lm dissolution[ Under a small amplitude ac perturbation\ we obtain from eqs[ "0Ð1# the expression for the faradaic impedance ð05\ 06Ł] 0467 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 DiF i B""0−a#¦iS Soo9 a:ðjv¦iS SŁ#:dF [ DE S "3# To derive the total impedance\ the high!frequency capacitance of the _lm\ CF\ and the faradaic pseudocapacitance\ C9\ have to be added in an appropriate manner] ZF "iS B""0−a#¦iS Soo9 a:ðjv¦iS SŁ#:dF ¦jvCF #−0 ¦jvC9 [ "4# For the _lm thickness vs[ potential relation\ an equation similar to that of Macdonald et al[ ð4\ 00Ł was adopted since it has been reported in the literature that the _lm thickness also grows linearly with potential in the transpassive region ð17\ 18Ł] dF "0−a#E:E[ 3[0[1[ Steady state current and impedance at the metal:_lm interface The charge balance at the metal:_lm interface gives ðFig[ 7"a#Ł] iM:F F"2k0 ¦3:2k1 #iS [ "5# Assuming an exponential "Tafel!like# dependence of the rate constants on the potential drop at the metal:_lm interface\ i[e[ kiki9 expðbi "0−a#EŁ\ i0\ 1\ the following expression is obtained] ZM:F −0 F"2b0 k0 ¦3:2b1 k1 #¦jvCM:F \ "6# where CM:F is the interfacial capacitance[ 3[0[2[ Steady state current and impedance at the _lm:solution interface The assumptions of Tafel dependence of the rate constants on the potential drop at the _lm:solution interface "kiki9 exp"bi aE#\ i2 to 5# and Langmuir adsorption of the intermediate lead to the following charge and material balances ðFig[ 7"b#Ł] iF:S F"2k2 gFe ¦3:2k3 ¦k4 gCr ¦1k5 u0 #\ "7# bdgFe k5 u0 xFe −k2 gFe xCr \ dt "8# bdgCr k5 u0 xCr ¦k2 gFe xCr −k4 gCr \ dt bdu0 k4 gCr −k5 u0 [ dt Obviously gFe¦gCr¦u00\ dgFe:dt¦dgCr:dt¦du0:dt9\ xCr¦xFe0\ where xCr and xFe are the mass fractions of Cr and Fe in the oxide _lm bulk[ The steady state current is obtained setting the above derivatives to zero] iF:S\SS F"2k2 gFeSS ¦3:2k3 ¦2k5 u0SS #\ "09# u0SS k2 k4 xCr :ðk4 k5 xFe ¦k2 xCr "k4 ¦k5 #Ł\ "00# M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0468 gFeSS k4 k5 xFe :ðk4 k5 xFe ¦k2 xCr "k4 ¦k5 #Ł[ The impedance of the _lm:solution interface is obtained by a _rst order Taylor expansion of eqs[ "7Ð8#] 6 ZF:S −0 R t−0 ¦F "2k2 −k4 # 7 dgFe du0 ¦"1k5 −k4 # ¦jvCF:S \ dE dE "01# where R t−0 aF"2b2 k2 gFeSS ¦3:2b3 k3 ¦"b4 ¦1b5 #k5 u0SS #\ "02# du0 "X1 Z0 −k4 X0 #:ðZ0 Z1 ¦k4 k5 xFe Ł\ dE dgFe "X0 Z1 ¦k5 xFe X1 #:ðZ0 Z1 ¦k4 k5 xFe Ł\ dE X0 aðb5 k5 xFe u0SS −b2 k2 xCr gFeSS Ł\ X1 a"b4 −b5 #k5 u0SS \ Z0 jvb¦k2 xCr \ Z1 jvb¦k4 ¦k5 and CF:S is the capacitance of the _lm:solution interface[ The total impedance is then calculated as the sum of the impedances of both interfaces and of _lm bulk "Equations "4\ 6\ 01Ð02##[ 3[1[ Comparison with the experimental results The simulated polarization curve and impedance spectra for the FeÐ01) Cr alloy in the range 9[5Ð0[9 V are presented in Fig[ 8"a\b#\ whereas the corresponding simu! lations for the FeÐ14) Cr alloy are shown in Fig[ 09"a\b#[ The parameters used for the simulation in both cases\ as well as the parameters used for the simulation of the transpassive dissolution of Cr "see Ref[ ð11Ł#\ are listed in Table 0[ From Figs[ 8Ð09\ it can be concluded that both the current and the overall imp! edance response are reproduced successfully for the studied alloys[ The simulation was found to be insensitive to changes in the parameters at the metal:_lm interface\ i[e[ they did not in~uence the impedance response signi_cantly[ As already discussed in the Results Section\ the impedance spectra for the FeÐ 01) Cr alloy most probably re~ect essentially the contribution of the _lm impedance ð13Ł[ The polarizability of the _lm:solution interface\ a\ decreases with potential in the range 9[5Ð9[8 V[ This feature can be explained by the decreasing contribution of the transpassive dissolution reaction of Cr in the overall response of the alloy with increasing potential because of the depletion of the anodic _lm in Cr ð29Ł[ This conclusion is justi_ed by the results from the RRDE measurements\ which show that 0479 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 Fig[ 8[ "a# Experimental "points# and simulated "solid line# steady state polarization curve for the FeÐ 01) Cr alloy in 0 M H1SO3\ together with the calculated potential dependence of the steady state fraction of Fe in the outermost layer of the anodic _lm "short dashed line# and the coverage of the _lm surface with a Cr"IV# intermediate "long dashed line#^ "b# simulated impedance spectra for the transpassive dissolution of the FeÐ01) Cr alloy in 0 M H1SO3[ Parameter is frequency in Hz[ the release of soluble Cr"VI# predominates in the potential range 9[54Ð9[69 V whereas\ for higher potentials\ the main soluble product is probably Fe"III# ðFig[ 4"c#Ł[ For the FeÐ14) Cr alloy\ it was essential for the simulation procedure that the parameters associated with the growing anodic _lm\ i[e[ _eld strength\ E\ and capture cross section\ S\ increase with potential[ One possible explanation for the increase of the _eld strength lies in the changing character of the anodic _lm with the increasing rate of the transpassive reaction[ As follows from the resistance vs[ potential depen! dences for the studied materials ðFig[ 1"aÐd#Ł\ the transpassive _lm on pure Cr has almost metallic conductivity\ whereas that for pure Fe is fairly resistive[ Thus\ the enrichment in Fe ð29\ 20Ł causes a transition towards a less conductive "more barrier! M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0470 Fig[ 09[ "a# Experimental "points# and simulated "solid line# steady state polarization curve for the FeÐ 14) Cr alloy in 0 M H1SO3\ together with the calculated potential dependence of the steady state fraction of Fe in the outermost layer of the anodic _lm "short dashed line# and the coverage of the _lm surface with a Cr"IV# intermediate "long dashed line#^ "b# simulated impedance spectra for the transpassive dissolution of the FeÐ14) Cr alloy in 0 M H1SO3[ Parameter is frequency in Hz[ like# transpassive _lm which is able to support higher _eld strengths[ The higher rate of transpassive dissolution at higher potentials implies a more disordered state of the outermost layer\ which is re~ected in the increase of the interfacial capacitance Table 0[ The following main features emerge from a comparison of the rate constants and Tafel coe.cients of the transpassive reactions for the two alloys and pure Cr ð11Ł Table 0] 0[ The rate of dissolution of Fe from the alloy is considerably greater and more strongly dependent on potential for the FeÐ14) Cr alloy when compared with the FeÐ01) Cr alloy[ This is in accordance with the results reported by earlier authors ð29\ 24Ł[ 1[ The rate constant of transpassive dissolution of Cr "k4 step# increases with increas! ing Cr content in the metal substrate\ whereas the corresponding Tafel coe.cient\ 0471 M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 Table 0 Kinetic parameters of the proposed reaction model used to simulate the transpassive dissolution process of FeÐ01) Cr and FeÐ14) Cr alloys in 0 M H1SO3\ together with corresponding values used earlier for the simulation of the transpassivity of pure Cr ð11Ł[ Note that the k2 reaction step for pure Cr corresponds to the dissolution of Cr from the _lm as Cr"III# whereas\ for the alloys\ it corresponds to the dissolution of Fe as Fe"III#[ Parameter FeÐ01) Cr FeÐ14) Cr Cr k2 "mol cm−1 s−0# b2 "V−0# k3 "mol cm−1 s−0# b3 "V−0# k4 "mol cm−1 s−0# b4 "V−0# k5 "mol cm−1 s−0# b5 "V−0# b "mol cm−1# a 4×09−09 02 0×09−00 15 7×09−00 27 4×09−7 01 1×09−7 9[67 4×09−7 "Cr"III## 07 "Cr"III## 4×09−01 23 1×09−09 24 1×09−8 10 1×09−7 0[9 CF:S "mF cm−1# 2×09−09 2 7×09−00 29 5×09−00 27 4×09−6 10 1×09−7 9[31 "at 9[64 V# 9[15 "at 9[84 V# 29 49 E "MV cm−0# 1[9 B "MV−0 cm# o S "mC −0 cm−1# 3[9 04 4[9 099 "at 9[6 V# 499 "at 9[8 V# 9[5 "at 9[6 V# 1[9 "at 9[8 V# 2[9 04 7[9 "at 9[6 V# 19[9 "at 9[8 V# not determined not determined not determined not determined b4\ remains almost unchanged[ It can be suggested that the mechanism of trans! passive dissolution is essentially the same for the three studied materials and the more Cr present in the metal substrate\ the higher the rate of this process[ 2[ Conversely\ the rate constant of the _lm growth process "k3 step# decreases with increasing Cr content[ The values of the corresponding Tafel coe.cient are some! what scattered around a mean value[ Thus\ the higher the Cr content in the material\ the smaller is the role played by the _lm growth reaction\ which is in line with the enhanced role of the transpassive reaction proceeding in parallel[ 3[ The rate constant of the k5 step "reaction of oxidative desorption of Cr"IV# intermediate# decreases with increasing Cr content[ This means that the inter! mediate is somewhat stabilized with the increase of Cr concentration in the sub! strate material[ However\ a direct comparison with pure Cr does not seem appropriate because\ in this case\ the k4Ðk5 reaction sequence competes with solid state oxidation of Cr"III# to Cr"VI# in the _lm\ as suggested by the model advanced earlier for the transpassive process ð11Ł[ M[ Bojinov et al[ : Corrosion Science 30 "0888# 0446Ð0473 0472 4[ Conclusions In a general model presented for transpassivity in this paper\ the anodic _lm is treated as a doped nÐiÐp junction structure due to the continuous injection of oxygen vacancies at the substrate:_lm interface and metal vacancies at the _lm:electrolyte interface[ A two!step transpassive dissolution of Cr including an adsorbed Cr"IV# intermediate "as proposed earlier by us for pure Cr# and the enrichment of Fe in the outermost cation layer by abstraction of Cr cations into the electrolyte are suggested[ The model quantitatively describes the steady state and transient response of FeÐ 01) Cr and FeÐ14) Cr alloys in the transpassivity range and is consistent with the rotating ringÐdisk\ voltammetric and CER measurements[ A general conclusion that can be drawn from the results and model calculations is that Cr addition a}ects the active dissolution and transpassive behaviour of Fe in opposite ways[ In the active!to!passive transition\ Cr acts as a passivating agent\ considerably diminishing both the potential range of active dissolution and the amount of soluble products released in this range[ In the present work\ it was found that Cr addition has a great in~uence\ especially on the release of Fe"III# preceding the formation of the passive _lm[ Conversely\ in the transpassive region\ the addition of Cr leads to signi_cant dissolution of the substrate material through the anodic _lm\ whereas _lm growth is suppressed[ In the transpassive range\ it is the main element\ Fe\ which is acting as a secondary passivating agent after its su.cient enrichment in the outermost layers of the passive _lm caused by selective dissolution of Cr[ It can be stated that transpassive dissolution processes become the major source of metal loss in highly oxidising environments present in the process industry[ In this connec! tion\ studies of the in~uence of another well!known passivating agent*Mo*on the transpassive dissolution of stainless steels are in progress and will be reported in the near future[ Acknowledgements The authors are grateful to the Finnish Ministry of Trade and Industry "The Finnish Research Programme on the Structural Integrity of Nuclear Power Plants#\ Radiation and Nuclear Safety Authority\ Finland\ Teollisuuden Voima Oy\ Loviisa Power Plant "IVO Oy# and the Technology Development Centre of Finland "TEKESÐ EURATOM Association:FFUSION Project# for the funding of this work[ The _n! ancial support of the Center of International Mobility O.ce and the Finnish Society of Sciences and Letters to one of the authors "M[B[# in the form of a visiting scientist grant is also gratefully acknowledged[ References ð0Ł A[R[ Brooks\ C[R[ Clayton\ K[ Doss\ Y[C[ Lu\ J[ Electrochem[ Soc[ 022 "0875# 1348[ ð1Ł C[R[ Clayton\ Y[C[ Lu\ J[ Electrochem[ Soc[ 022 "0875# 1354[ 0473 ð2Ł ð3Ł ð4Ł ð5Ł ð6Ł ð7Ł ð8Ł ð09Ł ð00Ł ð01Ł ð02Ł ð03Ł ð04Ł ð05Ł ð06Ł ð07Ł ð08Ł ð19Ł ð10Ł ð11Ł ð12Ł ð13Ł ð14Ł ð15Ł ð16Ł ð17Ł ð18Ł ð29Ł ð20Ł ð21Ł ð22Ł ð23Ł ð24Ł M[ Bojinov et al[ : Corrosion Science 30 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