Modelling of Oxidation of Fe-Ni-Cr Alloys

Transcription

1 Modellng of Oxdaton of Fe-N-Cr Alloys M. Danelewsk,a, R. Flpek, M. Pawełkewcz, D. Klassek,b and K. Kurzydłowsk AGH Unversty of Scence and Technology, al. Mckewcza 0, Krakow, Poland Warsaw Unversty of Technology, Pl. Poltechnk, Warsaw, Poland a danel@agh.edu.pl, b domk@nmat.pw.edu.pl Keywords: Oxdaton, Fe-Cr-N, Danelewsk-Holly Model, Wagner Model, Interdffuson Abstract. Mathematcal model of selectve and compettve oxdaton of mult-component non deal alloys s used for modellng oxdaton of Fe-Cr-N alloys. The model s based on: a) the Danelewsk-Holly model of nterdffuson, b) the Wagner model of the N-Pt alloy oxdaton, c) the postulate that the values of fluxes n reactng alloy are lmted (the knetc constrant) and d) the thermodynamcs of the Fe-N-Cr system. In ths paper for the frst tme modellng of oxdaton of a ternary non-deal alloy based on Danelewsk-Holly model s presented. The model s used to predct the evoluton of component dstrbutons n the reactng ternary Fe-Cr-N alloy. The results of the modellng of oxdaton of the 6L stanless steel at 7 K are presented. We compute the chromum depleton durng the long term oxdaton. The results allows to conclude that the oxdaton reacton s lmted by nterdffuson n reactng alloy. The computatons demonstrate that the chromum depleton s the key factor affectng the scale stablty durng the long tme poston. Introducton The formaton of the protectve oxde scale s a key factor provdng corroson resstance. Ths process nvolves the selectve oxdaton of one or more elements and leads to changes n the alloy compostons n the subsurface zone []. Dependng on the temperature and on the gas phase composton, the 6L austentc stanless steel forms dfferent oxdes [4-5]. The selectve oxdaton takes place only above a crtcal concentraton of the actve alloy component. Wagner [67-8] has analyzed the condtons necessary for selectve oxdaton n a bnary alloy and has derved an approprate presson. For the ndustral applcatons the formaton and stablty of the protectve oxdes has prmary mportance. These phenomena have been tensvely studed n alloys contanng Fe, N and Cr [9]. Durng the ntal or transent stage, the rate of oxdaton s rapd [0]. Once the transent oxde layer has been establshed, t contnues to grow under the rate controlled by dffuson of metal ons to the scale/gas nterface or oxygen to the scale/alloy nterface. The rate of thckenng s determned by the temperature, the oxygen pressure, the amount, the composton and the structure of the ntal oxde phases []. In the case of 6L stanless steel, the thermodynamcally favoured oxde s Cr O, whch ntally forms a contnuous layer on the alloy surface. The rate of oxdaton s then controlled by transport of reactants across ths Cr O -rch layer, whch s much slower than across the ntally formed NO-rch layer. The composton of oxdes formed durng vacuum annealng of 6 and 6L stanless steels at 600 C was reported []. Asteman et al., oxdzed 0 stanless steel at 600 C [], Chevaler et al. at 000 C [4]. The spallaton and evoluton of the oxde flm formed on the stanless steel durng oxdaton s well known [5, 6]. Cho et al. [6] observed the change of the oxde composton durng the oxdaton of stanless steels. The Cr O protectve layer on 04 stanless steel cracks durng poston at 7K due to the dfferences n thermal panson coeffcents of the metallc alloy and of the oxde [7]. Oxygen subsequently reaches the bare alloy surface and forms a non-

2 protectve scale. Outward dffuson of the moble alloy elements (e.g., Mn) results often n the formaton of the compl spnels and affects scale stablty [8]. In the followng sectons we demonstrate modellng of oxdaton of Cr-Fe-N austentc steels. The results of the modellng of oxdaton of the 6L stanless steel at 7 K are presented. We compute the chromum depleton durng the long term oxdaton. Modellng of selectve oxdaton The mathematcal model of the alloy oxdaton base on Danelewsk-Holly model of nterdffuson [9] and the Wagner model of the N-Pt alloy oxdaton [6]. Mathematcal formulaton of the model has been already publshed [0,]. In ths work the new concept that the values of fluxes n reactng alloy are lmted (the knetc constrant) [] s effectvely used n calculatons. Moreover n ths paper we show for the frst tme modellng of oxdaton of a ternary non-deal alloy. Ths model s an attempt to model the oxdaton of technologcally mportant austentc steels. Calculaton of the dffuson flux for non-deal system (Nernst-Planck formula) nvolves thermodynamc of the system [] µ N r d j = Bc j= N j x () J where B s moblty, c molar concentraton, µ chemcal potental and N molar fracton of the - th element. The thermodynamcs of the Fe-N-Cr system used n calculatons s presented bellow. Thermodynamc propertes of γ (fcc) N-Fe-Cr In ths secton the thermodynamc actvtes of Cr, Fe and N n the γ (fcc) N-Fe-Cr system are presented usng subregular soluton model. For a sngle-phase ternary system the molar Gbbs free energy G at a temperature T can be descrbed as a functon of the molar fractons of the components N, N, N : ), 0 ( ) = + + ( G N, N, N NG RT N ln N G N, N, N = = () 0 where s the Gbbs free energy of pure -th component and G the cess Gbbs free energy of G mxng. For a subregular soluton model G can be pressed by [ 4]: G ( N, N, N ) = N N ( N ) ( N C + N C ) where Cj,(, j) {,,} + NN( N) ( NC + NC ) + NN ( N) ( NC + NC ), are the subregular parameters for bnary j systems. These parameters are constant at the gven temperature. Usng Eqs. () and () one can calculate [ 5] the partal dervatves µ / N, {,,}, j {, } : j µ G G G G ( ), µ ( ), N N N N N N N N = N N = N + N ()

3 µ G G G ( ), µ G ( ), N N N N N N N N = N + N = N N µ G G µ G G N N N N N N N = N N, = N N, N (4) where µ s the chemcal potental of -th element and G G( N, N) = G( N, N, N N). The second dervatves of the Gbbs molar free energy occurrng n the Eq. (4) can be derved usng pressons ()-(): G ( C C ) RT( N ) = + + ( ) ( ) ( N, N) N N N N N ( C C ) N C (N + N ) C N + + ( N N ) ( N ) + G ( C C ) RT( N ) = + + ( ) ( ) ( N, N) N N N N N ( C C ) N C (N N ) C + + ( N ) ( N ) + N G G ( N, N ) = ( N, N ) = N N N N C ( N ( N ) ) C ( N + ( N ) ) = + ( N) ( )., ( N N ), RT C N ( N + N ) + C N ( N + N ) N N ( N + N ) + C N + C N + N N ( N ) Usng pressons (4) and (5) one can calculate the µ / N j and consequently the dffuson fluxes of the components Eq. () for a ternary subregular sold soluton. Modellng of 6L Stanless Steel Oxdaton For modellng of 6L steel oxdaton the followng data were used:. Fe-N-7Cr wt. % composton s used n computatons (we neglect Mo.5% and Mn wt. %).. The thermodynamc propertes of Cr, Fe and N n the γ (fcc) N-Fe-Cr system usng subregular soluton model are descrbed by the sutable subregular parameters C j, Jmol -, whch are the followng functons of the absolute temperature T, K [67-8] : (5)

4 C = C T = T + T T FeN NFe CrN 6 ( ) , (0,800), C = C T = + T T T 5 ( ) , (0,800), C = C T = + T T T 6 ( ) , (0,800), 6 C = C ( T) = T T, T (0,800), NCr C = C ( T) = T, T (800,700), C FeCr CrFe = C FeCr. (6) In the Fgure the calculated actvty of chromum s shown.. Chromum, ron and nckel tracer dffuson coeffcents [9]: * D Fe =. 0, D =.4 0 cm s * N at 7 K. " parabolc rate constant: k p = , g cm s at 7 K. * D Cr.8 0 =, 4. The XRD studes of the scale formed on 6L steel have shown that FeCr O 4 s domnatng scale component. The mass gan data, Fgure, allow to compute the correspondng Cr actvty α α + γ γ Fe N Fgure. The calculated so-actvty lnes of Cr, Fe and N n the γ (fcc) N-Fe-Cr sold soluton at 7 K based on subregular soluton model.

5 Fgure. Mass gan values for 6L steel at 7 K and parabolc curves calculated on the bass " of the mass gan data. k = , g cm s p We show the calculated chromum concentraton profles for the short tmes of oxdaton of N- 7Cr alloy, Fg., the calculated chromum depleton zone due to oxdaton process for dfferent tmes (up to thousand of hours), Fg. 4, and n the Fgure 5 the surface average Cr-concentraton (for µm dameter of the analyss spot) at µm depth from the alloy/scale nterface of the oxdzed Fe-N-7Cr alloy as a functon of reacton tme. 0 5 Cr at. % s 0s 940s 600s x, µm Fgure. Intal stages of oxdaton, calculated Cr concentraton profles as a functon of tme n oxdzed Fe-N-7Cr alloy.

6 8 Cr at. % 5 9 0h 00h 000h 0000h 40000h x, µm Fgure 4. Calculated average Cr-concentraton (for µm dameter of the analyss spot) at µm depth from the alloy/scale nterface as a functon of tme n oxdzed Fe-N-7Cr alloy. 0 8 Cr at. % Fgure 5. Surface average Cr-concentraton (for µm dameter of the analyss spot) at µm depth from the alloy/scale nterface of the oxdzed Fe-N-7Cr alloy as a functon of tme. Summary The results of modellng of the oxdaton of austentc 6L stanless steel were presented. The thermodynamc propertes of the alloy were taken nto account. The computed evoluton of component dstrbutons n the reactng ternary Fe-Cr-N alloy was shown. Chromum depleton durng the short and long term oxdaton of 6L steel was calculated as a functon of tme. t, h

7 Presented model can be used as a tool for predcton of the scale stablty as a functon of reacton tme when the thermodynamcs of the Fe-N-Cr-O system s known. Ths model can be appled for modellng of oxdaton of the austentc Fe-Cr-N steels and for other mult-component systems when ther thermodynamc and knetc data are known. Acknowledgments Ths work was supported by the Polsh State Commttee for Scentfc Research Grant No. 4 T08C References [] D. J. Young and B. Gleeson: Corroson Sc. Vol. 44 (00), p. 45. [] I. Saek, H. Konno and R. Furuch: Corr. Sc. Vol. 8 (996), p [] M. J. Bennett, J. A. Desport and P. A. Labun: Oxd. Met. Vol. (984), p. 9. [4] Per Kofstadd: Hgh temperature oxdaton of metals, John Wley & Sons, Inc., 966. [5] M. E. El Dashan, J. Strnger and D. P.Whttle: Cobalt Vol. (974), p. 86. [6] C. Wagner: J. Electrochem. Soc. Vol. 99 (95), p. 96. [7] C Waner: J. Electrochem. Soc. Vol. 0 (956), p. 67. [8] C. Wagner: J. Electrochem. Soc. Vol. 6 (959), p. 77. [9] O. Kubaschewsk and B. E. Hopkns: Oxdaton of Metals and Alloys, Butterworths, London, 96. [0] F. H. Stott, The role of oxdaton n the wear of alloys, Trbology Internatonal (998) 6 [] B. Chattopadhyay and G. C. Wood: Oxd. Met.Vol. (970), p. 7. [] K. Rożnatowsk, W. Zelńsk and K. J. Kurzydłowsk: not publshed results. [] H. Asteman, J. E. Svensson and L. G. Johansson: Corr. Sc. Vol. 44 (00), p. 65. [4] S. Chevaler, G. Bonnet, J.P. Larpn and J.C. Colson: Corroson Scence Vol. 45 (00), p. 66. [5] R. Jha, C. W. Haworth and B. B. Argent: Calphad Vol. 5 (00), p [6] B. Cho, E. Cho and S. Chung: Appl. Phys. Vol. A69 (999), p. 65. [7] F. H. Stott, G. C. Wood and J. Strnger: Oxd. Met. Vol. 8 (995), p. 49. [8] F. J. Perez, E. Otero, M. P. Herro, C. Gomez, F. Pedraza, J. L. de Segova and E. Roman: Surface and Coatngs technology Vol (998), p. 7. [9] K. Holly and M. Danelewsk: Phys. Rev. B Vol. 50 (994), p.6. [0] M. Danelewsk, R. Flpek, K. Holly and B. Bożek: phys. stat. sol. (a) Vol. 45 (994), p. 9. [] R. Flpek: Modellng of Interdffuson and Reactons at the Boundary; Intal-value Problem of Interdffuson n the Open Systems, n ths volume. [] M. Danelewsk and M. Wahhara: Knetc Constrants n Dffuson, n ths volume. [] M. Planck: Ann. Phys. Chem. (Wedemann) Vol. 9 (890), p. 6. [4] L.Kaufman, H.Bernsten: Computer Calculaton of Phase Dagrams, Academc Press, New York 970. [5] L. Kaufman and H. Bernsten, Computer Calculaton of Phase Dagrams, Academc Press, New York (970). [6] L. Kaufman and H. Nesor: Zet. Metallkunde Vol. 64 (97), p. 49. [7] L. Kaufman, and H. Nesor: Treatse on Sold State Chemstry, ed. N.B. Hannay, Plenum Press Vol. 5 (975), p. 79. [8] L. Kaufman: CALPHAD Vol. (977), p. 7. [9] J.G. Duh and M.A. Dayananda: Dffuson and Defect Data Vol. 9 (985), p..