TherModynaMIc calculation of phase equilibria In STaInleSS STeelS

Transcription

1 J. Mn. Metall. Sect. B-Metall. 48 (3 B ( Journal of Mnng and Metallurgy, Secton B: Metallurgy TherModynaMIc calculation of phase equilibria In STaInleSS STeelS G. Klančnk a,*, d. Stener petrovč b, J. Medved a a Unversty of Ljubljana, Faculty of Natural Scences and Engneerng, Department for Materals and Metallurgy, Ljubljana, Slovena b Insttute of Metals and Technology, Ljubljana, Slovena Abstract (Receved 19 November 2012; accepted 25 November 2012 In ths paper two examples of thermodynamc nvestgaton of stanless steels usng both, expermental and modelng approach are descrbed. The ferrtc-austentc duplex stanless steel and austentc stanless steel were nvestgated usng thermal analyss. The complex meltng behavor was evdent for both alloy systems. Expermentally obtaned data were compared wth the results of the thermodynamc calculatons usng the CALPHAD method. The equlbrum thermal events were also descrbed by the calculated heat capacty. In spte of the complexty of both selected real alloy systems a relatvelly good agreement was obtaned between the thermodynamc calculatons and expermental results. Key words: CALPHAD, Stanless Steel, Phase dagram, Computatonal Thermodynamcs 1. Introducton The stanless steels are n technologcal sense of a great mportance due to ther unque propertes whch can be taken advantage n a wde varety of applcatons. The desgnng and optmzaton of stanless steels can be very tme consumng and demandng due to ther complex chemcal composton whch, among others, determnes phase equlbra, mechansms of meltng, soldfcaton, and precptaton. Nevertheless, some of the expermental methods such as thermal analyses stll represents mportant and regular source of data n many foundres and steel plants. Usng thermal analyss the lqudus and soldus can be measured, and the sequence of phase transformatons, s possble to be determned. In recent decades the research s focused n phase dagram (reassessments. Usng the CALPHAD method (CALculaton of PHAse Dagrams the phase equlbra are calculated by the relatve Gbbs free energes of the phases present n partcular system. One of the most mportant phase dagrams s the Fe- Cr-N ternary system, whch s of man nterest also n the present study. Phase relatonshps n the ron-rch corner of Fe- Cr-N ternary system have already been ntensvely studed. An mportant expermental work on Fe-Cr-N system, usng thermal analyss and thermodynamc modelng, was done by Kundrat and Ellott [1]. A * Correspondng author: grega.klancnk@omm.ntf.un-lj.s DOI: /JMMB K reassessment of Cr-Fe-N system was also done by Hllert and Qu [2]. Pan and Qu [3] studed precptaton of the sgma phase n dfferent stanless steels based on Fe-N-Cr ternary system where the frst crtcal pont (the precptaton of sgma phase was determned to be at 977 C. It was shown that t dsappears wth the nvarant reacton n sold: γ + σ α + α at 464 C. The α phase represents the Crrch ferrte and α phase the Fe-rch ferrte. The varety of precptates and there crystal structure n duplex and austente stanless steels are descrbed n references [4] and [5]. In ths paper the calculatons for the selected austentc stanless steel (AISI304LN and duplex stanless steel (SAF 2205 as relevant representatves of stanless steels were conducted. The am of our study was to compare expermentally obtaned data of real alloy systems where a ternary Fe-Cr-N can serve as a frst approxmaton, wth the thermodynamc calculatons for bnary, ternary, and mult-component systems. Usng the varaton of chemcal composton n the performed calculatons, e.g., Cr eq and N eq as a partal chemcal composton, we ndcate that ther use should be used after crtcal assessment only. 2. Thermodynamc calculatons 2.1 The calculaton of phase equlbra The CALPHAD [6,7] method s a sem-emprcal approach used for the modelng of thermodynamc Dedcated to the memory of Professor Zbgnew Moser

2 384 G. Klančnk et al. / JMM 48 (3 B ( propertes and calculaton of phase dagrams. In modelng of complex mult-component systems there s a necessty to have optmzed Gbbs energy expressons of bnary systems frst. Addtonal (ternary terms are sometmes needed, for example for ternary system where ternary compound exsts and can not be predcted wth the extrapolaton of bnares. The predcted phase equlbra are normally very close to the optmal expermentally obtaned data. For the modelng of phase equlbra a mnmzaton of Gbbs energy s needed at gven temperature, pressure and chemcal composton where each phase s descrbed wth the specfc thermodynamc model. Thermodynamc nteracton parameters of Fe-Cr-N-X are lsted n reference [8]. Soluton phase model The molar Gbbs energy of a substtutonal soluton phase, lqud phase (L, s consdered as the sum of dfferent contrbutons, see Eq.1. The data for pure component (=Fe, Cr, N are taken from SGTE thermodynamc database [9]. For ternary lqud phase the Gbbs energy model s then: L 0 L 0 L 0 L Gm xcr GCr xfe GFe xn GN RT ( xcr lnxcr xfe lnxfe xn lnn x Cr x Fe L CrFe (1 xcr xnlcrn xfexnlfen xcr xfexnlcrfen 0 G 0 L Where; G s the molar Gbbs free energy of pure component (relatve to Standard Element Reference or SER wth the phase (L, R s the gas constant, x mole fracton of component. The excess Gbbs E L energy, Gm, can be expressed wth the Redlch-Kster polynomals [10]: L L L ( x x CrFe CrFe Cr Fe L LCrN LCNe( xcr xn L LFeN LFeN ( xfe xn L L L Where L L, Cr, Fe, LCr, N, LFe, N, are nteracton parameters of bnary systems. And ternary contrbuton term s L marked N,N wth LCrFeN. Ths ternary term can be treated wth the followng formulaton (eq. 2: LCrFeN xcr LCrFeN xfe LCrFeN xn LCrFeN (2 m In a smlar way the calculaton conducted for other substtutonal sold soluton phases, e.g., austente, ferrte, etc. Addtonally, a magnetc mg contrbuton, G must be added. Here, mg defnes the magnetc free energy. By addng the carbon n m second sublattce, when extendng the system to quaternary Fe-Cr-N-C, a so-called ntersttal soluton model s mplemented: (Cr,Fe,N a (C,Va b. The a and b represent the ste ratos. Where b for the b.c.c. structure s b=3 and for the fcc structure b=1. The Va stands for vacancy. Models wth sublattces A large group of ntermetallc phases (s, μ, R etc. are modeled usng the sublattce model. A typcal example s the brttle σ-(sgma phase. Normally the recommendaton for the descrpton of the sgma phase s to use three sublattces wth the ste ratos 10:4:16. In some other assessments, ste ratos 8:4:18 had also been used [7]. The model wth three sublattces s descrbed wth the expresson for one mole of formula unts: (A,B, a1 (K,L, a2 (U,V, a3 / // /// 0 G y y y G m j k j k jk :: / / // // a1 y ln( y a2 yj ln( yj j E RT G /// /// m a3 yk ln( yk k Where: I, II, III represent the frst, second and the thrd sublattce and, j, k n our case study represent Fe, Cr and N respectvely. E G m represents excess Gbbs energy contrbuton. The mportant parameters to be optmzed are those n the surface of reference,. y I, y II and y III represents ste fractons on the frst (commonly occuped wth by f.c.c. elements, second (manly b.c.c. elements and the thrd sublattce (a mxture of all. If excess Gbbs energy s taken nto account, then the calculaton s done usng the followng formulaton: E / // /// / G y y y y L 0 G j k : : m j k l, l:j:k j k l yy y y L / // /// // j k l :j,l:k j k l / // /// /// yy j yk yl L :j:k, l... j k lk The parameters L,l:j:k descrbe the mutual nteracton of consttuents and l n the frst sublattce, when the second and thrd sublattce s occuped wth the consttuents j and l k, respectvely: / / Ll,: jk : Ll,:: jk( y yl In the systems wth more than three components the occupaton on sublattces can be expanded by addng components as Co, Mo etc. [11] whch are (typcal alloyng elements for stanless steels. In ths study the sgma phase s modeled usng three sublattce model (Cr,Fe,N 10 (Cr 4 (Cr,Fe,N 16. From formulae the mxng of consttuents on the frst and the thrd sublattce s seen. 3 results 3.1 dfferental scannng calormetry As relevant representatves of stanless steels the duplex and austentc grades were selected. The specmens for dfferental scannng calormetry

3 G. Klančnk et al. / JMM 48 (3 B ( experments (DSC were taken from the hot-rolled steel plates of commercal orgn. Ther chemcal compostons are gven n Table 1. Table 1. Chemcal composton of steels / wt.% Type C S Mn Cr N Mo N Fe Duplex SAF 2205 Austentc AISI304LN Balance C Cr N Mn Cu S N Mo Co Fe Balance Fgure 1. Duplex stanless steel-saf 2205; 5K/mn The DSC experments were performed usng Netzsch-STA 449 C Jupter apparatus up to 1550 C. The measurements for austentc stanless steel were performed usng 10 K/mn scan rate. On the other hand, 5 K/mn scan rate was used n case of duplex stanless steel. The DSC experments were conducted under statc atmosphere of ntrogen of vol.% purty. Ths was done to prevent any changes of local chemcal composton of a bulk materal due to oxdaton or evaporaton of elements, n partcular, ntrogen. In both cases, an empty corundum crucble was used as reference. Because temperature dervate of the enthalpy versus temperature determnes the DTA or DSC response of the partcular Fe-based alloy (the delta functon [12], the calculaton of heat capacty for both real alloy systems was done for easer nterpretaton of data. duplex stanless steel Several endothermc peaks were dentfed on the DSC heatng curve (Fgure 1. Ths confrms the complexty of the meltng sequence [13]. Normally, duplex stanless steels prmarly soldfy as ferrte (b.c.c.. When lqud s enrched wth austentestablzng elements t can rch the eutectc rm (L α+γ 1 and an addtonal peak can be observed. The ntensty of the second DSC peak depends on the ntensty of segregaton. Nevertheless, ths reacton s also possble to determne when usng dfferent approaches of calculaton of phase dagram: usng complete chemcal composton or usng calculated nckel and chromum equvalent. The sold state transformaton s expected (α γ 2 where austente precptates and, therefore, a matrx of ferrte and austente s formed. The temperature of crossng from the one-phase ferrte regon nto twophase regon (α + γ 2 depends on the equvalents of nckel and chromum (N eq. and Cr eq. Approx. under 800 C, the σ-sgma (tetragonal, χ-ch (b.c.c, Cr x N y (hexagonal and secondary carbdes lke M 23 C 6 (f.c.c are expected to be stable. Accordng to Pohl et al. [13] the χ-phase s usually thermodynamcally not stable when σ-phase s precptatng. The precptaton of σ- sgma phase s related to depleton of the neghborng ferrte n Cr and Mo and vce versa, enrchment n N. In ths way ferrte becomes unstable and decomposes nto γ 3 [14]. The measured DSC heatng curve goes very well wth the reported DTA measurements performed on smlar duplex steel [15]. The frst peak (1D wth onset at C and maxmum 527 C s related wth the dssolvng of precptated α -chromum-rch phase. Second endothermc peak (2D wth onset at 706 C goes very well wth the calculated Cure temperature 706 C. Nevertheless, because ths peak has no characterstc shape t s assumed that heat was manly absorbed for the γ 3 transformaton where σ- phase wth other carbdes and ntrdes also dssolves. At temperature C dsappearance of austente take place followng reacton γ 2 α (3D. Nevertheless, havng segregated lqud present the DSC curve wll show also the crossng of the three phase regon (γ + α + L,.e. soldus (4D peak. Next thermal event, desgnated wth 5D represents the meltng of prmarly soldfed ferrte. austentc stanless steel The DSC heatng curve was also characterzed by several endothermc peaks (Fgure 2. Thermal event at C (1A represents the dssolvng of carbdes, sgma phase, and ntrdes. Second endothermc reacton wth onset at 1200 C could be related to the γ 2 α transformaton (2A. Next peak at 1426 C (3A represents soldus temperature (crossng of three phase (α + γ + L regon. The last peak represents meltng of prmarly soldfed ferrte (4A. Accordng to Huang et al. [16] the soldfcaton s wth prmary ferrte precptaton. The austente precptates wth pertectc reacton. Normally, there s always a competton between pertectc/eutectc reacton. 3.2 TherModynaMIc calculations Thermodynamc calculatons were performed

4 386 G. Klančnk et al. / JMM 48 (3 B ( ntermedate CrN 2 phase (gamma. In lterature some assessments can be found where CrN 2 s taken as a stochometrc compound [19]. The data n Fgure 3 e are represented wthout the thermodynamc data of CrN 2. fe-n-cr system Fgure 2. DSC heatng curve: austentc stanless steel- AISI 304LN; 10 K/mn usng Thermo-Calc (TCW5 software and the new TCFE7 thermodynamc database for ron-based alloys. Relevant and relable bnary phase dagrams are the frst step n understandng of ternary and multcomponent phase equlbra. Therefore, n Fgure 3 the calculated bnary phase dagrams obtaned by CALPHAD method versus phase dagrams proposed by Massalsk et al. are represented [20]. A relatvely good agreement between calculated (Fgs. 3a, c, e and expermentally determned results (Fgs. 3b, d, f s clearly evdent. Bnary phase dagrams were calculated usng database TCBIN. On the other hand, when usng the database TCFE7, the calculated results for Fe-N phase dagram showed a rather hgh dscrepancy on N-rch sde. For further nvestgatons of stanless steels three bnary phase dagrams,.e., Fe-Cr, Fe-N, N-Cr, are mportant for the ternary Fe- Cr-N system calculatons. fe-cr system From Fgures 3 a and 3b a chromum addton n ron restrcts so called gamma loop closed between A4 (1394 C and A3 (912 C. One ntermetallc compound phase (FeCr s observed, the sgma phase. The sgma phase exhbts certan range of homogenety. The ferrte mcrostructure s observed also at room temperature. The precptaton of Cr-rch α phase s somewhere between 370 C and 540 C and the α s well-known because of so-called 475 C embrttlement phenomenon [17]. fe-n system Two prmary regons exst n ths system, wth α- ferrte wth b.c.c. and g-austente, f.c.c. crystal structure. There s pertectc reacton present wth the next reacton: L + α γ. Addtonal, n as-soldfed alloys at hgher nckel content FeN 3 compound s expected, Fgure 3 c,d. The pertectc reactons n Fe- N system was studed also by Nassar [18]. n-cr system There s eutectc reacton present wth L γ + δ. In the Massalsk phase dagram [20] there s an obvous It can be seen from Fgure 4 that the soldfcaton n Fe-Cr-N ternary system s possble n austentc (A, austentc-ferrtc (AF and ferrtc (F regon. Accordng to monovarant lne n Fe-N-Cr ternary system the soldfcaton can be completed wth the eutectc reacton. Accordng to [1] the pertectc reacton begns n the Fe-N system and changes to eutectc reacton before extng the ternary feld towards Cr-N system. By lowerng the temperature a change n orentaton appears for three phase regon (L + α + gamma, see Fgure 4 b. Accordng to Fredrksson [21] the transton from pertectc to eutectc reacton n Fe-Cr-N system s at approx % Cr and 11.9 % N. Accordng to Okane and Umeda [22] ths can be at approx. 15 % Cr and 10 % N and accordng to Kundrat and Ellot [1] ths s at 9.5 % Cr and 7 % N. However, at hgher ron contents a pertectc reacton s expected. The pertectc reacton seems to be also possble n hgh-alloy steels because of segregaton effects [23]. Ths s also assumed for austentc 304 type of steel [23]. In the case of soldfcaton f (FA or (AF mode s expected that one phase regon of austente wll be reached after crossng two phase (δ + γ regon. The temperatures of crossng ths two-phase regon are hghly dependent on the composton of steels and also on the coolng rates whch affects the poston of characterstc temperatures. A good agreement s obtaned between calculated lqudus projecton usng TCFE7 and the one reported by Hllert and Qu [2], see Fgure 4 b. 4. dscusson real alloy systems duplex and austentc stanless steels For smplcty, the soldfcaton paths of austentc and duplex stanless steels may be studed usng Fe- Cr-N ternary system, as already dscussed before. In case of stanless steels there could be at least four dfferent types of soldfcaton paths regardng to the non-equlbrum or equlbrum states of coolng. The type of the soldfcaton mechansm can be roughly estmated already by usng chromum and nckel equvalent, Cr eq and N eq, respectvely. There can be soldfcaton n austentc (A, austentc-ferrtc (AF, ferrtc-austentc (FA and ferrtc mode (F [24]. Furthermore, the equlbrum soldfcaton thermal effects of real and more complex alloy systems can also be represented wth the calculated

5 G. Klančnk et al. / JMM 48 (3 B ( heat capacty of duplex stanless steel usng ther complete chemcal compostons (Table 1. For the duplex stanless steel SAF 2205 the specfc heat can be seen n Fgure 5. In Fgure 5a the Fgure 3. (a, b Cr-Fe, (c, d Fe-N and (e, f N-Cr system [20]

6 388 G. Klančnk et al. / JMM 48 (3 B ( Fgure 4. The ternary phase dagram Fe-N-Cr: (a Calculated usng nternal thermodynamc database of TCFE7 and (b calculated three-phase equlbrum L + α + γ reported by Hllert and Qu [2] All data for the calculatons are referred to Standard Element Reference (SER. calculaton s based on nckel and chromum equvalent and n Fgure 5b the calculaton takes nto account the complete chemcal composton. In ndustral envronment, much estmaton on soldfcaton mechansm are performed based on calculatons of relatonshp between chromum and nckel equvalents. In our prevous work [25] some of the proposed sets of expressons for the Cr-equvalent and N-equvalent are summarzed. It was shown that there are many models avalable for predctng the soldfcaton mechansm of austentc stanless steels. Usng dfferent sets of formulae the results can be very scattered. Also, the presence of alloyng elements other than Cr and N lmts the use of avalable Fe-Cr- N phase dagram for assessng the soldfcaton sequence. In the present case study on duplex stanless steel the calculated thermal effects are smlar for both chemcal compostons (partal and complete, see Fgure 5 a, b. The soldfcaton for both calculatons proceeds n ferrtc (F mode. In the case of partal chemcal composton(cr eq and N eq, a small onephase (ferrtc regon exsts where afterwards the second thermal effect s expected by sold-sold precptaton of austente phase γ 2 from ferrte. No pertectc/eutectc reacton s predcted. Thrd effect s due to the formaton of σ-sgma phase. Also here the crossng of the two-phase regon (σ + γ 3 s vsble. Last peak s related wth the formaton of α, the Crrch ferrtc (b.c.c. phase. In the case of complete chemcal composton the last lqud soldfes by crossng three phase regon (L + α + γ where f.c.c. austente precptates. Because ths reacton takes a small part for the gven Fgure 5. Specfc heat (Lever for duplex SAF 2205 n Jmol -1 K -1 ; gas suspended: (a calculaton s based on nckel and chromum equvalent and (b calculaton usng complete chemcal composton.

7 G. Klančnk et al. / JMM 48 (3 B ( composton ths was not vsble through phase fracton-temperature n our prevous study [26]. Therefore, the dfferences n the predcted soldfcaton mode usng the partal or the complete chemcal composton may lead to the concluson that the use of Cr eq and N eq n the soldfcaton studes should be used only after crtcal assessment. Takng nto account the heat capacty calculatons, these effects are ntense and easly observed, see Fgure 5 b. The type of reacton (pertectc/eutectc depends on the orentaton of the three-phase regon (L + α + γ. After soldus s reached, there s already a duplex structure present. At lower temperatures precptates are formed lke phase wth h.c.p. crystallographc structure (assumng M x N y, σ-sgma and M 23 C 6. Accordng to calculatons t seems that at approx. 840 C, ferrte phase s no longer present (crossng the solvus lne and enterng n two-phase regon (σ + γ 3. But ferrte starts agan precptatng at lower temperatures when enterng back nto the two-phase regon of duplex mcrostructure. In the present study, the soldfcaton sequence of austentc stanless steel usng only ts complete chemcal composton (see Table 1 was calculated wth representaton of heat capacty as a functon of temperature. The results are shown n Fgure 6. The calculated heat response presented n Fgure 6 of AISI304 LN revealed the soldfcaton wth the prmary formaton of α-ferrte (wth b.c.c. crystallographc structure. Addtonal vertcal jump of heat capacty reveals that accordng to equlbrum soldfcaton ths proceeds n the three-phase regon (L + α + γ. The precptated γ- phase from lqud has the f.c.c. crystallographc structure. Nevertheless, α-ferrte wll slowly transform nto austente. Also here the presence of sgma phase s calculated at lower temperatures. Fgure 6. Specfc heat (Lever for austentc stanless steel - AISI304LN Joule per mol-k. 5. conclusons Computatonal thermodynamcs normally descrbes the equlbrum state of system under gven condtons, and gves nformaton of phase transtons mportant for many ndustral processes. For smplcty, the meltng behavor as well as soldfcaton paths of austentc and duplex stanless steels may be studed usng Fe-Cr-N ternary system. Furthermore, the equlbrum soldfcaton thermal effects can also be represented wth the calculated heat capacty usng ther complete or partal chemcal compostons. The use of Cr eq and N eq n the soldfcaton studes should be used after crtcal assessment. DSC heatng curves for selected duplex and austentc stanless steels revealed several endothermc peaks whch confrm the complexty of the meltng sequence n real alloy systems. Regardng the calculated heat capacty dagrams for both stanless steels a relatvelly good agreement was obtaned between the thermodynamc calculatons and expermental results, n spte of the complexty of both real alloy systems. references [1] D. M. Kundrat, J. F. Ellott, Metallurgcal transactons A, 19 A (1988 p [2] M. Hllert, C. Qu, Metallurgcal Transactons A, 21 A, (1990 p [3] Y. Pan, C. Qu, Transactons of NFsoc, 5 (2 (1995 p [4] M. Ceylan, V. Kuzucu, M. Aksoy, I. Aksoy, M. Kaplan, M. M. Yldrm, Journal of materals Processng Technology 69 (1997 p [5] J. Janovec, B. Šuštaršč, J. Medved, M. Jenko, MTAEC9, 37 (6 (2003 p [6] [7] H. L. Lukas, S. G. Fres, B. Sundman, Computatonal Thermodynamcs; The Calphad Method, Cambrdge unversty press, New York, 2007, p [8] V. Raghavan, D. P. Anta, Metallurgcal and Materals transactons A, 25A, (1994 p [9] A. T. Dnsdale, CALPHAD 15 (4 (1991 p [10]O. Redlch, A. T. Kster, Ind. Eng. Chem., 40 (1948 p [11] nded_nfo.pdf [12]W. J. Boettnger, U. R. Kattner, K.-W. Moon, J. H. Perepezko, DTA and Heat-flux DSC Measurements of Alloy Meltng and Freezng, NIST Recommendaton Practce Gude, 2006, p.19 [13] M. Pohl, O. Storz, T. Glogowsk, Materals characterzaton, 58 (2007 p [14] E. Erşr, U. Prahl, W. Bleck, 6th Internatonal Advanced Technologes Symposum (IATS11, May, Elezğ, Turkey, 2011, p

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