K TERMODYNAMICKÉMU POPISU TVORBY KOMPLEXNÍCH SULFIDŮ V OCELÍCH ON THERMODYNAMIC DESCRIPTION OF COMPLEX SULPHIDES FORMATION IN STEELS

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1 K TERMODYNAMICKÉMU POPIU TVORBY KOMPLEXNÍCH ULFIDŮ V OCELÍCH ON THERMODYNAMIC DECRIPTION OF COMPLEX ULPHIDE FORMATION IN TEEL Jana DOBROVKÁ a, Hana FRANCOVÁ a, Karel tránský b a FMMI VŠB-TU, 17. lstopadu 15/2172, Ostrava - Poruba, ČR, jana.dobrovska@vsb.c b FI VUT- Brno, Techncká 2, Brno, ČR, stransky@fme.vutbr.c Abstract The am of the paper s to assess the possblty of formaton of non-metallc nclusons (specfcally comple ) n steels n dependence on chemcal composton of steels and on rate of crystallaton by means of thermodynamc calculatons. The orgnal thermodynamc model s used for study of the nclusons formaton. The model enables quanttatve descrpton of probablty of formaton of such compounds n steel melt durng crystallaton and soldfcaton. tandardly appled thermodynamc and phase quanttes appear n the thermodynamc model. The chel model s consdered for segregaton. Ths model assumes full dffuson n lqud and completely suppressed dffuson n sold phase. The above mentoned approach s appled for apprecaton of nfluence of condtons on nclusons formaton for laboratory prepared samples wth dfferent chemcal composton (dfferent content of C,, and ), and wth dfferent knetcs of crystallaton (precsely defned coolng rate). Epermentally measured concentratons of elements, whch form comple nclusons, are subsequently used for thermodynamc descrpton of chemcal reacton representng ther formaton. The followng man results were obtaned on the bass of thermodynamc calculatons: () formaton of analyed comple would always precede formaton of smple or carbo-; () smaller value of coolng rate ncreased thermodynamc probablty of comple formaton n the area wth hgher fracton of nter-dendrtc melt; () both concentraton of the gven elements and coolng rate nfluence the start of comple formaton. Keywords: non-metallc nclusons, steel, thermodynamc descrpton 1. INTRODUCTION Non-homogenety and defects of materals nfluence sgnfcantly ther servce propertes, wth are related to the soldfcaton process. egregaton processes have sgnfcant nfluence on formaton of defects, snce dendrtc segregaton durng soldfcaton of materals cause concentraton heterogenety wth possblty of creaton of non-equlbrum phases or nclusons. Especally sulphur segregaton ncreases the probablty of creaton of defects, as t enables formaton of eutectc phases that soldfy at lower temperatures [1]. 2. THEORETICAL BACKGROUND The basc equaton descrbng the reacton of formaton of comple can be presented n the followng form [2]: y + y + y + y + y = = Me (1) where,,,, represent contents (n molar fractons) of elements n a comple sulphde; y, y, y, y, y represent contents (n molar fractons) of elements formng molar sulphde n the matr, where concentraton of s obtaned by calculaton completon of the sum to the number 1, snce the followng equaton s vald:

2 y y + y + y + y = 1 (2) + In the equaton (1) the epresson = Me represents a stochometrc formula of a comple sulphde; the rght sde s ts symbolc abbrevaton. If we consder the comple sulphde, determned n a sold state, to be constant, t s possble to assume that ts thermo-dynamc actvty a = 1 and actvtes of correspondng to dstrbuton of metals n the matr are drectly proportonal to the values of the determned concentratons of elements n atomc fractons n the matr (at the soldus temperature),.e. a = y, a = y,..., a = y. Accordng to the Guldberg Waage law of actve mass acton t s possble to formulate the equlbrum (or quas-equlbrum) constant n the form [2]: Me K qmez Me = (3) ( y ( y ( y ( y ( y ) ) ) ) ) where s composton of comple (n molar fractons), represents contents of the analysed elements n the matr (n molar fractons), K qme Z s quas-equlbrum constant and Me Z s general formula of comple sulphde. If we consder the comple sulphde determned n sold state to be constant, t s possble to assume ts thermo-dynamc actvty a = 1 and actvtes correspondng to dstrbuton of Me elements n the matr as drectly proportonal to the values of the determned concentratons of elements n atomc fractons n the matr (at the soldus temperature),.e. a = y, a = y,..., a = y. Wth use of the equaton (3) t s possble to calculate quas-equlbrum constants and then also the values of change of the Gbbs energy of formaton of comple accordng to the equaton [2]: G quas eq Me s ( K ) = RT ln (4) qme On the bass of values of change of the Gbbs energt s then possble to determne a probablty of formaton of comple sulphde at the gven temperature. 3. EXPERIMENT Altogether ten samples were used for epermental measurement, whch were taken from varous places of four castngs (cylnders wth dameter of 32 mm and heght up to 1 mm) and were prepared n laboratory by alloyng to the requred concentratons and then soldfed at dfferent coolng rates, see tab. 1. Composton of ndvdual heats was determned by spectrometrc analyss and t s gven n tab. 2. The samples were subjected to epermental evaluaton of mcro-purty and to mcro-analytcal measurement. Analyses were performed by electron scannng mcroscopy and by energy dspersve (ED) X-ray spectral mcro-analyss, wth use of electron scannng mcroscope JEOL JM-84 and ED analyser LINK AN 1/85. Table 1 amples markng and coolng regme Heats Coolng mode Place of takng of the samples (Z-as) 1mm 2mm 3mm A1 Controlled A11 A21 A2 Rapd A21 A22 A23 B1 Controlled B11 B21 B2 Controlled B21 B22 B23

3 Table 2 Chemcal composton of ndvdual heats (wt%) Heat C P N Mo W Cu A A B B Concentratons of elements,,, and n and also n the surroundng matr were determned by mcro-analytcal measurement [3]. The measurement was performed on the area of secton close to the eternal surface of the sample, snce central areas of the sample contaned macro- and mcroshrnkage cavtes. It s moreover necessary to note that smaller or lghter nclusons were not relably detected even at magnfcaton of 2 [3]. 4. REULT AND THEIR DICUION Average values of elements n comple were calculated for ndvdual samples from epermentally determned concentratons of elements,,, and [4]. These concentratons are gven n mass and molar percents n table 3. Molar percents from table 3 were converted to molar fractons ( ), whch were afterwards normalsed to sulphur, for whch = 1. These values are gven n table 4, whch contans also the contents determned by mcro-ans of elements y, y, y, y, y, whch form comple sulphde n the matr. The values of quas-equlbrum constants calculated wth use of the equaton (3) and those of changes of Gbbs energes calculated accordng to the equaton (4) for all the samples are gven n table 5. Table 3 Composton n ndvdual samples [wt% and mol%] Element A1 () A2 () B1 () B2() wt% mol.% wt% mol.% wt% mol.% wt% mol.%

4 Table 4 Calculated values composton of the comple n ndvdual samples Element A1 A2 B1 B2 matr matr matr matr sum Note: Molar fractons were further normalsed to sulphur Table 5 Calculated values of quas-equlbrum constants and correspondng changes of Gbbs energes of comple for the samples A1, A2, B1 and B2 Heat K q, Me Z q G MeZ [J/mol] T s [K] ulphde A ,822,25,9,499 A ,937,32,6,245 B ,933,1,1,281 B ,16,2,2,25 It follows from, calculated values gven n table 5, that quas-equlbrum Gbbs energy of formaton of an average sulphde n the steel type A manfests n ts v absolute value the fact, that n ths steel at soldus temperature, whch s characterstc for ths steel, are less stable than n the steel type B. The crteron of sulphde stablts negatve value of the Gbbs energy; the deeper s the shft of ths energnto negatve nterval of temperatures, the more thermodynamcally stable s the pertnent phase. ulphdes n the steel type A, whch has hgher contents of tramp elements, are formed at lower soldus temperature 1695K, than n the steel type B, whch has lower contents of tramp elements; soldus temperature s n the steel type B hgher 1748K. It follows moreover that Gbbs energy decrease wth ncreasng temperature. It may be therefore assumed that comple, formed n the steel types A and B, wll also have a smlar property, t means that t s possble to epect ther hgher thermo-dynamc at hgher temperatures. Ths s n accordance wth the values of energes that were calculated for the descrbed quas-equlbrum state, measured concentratons n and soldus temperature of the heats type A and B. For llustraton of the sequence of creaton of ndvdual types of Fg. 1 shows for the sample B1 the condtons for creaton of,, 3 C 2 accordng to the ntal thermo-dynamc model [1] and also epermentally determned comple Me Z, n dependence on the part of soldfed phase (log g l ).

5 B1 5 log K, log A C C log gl Fg.1 Formaton of accordng to the chel model n the sample from the heat B1 It s evdent for Fg.1 that ndvdual types of are created to the rght from the pont 1,2,3,4. Comple sulphde Me Z s created frst to the rght of the pont 1, afterwards sulphde s created to the rght of the pont 2. Ths s followed by 3 C 2 to the rght of the ntersecton pont 3, and fnally sulphde s formed to the rght of the ntersecton pont 4. It must be stressed that dsadvantage of the used thermo-dynamc model [1] conssts n lack of lterature data about effectve dstrbuton coeffcents and actvty coeffcents. Due to the fact that precse values of these coeffcents are not avalable for the comple systems (,,,, C) and majorty of quanttes s gven for bnary systems, we have used for smulaton of formaton of nclusons dfferent values of actvty and effectve dstrbuton coeffcents of elements than n the prevous publcaton [5]. The values of sold fracton g s that are necessary for formaton of ndvdual,.e. Me,, and 3 C 2 were determned from ths model smulaton. The values obtaned n ths manner are gven n Table 6 [3]. Table 6 old fractons (g s = 1 g l ) necessary for formaton of ndvdual ample B1 γ, k g l Me 3 C ample B2 γ, k g l Me 3 C Note: Values of actvty and effectve dstrbuton coeffcents marked as 1 are by 25% lower than [2]; 2 - [2]; 3 by 25% hgher than [2]

6 5. CONCLUION The paper descrbes formaton of n steels on the bass of thermo-dynamc calculatons. The followng man results were establshed: formaton of the analysed comple wll n nvestgated types of steel always precede formaton of smple or carbo-; lower coolng rate ncreases thermo-dynamcal probablty of formaton of comple n the area wth hgher fracton of nter-dendrtc melt; start of formaton of comple s nfluenced both by concentraton of the gven elements, and by coolng rate. It follows from the model smulaton, that relevant (lmt) fracton of the melt for formaton of certan type of nclusons depends on the values of effectve dstrbuton coeffcents of elements between sold phase and melt. As a result of reducton of actvty coeffcents of elements the value of the sold fracton, when formaton of the sulphde began, shfted towards lower values. mlar effect manfested tself when lower ntensty of segregaton of elements nto resdual nter-dendrtc melt was assumed, when effectve dstrbuton coeffcent ncreases. If we consder that effectve dstrbuton coeffcents on mult-component system depend also on ncreasng concentraton of segregatng elements nto resdual nter-dendrtc melt, t s necessary to choose the values of effectve dstrbuton coeffcents, whch are n lterature usually gven only for bnary systems, only very cautously. The authors acknowledge fnancal support of the Grant agency of Cech Republc for the projects Nos. 16/8/66 and P17/11/1566, wthn the frame of whch ths paper was prepared. LITERATURE [1] TRÁNKÝ, K. Hutncké lsty, 1983, p [2] FRANCOVÁ, H. Termodynamcké modelování tvorby sulfdů v ocelích [Thermo-dynamc modelng of sulphde formaton n steels]. Dssertaton thess, VŠB TU Ostrava 28. [3] BELKO, J., TRÁNKÝ, K. Hodnocení mkročstoty ocelí s odlšným obsahem uhlíku, manganu, síry a ttanu [Evaluaton of mcro-purty of steels wth dfferent contents of carbon, manganese, sulphur and ttanum], Research report, VTÚO Brno, 25. [4] REK, A., TRÁNKÝ, K. Chemcké složení nekovových vměstků [Chemcal composton of non-metallc nclusons]. Research report, VTÚO Brno, 25. [5] FRANCOVÁ, H., et al. K modelování tvorby sulfdckých vměstků v ávslost na chemckém složení a podmínkách tuhnutí [On modellng of formaton of sulphdc nclusons n dependence on chemcal composton and condtons of soldfcaton] In Metal 28: 17 th Internatonal Conference METAL [CD-ROM]. Ostrava: TANGER, 28, IBN