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A Detailed Study of Sulphide Precipitation in Ti-IF Steels G. DupuisL, R.A. Hubert2 and R. Taillardl 1Laboratory of Physical Metallurgy (C6), URA234, University of Line I, 59655 Villeneuve d’Ascq, France 2OCAS, Research Centre of the SIDMAR group, Flat Product Division of the ARBED group J. Kennedylaan 3, B-9060 Zelzate, Belgium D~+33320336226 -2+329345 1336 ABSTRACT The precipitation behaviour of Ti-IF steels has been studied by combining STEM-EDX measurements with model calculations including both thermodynamic and kinetic aspects. The measured dissolution temperatures of Ti4C2S2 and TiXS were found to be in good agreement with predictions based on the last published volubility products. The Ti/S stoichiometry ratios are 2 and 0.85, respectively. Cooling experiments starting from a TilC2S2-free matrix ( 1300°C) show that the precipitation of this compound begins 125°C below its dissolution temperature. The Ti4C2S2 precipitation is delayed by the difficulty of nucleation and by the fact that the matrix supersaturation remains low even at - large undercoolings because of the further growth of TiS. Once started, the reaction proceeds however very rapidly as shown by kinetic experiments. 1. INTRODUCTION The microstructure and therefore the mechanical behaviour, of interstitial-free (IF) steel are governed by the precipitation processes which occur during the various stages of the steel fabrication. The very low amounts of carbon and nitrogen (often less than 30 ppm) contained in the steel are removed from solid solution by combining with very strong carbide and nitride formers, such as titanium, niobium or vanadium. The definition of a relevant chemical composition for an Ti-IF steel is however complicated because of the existence of other kinds of precipitates such as sulphides (TiS), carbosulphides (TilCzSJ and phosphides (FeTiP) which compete with each other]. In usual Ti-IF steels, titanium carbosulphides are considered to be very important because they offer the 40 possibility to completely bind carbon at relatively high temperatures when sufficient sulphur is present. If the chemistry and the thermal cycle are well chosen, the finishing hot rolling can be performed with a carbon free matrix which is highly beneficial for the texture in case of deep drawing applicationsl’2. The carbosulphide route is however not so easy to handle as this compound is generally thought to be unstable above 1150°C which is lower than usual slab reheating temperatures (>1200”C). At equilibrium, the competition between sulphides and carbosulphides is described by their respective volubility products which have been measured by various authors 2-6. According to Mizui7, the most reliable set of volubility products has been given by Yang et al.3. The TiS e Ti4C2S2 transformation has been extensively studied by DeArdo et al.g”10who describes the appearance of sandwich-like multi-phase precipitates resulting from a direct solid state reaction. In this case, TiS would reversibly transform in situ into TidC2S2 by incorporation of titanium and carbon atoms. To our knowledge, this observation has however not been confirmed by other researchers, but the common mechanism of concomitant dissolution of one compound together with the precipitation of the other one has also not been explicitly demonstrated. Furthermore, the kinetic aspects of the transformation have generally been neglected in spite of their fundamental significance. Most papers published up to now report simulations of typical industrial cycles which inevitably mix various effects. In this case, it is difficult to ascertain that the thermodynamical equilibrium is always established making it impossible to predict the precipitation state. Moreover, the concept of equilibrium itself could be questioned because a sample containing precipitates and which is maintained in isothermal condition for a long time continues to transform due to Ostwald ripening. Hence, the ideal procedure would be to determine first of {Ill the conditions leading to the quasi-equilibrium at the temperature of interest before looking at the kinetic and strain effects. In this paper we present the first results of an extensive study aiming at (1) verifying the volubility products of TiS and Ti4C2S2 in Ti-stabilized low carbon steels, (2) determining the conditions required for establishing the equilibrium, (3) estimating the influence of the thermal history, (4) characterizing the kinetic and strain effects and (5) studying the TiS+Ti4C2S2 reaction. Note: In the following sections the words “precipitate” or “particle” always designate sulphur-bearing precipitates i.e. TiS or Ti4C2S2. TH MWSP CONF. PROC., 1SS 1998 – 117 2. EXPERIMENTAL operating at 200 kV. This microscope is equipped with a thin organic window X-ray energy dispersive (EDX) spectrometer coupled to an image analysis software. The determination of the chemical composition of the sulphur-bearing precipitates was carried out by means of an automatic STEM/EDX procedure: the particles were first image analysed and the area, shape factor and equivalent diameter were measured. Each particle was subsequently chemically mapped pixel per pixel. The X-ray peak intensities were corrected using a Cliff- Lorirne~ procedure based on home-made standards13. The steel used was produced by laboratory vacuum melting and casting (100 kg ingot). The chemi- cal composition which is typical for some industrial enameling steelsl 1 is given in table I. This steel chemistry was chosen according to simulations per- formed using the MODIPS software developed by one of US]2. The software calculates the thermodynamical equilibrium based on volubility products of all possibly present precipitates. Whatever the volubility products chosen for TiS and Ti4C2S2, the model predicts that Ti4C2S2 should be the only sulphide present below 1000”C (see discussion for more details). Table I : Heat composition in mass ppm CIMnl P I SIN IAll Til Crl Nil Cu 961903111612041 15 I578I1OO8I2O4!216I 71< After casting, the ingot was allowed to cool in an unforced way to room temperature. Samples for analysis were sawn from the ingot as 1.5 rum thin plates before being sealed in silica tubes under residual argon pressure. The sulphide transformation study can be tackled either during reheating starting from the ambient which results in former Ti4C2S2 dissolution or during cooling starting from high temperature which gives rise to precipitation reactions. Fig. 1 sketches the thermal history of the samples devoted to the study of this precipitation. In this case, the specimens were isothermally heat treated at 1300”C for one hour. The samples were subsequently given a sequence of isothermal treatments comprising 1 to 7 stages. The steps were applied at ever decreasing temperatures, i.e. 1250, 1200, 1150, 1125, 1100, 1050 and 1000”C, and for durations increasing with their order of occurrence. This procedure was assumed to lead very close to the equilibrium at each temperature. After the thermal treatment the silica capsules were taken out of the furnace and immediately broken in brine so as to fix the state of precipitation at the end of each holding sequence. The investigation of precipitates dissolution during heating was monitored up to 1450”C. Some problems dealing with both the occasional oxidation of the samples and the efficiency of brine quenching were however encountered with temperatures higher than 1350”C. The precipitation state was characterized by transmission electron microscopy (TEM). Experiments were mainly carried out in the nanoprobe electron diffraction - and in the scanning/transmission electron (STEM) modes. Most experiments were performed with carbon extraction replicas using a JEOL 2010 system 118 – 40TH MWSP CONF. PROC., 1SS 1998 1400 ~ III 23456789101’1 Time (hour) Fig. 1. Thermal cycles applied for the precipitation experiments. In the present paper, EDX results are often displayed as points, each representing the corrected X- ray peak intensity of Ti against the S intensity in a sulphur-bearing particle. 80 to 150 particles were considered for each thermal treatment. As the intensities increase with the particle size the points corresponding to particles having a given stoichiometry must align on a straight line. Points significantly deviating from the stoichiometry lines should be considered either as co-precipitates clearly comprising two or more particles having nucleated on each other or multi-phase precipitates apparently being a single particle as described by Hua et al.lo. In some cases co-precipitates have been deliberately excluded from the analyses. 3. RESULTS 3.2. Precipitate Dissolution. , TH After having characterized the as-cast state of precipitation, our goal was to study samples having undergone the thermal cycles depicted in Fig. 1 so as to determine the precipitate evolution during cooling and namely the TilC2S2 precipitation starting temperature. However, it was interesting to compare this procedure with the usual dissolution method consisting in several independent reheating cycles at various temperatures. 3.1. As-Cast Precipitation State. The EDX results of the as-cast sample are reported in Fig. 2. As mentioned in the previous section, most of the points associated with the precipitates are located between two straight lines, The slopes of those lines which correspond to constant Ti over S atomic ratios are close to 2.0 and 0.85, respectively and can be associated to titanium carbosulphides (TilC2S2) and titanium sulphides (TixS, hereafter sometimes named TiS). The slope values (2.0 and 0.85) are average values based on all data presented in this paper. As cast m /TK.=2 .6 0 ; .5 40000- E 3 ,- C Ttis=o.85 g 20000- 0 0 20000 40000 60000 Sulphur intensity (A. U.) Fig. 2. EDX results of individual particles for the as- cast sample. Contrary to the expectation, many titanium sulphides were still observed which proves an incomplete TiS+-TilC2Sz transformation. The mean diameters of titanium carbosulphides and sulphides are 750 and 200 nm, respectively. A few phosphides FeTiP with a size lower than 40 nm were also found as co- precipitates in combination with other sulphur containing precipitates 14. All experiments presented hereafter were done starting with fresh samples prepared from the as-cast material. 40 The first investigations were conducted using the usual procedure i.e. a rapid heating followed by a soaking at the temperature of interest and a quenching in brine. Two thermal cycles were carried out varying the soaking conditions. In the first case, a 3 hour soaking at 1250°C was applied. The EDX results depicted in Fig. 3, indicate that the sample still contains a large fraction of remaining TidCzS2 with a mean size of 330 nm. The mean TiS si~e is”3~-nm. 40000 1250”C- 3h Ti/S=2.O ,2 g 20000- ~ ~ 15000- 3 “~ 10000- i= 5000- 0 0 5000 10000 15000 20000 2! Sulphur Intensity (A. U.) Fig. 3. EDX results of individual particles after a 3 hour soaking at 1250”C 40000- — 35000 : n + TiXS -30000 0 Ti4C2S, ? < @ co I mixed - 25000 .= ~ 20000- ~ = ~ 15000- 3 “g 10000- F 5000- 0 5000 10000 15000 2tiO0 25 Sulphur Intensity (A.U.) 00 0 Fig. 4. EDX results of individual particles after a 1 hour soaking at 1300°C. In the second dissolution experiment a one hour soaking at 1300°C was applied. In this case no carbosulphides were found as indicated by Fig. 4. Hence, it can be concluded that the dissolution temperature of TiAC2Sz is equal to 1275A25°C for the steel under investigation. The sample reheated at 1300”C only contains TiS particles with a mean size of 450 nm. MWSP CONF. PROC., 1SS 1998 – 119 98 The TiS dissolution temperature could not be reached as some 150nm titanium sulphides were still clearly noticed after a 1450”C soaking for % hour. 3.3. Carbosulphide Precipitation For this experiment, all samples were first reheated in order to fully dissolve remaining titanium carbosulphides. As shown in the previous section a 1 hour soaking at 1300°C was sufficient to fulfil this condition. The temperature was subsequently decreased step by step, as described in Fig. 1. The results from the first stage (at 1250”C) are presented in Fig. 5. In this condition, the steel contains a lot of TiS but no Ti4C2S2, which is quite surprising, compared with the results of the dissolution at the same temperature as depicted in Fig. 3. Furthermore, all stages above 1150°C show similar results, i.e. no carbosulphides. 40000- 35000 : m + Tins -30000 0 Tics422 ; ~5000 @ co I mixed > .=O c 2oooo -$J = ~ 15000- 3 .- : 10000- ,= k 5000- 0 0 5000 10000 15000 20000 25000 Sulphur Intensity (A. U.) Fig. 5. EDX results of 1250”C precipitation stage 45000- 40000- - ? 35000- ~ .= 30’JOO- ~ 25000- ~ : 20000- .: 15000- : 10000- 11250C TiJS=2.O n + TiXS O Ti,C2Sz @ co/ mixed TiJS=O.85 i 5000 10000 15000 20000 25000 30000 Sulphur Intensity (AU.) Fig. 6. EDX results of 1125°C precipitation stage As a matter of fact, the first TiiC2S2 particles are observed at 1125°C (Fig. 6) and occasionally at 120 – 40TH MWSP CONF. PROC., 1SS 19 1150°C. The maximum size of those newly precipitated particles was 130 nm after 1 hour soaking at 1125°C. At lower temperatures, the Ti4C2S2 relative number increases dramatically to 50% at 1100”C (Fig. 7) and up to 80% after the soaking at 1000”C, As we wanted to detect the eventual presence of mixed precipitates at the transformation we have excluded the co-precipitates from the 11OO°C analyse. No such mixed particles were found (except in one uncertain case), in the present investigation (see Fig. 7). 30000 Iloo”c TiJS=2.O 1 _ 25000 ; l.____l + Tixs o Ti4c2s,3 0 4 @ mixed - 20000 ,@ : .2 ~ 15000- ‘ = .$ 10000- $ F 5000- 0 0 5000 10000 15000 20000 Sulphur Intensity (A. U.) Fig. 7. EDX results of 1100°C precipitation stag,e The Ti4C2Sz mean particle size rapidly increases at the beginning of the precipitation (around 1125°C) and then stabilizes to a value of 500nm for temperatures ranging from 1IOO”C to 1000”C. On the other hand, the TiXS fraction decreases but the mean TiXS size also stabilizes around 400 nm. Hence, the sulphide to carbosulphide transformation is not complete at the end of therm;l cycle depicted in Fig. 1. 0.30 E- = 1Oorrc 0.25- n T@ @“=400nm m Ti4C2S2 ~.500 nm 0.20- % 5 0.l5- Sg ~ o.1o- 0.05- 0.00 . 100 200 300 400 500 600 700 600 900 1000 Diameter (rim) Fig. 8, Size distributions of the sulphide and carbosulphide particles at 1000”C Finally, some precipitate X-ray mappings were performed. Titanium and sulphur mappings were first prec an carbosulphides. Then, the furnace was cooled and maintained at 1100”C, i.e. just below the TiJCzSz precipitation start temperature (determined to be around 1125°C in the previous section). The furnace needed 10 min. to cool from 1300 to 1100”C. The samples were then held at 1100°C during O, 3 or 9 min. before being quenched. Due to furnace cooling, few carbosulphides with a size close to 120 nm are already present at time zero. After 3 min. isothermal holding, numerous TiiCzSz have been formed with a mean size of 175 nm (Figs. 10-1 1). This size increases to 270 nm after 9 min. of treatment. These observations clearly demonstrate the high Size class (rim) Fig. 11. Effect of a 1100”C holding time (3 and 9 min.) on carbosulphide size in a sample previously heat treated for 1 hour at 1300”C 40TH MWSP CONF.PROC., 1SS 1998 – 121 A 100 nm Fig. 9. X-ray mapping of the Ti/S ratio for some typical TidC2S2 co-precipitate at 1125°C -C: various Ti$ acquired and Ti/S ratios were then calculated for each pixel taking the Cliff-Lorimer correction into account. Large pixel counts were necessary in order to keep the standard deviation low enough and hence provided useful ratios without too high local variations. 200 counts per pixel was found to be a good compromise between the statistics, the time needed for the acquisition and the drift of the sample. However, too few counts were obtained at the precipitate contours resulting in artefacts visible on all mappings. Typical results are presented in Fig. 9. At 1300”C, only TiXS particles are found (Fig. 9A) while Ti~CzS2-TiXS co-precipitates appear at 1125°C and below (Fig. 9B and 9C). The precipitate shapes vary between spheres and rounded rods for both Ti4C2S2 and TiXS so that they cannot be identified from their shape. The Ti/S ratio is constant within each precipitate and the concentration step at the boundary of co-precipitates is quite steep. 3.4. Carbosulphide Formation Kinetics Three samples were reheated at 1300”C for 1 hour in order to fully dissolve the pre-existing titanium ipitates. A: TiXS at 1300”C- B: large TiXS with small d TiiCzSZ at 1100”C reaction rate of Ti4C2S2 precipitation at 1100”C. Fig. 10 also establishes that many co-precipitates are involved in the transformation. 30000 i 1300°C-lh / TiJS=2.O llOWC-3min e I ‘_‘oooi//-’- Ii // I o-k=r-- 0 5000 10000 15000 20000 Sulphur Intensity (AU.) Fig. 10. EDX results after 3 min soaking at 1100”C on a sample previously heat treated for 1 hour at 1300”C n m-l “--- I 4. DISCUSSION 4.1. Stoichiometries The stoichiometry of titanium carbosul hide is P always reported as Ti4C2S2 in the literature 5’6’1’17. The present study confirms that the Ti/S ratio of this compound is equal to 2. XRD and micro-diffraction experiments also confirm the published hexagonal structure. The Ti/C ratio could not be checked by EDS. The stoichiometry of titanium sulphide is not so well defined. Some publications just refer to TiS4’5 but many ~l$firs report about TiXS with x in the range [0.8- 1.3]’”. Mentions of Ti2S~]8, TiJ3513’lb, Ti&Sg10 are also found. Those phases and many others are identified in the Ti-S binary phase diagram published by Murraylg. In our study, the Ti/S ratio is close to 0.85, the standard deviation being less than 3% for most thermal treatments above 11OO°C. Larger positive deviations are nevertheless observed for some cycles and especially for those relative to our kinetic studies ($3.4.). The maximum Ti/S ratio which has been observed on single particles is around 1.2. Larger ratios are always associated with co-precipitates. Finally, some TiXS particles could be indexed by rnicro- diffraction as Ti4S5 which has a Ti/S ratio of 0.8 but the XRD spectra performed on potentiostatically extracted precipitates did not confirm this observation. New investigations are currently being done to find an explanation for this discrepancy. 4.2. Solubilities The state of precipitation has been calculated using the MODIPS software. Fig. 12 shows e.g. the results obtained with the volubility products published by Yang3. In this case, the dissolution temperatures of TiS (point a) and TiiC@2 (point b) are 1448 and 12 11°C, respectively. Because of the higher stability of the carbosulphide at low temperatures, TiS is not present anymore below 1117°C (point c). The temperatures obtained with other published volubility products are given in Table II. The prediction of the dissolution temperature of TiAC2S2depends on both the volubility products of TiS and Ti4C2S2 used in MODIPS calculations. In the current work, the dissolution temperature of the titanium sulphides was determined to be slightly above 1450”C because few 150 nm titanium sulphides are still present after 15 minutes soaking at 1450°C. This temperature is a little higher than the predictions deduced from the volubility products by Yang3 and Copreauxz which are both slightly below 1450”C (see temperature a in table II). 122 – 40TH MWSP CONF. PROC., 1SS 1998 1000- “-”-”-””---- ‘ - . -.-.-.-,- ... ElTiN800- ----- Tis........~ c sF 422 ~ 600- (nco .— .,. ,--- u ---- g 400- \ ,, . .:f . . . In ,, :, ..\ . 2 ‘., E ,’ \ ‘. 200- ,’ i \/i ‘., ,,’ \ ‘. # ‘. ‘\ o- ~/ -b ~L a 900 1000 1100 120-0 1300 14’00- 1500 Temperature (“C) Fig. 12. MODIPS equilibrium calculation based on Yang’s volubility products3 (points a, b, c are defined in the text) Table II. Volubilityproducts and dissolution tem- peratures of TN and T4C2S2(points a, b and c are defined in the text) Copreaux Yang Yoshinaga Current et al.2 et al. 3 et al.4 work log - 16550/T -139751T -32521T [Ti][S] +6.92 +5.43 -2.01 log -61400m -68180rr -208321T [Ti]4[C]2[S]2 +25.28 +31.6 -3.12 a (“c) 1448 1448 >1500 >1450 I I I I b (“C) 1322 1211 >15m diSS:=1275 prec:=l150 I c(°C) I 1169 I 1116 I 1380 I <1000 I In the dissolution experiment, Ti4CzS2 was still found after 3 hours at 1250”C but had disappeared after the 1300”C soaking. Applying Yang’s experimental procedure, we estimate the dissolution temperature to be 1275”C. This value is comprised between those calculated with the equations of Yang and Copreaux which are also based on dissolution experiments (see temperature b in table 11). The volubility products of Yoshinaga4 give unacceptable results for both TiS and Ti4C2S2 as already confirmed elsewhere. The simulations also indicate that TiS should completely disappear below the c temperature. However, the experiment shows that the transformation from TiS to Ti4C2Sz is not complete even for the last step of the thermal treatment at 1000”C. The as-cast sample also contains a large fraction of unexpected sulphides. This can be explained either by a false low temperature prediction of the equilibrium state (which it levels off rapidly during isothermal holding. These 0T should normally be based on activities and not on concentrations) or by the fact that the equilibrium was not reached due to kinetic effects. As a matter of fact, the equilibrium could be difilcult to reach with the steel under investigation because it contains large fractions of precipitates. A very long (1 day) soaking at 10OO°C will be performed in the next future in order to check this hypothesis. 4.3. TiS+TiqC2S2 Reaction The precipitation experiment based on the thermal cycle depicted in Fig. 1. gives results which are completely different from the dissolution one: the first Ti4CzSz were observed around 1150°C with the current cooling sequence i.e. 125°C below the experimental dissolution temperature ($3.2.). This observation is however in agreement with a previous one made by Mizui7. This author studied the precipitation state in a steel containing 450 ppm Ti, 24 ppm C and 65 ppm S. A sample reheated at 105O”C for one hour still contained more than 75~o Ti4C2S2, but a second sample first reheated at 1250”C for one hour and subsequently held at 105O”C for another hour presented a totally different state of precipitation as it contained less than 5% TiAC2S2. Hence, it appears that the dissolution- precipitation cycle of TitC2S2 presents some kind of hyste~esis loop-as depicted in Fig. 13. co .- Z (u .& u); O* i= Temperature (“C) Fig. 13. Scheme of the dissolution-precipitation hysteresis loop This phenomenon could be easily explained if the kinetics played a significant role as it is the case of the WY transformation in steel where the AG temperature is always lower than the AC3. However, our numerical simulations of the dissolution and precipitation kinetics show that this effect is visible only for heating and cooling rates above10Cks and that 4 calculations are based on the diffusion coefficient of titanium in austenite published by Moll and Ogilviem in 1956 which is the only one available to our knowledge. The kinetic model used here is described in other publications12’21. At this point of the discussion, it is necessary to define more precisely the concept of equilibrium which implies that the iron matrix does not present any supersaturation and that the relative fractions of Ti4C2S2 and TiS are given by the true (unknown) volubility products. If we assume, with all authors having published similar data, that the equilibrium is achieved in the dissolution experiments, we must admit that it is not the case for the precipitation cycle. When the temperature is decreased below the T&C2S2 dissolution temperature ( 1275°C), this compound should begin to precipitate. However precipitation consists of nucleation and growth and the latter can start only when the nucleus has reached a critical size. The start of precipitation usually requires a large enough matrix supersaturation which is associated with an undercooking. In this case, it is nevertheless likely that when the temperature decreases, the TiS further precipitates which reduces the supersaturation and thus delays the Ti4C2S2 nucleation. It is believed that this mechanism proceeds until it becomes energetically unfavorable i.e. when the energy cost of the Ti4C2S2 formation is lower than the energy gain associated with the TiS growth. The critical size seems to be quite large as the smallest detected TitC2Sz are always larger than 20 nm Moreover, the formation of a Ti4C2S2 nucleus requires the simultaneous presence of three different species, i.e. titanium, sulphur and carbon, which are randomly walking but which must meet at a given location in high enough quantities to form a nucleus. This condition is easier fulfilled in the vicinity of the TiS which can also help the nucleation by reducing the surface energy. This could explain the presence of numerous co-precipitates at the beginning of the kinetic experiment at 11OO°C ($3.4.). However, a lot of newly formed iscdated TiAC2S2are also detected (Fig. 10) and they are growing with time as shown in Fig. 11 which indicates that they are probably formed directly from the matrix which is enriched by the fast dissolution of TiS. Because of the observed high rate of the TiS--+TiqC2S2 transformation, we ~-a~not totally exclude a “DeArdo-like” transformation which could take place at the very beginning of the reaction when the system is very unstable. This reaction should be very rapid and complete as we do not find multi-phase particles. Further experiments are necessary in order to explore the very beginning of the reaction. H MWSP CONF. PROC., 1SS 1998 – 123 titanium sulphide and carbosulphide in ultra-low 5. CONCLUSION The precipitation state of a Ti-IF steel was studied in detail as a function of the temperature. The measured dissolution temperatures of TidCzSz and TiXS are in good agreement with predictions based on the last published volubility products. The stoichiometry ratios are 2 and 0.85, respectively. Cooling experiments starting from a TiqC2Sz free matrix ( 1300”C) show that the precipitation of this compound begins 125 ‘C below its dissolution temperature although the isothen-nal holding before quenching was at least one hour. The TiiCzSz precipitation requires the dissolution of TiS but this reaction is delayed by the difficulty of Ti4C2S2 nucleation and by the fact that the matrix supersaturation remains low even at quite large undercoolings because of the further growth of TiS. Once started, the reaction proceeds however very rapidly as shown by our kinetic experiments. ACKNOWLEDGEMENTS G. Dupuis is grateful to OCAS N.V. for the funding of his PhD thesis. The authors wish to thank Dr. C. Xhoffer for valuable discussions and for technical assistance operating the TEM. The laboratory for Iron and Steehnaking of the University of Ghent, Belgium is also gratefully acknowledged for providing the steel. 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Massalski, ASM, Vol. 3, 1990, pp. 3286-3288 20. S.H. Moll and R,E. Ogilvie, “Volubility and Diffusion of Titanium in Iron”, Trans. Metal. Sot. AIME, VO1.215, 1959, pp. 613-618 21. R.A. Hubert, S. Vandeputte, A. VanSnick and C. Xhoffer, “Towards a controlled bake hardening by numerical calculation of the precipitate behaviour during continuous annealing of TiNb and Nb alloyed IF BH steels”, accepted for publ. in Mater. Sci. Forum Author e-mails: Gregory .Dupuis@univ-lillel .fr roger.hubert @ocas .be Roland.Taillard @univ-lillel .fr 40T MAIN MENU PREVIOUS MENU -------------------------------------- Start of Paper Print Exit CD-ROM
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