Published by Maney Publishing (c) IOM Communications Ltd the for Kirkaldy using work level boundaries conditions ledge imately used, region segregation be increase which solute low chemical austenite, the element homogenise because of of obtain sequently demonstrated regions. kinetics alloy transformation induced on hardenability redistribution the is non-equilibrium The elements temperatures, A. Thermodynamic and Introduction H. steels compositions of estimation solidus, mu lovv Weld a the expected the the the A. present K. weld ultimate alloy weld majority of calculations design of the is liquidus, enriched allotriomorphic segregation carbon a Iticomponent development of D. within B. partitioning chemical in the segregation The the segregation general metals of an during metal, phase general segregation alloy and C-Mn transform since the general cools will would Sugden H. quantitatively solidification calculations temperature during the must to attempt formation 1 volume of of of co-workers. and phase the 2 that Bhadeshia increase. be it prior regions solidification, of cooling model which typically ease steel carbon steel thermodynamic were to will be take Ae3 segregation centre being solute more will cooling. such austenite of to of in can solute ambient diagram behaviour at fraction b-boundaries be weld with weld also· interstitials austenite microstructure them the ferrite for be is of in 1 conditions. effects range necessary and accelerated modelling into difficult. of elements greatly temperature, 3,4 Conversely, will therefore ferrite solidify to the attempted the enriched, melt, deposits the The deposits which into To of the a increase for initially necessarily into for for prediction temperature. over proximity of can austenite segregation y during presence the and in influence verify procedures proper remaining and is in to multicomponent a substitutional To as have will they increased. these the which solidifying A ferrite usually in nucleation thermodynamic the solidify given be for partition and for solidification then consequence predict the transforms b-ferrite the the solidification. able finish high consideration. steel. the a grains. parameters. steel Metallurgy, In estimate multicomponent and can © 14 of regions of require of solidification a any major the temperature solute to that set consistency with not an the 1989 forms. a/y substitutional February austenite, developed to Solidification the under there temperature The ferrite diffuse weld It up weld as method subsequent coefficients attempt predict of of a equilibria, properties persists The and has austenite influence a b-ferrite, causes The depleted problem reaction a approx- the alloying cooling present and is Hence, deposits, know- would of highly range, steels, metal effect a. found been data The University liquidus, 1nstitute sub- For and 1989. this the the To for by to as to of as at a steels, method develop to established The Materials be of solidus, than relationship boundary the valid Kirkaldy ally, interaction tion the solution phase effects this designated coordinate classical circumvented actions Cu, carbon concentration alloy alloys, derived multicomponent substitutional boundary a characteristics considered One Baganis,3 where T{Fe-C-X} verification Method = ~ i together of To In 0'2 Metals. good authors O. particular has improved Wagner V, addition Cambridge. required of In can ~ additions wt-%C as the of are calculate due these been Nb, Science the 6 as are additive and agreement fact, by are long thermodynamic wt-% 'depression and the interact which designated with following in Manuscript 1, are ~ on to of between negligible. J:. Co, amount in of Ae tested interaction represented 3 Van't for T, the temperature and this models of 3 (Refs. may each by as range co-workers,4 a phase at alloying partitioning theory in most of The thermodynamic analysis and and substitutional are W phase Kirkaldy binary transformation is the ~ the the a the is determining the infinite system T against used with between as phase individual Technology be Hoff not 5, the additive temperature for elements equality description, of values alloying of as total Department important boundary is temperature i( The received of boundary 6). found. elements, Fe-C silicon in strictly parameters Xi = the experimental much other procedures by 4, dilution changes (see boundary, In the is the 2-n). a and interactions (i alloying coefficients experiment prediction empirical is large so as = the found that of i system. elements elements present the element. freezing greater. the This content 25 Ref. 3 solute and O-n). correct long Baganis temperatures The modelling that the October in deviation analysis from is factors iron August for of temperature amount resulting it same the 5). k, and that deviation element have given procedure chemical mole A due as Materials 8 The ceases concentrations the 7 coefficients Gik(i work, elements. of data and pure In and general is between is Si, ~ solute-solute point' the and the as this 1989 T to microstructures 1988; been < started change designated phase of which of =1= fractions by Mn, multicomponent other of is theory. from from saying the Fe-C above available this 1 content for k, published silicon, corresponding to assumption Kirkaldy calculated summing wt-%. potentials the used at temperature deviation i Ni, relationship infinalform Science Vol. follows elements addition and problem retain individual boundary J: known However, in MSTj975 must system with a Fe-C-X assump- that Cr, to in 5 carbon due especi- k is above phase inter- as each as data > Mo, and 977 less and the the the the the for be to as in in in of of 0, 1) is is is a Published by Maney Publishing (c) IOM Communications Ltd 9 978 the where the denote activity where higher difference equation, boundary for coefficients Materials the and XiYi B Similarly The L\T A crystal Location which austenite two form i y (2). = _ - Sugden y X = o X~ {L\ the _ - A?-[1+Xf(1-Xf)(eii-eI1A~A?)J and coefficient 2 phases Eventually, RT~ Wagner-Taylor RT Science Xi o = °G is temperature (After between L\ [X austenite L o L for 1- Yi the °GY lower of and and L _(X)2 were i f LJ " = exp L\ n carbon(n which Li= -+ mole 2 the and ° Bhadeshia 2 liquid/liquid L Ref. H A.X~ for (L\ 1 = 1 temperature 1 then the this Xi and A Technology octahedral eeL the °G fraction °Gi 1 are L ~ 16) RT and 11 is + gave Gibbs = liquid iron, -+ the -eY (1 - in substituted expansions L) 1) R °G - y 11 equilibrium. Liquidus, mole is or X the O of (A)2]} and phase L phases, 1)L\ free the component or, 1 component phases, temperature interstices October fraction the ° universal H energies boundary more solidus, 0] superscripts into respectively. for exp For T 1989 of generally, exp i equations i is B iron, gas the Ae example, (.) 3 of and deviation for the B Vol. constant. the temperatures, Yo Y where iron activity in In and phase is 5 pure bcc this the the for (1) (2) (1) (3) in L (Mn, the The are calculated interaction energy where and and standard be The was multipass microstructure has temperatures history welds. and from et was using volume there potentially to routine from and and In Kaufman was standard eutectoid kinetics low.) iron lattice represented b-Fe be concentration out L\ transformation Prediction sites, range which even even interaction Kirkaldy (99'6/0'417) argued 4 This °G A 2. O 4. ai. o 3. 1. 200°C. able assessed those applying Fe-C-X n solute i by phase L\ overall W Cu incorporated written to a The atoms The Although Si, Values -+Y(T Kaufman = Bhadeshia being at the is °G, but 1 is of are This in n was considerable 3 changes extrapolate were Kaufman exp of additions. that The 1 to one fractions Ni, to saturation, = using that +eInxi method interest,14 molar Gibbs a program temperature. Ae 0·09 compositions elements for welds. Extrapolating respectively. known 3 and the > the parameters predict 1 very intention crystal the et be parameter [(L\ in = quantitatively. and Cr, requires to included, for carbon by the multicomponent equation 1183 of or might any 239 of wt-% weld values the of 13 °Gn/RJ;,)+ calculated 3 allow and maximum et probability in relationship accurate data per ai. Baganis Mo, the L\ enthalpy free useful, and six i curve et Therefore, described error exp ai.,13 into of to carbon °H Ae pure alloy. K) o 3 iron same the 13 (Ref. the of had In for ai. the steels. unit commonly carbon were and the 10 atom = influence be and· the energy of Edmonds a the were (L\ from -+ (X-Fe. for addition, using 11 and e it which 0·417 Ae3 is mechanical for (3) which detailed temperature this Y iron allowing, introduced been size reliable °GtfRJ;,) 4), atoms are fitting probability as the of unit necessarily were phases Ae Cu) multiplied values einXi] 3 used. changes J;, in at for In had low to Figure Kaufman to above. provided follows. and and The of solute known, further sites. of used L\ change as solubility at.-%. later Ae were used the welding, ferrite. 3 temperatures although, temperature give cell lower every °G the equilibrium alloy obtained o on, the their be for the an taken The over values other knowledge bcc L\ present program for in giving derived for (This -+ found 1 is A forMn, °H values dissolving calculation formulated corresponding reaustenitised o properties elements every initial inter data Y, is corrected steels L\ shows temperatures, Therefore, this accompanying 119 12 of series of only unit function only This an example, occupation the and since T current the negligible, e~ and the for ignores two if from can from entire values given in unit manner 1 1s in of alia, determination down cell carbon Bernstein. the has Ae step, by 0·004. from 3 assumption of to phase the low a Si, well as transformation of values in the L\ for carbon modifications longterm L\ cells, research the be work contains relevant been L\ of °H carbon Table temperature by Ni, principle temperature carbon growth the the into of zero. values °G of alloy a to tetrahedral Nb, °G o as there below 1 predicted, equations multipass Thus, would diagram. region since Kirkaldy is atom, very program the to J;, the 0 Cr, and thermal are so written relative for -+ welded the carried a Co, K rather atoms steels down Y L\ They 3 that, data is sub- sub- Ae, Mo, free rate was two and 3 aim low can the °G the the the are the the rt./y o for be of be V, to or in in of Published by Maney Publishing (c) IOM Communications Ltd systems, were (typically Initiillly, 2 discrepancies Kubaschewski;17 data who ~ of calculated. application pancy For dent and assumption values As w I- w I- ::> 0:: w T ~ a.. w 0::: « I- w a.. w 0:: I- ::> 0:: ::!: « Fe-Mn u ~ °G~; Since = 0·5 showing Vertical Fe-C T 1000 Kirkaldy 1000 850 900 950 750 900 800 950 700 750 800 850 700 was (T this on calculated changed from determined wt-% was 0.0 0.0 Y. for + all temperature, and adopted. ~ Instead, T purpose, (0) five (b) T). the observed the of made Fe-X was and these Then, of sections were effect equation times). This by thermodynamic Fe-Mn 0.1 0.1 3 ~ overall a set Sugden Baganis by data less and °G~; are manganese observed a binary procedure between as Kirkaldy ~ loop Results 0'5°/0 the on discussed than T (3), verified Y were agreement I system, of 4 CARBON, and cannot between 0.2 0.2 Ae 3 but also phase was Mn program t and 0·1 with Fe-C-X Bhadeshia for used experimental was must and functions found, temperature K included and below. for a attributable be all the wt diagrams repeated was in trial from Baganis 700 obtained 0.3 0.3 be the correspondence - b Fe-Mn, successive °/0 a was' deduced excellent. phase silicon value and systematic alloying Liquidus, used Gilmour in and until seems the compiled from rerun 850°C to 0.4 0.4 were and of of to diagrams, iteratively. calculated However, iterations errors the program. elements ~ solidus, justified a adding et Fe-Nb binary Twas depen- discre- single value using al.,18 with with 0.5 0.5 by in Ae 3 temperatures, 19 large content cally Figure Wagner were increased expands, Swinden advised, ture * check together program With In because A (Ref. to At concentration relating source from work, experimental of as 3 Fe-Nb 1·6 0:: I- 0:: W a.. 0:: w 0 w a.. w « ::> t) l- w £:) u :!:: -ן L\ ° « GJ M Experimental Figures ~ ~ ~ ~ large °G manganese niobium Ae fact, Comparison 3 X Materials 850 900 800 750 °G~; °G~; 70~00 °GC% °G~; 2 of is 21). 1262 10- a be this that compared the Nb ~ in 3 adding knowledge temperature -+ deviation interaction °G~; of was this the with J so and and Y assumed Y Y Y uses 1 accuracy as and in mol- recalculation, . 0 K, = = = = At (Ref. 2a an Lf=2Xj (rather and that Ref.23 MEASURED excess the Ref.22 Science -RT 60·0-5·4 25·57T 2·1596 value Y applying restricted Woodhead,23 data illustrate in results in error and 0·5 data 0·5 was X&b and 1493 19). phase austenite austenite the of with data solute-solute 750 from wt-%Si, wt-%Mn, of for of ~ to In T than calculated coefficients molar was b line - in X = predicted two Therefore, and from is \ K, for the 4 6 the IX&bl 32640 on 10 X~b show a compositions be 6·0 ~ in x those Ae wt-%, well for 3 the the of 3 the to broad due pure °G~; Technology 10-T phases. K various activity program. -12·073T and X the negligible, phase X&b ideality Gibbs Aaronson unless 3 TEMPERATURE when less air 10- discrepancy the high who when equation two to for iron) Y. ferrite as as Fe-C-Mn 800 range = efj °0 phase and interactions ~ effect Kirkaldy stated than a field Recalculating a and established 1·2 free and steels °G~; other examples Kirkaldy the purity the mistake The function and gives for at X measured of and contracts. molar otherwise. eli 2 October boundary on and energy austenite 1 Ae 10- 3 low Y due equilibrium . conditions steels, wt-% alloying for disappeared. may , the X~b et ° . system. Fe-C-X 22 that 850 c alloy Domain 4 temperature in silicon al. of concentrations to from and could . Ae Ae to 3 and 3 be were 1989 = because the with temperature 20 . the values Andrews phase steels give was the 1·1 3 expressed elements. tempera- Baganis tempera- imposed . the In are original to realisti- used respect X~b X silicon alloys, solute Vol. found . 2 give* 10- their very field and Ae 900 979 3 the for (5) (4) (6) (7) to = is 5 Published by Maney Publishing (c) IOM Communications Ltd 980 4 prolonged medium good, Ni, tures experimental equilibrium metry at also agreement obtained Grange Over would However, mode to behaviour. the sequent these ternary compute seem temperatures been * binary Kirkaldy Prediction contain Ref. Equation LIQUIDUS Materials I- w ~ :::> c::: <{ w Il.. I- w ~ ~ I- w 0 u CI ~ w Il.. 1'+11. taken data for Sugden In °G~; c,ompared °Gl".; °Hi °G~; 720 the were to recent on typographical of prediction addition, phase require Mo, identified alloys, 1 -> the development a in carbon 3 in the Science heating, of solidification have standard {) l' 1'= et L and, isothermal to should = = = between series from = Kirkaldy 4 Although the 2 al.* Figure values. MEASURED last -26650+42'69T-0'017T 430 3500-2'308T 1185-150'3 Cu, peritectic - the results and at years TEMPERATURE attempt of in .. diagram 5360 of in but been ferrite - line 24 predicting against a Appendix be trace low 740 Grange Tables O' of However, and using and Bhadeshia low errors; data would the of peritectic 305 cal knowledge et headed error 4, and their it predictions of experimental This 4 obtained a1. l the alloy mol-, T verified. Technology equation the heating. Ae of Co. has to ideality and 3 wt-%C+216(0'865 alloy 1-3 part Ae cal of the is were experimental 3 contain cal experimental required ferrite being 1, be L1 l calculations Ae \ model is mol-, 3 the mean a calculated reader .. °Gl-> the mol-I, It temperature the equations multicomponent become TEMPERATURE" austenite not consisting several of 760 liable determining in standard steels not Liquidus, can being temperature, the the Kirkaldy This L, less - liquidus weld of transformed (3) agreement is not and apparent region 5630 not not the referred following included phase steels be to were the had October cal phase than 650. 5 2, L1Gf work,24 apparent2,26 of 3100. slightly .. state mode measurements yield metal solidi, seen mol-l, wt_%C)4'26 14, data. do of data solidus, 780 steel's -> been commercial and to values as containing diagram superscripts ± L. already 17, and ,OC factor errata: boundaries an not the overshoot that higher 10K. with the 1989 in of not the 18, from less and microstructure. to other as steels applied analysis present 3 seem Baganis that 2 Ae solidification solidification 3 K, 0·17T. austenite 21, temperature with the accuracy in than the Data 'for the for not found than 800 Vol. and Ref. are peritectic temperatures, does the that text analysis; Mn, to general is purity. dilato- 1115. several results omitted. widely bib of on of 22 10 5 were and have very 24 true sub- Ae 3 the not did the the also +y on K. Si, 19 in of to Table 205 204 Steel 4 203 202 201 no. 206 209 207 211 213 2 6 and 216 1 214 3 5 8 7 26 for line. 25 ASM Benz respectively, equilibrium Ref. Data content To present These ~ diagrams discrepancy Although the in As The mental values liquidus newly thermal wide obtained are since Table temperatures Experimental °G; ~ M ~ 7;,(j.-. ~oGlt;L=1'20x104-8'50T 7;,y+(j 7;,y.-. 7;,y+L To the with 30. the discover value phase °G; given M °Glt for 28 compositions C 0'36 0·19 0·18 0·12 0·11 0·29 0·35 0·30 0·81 0·48 0·58 0·89 Also, 0·69 0·20 0·52 0·66 0·004 0·001 1·01 1·01 1·48 1·20 data range 1 and assess two 2 published these program (j+L y+L (j for -> steels -> austenite work -> data and the X~ and analysis temperatures (j L L steels Compositions, (j at were compositions of in = general = 27 = the functions = = = = the Elliott Si 0·10 0·06 0·27 0·40 0·44 0·27 0·12 0·21 0·24 0·41 0·31 0·99 0·43 0·11 0·32 0·23 0·25 0·25 0·23 0·22 0·55 0·53 Ae and the was 3 was to plotted of 201-216 ~ ~ phase are if the 1666 1809 ~ 1793 9·25 Table 2·72 1783 were ~ of T liquidi, °Glt; °G~; generated and be any equation °G; steels to M lowest analysed, program, a experimental Mn < < < < for found overall at the set liquidus expected x + X - new -146'7(wt-%C) 0·13 0·04 -164'0(wt-%C) 0·58 0·67 0·04 0·04 0·72 0·90 0·46 0·62 0·33 0·85 0·14 0·02 1·42 1·26 1·53 1·25 0·02 0·02 0·02 0·02 increase of agreement 3 3 1. 10 taken L. 10 1122(wt-%C) 201'3(wt-%C) a data in y diagram each are taken L calculated to did + the steels have variety Kirkaldy For curve solidi, of Fig. has for Cr -7'22T ~ cooling -1'28T} < for zero then ° accuracy 0·07 0·01 0·08 0;92 0·30 0·08 0·02 0·06 0·02 0·81 0·02 0·03 0·04 0·03 0·02 0·04 L 0·02 0·03 1·11 1·55 1·07 a 0·02 for steels given values Glt: of from solute not a low as from wt-% this been wide 5. the the to been temperature given was each and low a It Mo combined of data < < so < < alloy the was Ref. seem be accuracy 0·02 0·02 0·024 0·016 0·06 0·03 0·07 0·01 0·06 0·02 for 0·21 0'19 0·012 0·007 0·005 rates 0·01 0·07 Fe-Mn analysis, function 0·02 0·02 0·02 0·02 can in et calculated. cooling estimated element range Jernkontoret,29 were values that - -16'74(wt-%C)2 4 measured - solidification element. 29 al. alloy in of from .. which closest Kirkaldy lines steels 2949(wt-%C) excellent, 7'869(wt-%C)2 Ni be < < (0'1 and to Table the 0·05 0·05 0·015 0·13 0·02 0·03 0·03 0·05 0·02 0·03 0·15 0·02 0·07 0·02 0·015 0·04 0·03 0·02 1·05 0·02 0·02 give dilute suspect, of seen system, Howe,30 to multicomponent loop rates. of of data for match for K could were program, steels, L?=2Xi from give In to From the S-l) carbon that 1 steels by Cu 0·08 0·02 0·05 0·07 0·12 0·07 0·03 0·04 0·07 0·03 0·04 0·04 binary et was the a this are from equilibrium. In 4 final the ranges be al. calculated, and differential systematic were were agreement values published giving the in ~ 1-26 Nb 0·03 addition, included manner, listed verified. liquidus carbon due experi- 6 Ref. for . result. in which phase Fe-C used, wt-% used. V from 0·02 0·04 0·02 0·04 0·14 (8b) (8d) of (8a) (10) (8c) the the for (9) to 29 7;, in a Published by Maney Publishing (c) IOM Communications Ltd 5 is 8 continuous attributable the 26 7 6 4 3 204 25 5 2 1 216 214 213 211 209 207 206 205 203 202 201 Steel Table no. The equilibria libria calculable. calculations One SOLIDIFICATION may austenite tion a::: w data stable the ::::> (f) I- a.. w I- ::::> Q ::::> W ~ a::: <{ w Cl :J 0 ...J oe:t I- ...J u ::::> U oe:t u excellent and austenite low Predicted 1540 1520 1500 1480 1440 1460 1420 14f200 liquidus Ae, small 3 31 and be indicate,32 should 2 particular formation 30 Austenitic Austenitic Austenitic Austenitic Austenitic Austenitic Austenitic Austenitic Austenitic solidification Ferritic Ferritic Ferritic Ferritic Ferritic Ferritic Ferritic Ferritic Primary Ferritic Ferritic Ferritic Ferritic Ferritic kinetically alloy the cooling • o or temperatures Measured in differences MEASURED cooling Primary Primary perhaps High 1420 surfaces is and the ferrite solidification; and slight also steels that Fe-C of Sugden conditions, measured actually mode advantage cooling favoured. 1440 be that conditions. one and, Austenitic Ferritic overestimation the to LIQUIDUS of in and AS for considered, the system these phase the Gibbs y/y temperature, 1530 1408 1456 1464 1476 1470 1505 1483 1501 1506 1507 1514 1529 1437 1472 1451 1495 1503 1503 1459 1474 1515 Measured of in and 1460 measurements PRIMARY predicted primary better Solidification + rates 22 general, other data liquidus Depending steels Bhadeshia L two Solidification TEMPERATURE" may means low free of phase 1480 .. liquidus are . can phases than since phase °C occur using energy may alloy for the ferrite temperatures that taken values boundary 1500 AUSTENITE obviate the up'on that close metastable solidify being is steels Liquidus, means when temperature, 1532 1534 1419 1465 1470 1500 1516 1454 1485 1504 1508 1458 1507 1516 1520 1523 1441 1477 1482 1505 1479 1514 Predicted 00 metastable between therm~chemi~al I the liquidus from DC and achieved for the 1520 proximity o made o eqUlhbnum stable nucleation th~t. directly IS composi- liquidus Refs. primary liquidus solidus, various readIly phases °C for 1540 under being m~ta- equi- one. for 29 22 as of Ae 3 temperatures, w 0:: .- ::> 0.... w 0:: w .- 2: U 33 <{ 216 214 213 211 209 206 207 205 204 203 202 201 Table no. Steel solidus to the amount allow process. in the distribution in welding solidiqcation elements precipitation. solubilities cementite Solidification than seen lating system indicated segregation solidification of cementite cementite PREDICTION 6 1526 Figure 1000 1200 1400 austenite 1600 the verify -- cementite Fe-C 800 solidification differences - phases Materials °C that the - 3 the the 1400 1300 1425 1450 1445 1340 1370 1440 1460 1460 1455 1460 Solidus Measured - Fe b-phase temperatures has since of melting stable in boundaries solidification Calculated by the austenite the 6 phase equilibria formation system. that This eventual equilibria and is ferrite been and and shows of Science full temperature, process Specifically, solidification directly then of accuracy melting boundaries (After the subsequently in above diffusion 5 phase consequently range OF lines diagram, behaviour an point constructed is of solidus 1410 1318 1450 1459 inclusions solute 1440 1321 1383 1442 1467 1470 1460 1471 proceeds Predicted Since the segregation alloy and two austenite-cementite SOLIDIFICATION is and of influenced Ref. of and by compositions point of the of much °C of austenite-graphite ranges and an Technology CARBON, 10 orders the the solidification rates b-Fe. austenite with where solute dashed the 17); and the segregation, as peritectic inhomogeneous has of alloy. diffusion form. less according austenite in boundaries in segregation austenite program yaustenite, measured in y-Fe a for of may by 151 119 104 Solidification Measured the the profound the 83 70 than 53 58 46 61 47 60 54 elements finite ferrite 15 Therefore, magnitude lines. for the steels is stable program weld temperature, be with equilibria at. October rate low during form ranges will only freezing directly to but liquidus. at -°10 and This of of analysed during alloy with RANGES and boundaries 20 significance result range, have the predicting L graphite of the solid substitutional solidi rv it 136 137 Predicted also liquid an 1989 in greater of 75 46 64 47 58 96 65 46 by 60 52 the 10 was steels metastable austenite- respect range austenite- austenite- related austenitic austenite, the °C It a not K different extrapo- primary and so in crucial ferritic can phase Vol. lower steels than only and that and can 981 the the the are be to to in 5 Published by Maney Publishing (c) IOM Communications Ltd ~ w a.. o Vl .- Ei .- :::> ~ U I- W Vl ~ o :::> w :::E a.. < o ~ Materials ~ < z ~ w :J o L;: < o z o u ~ .- w o Vl a.. ~ w o U u 0·11 temperatures Table approximation, tectic analysed. diagram sections the temperature As steels. using algorithm 982 7 8 Figures 1500 1450 1300 1400 1350 120 100 140 160 temperature with binary multicomponent indicates (0'17 Experimental other range Experimental 80 40 60 and Sugden the 3 as These the lists wt-%C Science 1 for 0·12 steels, through b-ferrite, For • o computer 300 MEASURED MEASURED 40 of 9a is C C Fe-C liquidus, and measured data < > 12 and change 0 and and an steels wt-%C 0.17 0.17 it . and by . low and the excellent b equilibrium was Bhadeshia corresponds solidification are 60 and the and the extrapolation 201 of show wt wt model. 1 SOLIDUS it Technology SOLIDIFICATION solidification alloy l'O%Mn 350 and in plotted calculated calculated % steels; can % and b-solidus and line Fe-C-Mn solidification calculated range line the 80 which \ steels be predictor The predicted of 202, entire TEMPERATURE, Liquidus, of in seen ideality and phase ranges data 1 ideality figures Figs. to which from 400 100 solidify was of given October values \ range that of peritectic 0 RANGE the and peritectic values 7 values of estimated, the and for solidus, are diagram respectively mode the show and in b-solidus 12 120 of through both for austenite Fe-C-Cr 1989 the Table thermodynamic 1 2'0%Cr, ,oe ,0 the 450 from 8, of solidification e region two for Jernkontoret for low Ae 3 respectively. the steels. the 140 point Vol. and 1 to alloys) line. the constant temperatures, contain solidus. solidus Ref. solidus solidus (wt-%) drawn a phase 5 alloy peri- thus 1500 first For on 29 160 and 9 The for partition element istic tectic vertical in respectively. cularly mination application Calculation when sion b-phase austenite cooling b-ferrite among of systems I-- ~ 0::: u w ~ a. W 0::: ~ 0::: :J W w c::: :J W I-- w ~ a. o alloying simplicity, diagrams 1500 maintained by Phase 1350 microscopic 1350 1550 1400 1450 1450 1400 trends 1550 phase partition value of and chromium computer since, section the rates entails field the or in o o coefficients phase of Ae compositions in ( 3 (0) diagrams austenite an elements, b) showing elements of b-field Although, compositional partition for for 0-2 0'2 encountered were coefficient temperatures alloy y three time thermodynamic of as of field equilibrium a manganese, is y the model 0,4 dilute OA straight present, partition and constructed consuming system. and of and the the phase to phase for coefficients for the solute CARBON, 0-6 0'6 solution contraction of liquid contribution the a level (it in low exact a concomitant line) change. a should can diagram, To and 0·8 0'8 cannot welding solute peritectic partition elements Fe-C-Mn should alloy iron of experiments. be coefficients calculations determine composition containing the using micro 1-0 seen. is wt also steels Depression element is corresponding of be 7 it a are be negligible. - from for coefficient is 0/0 logical be 1·2 Stabilisation the points segregation contraction region predicted and fairly possible· noted multicomponent noted. the the small is austenite Therefore, to "4 of a b equilibrium high, step, L of interaction generated the the character- has that, Fe-C-Cr; Since amounts the to between 1·6 L from expan- phases of deter- of it of parti- do been peri- field can the for the the the 1·8 an so a Published by Maney Publishing (c) IOM Communications Ltd coefficient general its equation multicomponent an the the equation The experimental where use (xt/Xr) Values Summary Standard been major element composition librium, ture from is austenite also be Table 0·70 0·74 0·50 0·83 0·88 0·80 0·84 0·94 0·95 0·96 0·86 0·83 0·95 0·90 0·92 0·95 0·75 0·95 0·66 0·73 0·91 Ref. Measured Ref. Ref. (X~/X~) Xi Agreement A.i not binary assumed accurate mel of various 34 36 35 be reason at = = the calculated 4 more influenced alloying t ------~-o-G-. calculated. exp XrAi for which and linear 1 1 may the is (3). (11) liquidus. free in and + coefficients Prediction and 1\ Y G that solute for the determined detailed between (Fig. thermodynamic 11 RT For (i.e. L proportions data. ( for energy be .X describes ternary o °Gi these both series the 1 0·50 0·50 0·84 0·72 0·88 0·78 0·77 0·50 0·50 0·84 0·88 0·78 0·72 0·50 0·50 0·84 0·72 0·78 0·78 0·72 0·78 elements Predicted segregation equilibrium necessary. and Fe-C-X solidification Sugden example, the exp lOb) by + The elements. By poorer X have the Gli changes models austenite L subsequent (Wagner)· __ partition alloys are RT of is partition o considering qualitatively ferrite using L) and 1 not themselves I liquidus given of transformation between for 7 agreement , have occurring However, determination and Bhadeshia obvious, partItIon these 36 and the as of and the coefficient expansion to in 0·50 0·60 0·95 0·87 0·95 0·70 0·74 0·50 0·75 0·95 0·50 0·78 Measured (xr/X~) been activity b-ferrite diffusion y-L the liquid describe the equilibrium two Table b-Fe relationship austenite been the during used for alloy although transformation, in steel coefficients iron phases Liquidus, relative data future and 4 used (Fig. temperatures. of solidification of during to partitioning of together elements) at a (XUXr) solidification are for evaluate the given equilibrium liquid to lOa) a even work, and 0·62 0·69 0·90 0·36 0·28 0·36 0·82 0·77 0·62 0·69 0·82 0·78 effects partition . Predicted tempera- given iron generate solidus, in activity cooling of is . solute equi- have their with here iron fair. and (11) can the the the as in of in A Ae 3 temperatures, mental Nb, Kirkaldy steels obtained dually, calculated, shown addition, revised the the using Fe-Nb the Mo, elements U -oJ computer describes < U ::::> -oJ U -I u ::> -I ~ w CL multicomponent ~ ~ z u o b L: u w z .- (/) agreement. ~ w Q w ~ c:: ::> :::!: ~ ~ ::::> :::!: c.. < i= z o b ~ U z ~ o u w ~ 10 The 0.0 participating 0.2 Materials 0.4 0.6 0.8 0.0 0.2 resultant 0.6 0.8 0.4 1.0 1.0 binary W, elements Cu, equilibrium b Calculated 0.0 0.0 empirical containing austenite to data and peritectic EXPERIMENTAL systems values Co) V, (b) on by be and the (a) discrepancies program with Fe-C for Nb, for and A valid line Science the calculation have deviation influence Baganis,3 for the 0.2 good the have 0.2 data each for phase W, Ae of phases steels 3 and region for up system and ~ been first liquidi ideality line partition and °G, and o has significant equilibrium been to phase to EQUILIBRIUM ability a liquid compositions of and time \ ~-ferrite of of in incorporated estimate have experimental Co. Technology the 1·8 0.4 ~ of with is the ideality been and 0.4 resolved. the °H, low o found boundary then wt-%C. its the iron phase to phase \ been multicomponent solidi accuracy the and coefficients concentrations additions written phase predict found. the temperature PARTITION to and 0.6 boundary for compared The boundary Fe-Mn, of ~ Using 0.6 be Gibbs October to being low a have diagram in liquid program New evaluated. values range which the the of alloy o extremely • COEFFICIENTS the Mn, treated free 0.8 been program ~ o • Ref.34 Ret.36 solidification is 1989 Fe-Ni, elements with from of of 0.8 of system of method steels accurately calculated iron Ref.34 Ref.35 Ref. Si, energy low has low for has used. alloying. Results experi- Ni, that indivi- solute 36 Vol. alloy good alloy been been 1.0 and and and and 983 the Cr, (V, In of of of 5 1.0 Published by Maney Publishing (c) IOM Communications Ltd gation, C set modifications fair. elements made range, largest it and 984 with Mo the inadequate sources, with Acknowledgments continues. source Group discussions laboratory support The Research References Materials 4. 2. 3. 5. 1. is The ~ of inability B. metallurgy J. 495-501. J. AIME. 495-504; Warrendale, Proc.), M. Stereol., 222-224; 'Hardenabi1ity L. < liquid only This 1'8%, authors iron Sugden s. S. GRETOFT, to alloying pleasure which S. 1'5%, practical STRANGWOOD data proportion at was KIRKALDY DARKEN i.e. and between estimate KIRKALDY, Science strictly model Council the as (ed. iron, Mn facilities experimental the 1986, with will 1987, 1953, to balance strongly also and are one of University to to H. D. elements, account PA, < limitations and limitations structural that be and has the 5, correct and and Professor Warrendale, members Tokyo, Bhadeshia grateful concepts K. V. obtained. b- 3'0%, component. the and of (2), The R. refined and B. Doane D. and at Fe-FeC (including been agreement 3 steels E. influences Technology w. the amount 365-371. H. to A. the Metallurgical for BAGANIS: Ni H. McGraw-Hill. GURRY: liquid in for of data steels', BHADESHIA, ESAB to shown with THOMSON, of solute-solute as and of used authors K. University of < Cambridge. the D. Finally, infinitely PA, Liquidus, the the 2'5%, the development D. for phase the It of iron, Si) J. following applications Hull the 'Physical (Conf. Metall. with in AB, The theory H. Science to S. is program partitioning the October ~ Phase welding amount Kirka1dy), Society anticipated and and Cr predict and BHADESHIA: an acknowledge diagram 1'0%. Metallurgical for Sweden, observed dilute pure Proc.), solidus, of Trans., < chemistry itself, attempt L.-E. interactions, between E. the range: Cambridge. and Transformations 2'5%, 1989 of result This of to binary of fabrication. accurately A. solutions, (ed. SVENSSON: AIME. provision of Ae in the 82-125; solute 3 for 1978, for Engineering steel', results BAGANIS: in covers that (all particular any J. Co from has Vol. of austenite Society program temperatures, financial alloying 'Welding Y. systems 9A, helpful metals', < wt-%) segre- (Conf. given Koo), 'been these since 5 1978, It Acta was and two 2%, the the (4), of of in is 20. 21. 23. 22. 25. 24. 11. 10. 28. 27. 26. and 30. 29. 12. 32. 31. 16. 15. 14. 13. 35. 34. 33. 19. 18. 17. 36. 9. 6. 8. 7. E. H. H. A. J. H. 28, C. P. Sci. Vol. H. London, H. R. 209, O. M. L. L. M. 209, York, D. H. K. R. R. 61, K. 781-796. Springer- 504. T. A. M. 1225. 113. 563; T. H. H. 1963, (3), (10), Stockholm, 'A A. Z. Z. 1972, (10), 68. 1976, phase B. 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