Interfacial segregation at Cu-rich precipitates in a high-strength low-carbon steel studied on a sub-nanometer scale

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1 Acta Materala 54 (2006) Interfacal segregaton at Cu-rch precptates n a hgh-strength low-carbon steel studed on a sub-nanometer scale Deter Ishem *, Mchael S. Gaglano, Morrs E. Fne, Davd N. Sedman Department of Materals Scence and Engneerng, Northwestern Unversty, 2220 Campus Drve, Evanston, IL , USA Receved 13 January 2005; receved n revsed form 25 September 2005; accepted 4 October 2005 Avalable onlne 19 December 2005 Abstract The local composton of small, coherent Cu-rch precptates wth a metastable body-centered cubc structure n a ferrtc a-fe matrx of a hgh-strength low-carbon steel was studed by conventonal atom-probe tomography. The average dameter, ÆDæ, of the precptates s 2.5 ± 0.3 nm at a number densty of (1.1 ± 0.3) m 3 after drect agng at 490 C for 100 mn to a near-peak hardness condton, yeldng a value of 84 Rockwell G. Besdes Cu, the precptates contan 33 ± 1 at.% Fe and are enrched n Al (0.5 ± 0.1 at.%). Nckel and Mn are sgnfcantly segregated at the a-fe matrx/precptate heterophase nterfaces. The Gbbsan nterfacal excesses relatve to Fe and Cu are 1.5 ± 0.4 atoms nm 2 for N and 1.0 ± 0.3 atoms nm 2 for Mn. The reducton of the nterfacal free energy, calculated utlzng the Gbbs adsorpton sotherm, s 16 mj m 2 for N and 11 mj m 2 for Mn. Ó 2005 Acta Materala Inc. Publshed by Elsever Ltd. All rghts reserved. Keywords: Interface segregaton; Gbbsan nterfacal excess; Ferrtc steels; Precptaton hardenng; Nanostructure 1. Introducton Copper precptaton plays an mportant role n the hardenng of hgh-strength low-carbon steels [1 4]. The formaton of Cu-rch precptates durng thermal agng has been studed by many technques: atom-probe feldon mcroscopy (APFIM) [5 12], small-angle neutron scatterng (SANS) [8,13,14], hgh-resoluton and conventonal electron mcroscopy (HREM and CTEM) [15 17], theoretcal modelng [13], and computer smulaton [18]. APFIM, HREM, CTEM, and SANS studes ndcate that small Cu precptates have, at dameters less than about 5 nm, a metastable body-centered cubc (bcc) structure and are coherent wth the ferrtc a-fe matrx [5,14 17]. In the 5 10 nm dameter range, the precptates transform to a 9R structure [15 17], and eventually, at even larger dameters, gradually nto the stackng-fault-free face-centered cubc (fcc) equlbrum structure of pure Cu. * Correspondng author. Tel.: ; fax: E-mal address: shem@northwestern.edu (D. Ishem). Interfacal segregaton of N and Mn at the a-fe matrx/ precptate nterfaces has been observed by APFIM for Cu precptates 5 10 nm n dameter n Fe Cu N and Fe Cu N Mn alloys [7 9,19]. At ths sze, however, the precptates are larger than the crtcal dameter for transformaton and loss of coherency of about 5 nm, and thus lkely have transformed to a 9 R or faulted fcc structure and are no longer bcc and coherent wth the a-fe matrx. After neutron rradaton, N and Mn have also been found, employng APFIM and atom-probe tomography (APT), to be enrched n the nteror and n the vcnty of smaller Cu-rch clusters and precptates n nuclear pressure vessel steels and model alloys [9,19 24]. Thermodynamcs, knetcs, loss of coherency, and structural transformaton behavor under neutron rradaton, however, are consderably dfferent from the case of thermal decomposton. There s lttle quanttatve nformaton about the segregaton of solute atoms at the nterfaces of coherent bcc Cu-rch precptates smaller than 5 nm n dameter n thermally aged alloys. We address ths queston employng APT to nvestgate Cu-rch precptates n a newly developed hgh-strength low-carbon steel. A formalsm s /$30.00 Ó 2005 Acta Materala Inc. Publshed by Elsever Ltd. All rghts reserved. do: /j.actamat

2 842 D. Ishem et al. / Acta Materala 54 (2006) presented to descrbe quanttatvely segregaton by extractng the relatve Gbbsan excess, whch s the relevant thermodynamc quantty to measure segregaton at an nterface n a system wth more than two components, from local compostons measured by APT. Cu-rch precptates are studed n a newly developed Mo- and Cr-free low-carbon steel wth an excellent tensle strength, up to 700 MPa (100 ks). A Charpy V-notch test mpact fracture toughness of 64 J (47 ft lb) at 40 C was obtaned for specmens aged to a near-peak hardness condton wth a yeld stress of 712 MPa [3,25 28]. For a verson of ths steel wth 0.1 wt.% T added, the Charpy fracture energy at 79 C was greater than 360 J (264 ft lb), snce the specmen bent wthout breakng n the Charpy apparatus [26]. Commercal Cu precptaton-hardened steels need to contan N to prevent segregaton of Cu to gran boundares and thus prevent hot-shortness, that s, crack formaton durng hot rollng, and Mn addtons to getter sulfur mpurtes. From a technologcal pont of vew Cu alloyed steels contanng N and Mn are of sgnfcant nterest. Essentally the steel was developed by elmnatng the Mo and Cr from the U.S. NavyÕs hgh-strength low-carbon HSLA 100 steel and optmzng the precptaton-hardenng process [25]. The APT analyses presented here reveal a sgnfcant nterfacal segregaton of N and Mn at coherent bcc Cu-rch precptates wth an average dameter, ÆDæ, of 2.5 ± 0.3 nm. The Gbbsan nterfacal excesses relatve to Fe and Cu, determned by the methodology ntroduced n Secton 2.2, are 1.5 ± 0.4 atoms nm 2 for N and 1.0 ± 0.3 atoms nm 2 for Mn. 2. Methods 2.1. Expermental procedures The steel was fabrcated at the Ispat-Inland Inc. Research Center, East Chcago, Indana. A 45.5 kg (100 lb) laboratory heat was vacuum nducton melted, cast nto molds, hot rolled to 13 mm thck plates, and ar cooled. Subsequent hot rollng to 2.5 mm was followed by a cold rollng step to the fnal thckness of 1.6 mm. The average composton of ths steel, as provded by the Ispat-Inland Inc. Research Center, s gven n Table 1. Followng an austentzaton treatment at 1100 C for 0.5 h, the specmens were quenched drectly from ths temperature to dfferent agng temperatures and aged for 100 mn [3]. Drect agng was conducted for a fundamental study of the nucleaton and growth of precptates n ths steel [3,4]. The hardness was measured as an ndcator for strength and to track the course of the precptaton. A Rockwell hardness tester was utlzed, applyng a 10 kg mnor load, 150 kg major load, and a 1.6 mm ball correspondng to the Rockwell G scale. At least fve hardness measurements were recorded for each sample tested, wth the average beng logged as the actual hardness value, and the standard devaton as the uncertanty of that value. FIM tps were prepared by electropolshng, usng ntally a soluton of 10 vol.% perchlorc acd n acetc acd at 20 V dc at room temperature, and then a soluton of 2 vol.% perchlorc acd n butoxyethanol at V dc at room temperature for the fnal tp preparaton. Conventonal APT analyses were performed at a resdual pressure of Pa, utlzng a pulse voltage-to-dc voltage rato of 20% at a pulse repetton frequency of 1500 Hz. Vsualzaton and data evaluaton of the threedmensonal atom-by-atom datasets were performed wth custom software, ADAM 1.5, developed at Northwestern Unversty [29]. Composton profles wth respect to dstance from the a-fe matrx/precptate heterophase nterface were obtaned wth ADAM 1.5 usng the proxmty hstogram method or proxgram for short [30,31]. A 10 at.% Cu soconcentraton surface served as a reference surface for the proxgram analyss. Ths concentraton threshold provded a relable and topologcally stable representaton of the precptates, that s, the changes of the morphology, sze, and number of the precptates were small when varyng the threshold around 10 at.% Cu. Isoconcentraton surfaces were generated wth ADAM 1.5 employng the adaptve marchng cube algorthm. The parameters used to obtan a nose-free soconcentraton surface n ADAM 1.5 were a voxel sze of nm and a delocalzaton dstance of 1.0 nm [32]. No addtonal nose suppresson was appled, that s, the confdence sgma parameter of ADAM 1.5 [29 32] was kept at a value of zero. The dameter, D, of a precptate contanng n atoms n the reconstructon was equated to the dameter of the volume equvalent sphere: D 6 nx 1=3 p f ; ð1þ where the atomc volume, X, s equal to nm 3 for bcc Fe, and the overall detecton and reconstructon effcency, f, s estmated to be 0.6. The number of atoms, n, belongng to a precptate was determned employng the envelope method [33], based on clusters wth more than 20 Cu atoms separated not farther than a maxmum separaton dstance of 0.5 nm and employng an envelope grd spacng of 0.15 nm. Table 1 Average composton of the hgh-strength low-carbon steel under nvestgaton as determned by chemcal analyss provded by Ispat-Inland Inc Fe C S Nb Mn Cu N Al Concentraton (wt.%) Balance Concentraton (at.%) Balance

3 2.2. Determnaton of the relatve Gbbsan excess of solute at an nterface At constant temperature and pressure, the Gbbs adsorpton sotherm for a planar heterophase nterface n a system wth two phases, a and b, and n P 3 components s [34] dr Xn 3 C relatve dl ; ð2þ where r s the nterfacal free energy, l the chemcal potental of component, and the relatve Gbbsan nterfacal excess of component s gven by D. Ishem et al. / Acta Materala 54 (2006) C relatve c a C C cb 2 cb c a 2 c a 1 1 c a 1 cb 2 C cb c b 1 ca 2 cb 1 ca 2 c a 1 cb 2 ; ð3þ cb 1 ca 2 where c k s the concentraton of component n phase k = a, b. The quantty C relatve s ndependent of the poston of the dvdng nterface [35] and can be calculated employng Eq. (3) from the measured Gbbsan excesses, C, obtaned for a specfc choce of the poston of an nterface. The values C are determned utlzng proxgram concentraton profles for a specfc nterface [30,31] from C qdx Xp m1 c m c k ; ð4þ where q s the known atomc densty, Dx s the dstance between the p concentraton data ponts n the proxgram, and k = a on the matrx sde and k = b on the precptate sde of the heterophase nterface. The determnaton of nterfacal excesses C for one-dmensonal concentraton profles across gran boundares n a two-component system by a smlar method has been dscussed elsewhere [36,37]. One advantage of wrtng the Gbbs adsorpton theorem n the form of Eq. (2) s that the (n 3) values of dl ( = 3,..., n) can be vared ndependently, and therefore a coeffcent for the reducton of the nterfacal free energy at a respectve chemcal potental, l, s gven by or ol C relatve. ð5þ T ;p;l3 ;...;l 1 ;l þ1 ;...;l n Ths coeffcent can be obtaned drectly from the nterfacal excesses, C relatve, determned from Eq. (3). Usng HenryÕs law for dlute solutons, Eq. (5) can be rewrtten n the form or kt Crelatve ; ð6þ oc c T ;p;l3 ;...;l 1 ;l þ1 ;...;l n whch s used to determne the coeffcent of nterfacal energy reducton at a concentraton c due to segregaton of component at the heterophase nterface, wth a Gbbsan nterfacal excess C relatve. 3. Results Fg. 1. Isochronal hardness curve for 100 mn agng tme at temperatures n the range C, after quenchng from the austentzaton treatment at 1100 C for 0.5 h [3]. The flled crcle marks the condton used for the APT nvestgatons. Fg. 1 dsplays an sochronal hardness curve for 100 mn of drect agng at each dfferent temperature. The maxmum value for the hardness s 85.2 ± 0.1 Rockwell G, whch s obtaned at an agng temperature of 500 C. Each hardness value s the average of fve ndependent measurements, and the error s the standard devaton of the fve values. A near-peak hardness condton wth a hgh number-densty of nanometer-szed precptates was studed by conventonal APT. The Cu-rch precptates formed durng agng at 490 C for 100 mn are dstnctvely vsble n a three-dmensonal atom-by-atom reconstructon, Fg. 2, dsplayng the postons of ndvdual Cu atoms n the analyss volume. The spatal dstrbutons of the solute components Cu, N, S, Al, and Mn are shown n the three-dmensonal reconstructons n Fg. 3, representng a subset of the data of Fg. 2, contanng three Cu precptates. It s seen qualtatvely that N, Al, and Mn are enrched at the locatons of the Cu-rch precptates. When nterpretng Fg. 3, however, account must be taken of the fact that the reconstructon represents atomc densty rather than concentraton. In fact, durng feld evaporaton, the precptates develop a surface slghtly recessed wth respect to the average curvature of a tpõs surface, that s, a surface wth a larger radus of curvature, snce Cu has a lower evaporaton feld (30 V nm 1 ) than does Fe (36 V nm 1 ) [38]. Consequently, atoms feld-evaporatng from the Cu-rch precptates are projected toward the detector at a lower magnfcaton than atoms feld-evaporated from the a-fe matrx. Ths causes an apparent hgher atomc densty for the precptates than the matrx n the threedmensonal reconstructon, snce the parameters used for the reconstructon are calbrated wth respect to the a-fe matrx. Fortunately, ths effect affects only the two lateral dmensons of the reconstructon. The thrd dmenson, the depth, vertcal n Fg. 2, s not affected and the precptates therefore appear slghtly elongated along ths drecton. Ths dstorton of a reconstructed Cu

4 844 D. Ishem et al. / Acta Materala 54 (2006) Fg. 2. Postons of Cu atoms n an APT reconstructon, nm 3 n sze, obtaned from a steel aged at 490 C for 100 mn. Body-centered cubc Cu-rch precptates wth an average dameter of 2.5 ± 0.3 nm have formed, at a number densty of (1.1 ± 0.3) m 3. precptate n an a-fe matrx, resultng from ths local magnfcaton effect, has been nvestgated n greater detal employng computer smulaton [39]. To determne the average precptate dameter, ÆDæ, ndependently of the dstortons due to the local magnfcaton effect, the dameter of a volume equvalent undstorted sphere s calculated from the number of atoms n each precptate employng Eq. (1). Only precptates fully contaned n the reconstructon volume, that s, whch are not cut by the surface of the reconstructed volume, are taken nto consderaton. The average dameter s ÆDæ = 2.5 ± 0.3 nm. At ths dameter, the precptates are expected to have a metastable bcc structure and to be fully coherent wth the a-fe matrx. The reconstructed volume dsplayed n Fg. 2 contans 30 Cu-rch precptates, of whch 15 are cut by the surfaces of the reconstructon volume. Countng the cut precptates as one-half, a number densty, N v, of (1.1 ± 0.3) m 3 s obtaned. The proxgram method [30,31] s used to determne both matrx and precptate composton and nterfacal segregaton. Snce the proxgram measures compostons wth respect to dstance from an soconcentraton surface, wth no restrctons on the morphology of a precptate, the elongated shape of the precptates due to the local magnfcaton effect does not affect ther measured composton. Lkewse, for the proxgram, t does not matter f a precptate s cut by the surface(s) of the reconstructed volume. Isoconcentraton surfaces drawn at the 10 at.% Cu level are used to delneate the Cu-rch precptates and to defne the orgn of the proxgram, servng as a fducal mark for measurng dstances nto a precptate (postve values) and a-fe matrx (negatve values). Fg. 4 dsplays the proxgram concentraton profles for an ndvdual precptate. The center regon of ths precptate s represented by the last data pont on the rght-hand sde of the dagram (postve dstances) and s enrched n Cu to 69 ± 4 at.%, Fg. 4(b), and contans 29 ± 4 at.% Fe, Fg. 4(a). Nckel and Mn are enrched n the nterfacal regon near the orgn of the dagram, Fg. 4(c) and (d), wth peak concentratons of 2.8 ± 0.4 at.% N and 2.6 ± 0.4 at.% Mn, respectvely, whch s a sgnfcant enrchment by a factor of 3 and 5, respectvely, wth respect to the a-fe matrx concentratons of 0.95 and 0.55 at.%. The precptate contans 0.5 ± 0.2 at.% Al, averaged from the last two data ponts n Fg. 4(e), whch s an enrchment by a factor of 10 wth respect to the a-fe matrx concentraton of only 0.05 at.% Al. To mprove the statstcs and to extract quanttatve average values for concentratons and nterfacal excesses, a proxgram of all precptates n the reconstructed volume, Fg. 2, was calculated and s dsplayed n Fg. 5. Snce all precptates are enveloped by a 10 at.% Cu soconcentraton surface, the proxgram corresponds to a weghted superposton of concentraton profles across the nterfaces of all precptates, wth all profles algned wth the 10 at.% Cu level at the orgn of the ntegral proxgram. A complete set of phase concentratons for all elements for Cu-rch precptates and the ferrtc a-fe matrx derved from Fg. 5 s provded n Table 2. The center regon of the precptates,

5 D. Ishem et al. / Acta Materala 54 (2006) Fg. 3. APT reconstructons of three Cu-rch precptates, showng the spatal dstrbutons of Cu, N, S, Al, and Mn atoms. The reconstructed volume s 2 nm n thckness and has a lateral cross-secton of nm 2. Fg. 4. Proxgram concentraton profles for (a) Fe, (b) Cu, (c) N, (d) Mn, (e) Al, and (f) S for an ndvdual Cu-rch precptate. The orgn s defned by a 10 at.% Cu soconcentraton surface. that s, the plateau regon consstng of the last two data ponts at the rght-hand sde of Fg. 5, has an average Cu concentraton of 64.0 ± 1.0 at.% and an average Fe concentraton of 33 ± 0.9 at.%. These concentratons are very close to the ones gven above for a sngle precptate. An Fe concentraton ths hgh n precptates wth ÆDæ = 2.5 ± 0.3 nm or less s consstent wth prevous atom-probe studes [6,7] of Cu-rch precptates of smlar Fg. 5. Proxgram concentraton profles for (a) Fe, (b) Cu, (c) N, (d) Mn, (e) Al, and (f) S for all Cu-rch precptates n Fg. 2, wth respect to a 10 at.% Cu soconcentraton surface. The cross-hatched areas n (c), (d), (e), and (f) correspond to the Gbbsan nterfacal excesses of N, Mn, Al, and S, respectvely, at the nterfaces of the precptates. sze n thermally aged alloys. SANS experments, however, ndcate that precptates wth ÆDæ larger than 1 nm are essentally devod of any Fe [13,24], even though some Fe (10 at.%) can obvously not be accounted for by the SANS technque, as dscussed n [24]. The N and Mn

6 846 D. Ishem et al. / Acta Materala 54 (2006) Table 2 Average compostons (at.%) of Cu-rch precptates and ferrtc a-fe matrx as measured by APT Fe C S Nb Mn Cu N Al Interor of precptates 33.0 ± 0.9 ND 0.60 ± 0.14 ND 0.76 ± ± ± ± 0.10 Ferrte matrx ± 0.02 ND 0.99 ± 0.01 ND 0.55 ± ± ± ± The concentraton values for p the precptates are based on 3017 atoms, and for the a-fe matrx on 636,202 atoms; ND, not detected. The error gven for each concentraton s r c ffffffffffffffffffffffffffffffffffffffffffff cð1 cþ=n, where N s the total number of atoms detected. concentratons n the centers of the precptates, 1.2 ± 0.2 at.% N and 0.76 ± 0.16 at.% Mn, are not strongly enhanced wth respect to the a-fe matrx concentratons of 0.95 ± 0.01 at.% N and 0.55 ± 0.01 at.% Mn, respectvely. Alumnum, however, s, as noted above for a sngle precptate, strongly enrched, by a factor of 10, n the nteror of the precptates wth 0.50 ± 0.10 at.% Al n the precptate center versus ± at.% Al n the a-fe matrx. The core of the Cu-rch precptates s depleted n S, wth a core concentraton of 0.60 ± 0.14 at.% S versus a matrx concentraton of 0.99 ± 0.01 at.%. An a-fe matrx/precptate nterface locaton s ndcated n Fg. 5 by the vertcal lne. The nterface poston s arbtrarly chosen at the locaton wth the mean value of matrx and precptate Cu concentraton, and thus t s not dentcal wth the orgn of the proxgram. As dscussed prevously, relatve nterfacal excesses, C relatve, are ndependent of the specfc poston of the dvdng nterface. Also, because of the possblty of an on trajectory overlap effect, due to the reduced local magnfcaton, the nterface may appear broader n the proxgram concentraton profle than n realty. Any artfcal ntermxng across the heterophase nterface that results n a lnear superposton of matrx and precptate atoms does not, however, affect the ndvdual nterfacal excesses, C, snce the matrx and precptate concentratons are used as reference concentratons, whch are subtracted n Eq. (4). Nckel and Mn show sgnfcant segregaton peaks at the nterface wth concentratons of up to 2.5 at.% N and 1.8 at.% Mn, respectvely, Fg. 5(c) and (d), correspondng to enhancement factors of 2.6 for N and 3.3 for Mn. Interfacal excesses, C, are determned from the area under the concentraton curves as plotted n Fg. 5, employng Eq. (4), the precptate and matrx concentratons gven n Table 2, and the atomc densty of Fe (85 nm 3 ). Sgnfcant postve relatve Gbbsan nterfacal excesses wth respect to Fe and Cu, C relatve, exst for N (1.5 ± 0.4 atoms nm 2 ) and Mn (1.0 ± 0.3 atoms nm 2 ). When normalzed by the atomc densty of a (110) lattce plane of the ferrtc a-fe matrx, 17 atoms nm 2, these values correspond to cumulatve projected excesses of 0.09 ± 0.02 monolayers (ML) for N and 0.06 ± 0.02 ML for Mn. The normalzaton of the Gbbsan excess to unts of ML, however, does not mply that the solute atoms are actually located n one atomc layer. Alumnum has only a slght tendency to segregate at the nterface, wth an excess of 0.24 ± 0.23 atoms nm 2 (0.01 ± 0.01 ML), and S, f there s an nteracton wth the nterface at all, has a slght tendency toward depleton at the nterface wth a negatve excess of 0.10 ± 0.11 atoms nm 2 (0.006 ± ML). Segregaton and depleton at an nterface are thermodynamcally both possble, accordng to the Gbbs adsorpton sotherm. 4. Dscusson Whle Al segregates only weakly at the a-fe matrx/ precptate heterophase nterface, f at all, t s strongly enrched n the nner portons of the precptates, 0.5 ± 0.1 at.% Al, compared wth a value of only ± at.% Al n the a-fe matrx. These values of matrx and precptate concentratons, c m and c p, result n a parttonng rato, K = c p /c m, of K =10±2. A value of K ths large ndcates a strong attractve nteracton for Al atoms n bcc Cu. The bnary Al Cu system possesses a stable bcc Cu(Al) sold soluton phase n the concentraton range at.% Al [40] wth a lattce parameter of nm [41]. Ths ndcates that Al addtons stablze thermodynamcally the bcc Cu phase, even though fcc Cu can dssolve up to 19.7 at.% Al [40]. Knowledge of ths stablzng effect of Al on bcc Cu precptates may be of technologcal mportance for optmzng the benefcal effects of bcc Cu precptates n steels. Nobum and C are not present n the entre three-dmensonal reconstructon dsplayed n Fg. 2. Ths s consstent wth the formaton of large nobum carbde precptates, at a number densty below m 3, whch s too small a value to be detected by the random-area analyss technque employed by conventonal APT. Nobum carbde precptates are detectable usng a selected area analyss approach [42] and by LEAP TM tomography. Next, we dscuss the consequences of lmted sold-state dffuson for the knetcs of precptaton and nterfacal segregaton. The three-dmensonal pffffffffffffffffffff root-mean-squared (RMS) dffuson dstance s hx 2 3D p ffffffffffffffffffff 6D X t, where D X s the mpurty dffusvty of the solute speces at 490 C and t s tme; for mpurty dffuson of atomc speces X n ferromagnetc a-fe the values are lsted n Table 3 [43 48]. The three-dmensonal RMS dffuson dstance calculated for Cu, 6.2 nm, s almost dentcal to half the average surface-to-surface nter-precptate spacng hs 3 1=3 4p N V 1 2 hd

7 D. Ishem et al. / Acta Materala 54 (2006) Table 3 pffffffffffffffffffff One- and three-dmensonal RMS dffuson dstances, hx 2 1D p ffffffffffffffffffffff pffffffffffffffffffff 2D X t and hx 2 3D p ffffffffffffffffffffff 6D X t, where D X s the dffusvty of solute speces X at 490 C and t = 100 mn, for self-dffuson of Fe, and mpurty dffuson of the solute elements Cu, N, Al, Mn, and S, n ferromagnetc a-fe qffffffffffffffffffffff D X [m 2 s 1 ] Ref. hx 2 1D p ffffffffffffffffffffff qffffffffffffffffffffff 2D X t; hx 2 3D p ffffffffffffffffffffff 6D X t; t = 100 mn [nm] t = 100 mn [nm] Fe [43] Cu [44] N [45] Al [46] Mn [47] S [48] D X s calculated from the actvaton energy and pre-exponental factor provded by the respectve reference lsted. of 6.1 nm. Ths mples that the dffuson zones of neghborng precptates overlap and the formaton of Cu-rch precptates has proceeded past the growth stage. Hence, the decomposton reacton s most lkely n the growth and coarsenng regme. The three-dmensonal RMS dffuson dstance for N, 8.6 nm, s slghtly larger, and the ones for Al (39 nm), Mn (23 nm), and S (35 nm) are much larger than the dffuson dstance of Cu, mplyng that N, Al, Mn, and S can redstrbute on a length scale that s larger than that for Cu. For a dscusson of a possble knetcally nduced, dffuson-lmted nterfacal segregaton due to solute ple-up n front of the movng matrx/precptate nterface, we pffffffffffffffffffff use the p one-dmensonal ffffffffffffffffffff RMS dffuson dstance, hx 2 1D 2D X t, whch provdes a conservatve estmate for a comparson wth the extent of the nterfacal segregaton zone measured n the proxgram concentraton profle because the atoms are dffusng n three dmensons, snce the proxgram folds the three-dmensonal precptate geometry nto a one-dmensonal profle [30]. The one-dmensonal RMS dffuson dstances of the solute elements (see Table 3) s 3.6 nm for Cu, 5.0 nm for N, 22 nm for Al, 13 nm for Mn, and 20 nm for S. All these dffuson dstances are sgnfcantly larger than the spatal extent of the zone of nterfacal segregaton of 1 2 nm, and, consequently, solute dffuson n the matrx s suffcent to establsh at the least local metastable equlbrum, and thus the solute enrchment at the precptate nterfaces s not domnated by a dffuson-lmted ple-up effect n front of the movng nterface of a growng precptate. A thermodynamc drvng force must therefore exst for the observed nterfacal segregaton. For a dscusson of a potental elastc nteracton between solute atoms and the a-fe matrx/precptate nterface, we frst estmate the lnear lattce parameter msft, e, between the a-fe matrx and the bcc Cu-rch precptates. The lattce parameter for bcc a-fe at room temperature s a 0 = nm [49], and, wth the thermal expanson data gven by [50], a 0 = nm at 0 K and a 0 = nm at 490 C. For bcc Cu or Cu-rch bcc Cu Fe sold solutons there s, however, to our knowledge no drectly expermentally measured lattce parameter avalable. Lattce parameter measurements of mechancally alloyed Cu Fe alloys [51] suggest a postve devaton from VegardÕs rule, wth a smlar atomc volume for both fcc and bcc sold solutons. The lattce parameter values gven n [51] result n a lattce parameter msmatch of 0.6% between bcc a-fe and bcc Cu 33 at.% Fe. A lattce parameter a 0 equal to nm has recently been calculated for bcc Cu 33 at.% Fe usng cluster-expanson generalzedgradent approxmaton densty-functonal theory calculatons [52], resultng n e = 0.85%, at 0 K. An earler molecular dynamcs smulaton [53], employng emprcal potentals, calculated a value of a 0 equal to nm for pure bcc Cu at 0 K, equvalent to the comparatvely large value of e = 3.2%. Better potentals, however, result n smaller values, a 0 = nm or a 0 = nm, correspondng to e = 0.9 or 0.7% [53 55], respectvely, at 0 K. Assumng that the thermal expanson coeffcent of bcc Cu, whch s not known, s not very dfferent from bcc a- Fe, then e s less than about 1% at all temperatures consdered. Values of e smaller than 1% are also n agreement wth estmates of the bcc Cu lattce parameter from fcc Cu (a 0 = at room temperature) by smple geometrc consderatons: Frstly, e = 0.3% results by equatng the atomc volumes of bcc and fcc Cu. Secondly, e = 0.1% results by calculatng the next-neghbor dstance and takng nto account, followng Goldschmdt [56], a 3% contracton for a reducton of the number of next-neghbor atoms from 12 to 8. Thus, snce the lnear lattce parameter msmatch, e, between bcc a-fe and bcc Cu 33 at.% Fe s about 1% or less and the lnear msmatch of N or Mn solute atoms n a- Fe s only 1.52 or 1.60%, respectvely [57], elastc nteractons cannot account for the nterfacal segregaton, as dscussed n Ref. [58], and very lkely electronc (chemcal) effects come nto play [61]. Eq. (6) s used for calculatng a coeffcent of the reducton n nterfacal free energy or oc T ;p;l3 ;...;l 1 ;l þ1 ;...;l n at a solute concentraton c of component, due to the Gbbsan nterfacal excess of ths solute component. The value for N s 1579 mj m 2 (at.fr.) 1 and for Mn t s 1620 mj m 2 (at.fr.) 1. These values are more than one order of magntude larger than the value of 114 mj m 2 (at.fr.) 1 reported for the segregaton of S at gran boundares at 550 C n an Fe 3 at.% S alloy nvestgated by onedmensonal atom-probe mcroscopy [36], but more than one order of magntude smaller than the value of 100,000 mj m 2 (at.fr.) 1 obtaned for segregaton of Sb to gran boundares n Fe 0.03 at.% Sb at C by Auger spectroscopy [59] and 119,000 mj m 2 (at.fr.) 1 measured for the segregaton of P to the gran boundares of an Fe at.% P alloy employng a technque based on equlbratng the contractle forces of thn fols [60]. Approxmatng the unknown dependence of the nterfacal free energy on solute segregaton by a lnear relatonshp,

8 848 D. Ishem et al. / Acta Materala 54 (2006) a value of the total reducton of the nterfacal free energy due to the gven nterfacal excesses s estmated by multplyng the coeffcent of reducton by the solute concentraton. Wth the values gven, the nterfacal energy of the a- Fe matrx/precptate heterophase nterface s reduced by 16 mj m 2 due to N segregaton, and by 11 mj m 2 due to the segregaton of Mn. The sum of these values (27 mj m 2 ) represents 10% of the nterfacal energy of 270 mj m 2 of bcc Cu precptates n a bnary Fe 1.38 at.% Cu alloy determned from precptaton knetcs [13]. These values for the reducton of nterfacal free energy are comparable wth the 10 mj m 2 reducton measured by APT for Mg segregaton at coherent nterfaces of Al 3 Sc precptates n an Al 2.2 Mg 0.12 Sc at.% alloy [61]. 5. Summary and conclusons 1. APT was utlzed to characterze nanometer-szed Curch precptates wth a metastable bcc structure that formed n the ferrtc a-fe matrx of a recently developed precptaton-hardened hgh-strength low-carbon steel. 2. After drect sothermal agng at 490 C for 100 mn to a near-peak hardness condton of 84 Rockwell G, the precptates have an average dameter of 2.5 ± 0.3 nm at a number densty of (1.1 ± 0.3) m The core regons of the Cu-rch precptates contan 64 ± 1 at.% Cu and 33 ± 1 at.% Fe. Al s enrched n the precptates to 0.5 ± 0.1 at.%, whch mples a parttonng rato of 10 ± 2 wth respect to the ± at.% Al n the a-fe matrx. Nckel and Mn do not partton sgnfcantly; and the precptates are depleted n S. 4. Nckel and Mn are segregated at the a-fe matrx/precptate heterophase nterface wth Gbbsan nterfacal excesses relatve to Fe and Cu of 1.5 ± 0.4 nm 2 and 1.0 ± 0.3 nm 2, respectvely. Alumnum has only a slght tendency toward segregaton, and S s depleted at ths heterophase nterface. 5. A coeffcent of reducton of nterfacal energy s calculated drectly from the relatve nterfacal excesses. The coeffcents are 1579 mj m 2 (at.fr.) 1 for N and 1620 mj m 2 (at.fr.) 1 for Mn. Total reductons of the nterfacal free energy of 16 mj m 2 for N and 11 mj m 2 for Mn are estmated. The sum of these energes s 27 mj m 2, whch amounts to 10% of the nterfacal energy of 270 mj m 2 [13]. Acknowledgements The authors thank Dr. Shrkant P. Bhat, Ispat-Inland Inc., for the provson of the steel used n ths study and the bulk chemcal composton. The atom-probe tomographc experments were performed n the Northwestern Unversty Center for Atom-Probe Tomography (NUC- APT). The nstruments n ths Center were purchased wth funds from the Offce of Naval Research and the Natonal Scence FoundatonÕs nstrumentaton programs. Fnancal support by the Offce of Naval Research, Grant Nos. N and N , Drs. George Yoder and Jule Chrstodoulou, program drectors, s gratefully acknowledged. References [1] Smth CS, Palmer EW. 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