NANOSEGREGATION PHENOMENA AT GRAIN BOUNDARIES OF METALLIC MATERIALS

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1 Acta Metallurgca Slovaca (117-13) 117 NANOSEGREGATON PHENOMENA AT GRAN BOUNDARES OF METALLC MATERALS Leček P. 1 Janovec J. 2 Konečná R. 3 1 nsttute of Physcs Academy of Scences of the Czech Republc Na Slovance Praha Czech Republc 2 Slovak Unversty of Technology Faculty of Materal Scence and Technology Dept. of Materal Engneerng Bottova Trnava Slovaka 3 Unversty of Žlna Faculty of Mechancal Engneerng Department of Materals Engneerng Unverztná Žlna Slovaka e-mal: pavel.lecek@fzu.cz ozef.anovec@stuba.sk radomla.konecna@fstro.utc.sk NANOSEGREGAČNÍ JEVY NA HRANCÍCH ZRN KOVOVÝCH MATERÁLŮ Leček P. 1 Janovec J. 2 Konečná R. 3 1 Fyzkální ústav Akademe věd České republky Na Slovance Praha ČR 2 Slovenská techncká unverzta Materálovotechnologcká fakulta Katedra materálového nžnerstva Bottova Trnava Slovensko 3 Žlnská unverzta Stronícka fakulta Katedra materálového nžnerstva Unverztná Žlna Slovensko e-mal: pavel.lecek@fzu.cz ozef.anovec@stuba.sk radomla.konecna@fstro.utc.sk Abstrakt Hrance zrn značně ovlvňuí vlastnost polykrystalckých materálů používaných pro techncké aplkace. Tento vlv e důsledkem rozdílné energe hranc zrn a obemu a následně důsledkem nterakce hranc zrn s ostatním porucham krystalové struktury např. bodovým porucham č dslokacem vedoucí k podstatnému snížení celkové Gbbsovy volné energe systému. Zeména eden typ takové nterakce nterakce hranc zrn s atomy příměsí (nanosegregace na hrancích zrn) e velce významný neboť díky úzkému vztahu nanosegregace a nterkrystalcké koheze výrazně ovlvňuí mechancké chování materálů. Pro zlepšení mechanckých vlastností techncky využívaných materálů navrhl Tadao Watanabe v osmdesátých letech mnulého století koncepc nženýrství hranc zrn která spočívá v produkc polykrystalckých materálů s optmálním vlastnostm řízením charakteru a dstrbuce hranc zrn. Pro tuto moderní koncepc e však nezbytně nutná znalost co nevětšího rozsahu vlastností šrokého spektra hranc zrn. Jednou z nedůležtěších vlastností které ovlvňuí chování polykrystalckých materálů a která tak nutně musí být brána v úvahu v koncepc nženýrství hranc zrn e nanosegregace příměsí na hrancích zrn. Chemcké složení ednotlvých hranc zrn může být určeno buď expermentálně pomocí nerůzněších technk analýzy povrchů (např. AES ESCA SMS) nebo smulováno metodam teoretckého modelování ako sou Monte Carlo nebo molekulární dynamka. Oba tyto přístupy však maí vážná omezení která nedovoluí získání potřebných údaů pro rozsáhlé spektrum příměsí hranc zrn. Proto e akákol předpověď takových dat velce perspektvní a žádoucí. Detalní analýza vlvu rozpustnost příměsí v pevném stavu na Gbbsovu volnou energ segregace příměsí na hrancích zrn vedla k formulac dvou vztahů. Prvním e tzv. dagram segregace příměsí na hrancích zrn [ ln ( T )] H ( ) H ( J 1) + vr T

2 Acta Metallurgca Slovaca (117-13) 118 vztahuící standardní molární entalp segregace příměs na hrancích zrn H k údaům o rozpustnost příměs v pevném stavu T ln (T ) a odrážeící ansotrop segregace příměsí na hrancích zrn H ( 1). Druhá závslost tzv kompenzační ev mez entalpí a entropí ukazue úzký vztah mez standardní molární entalpí H a standardní molární entropí S segregace příměs na hrancích zrn S H +. p Tc Na základě těchto dvou vztahů lze předpovědět segregac lbovolné příměs na lbovolné hranc zrn v α-železe. Tato předpověď která poskytue podstatné rozšíření databáze o segregac příměsí na hrancích zrn e testována porovnáním výsledků expermentálního měření segregace na hrancích zrn v polykrystalckých materálech bnárních pseudobnárních a mnohosložkových systémů. Jeí perspektva e rovněž ukázána na příkladu předpověd chemckého složení hranc zrn ve dvou techncky používaných materálech: nízkolegované fertcké ocel a fertcké fáz ltny s kulčkovým graftem. Díky zcela obecnému odvození výše uvedených vztahů může být naše metoda predkce snadno rozšířena na různé základní materály a různá rozhraní např. volné povrchy č fázová rozhraní. Abstract Gran boundares strongly nfluence the propertes of polycrystallne materals whch are used for practcal applcatons. Ths effect orgnates from the energy dfference between the nternal nterfaces and the crystal volume and consequently from an nteracton of the gran boundares wth other lattce defects such as pont defects and dslocatons resultng n substantal reducton of the total Gbbs free energy of the system. One representatve of such nteracton the nteracton wth the solute atoms (nanosegregaton at the gran boundares) s of hgh mportance because t predomnantly affects the ntergranular coheson and n consequence the mechancal behavor of the materals. To mprove the mechancal propertes of the techncally used materals the concept of Gran Boundary Engneerng was proposed n 198s by Tadao Watanabe to produce the polycrystals wth optmum propertes by controllng the gran boundary character dstrbuton. For ths purpose the knowledge of the broad spectrum of propertes of the broad spectrum of gran boundares s needed. One of the most mportant propertes whch affects the behavor of polycrystallne materals and whch has thus be consdered n the Gran Boundary Engneerng concept s the nanosegregaton of the solutes at the gran boundares. The chemcal composton of ndvdual gran boundares can be ether measured expermentally usng varous technques of surface analyss (for example AES ESCA and SMS) or smulated by the methods of theoretcal modelng (for example Monte Carlo and molecular dynamcs). Both these approaches however have serous lmtatons whch do not allow provdng us wth the data for a broad spectrum of the solutes and for a broad spectrum of the gran boundares. Therefore any predcton of such data seems to be very prospectve and desrable. A detal analyss of the effect of the sold solublty on varatons of the Gbbs free energy of nterfacal segregaton resulted n formulaton of two smple expressons. One of them s the so-called gran boundary segregaton dagram [ ln ( T )] H ( ) H ( J 1) + vr T relatng the standard molar enthalpy of solute segregaton H to the sold solublty data T ln (T ) and reflectng ansotropy of gran boundary segregaton H ( 1). The other

3 Acta Metallurgca Slovaca (117-13) 119 expresson so-called the enthalpy-entropy compensaton effect shows a close relatonshp between the standard molar enthalpy H and the standard molar entropy S of gran boundary segregaton S H +. p Tc Based on the above two relatonshps the segregaton of any solute at any gran boundary of α-ron can be predcted. Ths predcton whch offers a substantal extenson of the database on gran boundary segregaton s tested by comparng wth the lterature data on expermental measurement of gran boundary segregaton n polycrystallne materals of bnary pseudobnary or multcomponent systems. n addton the potency of the predcton method s shown to dsplay chemcal composton of the gran boundares n two techncally used materals the low-alloy ferrte steel and the ferrte phase of the nodular cast ron. Due to the generalty of the dervaton of the above relatonshps the proposed predcton method can be smply extended to dfferent matrces and types of the nterfaces (free surfaces phase nterfaces). Keywords: segregaton gran boundares predcton thermodynamcs ferrte alloys ntroducton Structural defects nfluence the propertes of materals. For example nteracton between dslocatons and fne precptates durng formng and thermomechancal treatment gve rse to strengthenng of metals and alloys. One of the most mportant classes of defects affectng the mcrostructure of polycrystals are nternal nterfaces and especally gran boundares separatng adacent grans. The bonds between ndvdual atoms n the gran boundary are altered as compared to the bulk crystal [1]. Gran boundares thus possess hgher energy and consequently dfferent propertes than the crystal nteror. Snce the gran boundares n polycrystals create a three-dmensonal web spread throughout the materal and thus represent a self-standng lnk n materal structure wth dfferent mechancal electrc and magnetc propertes they substantally contrbute to the behavour of the materal. Let us emphasse that the propertes of gran boundares are usually worse than those of the crystal nteror. t sgnfcantly lmts possbltes for practcal applcatons of polycrystallne materals. Moreover the gran boundares show the tendency to reduce the total energy of the system by nteracton wth other lattce defects such as solute atoms. t results n accumulaton (segregaton) of the solute atoms at the gran boundares to such extent that the nterfaces compared to the bulk may become qualtatvely dfferent n chemcal nature. Chemcal changes at the gran boundares may nduce degradaton processes n the alloys e.g. ntergranular embrttlement [2]. Gran boundary segregaton s a very mportant phenomenon whch affects the behavour of polycrystals to a large extent. Ths phenomenon covers all concentraton changes at a gran boundary supposng the character of a sold soluton s preserved [2]. t s worth notng that the lmt of solublty of a solute n a basc materal (matrx) may dffer at gran boundares and n bulk crystal [3]. f partcles of another phase appear at the gran boundares one must call t gran boundary precptaton. Gran boundary precptaton s contnuaton of gran boundary segregaton ndeed because new partcles grow at the nterface due to supersaturaton of the sold soluton at the gran boundary [4].

4 Acta Metallurgca Slovaca (117-13) 12 Fg.1 Schematc depcton of ndvdual classes of segregaton. (1) and (2) represent the concentratons of ndvdual compared regons L represents the length scale of the effect. Macro- and mcrosegregaton are connected wth the lquaton effects whle nanosegregaton represents the gran boundary segregaton Let us menton that the term segregaton s used n metallurgy to descrbe a wde range of phenomena. We can meet ths term often n relaton to soldfcaton processes. Durng soldfcaton of a molten alloy concentraton dfferences occur n the cast due to the lquaton. The lquaton effects can embrace areas of meter scale n the cast and of mcrometer scales between dendrtes and nterdendrte space. The former effect s referred to as macrosegregaton the latter effect to as mcrosegregaton [5]. n contrast the gran boundary segregaton concerns one or several atomc layers and s controlled by gran boundary energy. Thus t may be ultmately lmted to nanometer scale. On the other hand t can exhbt much larger concentraton dfferences than macro- or mcrosegregatons (Fg. 1). From the pont of vew of the above scale-based classfcaton the gran boundary segregaton can be called nanosegregaton. Thermodynamcs of equlbrum gran boundary segregaton As mentoned above the gran boundary segregaton s thermodynamcally favourable process whch leads to accumulaton of solute atoms at the gran boundary. The term equlbrum gran boundary segregaton s used to denote the very local redstrbuton of solutes at gran boundares caused by mnmsaton of the total Gbbs free energy of the system. t s supposed that chemcal potentals µ of all speces nvolved n sold soluton are constant throughout the system. At equlbrum there s parttonng whch results n gran boundary enrchment by surface-actve speces. The level of the enrchment s defned by the system parameters at equlbrum only and not by the alloy hstory and can be reproduced by reestablshng the dentcal physcochemcal condtons. A detal thermodynamc analyss [67] shows that the gran boundary segregaton can be descrbed as exchange of solute and matrx M elements between gran boundary and bulk B B + M + M B (1) The basc condton for equlbrum between the gran boundary and bulk s

5 Acta Metallurgca Slovaca (117-13) 121 µ + (2) B B + µ M µ µ M for each component ( M). Acceptng the general expresson for chemcal potentals µ µ + RT ln a where a s the actvty of the element n a sold soluton [8] we can wrte a M a B B M a a G exp (3) RT n eq. (3) the standard molar Gbbs free energy of segregaton G B B ( µ ) ( µ M µ M ) H T S µ (4) s defned as combnaton of the standard chemcal potentals of the pure elements and M at the gran boundary and n the bulk µ and µ B respectvely at the temperature and pressure of the system. H and S are the standard molar enthalpy and entropy of segregaton of solute at the gran boundary n matrx M. The chemcal potentals referrng to the gran boundary µ ntrnscally nvolve the contrbuton of the gran boundary energy [67] µ ξ A (5) where A s the partal molar area of speces at the gran boundary and ξ s the partal molar Helmholz free energy of speces n the nterface n the standard state. Snce generally a γ where γ s the actvty coeffcent of element [8] we can M 1 rewrte eq. (3) usng 1 as M J 1 J 1 M 1 M E G + G exp RT (6) n eq. (6) γ γ B E M G RT ln (7) B γ M γ s the excess molar Gbbs free energy of segregaton. Eq. (6) represents the general thermodynamc form of the segregaton sotherm. Snce the values of the actvty coeffcents n eq. (7) are not known G E s presently correlated accordng to models whch are based on sememprcal approaches. The smplest approach supposng deal behavour of all components n the system (.e. G E ) s called Langmur McLean segregaton sotherm [9]. t can be expressed for a bnary system as 1 1 G exp RT (8) Regular sold soluton model results n Fowler sotherm (n case of a bnary system) and n Guttmann sotherm (for multcomponent systems) [2479].

6 Acta Metallurgca Slovaca (117-13) 122 Effect of nterfacal energy on gran boundary segregaton There are many examples of expermental as well as theoretcal evdence of the effect of varous thermodynamc and structural varables (pressure magnetc feld gran boundary structure character of both solute and matrx elements) on gran boundary segregaton [9]. t s apparent from eqs. (4) and (6) that the nfluence of ndvdual parameters on gran boundary segregaton s prmarly nvolved n varatons of the values of G and consequently of the values of H and S. Addtonally temperature affects the values of the exponental term n eq. (6). The effect of bulk concentraton on gran boundary segregaton s also evdent from eq. (6). All above-mentoned effects as well as gran boundary composton contrbute to varatons of the values of G E n real systems. Let us now dscuss one of these effects the effect of the gran boundary energy. The varatons of the standard molar Gbbs free energy of segregaton G can be expressed by ts total dfferental d G G T P Ω G dt + P T Ω dp + G Ω (9) T P Ω n eq. (9) Ω are the ntensve varables of the system such as magnetc feld and gran boundary energy [1]. t s apparent that ( G / P) TΩ V ( V s the standard molar segregaton volume of solute ) and ( G / T) PΩ S [8]. n agreement wth eq. (4) the total dfferentals of the standard molar enthalpy and entropy of segregaton can be expressed analogously dω d H H Ω and T P Ω dω d S S Ω (1) T P Ω dω The changes n the gran boundary energy affect the values of the chemcal potentals of the solute and matrx element at the gran boundary (cf. eq. (5)) and thus the standard molar Gbbs free energy of segregaton. The changes of the gran boundary energy may be of dfferent nature but prncpally changes due to () gran boundary structure (ansotropy of gran boundary segregaton) and () nature of segregatng and matrx elements. Structural dependence of gran boundary segregaton can be dsplayed as an orentaton dependence of H [11]. An example of the ansotropy of solute segregaton at gran boundares of α-ron s shown n Fg. 2. On the other hand the dependence of the gran boundary segregaton on the nature of the solute can be represented by the dependence of H on the solublty of the solute n sold matrx * (T) [12] as shown n Fg. 3. n fact ths representaton s smlar to that between the gran boundary enrchment rato and the sold solublty revealed earler by Hondros and Seah [13]. Chemcal potental µ * of the solute n saturated bulk sold soluton s µ + RT ln a µ (11) where a * s the actvty of the solute n the system M at the solublty lmt * (T) [14]. Provdng the saturated bulk sold soluton of n M s consdered as another standard state the segregaton free energy of the solute G * can be expressed as

7 Acta Metallurgca Slovaca (117-13) 123 G ( µ B ) ( µ M µ B M ) G RT ln a µ (12) t can be smply shown that S [ T a ] ln S R (13) T P As the product on the rght-hand sde of eq. (13) T lna * G sol /R was proved to be nearly ndependent of temperature for varous systems [1314] the term n brackets of eq. (13) s neglgble. Consequently both entropy terms n eq. (13) are equal. Eq. (12) can be then rewrtten as H (14) H + RT ln a The plot of numerous pars of the values of actvtes and correspondng concentratons at the sold solublty level n varous systems found n [15] revealed a smple power relatonshp between these two values for dfferent systems and temperatures [14] a ) v ( (15) where the parameter v depends on matrx element M albet not on the nature of the solute element [14]. A combnaton of eqs. (14) and (15) provdes us wth [14] [ ln ( T )] H ( ) H ( J 1) + vr T (16) Eq. (16) represents a very mportant relatonshp between the standard molar enthalpy of segregaton of a solute element wth sold solublty * (at a temperature T ) and the product of logarthm of sold solublty and correspondng temperature. Let us emphasse that the product T ln * (T ) const. and therefore H ( * ) s ndependent of temperature. As was dscussed above H depends on the gran boundary structure. Ths dependence s ncluded n H J * () representng the standard molar enthalpy of segregaton of a solute wth unlmted sold solublty J * 1. t s apparent that the structural term H * () s ndependent of sold solublty and the solublty term vr[t ln * (T )] does not depend on gran boundary energy [14]. Ths concluson can be well seen from the plot of H vs. msorentaton angle θ and vs. [T ln * (T )] so-called gran boundary segregaton dagram [1416] (Fg. 4): the lnes onng the segregaton enthalpy of ndvdual solute elements at correspondng gran boundares are parallel. Eq. (16) and the gran boundary segregaton dagram represent an extenson of the model of Hondros and Seah [13] by consderng segregaton ansotropy ( H f()) and nondeal behavour of the sold solutons at solublty lmt (ν 1) [14]. n sense of eq. (1) we can wrte d H H T P Ω H d + T P Ω d (17)

8 Acta Metallurgca Slovaca (117-13) 124 Fg.2 Dependence of enthalpy of segregaton of slcon phosphorus and carbon on msorentaton angle of [1] symmetrcal gran boundares [11] Fg.3 Dependence of enthalpy of segregaton of varous solutes at general gran boundares on sold solublty data of α- ron. Full lne depcts the predcton (cf. eq. (16)); the scatter of ±5 kj/mol from the predcton s marked by the dashed lnes [12] where and reflect the changes of the gran boundary energy caused by changes n structure and nature of the solute respectvely. The total dfferental of the segregaton entropy can be expressed analogously. Evdently ranges of the values of and must exst for that a constant temperature T c s defned as [17] P T P T P T P T c S S H H S H T d d d d d d Ω Ω Ω Ω + + (18).e.

9 Acta Metallurgca Slovaca (117-13) 125 T d S d H (19) c Fg.4 Gran boundary segregaton dagram for [1] symmetrcal tlt gran boundares n α-ron [14] t follows from eqs. (4) (18) and (19) that d ( ) G G Tc P Ω d G + P Ω d (2) ntegraton of eq. (19) provdes H T c ( S + S ) and thus H G ( T ) c S (21) Tc Tc Therefore G (T c ) T c S whch s constant accordng to eq. (2).e. ndependent of any change of the gran boundary energy at T c. Eq. (18) represents the compensaton effect suggestng that the change of the standard molar enthalpy of segregaton d H caused by the change of the gran boundary energy s compensated by the correspondng change of the standard molar entropy of segregaton d S n a lnear way despte of the nature of the changes of the gran boundary energy. T c s the compensaton temperature [17]. S G (T c )/T c s the negatve confguraton entropy at T c [18] and s ndependent ether of the gran boundary structure or the nature of the segregated solute. Let us menton that the compensaton effect s completely general and holds for all consdered varables Ω n sense of eqs. (9) and (1) [17]. t s also worth notng that condton (2) does not represent an equlbrum condton and thus no transformaton can generally occur at T c. The compensaton effect for gran boundary segregaton n α-ron s shown n Fg. 5. t s seen that there exst two branches of the dependence S vs. H. t s because the compensaton effect may exst for the process only the nature and mechansm of whch reman the same when a varable changes. However the segregaton occurs ether on substtuton or at ntersttal postons representng dfferent mechansms. n Fg. 5 the upper and lower lnes

10 Acta Metallurgca Slovaca (117-13) 126 correspond to segregaton at ntersttal and substtuton postons respectvely but possess the same slope. t means that the compensaton temperature s ndependent of the mechansm of the segregaton (T c 93 K). Therefore we may well accept that T c s a characterstc parameter of the matrx element. S s dfferent for both branches ndeed [17]. Fg.5 Compensaton effect for segregaton n α-ron. Full symbols data for segregaton of carbon (squares) phosphorus (trangles) and slcon (crcles) at ndvdual gran boundares [11]. Empty symbols data from lterature measured for solute segregaton n polycrystallne α-ron [12] Let us notce that the above-demonstrated thermodynamc dervaton of the compensaton effect was performed generally and can be appled to any thermodynamc process or equlbrum state that s charactersed by changes of the Gbbs free energy despte of ts meanng as characterstc equlbrum change or actvaton energy. Ths s documented by observng the compensaton effect not only n varous nterfacal processes and states (e.g. gran boundary dffuson mgraton segregaton) but also n many felds of physcs chemstry bology medcne etc. [17]. Predcton of gran boundary segregaton Thermodynamc consderatons resultng n eqs. (16) and (21) were already used for predcton of gran boundary segregaton [1219]. For ths predcton few parameters are needed only: H * () v T c and S. The value of S reflects the mechansm of gran boundary segregaton (at substtuton and ntersttal stes). For gran boundary segregaton n α-ron these parameters are lsted n Table 1. A knowledge of the solublty of the solute n the M sold soluton * (T ) s only necessary to determne the values of H () and S (). Consequently the values of G () and gran boundary concentratons (accordng to eq. (8)) for any element at any gran boundary at any temperature for any bulk concentraton (supposng the condtons necessary for dervaton of eq. (8) are fulflled) can be determned. The predcted values of H and S for selected elements are gven n Table 2. The agreement between the predcted values of H and S for Al Cr N P Sb and Sn segregaton n α-ron and those found n lterature s surprsngly good as can also be seen from Fg. 5. n addton the predcted concentratons of boron (5.4at.%B at 673 K) and sulphur (8.6at.%S at 823 K) at general gran

11 Acta Metallurgca Slovaca (117-13) 127 boundares n respectve bnary systems wth α-ron are also n excellent agreement wth the expermental data found for polycrystallne alloys (4at.%B and 6at.%S at correspondng temperatures) [1219]. Table 1 Parameters needed for predcton of gran boundary segregaton (eqs. (16) and (21)) n α-ron [1219]. The parameters were determned from the measurements of slcon phosphorus and carbon segregaton at ndvdual gran boundares n α-ron [911] H * () General gran boundares 8 to 4.77 Vcnal gran boundares 2 to Specal gran boundares +5 to v S (J/(mol.K)) Substtuton segregaton ntersttal segregaton T c (K) Table 2 Selecton of predcted values of the enthalpy and entropy of segregaton of varous solutes at ndvdual gran boundares n α-ron (S substtuton ntersttal) [1219]. The data on sold solublty of the solute elements n α-ron were taken from [2] solute solublty [2] T (K) ste {13} (specal) H +6 kj/mol H (kj/mol) / S (J/(mol.K)) (1)/(34) (vcnal) H +2 kj/mol 45 [1] (general) H 6 kj/mol Al S 1 / +4 5 / 1 13 / 9 As / / / +31 B / 2 73 / / 33 C / / / +2 Co S / +5 / +5 8 / 4 Cr S 1 / +4 5 / 13 / 9 Cu S 23 / 2 27 / / 33 H / 1 57 / 5 65 / 14 Mg S 53 / / / 65 Mn S 14 / 1 18 / / 23 Mo S 16 / 12 2 / / 25 N / / / +17 Nb S 33 / / / 44 N S 8 / 4 12 / 8 2 / 16 O / / / 46 P / / / +22 S / 4 6 / 8 68 / 17 Sb / / / +24 S S 4 / +1 8 / 4 16 / 12 Sn / / / +3 T S 2 / / / 29 V S 4 / 8 / 4 16 / 13 W S 23 / 2 27 / / 33

12 Acta Metallurgca Slovaca (117-13) 128 Let us now apply ths predcton to complex α-ron based systems such as low-alloy ferrte steel and ferrte phase of nodular cast ron where ntergranular decoheson may also occur (Fg. 6). Although the nomnal compostons of these systems s well known t s necessary to fnd the real concentratons of ndvdual solutes dssolved n ferrte matrx of partcular materal at a chosen temperature. t s well known that a part of the solute atoms s usually bound n precptates and thus they do not partcpate n segregaton equlbrum. An estmate of the ferrte composton n partcular alloys may be calculated for example usng the THERMO-CALC program [2122]. n Tables 3 and 4 related to the chosen steel and nodular cast ron respectvely the bulk content of solute elements are compared to ther concentratons n ferrte. n case of the steel (Table 3) we compared predcted values of gran boundary concentraton ( P ) wth the expermental values ( E ) measured after equlbrum annealng at 853 K. The data n brackets are too low to be detected by Auger electron spectroscopy on ntergranular fracture surfaces (AES). Carbon was not consdered n determnaton of gran boundary composton (N) because ts segregated porton s hardly dstngushable from that present n carbdes as well as from that contamnated at the fracture surface durng measurements. The value of E P s n excellent agreement wth the value of P P but the predcted and expermental data for chromum dffer substantally. Ths dfference may orgn n the estmate of chromum concentraton n bulk sold soluton and/or n the quantfcaton procedure of AES. The predcted concentratons of molybdenum and vanadum are low and correspondngly they were not detected by AES. The concentratons of slcon and manganese are prncpally measurable by AES however the peaks of both elements are very close to those of ron and therefore t s complcated to dstngush them for such low concentratons. Gran boundary concentraton of carbon s under the detecton lmt of AES that ustfes neglectng the measured peaks of carbon that orgnated manly from the precptates and contamnaton effects. n any case t s remarkable that the method predcts (qualtatvely at least) segregaton of all solutes that was also measured expermentally. Nevertheless for complete predcton t s necessary to take nto account mutual nteracton between solute elements as to correlate the value of G E (eq. (6)). Untl now however there s no avalable way to predct these values. Table 3 Comparson of predcted and expermental data for a low-alloy steel. W nomnal bulk concentratons; sol calculated solute concentratons n ferrte at 853 K; E expermental values of gran boundary concentratons n polycrystals at 853 K; P solute concentratons at a general gran boundary at 853 K predcted for deal multcomponent Fe system. The data n bold may be compared [12] steel Cr Mo V S P C Mn S Ref. W (mass.%) [23] sol (at.%) E (at.%) N [1223] P (at.%) 2.7 (.3) (.6) (.7) 1.3 Table 4 Comparson of expermental data for nodular cast ron D1248 wth the predcted ones for 173 K. For meanng of symbols see Table 3 cast ron D1248 C Mn S P S Cr Mg Ref. W (mass.%) [24] sol (at.%) E (at.%) [24] P (at.%) 14 (.1) (.2) (.1)

13 Acta Metallurgca Slovaca (117-13) 129 Gran boundary composton of ferrte phase n nodular cast ron D1248 was treated smlarly (Table 4). As n case of the steel sulphur s supposed to be completely precptated n MnS and not partcpatng n segregaton. n contrast to the steel the amount of carbon dssolved n ferrte s hgh enough to take ts segregaton nto account. Addtonally the data of E P n Table 4 were measured at gran boundares of a slowly cooled materal that was not tempered for segregaton. t means that the segregaton state at the boundary was not developed durng changed temperatures and therefore these data cannot be ascrbed to a specfc temperature. As t s seen from Table 4 the values of P and E are n good qualtatve agreement: Gran boundary segregaton at 173 K was predcted for all solutes the segregaton of whch was found expermentally.e. for phosphorus slcon and carbon. The predcted nterfacal concentratons of manganese chromum and magnesum are low and correspondngly they were not detected by AES. One can expect that n equlbrum the concentraton of carbon and phosphorus should be hgher and that of slcon lower than the measured values of E. Due to domnant repulsve S P nteracton the content of slcon should be substantally suppressed. Nevertheless elements as slcon carbon and phosphorus wll appear at gran boundares n equlbrum whereas the other solutes present n the cast ron wll not reach measurable concentratons at the gran boundares [9]. Fg.6 SEM mcrograph taken n vcnty of a globular graphte partcle showng ntergranular decoheson n ferrte fractured prevalngly by cleavage. The arrow ndcates the ntergranular facet Conclusons Thermodynamc analyss of the effect of nterfacal energy on gran boundary segregaton revealed novel relatonshps between thermodynamc parameters of gran boundary segregaton. The dependence of the standard molar enthalpy of segregaton on both the solute sold solublty and the gran boundary structure resulted n constructon of the gran boundary segregaton dagram and n refnement of the earler model of Hondros and Seah. t was also shown that all thermodynamc parameters of gran boundary segregaton change wth changng the nterfacal energy evoked by changes of both the gran boundary structure and the nature of segregated element. The dependence of enthalpy and entropy of gran boundary segregaton on nterfacal energy can be represented by the compensaton effect. Both relatonshps the gran boundary segregaton dagram and the compensaton effect were successfully used to predct gran boundary segregaton of any element at any gran boundary n bnary systems and n complex systems such as steels and cast rons as well.

14 Acta Metallurgca Slovaca (117-13) 13 Acknowledgement Ths work was supported by the grants of the Czech Scence Foundaton (22/6/4) and of the Czech Slovak blateral co-operaton (37/26). The authors are grateful to Dr. Aleš Kroupa of PM AS CR for provdng assstance wth calculatons usng THERMO-CALC program. Lterature [1] Sutton A.P. Balluff R.W.: nterfaces n Crystallne Materals (Clarendon Oxford 1995). [2] Hondros E.D. Seah M.P. Hofmann S. Leček P: nterfacal and surface mcrochemstry. n: Physcal Metallurgy 4 th ed ed. by R.W. Cahn P. Haasen (North Holland Amsterdam 1996) pp [3] Chang L.S. Rabkn E. Straumal B.B. Hofmann S. Baretzky B. Gust W.: Def. Dff. Forum (1998). [4] Janovec J.: Nature of Alloy Steel ntergranular Embrttlement (Veda Bratslava 1999). [5] Blon H. Boetnger W.J.: Soldfcaton. n: Physcal Metallurgy 4 th ed. ed. by R.W. Cahn P. Haasen (North Holland Amsterdam 1996) pp [6] duplesss J. van Wyk G.N.: J. Phys. Chem. Solds and 1451 (1988). [7] duplesss J.: Sold State Phenom (199). [8] Gaskell D.R.: Metallurgcal thermodynamcs. n: Physcal Metallurgy 4 th ed. ed. by R.W. Cahn P. Haasen (North-Holland Amsterdam 1996). pp [9] Leček P. Hofmann S.: Crt. Rev. Mater. Sc. Sol. State 2 1 (1995). [1] Leček P.: Z. Metallkde (25). [11] Leček P. Hofmann S. Padar V.: Acta Mater (23). [12] Leček P. Hofmann S. Janovec J.: Mater. Sc. Eng. A n press. [13] Hondros E.D. Seah M.P.: Metall. Trans. A (1977). [14] Leček P. Hofmann S.: nterface Sc (1993). [15] Selected Values of the Thermodynamc Propertes of Bnary Alloys ed. by R. Hultgren P. Desa D. Hawkns M. Gleser K. Kelley (ASM Metals Park 1973). [16] Watanabe T. Ktamura S. Karashma S.: Acta Metall (198). [17] Leček P.: Z. Metallkde (25). [18] Rubnovch L. Polak M: Europ. Phys. J. B (21). [19] Leček P. Hofmann S.: Gran boundary segregaton ansotropy and predcton n: Encyclopeda of Materals: Scence and Technology Updates ed. by K. Bunshaw R.W. Cahn M. Flemngs E. Kramer S. Mahaan (Pergamon Amsterdam 22) #2115 pp [2] Kubaschewsk O.: ron Bnary Phase Dagrams (Sprnger Berln 1982); Massalsk T.B.: Bnary Alloy Phase Dagrams (ASM Metals Park 1987); Predel B.: Phase Equlbra of Bnary Alloys (Sprnger Berln 23). [21] Sundman B.: THERMO-CALC verson L (Royal nst. Technol. Stockholm 1997). [22] Kroupa A. Havránková J. Coufalová M. Svoboda M. Vřešťál J.: J. Phase Equl (21). [23] Janovec J. Grman D. Perháčová J. Leček P. Patscheder J. Ševc P.: Surf. nterface Anal (2). [24] Konečná R. Leček P. Ncoletto G. Bartuška P.: Mater. Sc. Tech. n press.