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A n E v a lu a tio n o f t h e F e - N P h a s e D ia g ra m C o n s id e r in gLo ng -Ran ge O rder o f N A tom s in y -Fe4N _ ,, and s -Fe2N _ ,B A R T J . K O O I , M A R C E L A .J . S O M E R S , a n d E R IC J . M I T T E M E I J E RThe chemica l po t en t ia l o f n i t rogen was de sc r ibed a s a func t i on o f n i t rogen con t en t fo r t he Fe -Nphases c~-Fe[N], 7' -Fe4N 1 x, and e-Fe2N ~_z. For c~-Fe[N], an idea l , rand om dist r ibut ion o f the ni t rog enatom s over the oc tah edra l in terst ices of the bcc i ron la t t ice was ass um ed; for y ' -Fe4Nl_x and e-Fe2N~_~, t he occu r rence o f a l ong- range o rde red d i s t r ibu t i on o f t he n i t rogen a toms ove r t he oc t ahedra linterst ices of the c lose packed i ron subla t t ices ( fcc and hcp, respect ive ly) was taken into account .The t heore t ic a l expre ss ions we re f i tt ed to n i t rogen-absorp t i on i so the rm da t a fo r t he t h ree F e -N phase s .T h e a / o t + y ' , o~ + y ' / y ' , y ' / y ' + e , and y ' + e / e phase bounda r i e s in the Fe -N phase d i ag ramwere ca l cu l a t ed f rom com bin ing t he q uan t i ta t i ve de sc rip t ions fo r t he absorp t i on i so the rms wi th t heknow n compo s i t i on o f NH3/H 2 ga s m ix tu re s i n equ i l i b r ium wi th coex i s t i ng c~ and y ' phase s and i nequ i l i b r i um wi th coex i s t i ng y ' and e phase s . Compar i son o f t he p re sen t phase bounda r i e s wi thexpe r imen ta l da t a and p rev ious ly ca l cu l a ted phase bounda r i e s showed a m a jo r improvem ent a s com-pa red t o t he p rev ious ly ca l cu l a t ed Fe -N phase d i ag rams , whe re l ong- range o rde r fo r t he n i t rogena toms in t he y ' and e phase s was no t a ccoun ted fo r .

I. I N T R O D U C T I O NTHEFe-N phase d i ag ram prov ides i n fo rma t ion e ssen t ia lfor the prac t ice of ni t r iding i ron and low-carbon stee ls . IUTo unde rs t and t he ( i n ) s t ab il i ty o f t he Fe -N p hase s , an ap -p ropr i a te m ode l fo r t he t he rmody nam ics o f t he se phase s i sr equ ired . Pre fe rab ly , such mo de l s fo r so l i d phase s a re ba sedon the c rys t a l la t t ic e o f t he phase conce rned .Fe -N so l i d so lu t ions can be conce ived a s com posed o f twointerpenetrating sublatt ices: the sublatt ice for the Fe atomsand the su bla t tice for the N a toms. The Fe subla t t ice can beconsidered to be ful ly occupied by Fe a toms. The N subla t -t ice , const i tuted by the o c tahedra l in terst ices of the Fe sub-la t t ice , i s par t ly occupied by N a toms and par t ly occupiedby vacancies V. In o~-Fe[N] (bcc Fe subla t t ice) and a lso inT-Fe[N] (fcc Fe sublatt ice), the nitrogen atoms are distrib-u t ed more o r l e ss r andomly ove r t he s i t e s o f t he i r ownsublattice. [z,3] In y'-Fe4N~ , (fcc sublattice) an d in e-Fe2N~_z(hcp Fe subla tt ice), the ni t rogen a tom s show long-range or-der (LRO) on the i r own subla t t ice . [~t~Recen t ly , mode l de sc rip t ions fo r t he t he rmodynam ics o fthe T ' -Fe4Nt_x and e-Fe2N~_~ phases were presented takinginto account the LRO of the ni t rogen a toms on the i r subla t -r ice . The behavior of the ni t rogen-absorpt ion i sotherms, de-pic t ing the dep endence o f the ch emical potent ia l of ni trogenon ni t rogen content , was descr ibed suc cessful ly a t severalt empe ra tu re s by us ing t he Gorsky-Bragg-W i l l i ams (GBW )approxim at ion for both y ' -ni t r ide and s Fromthe descr ipt ion of the ni t rogen-absorpt ion i sotherms of thevar ious Fe-N phases, the corresponding phase boundaries inthe Fe-N phase diagram can be ca lcula ted st ra ight forwardly

BAR T J. KOOI, form erly Graduate Student, Laboratory of Materia lsScience, Delft Unive rsity of Tech nology , is Postdoctoral S tudent,Materia ls Science Cent re , Department of Appl ied Physics , Universi ty ofGroningen, NL-9747 A W Groninge n, The Netherlands. MARCEL A.LSOMERS, Assis tan t Professor, and ERIC J . MITT EM EIJER , Professor,are wi th the Laboratory of Materia ls Science, Del ft Universi ty ofTechnology, NL-2628 AL Delft , The Netherlands.Manuscrip t submit ted June 14 , 1995.

by equa t ing t he chemica l po ten t ia l s o f n i t rogen and o f i ronfor the phases coexist ing in equil ibr ium. For this ca lcula t ion,knowledge i s requi red of ( the di f ferences in) the chemicalpotent ia ls for the standard sta te of both n i t rogen and i ron,/~ (=G ~) and /XFe (=Gve ) , fo r t he phase s conce rned . Da t afor G~ is avai lable f rom References 12 and 13; da ta forG~e are no t k now n. In th e studies p resen ted so far, ~4-z0] val-ues for the di f ference of G~e were evalua ted by f i t t ing ex-pressions obta ined for the equal chemical potent ia ls of i ronin coexist ing phases to exper imenta l composi t ion- tempera-ture da ta for the phase boundary concerned.W i thou t r e course t o expe r imen ta l phase -bounda ry da t a ,in the presen t work, the ni t rog en par t ia l pressures per ta iningto equ i l i b r ium o f ammo nia /hydro gen mix tu re s wi th coex-ist ing a and 3" phases and wi th coexist ing Y' and e phaseswere used to ca lcula te the a / a + y ' , a + "Y '/T', Y '/7 ' + E:,and y ' + e / e phase bounda r i e s i n t he Fe -N phase d i ag ramfrom the expre ss ions fo r t he n i t rogen-absorp ti on i so the rms .The re su l t s we re co mpared wi th ex i s t i ng expe r imen ta l da t afo r t he se phase bounda r i e s and wi th t he p rev ious eva lua -t i ons o f the F e -N phase d i ag ram.

I I . C H E M I C A L P O T E N T I A L O F N I T R O G E N I NF E -N P H A S E S ; N I T R O G E N - A B S O R P T I O NI S O T H E R M S

An eq ui l ibr ium sta te of the Fe-N phases T '-Fe4N~_ ande-Fe2N~_, cannot be a t ta ined in contac t wi th pure ni t rogengas a t a tmospheric pressure , because equi l ibr ium par t ia lp re ssu re s o f n i trogen am ount t o seve ra l GPa ' s fo r the i ronn i t r i de s ( a t no rma l t empe ra tu re s : 500 t o 1000 K) . Ammo-n ia /hydrogen ga s m ix tu re s a t a tmosphe r i c p re ssu re a re su i t-ab l e t o i nves t iga t e the t he rm odyn amics o f Fe -N phase s a ta tmosphe r i c p re ssu re because o f t he i r h igh v i r t ua l n i trogenpar t ia l pressure and the wide range of vi r tua l ni t rogen par-t i a l p re ssu re s t ha t c an be r ea l i z ed by va r i a t i on o f t he am-monia con t en t . The re fo re , t he Fe -N phase d i ag rames t ab l i shed f rom da t a fo r Fe -N phase s i n equ i l i b r i um wi thN H 3 / H 2 gas mix tu re s i s no t t he phase d i ag ram of i t s pu re

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c o m p o n e n t s F e a n d N 2 a t atmospher ic pressure~* At at-*In fact, the diagram usually referred to as the ge-N phase diagram isa quasibinary Fe-NH3-H phase diagram or can be interpreted as aprojection o f data of phase diagrams of Fe and N~ at various pressures(corresponding with the N 2 partial pressure of the NHJI-Iz gas mixtureholding for a data point).

mo sp h er ic p r es su r e , Fe - N p h ases w i th an eq u i l ib r iu m n i -t r o g en p a r t i a l p r es su r e h ig h er th an 1 a tmo sp h er e t en d tod eco mp o se in to Fe an d N 2 . Th u s , th e Fe- N p h ase d iag r amo b ta in ed f r o m eq u i l ib r iu m s tu d ies o f Fe - N p h ases w i thN H 3 /H2 g as mix tu r es i s a me tas tab le p h ase d iag r am ( c f th emetas tab le an d s tab le Fe- C p h ase d iag r ams) .T h e c h e m i c a l p o te n t i al o f n i t r o g e n i n a g a s p h a s e , / ~ . ~ ,co n s i s t in g o f an N H JH 2 mix tu r e can b e d e f in ed o n th e b as i so f th e h y p o th e t ica l eq u i l ib r iu m

,.+3 1NH3 ~ ~H2 + $N2w h e r e

1 3/ x s . - - ~ b % = / ~ 3 - ~ / x 2I f th e s tan d ar d s ta tes r e f e r to u n i t p r es su r e an d i f id ea l g aseso r co n s tan t f u g ac i ty co ef f ic ien t s can b e as su med , th e f o l -lo w in g h o ld s :

3/~ = 2 G~2 +1 _1 R T In PN2 = GNH3O_ ~ G n 2 ~ RT In rN [1]w i t h

PNH3rN ~ 3/2PHzw h er e G j r e f e r s to th e G ib b s f r ee en er g y p e r mo le o f j , p jr e f e r s to th e p a r ti a l p r es su r e o f , th e su p er sc r ip t o in d ica testh e s tan d ar d s ta te o f th e co mp o n en t c o n cer n ed , r N i s th e so -ca l led n i t r id in g p o ten t ia l , an d R an d T h av e th e i r u su a lmean in g s . Th e v i r tu a l p a r t i a l p r es su r e o f N : co r r esp o n d in gto an N H 3 /H2 mix tu r e c an b e ca lcu la ted f r o m E q . [ 1] .If equilibrium is attained between an imposed NH3fft--l_~mix tu r e an d an Fe- N p h ase , th e ch emica l p o ten t ia l o f n i -t r o g en in th e so l id Fe- N p h ase s ( =o r , T ' , e ) i s eq u a l to th a ti n t h e g a s p h a s e: / ~ = / . ~ . B y v a ri a t io n o f t h e c o m p o -s i t io n o f th e N H 3 /H z g as mix tu r e a t a ce r ta in t emp er a tu r ean d d e te r min a t io n o f th e eq u i l ib r iu m n i t r o g en co n ten t in th eFe- N p h ase , a n i t r o g en - ab so r p t io n i so th e r m i s o b ta in ed .Th er e b y , th r o u g h E q . [ 1 , th e ch em ica l p o ten t ia l o f n i t ro g eni n a n F e - N p h a s e c a n b e d e t e r m i n e d e x p e r im e n t a l l y a s af u n c t io n o f th e n i t r o g en co n ten t . F i t t in g o f a th eo r e t ica l d e -sc r ip t io n f o r th e c h emica l p o ten t ia l to th e ex p er imen ta l n i -t r o g en - ab so r p t io n i so th e r m d a ta p r o v id es v a lu es f o r th eu n k n o w n p ar amete r s in th i s d esc r ip t io n .A . o t - F e

Fo r n i t r o g en in f e r r i t e , a r eg u la r so lu t io n o f n i t ro g en o ni t s o w n su b la t t ice can b e as su med . Th e n i t r o g en co n ten t o nth e in te r s t it i a l su b la t ti ce i s so lo w th a t ex cess en th a lp y d o e sn o t h av e to b e tak en in to acco u n t . H en ce , th e ch emica lp o t e n ti a l o f n i tr o g e n i n f e r r i t e , / ~ , . , i s

~ , o = G ~ . ~ R T I n 1 - Y N , ~ ]

with YN,~ as the f ract ion o f in ters t i t ia l s i tes occ upie d by Na to ms . Fo r eq u i l ib r iu m w i th an am mo n ia /h y d r o g e n mix tu r e ,equating Eqs. [1] and [2] y ields an express ion for the n i-t r o g en - ab so r p t io n i so th e r m:YN,~ _ r ~ [3]

1 - Y N , ~ r ~ , ~with rN, . def ined as RT In rN, . = G N , , , - - G N H 3 + 3 G H / 2 .I t fo l lows f rom Eq. [3] that r~ ,~ can be in terpreted as then i t r id in g p o ten t ia l in eq u i l ib r iu m w i th f e r r i t e o f th e h y p o -thetical composition Fe2N3(YN,~ = 1 /2; th ree in ters t i t ia l s i tesper Fe s i te in bcc Fe) . S ince YN,~ is very sm all (m axim ally1.339-10 -3 at 863 K{2~I), th e d en o min a to r in Eq . [ 3 ] can b er ep laced b y 1 . F r o m an ev a lu a t io n o f l i t e r a tu r e d a ta , th ef o l lo w in g w as f o u n d f o r th e t emp er a tu r e d ep en d en c e o f th en i t r o g en - ab so r p t io n i so th e r ms o f oe -Fe ( 57 3 K < T < 863K ; see A p p en d ix )

[ 3 , ~ ] 9 0 9 6ln r ~ ,~ = - I n N ,~" = - 1 1.56 + T [ 4]wh ere r N is g iven in Pa - '/2 and T is g ive n in kelv in .

' F ,. y - e 4 N l _ ~ ,Lo n g - r an g e o r d er in g o f N a to ms in y '- Fe4 N~_ x imp l iesth a t th ese a to ms p r e f e r to o ccu p y o n e o f th e f o u r o c tah ed r a lin te r s ti ces in th e f cc u n i t ce l l o f th e Fe a to ms ( o r d er s i t e s) .To a r r iv e a t an accu r a te d esc r ip t io n o f th e av a i lab le ex p er -imen ta l d a ta f o r th e n i t r o g en - ab so r p t io n i so th e r ms o f y ' -Fe4 N ~_ , , i t w as sh o w n n ecessa r y to t ak e in to acco u n t th e( v er y lo w ) o ccu p an cy b y N a to ms o f th e o th e r , n o t p r e -fer red , octahedral in ters t ices (d isorder s i tes uJ) as well . Thechem ical po ten tial o f n i trog en in y ' -n i tr ide , /_~.~. , can bed esc r ib ed as a f u n c t io n o f n i t r o g en co n ten t an d temp er a tu r ew i t h t he s a m e a c c u r a c y b y a G B W a p p r o a c h a n d a W a g n e r -Sch o t tk y ( WS) ap p r o ach , a s w as sh o w n in Ref e r en ce 1 2 .

T h e W S a p p r o a c h i s m o r e c o n v e n i e n t m a t h e m a t i c al l y th a nth e G BW ap p r o ach an d i t i s th e r e f o r e ad o p ted h e r e :

P~ . r' = G ~ . r ' + R T I n 1 + \ 2 K r ' ] 2 g j [51wh ere 4AyN. , = 4yy .~. - - 1 , with YN.r' as the f ract ion of thein te r s t i t i a l su b la t t i ce o ccu p ied b y N a to ms , d esc r ib es th ed ev ia t io n o f th e co mp o s i t io n f r o m th e s to ich io me t r yFe4N(Fe4Nl+4Ays~. and 16/3 (Kr.)z is the equilibrium con-s tan t f o r th e ex c iaan g e o f n i t r o g en a to ms a t o r d e r s i t e s w i thn i t r o g en a to ms a t d i so r d er s i t e s . Fo r eq u i l ib r iu m w i th anamm o n ia /h y d r o g en mix tu r e , eq u a t in g Eq s . [ 1] an d [ 5 ]y ie ld s an ex p r ess io n f o r th e n i t r o g en - ab so r p t io n i so th e r m:

r__Ns _ { ~ l q_ (~..~_.~z2,12 .+_ A y N yr~ ' k 2 K r ' ] 2K, j [6]o o ow ith r N , r , d e f in ed as RT I n r N , /~= G N , r , - G N H3 +3 G ~ I t fo l lows f rom Eq. [6] that r~ , , , can be in terpretedas the n i tr id ing poten tial in equil ibr ium with y ' -Fe4N , _ . o fthe hypo thet ica l comp osit ion Fe4N, (YN,~, = 1 /4; one in ter -s t i t i a l s i t e p e r Fe s i t e in f cc Fe) . A cco r d in g to Ref e r en ce

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-2-

-4-

7 0 0 6 0 0temperature (~

500 400 300Eq.(14a)

E q . ( 1 4 b )

~zv -6-

XX 7

O~

9 Lehrer [23]+ Emm ett et a1.[26]zx Bm naue r et a1.[27]Comey, Turkdogan[28]o Barde se [291x Grabk e [30]Wriedt, et al. [31]m Podgurski, Davis [32][] Maldzin ski [25]

i i 1 1 I1.0 1.2 1.4 1.6 1.8x 10 "3( tem pera ture) -1 (K) "1

Fig . 1- -Le hrer d iagram , showing the n i t r id ing-potent ia l ranges of the Fe-N phases : the n i t r id ing poten t ia l , rN, a t the phase boundar ies is g iven asa funct ion of the temperature , T. Analy t ical express ions for the bounda r iesbetween the a-Fe and "/ -Fe4N~_ ~ phase f ie lds and the y ' -Fe4N,_ , and e-Fe:N ~ ~ phase f ie lds are g iven by Eqs . [13] and [14] , respect ively . T hedashed l ine cor responds to Eq. [14b] , to be d is t inguished f rom the so l idl ine cor responding to Eq. [14a] only for T < 673 K. The exper im entald a t a f r o m R e f . 2 3 d e t e r m in e a p h as e b o u n d a r y a s an i n t e r m ed ia t e b e tweendata ind icat ing the per iphery of the associa ted phase f ie lds .

12, the va lues for r~, r . and Kr. a re given by6.35" 103~ = -1 2 . 5 + [7a ]n rN. r, T

7.56 . 103In 4K r, = 2 .98 T [7b]w h e r e r~ , r , i s g iv en in Pa -~/2 and T i s giv en in ke lvin.C . e - F e 2 N I _ z

Long - range o rde r ing o f N a toms in e -Fe2N,_~ can be de -sc r ibed on t he ba s i s o f a s imple hexagona l un i t c e l l fo r t heinterst i t ia l subla t t ice conta ining six types of s i tes (A1, B1,C1 , A2 , B2 , C2) , wh ich r ep re sen t s i x sub l a t t i c e s fo r t hen i t rogen a toms . The GB W approach 221 was app l i ed t o t hein t e r s t i t i a l sub l a t t i c e occup ied by N a toms and V a toms(vacanc ie s )Y ~ The i n t e rac ti on am ong the a toms was ac -coun ted fo r by an exch ange ene rg y W ~,~ epre sen t i ng pa i r-wi se i n t e rac t i on i n t he d i r ec t i on pe rpend icu l a r t o t he ba sa lp l ane o f t he hex agona l un i t c e l l (s i te s deno t ed by t he samecha rac t e r A, B , o r C) an d an exchange ene rgy W P~ repre-sen t i ng t he pa i rwi se i n t e rac t i ons i n t he ba sa l p l ane o f t hehexagon a l un i t c e l l (s i t es deno t ed by t he sam e num ber 1 o r

2 ). O n th i s ba s i s , a ve ry good desc r ip t ion o f t he chem ica lpotent ia l o f ni t rogen in e-Fe2N~_~ as a funct ion o f ni t rogencon ten t and t empe ra tu re was ob t a ined i n Re fe rence 13. Forthe chemical potent ia l of in terst i t ia l s a t s i tes of type A1,A I ~ [ N . e the fol low ing holds, l3lo + [8]A ' tZ N , , G N , ~ + R T In 1 - A lyN,~J

( 1 - 2 A '~yN,~) W ~.~+ ( 1 - my N,~ + C'y N, ~) W[~,~whe re kyN, is t he f r ac t ion o f s i t es o f t ype k occup ied by Na toms. Ana logous equa t i ons ho ld fo r t he chemica l po t en -t ia ls of the interst i t ia l s a t the o ther types o f s ites. At equi -l ibr ium, the six chemical potent ia ls a re equal . Forequ i l i b ri um wi th an am mo nia /hydro gen mix tu re , equa t i ngEqs. [1] and [8] yie lds

In r___~N= In YN,~ + [9]o AIrN, ~ 1 - YN,~J

(1 - - 2 A2yN,et ~N,E ( __ El ~ / Wp,E"- - ~ + 1 - B 'yN. YN, R To o o oo de f ined a s RT In rN .~ = G~,~ - GNH3 + 3 GH 2/2 .i th rN,,I t fo l l ows f rom Eq . [9 ] t ha t r~ , , c an be i n t e rp re t ed a s t heni t r iding potent ia l in equi l ibr ium wi th e-Fe2N~_z hav ing thehypothet ica l composi t ion FeEN and A~yN, = myN, = C'yN, ~= AEyN. = B2yN, = CEyN. = 1/2 ( i . e . , a r andom d i s t r ibu t i on

of N a toms over a l l ava i lable si tes; one interst i t ia l s i te perFe a tom in hcp F e ) . Ana logous equa t i ons ho ld fo r the o the rtypes o f s i te s . Va lues fo r kyy , , can be ob t a ined numer i ca l l yf rom the se t o f s i x equa t i ons o f t ype Eq . [9 ] ( r e fe r t oRe fe rences 11 and 13 fo r numer i ca l r e c ipe s ) . Two so lu -t i ons pe r t a in ing t o d i s t i nc t o rde red conf igura t i ons o f t he Na toms, deno t ed A and B , we re foun d fo r exchange ene rg i e sW ~ . J R T < 0 and W ~ . J R T < 0 , imply ing mutua l r epu l s ionamo ng N a toms . Conf igura t i on B i s t he mos t s t ab le one fo rcom posi t ions near FeEN2/3; configu ra t ion A is the m ost s ta -b l e one fo r t he h ighe r n i t rogen con t en ts , up t o Fe2N. tmFrom f i tt i ng t he G BW mode l t o expe r imen ta l da t a fo rni t rogen-absorpt ion i sotherms of e -FezN~_, , i t was con-c luded i n Re fe rence 13 tha t , wi th in t he comp os i t ion r angeFe3N to Fe2N and t empe ra tu re r ange 673 t o 823 K inves-t i ga ted , conf igura t ion A i s dom inan t and t ha t t he exchangeene rg i e s c an be t aken d i r ec t l y p ropor t iona l t o t he t empe r -a tu re . Howeve r , t he n i t rogen con t en t s o f e -Fe2N,_z whicha re o f impor t ance fo r c a l cu l a t i on o f t he 7 ' / ( 3 , ' + e ) and (3" + e ) / e phase boun da r i e s a re gene ra l l y nea r o r be low tha tfo r F%N. For t he se compos i t i ons , i t was shown in Re fe r -ence 13 tha t (1) configura t ion B is more stable than con-f i gura ti on A and (2 ) t he p a rame te r s W P . , , W ~, , and In r~ob ta ined fo r conf igura t i on A app ly t o conf igura ti on B a swe l l . Hence , fo r c a l cu l a t ion o f the (7 ' + e ) / e phase bound-a ry , conf igurat i on B h as t o be adop ted fo r t he e phase us ingthe fol low ing va lues for the exch ang e energies5 t31

Wp c: , E = _ W N,E= _ 2 .98 [10a ]R T 4 .4 8 , R Tand fo r t he r e fe rence n i t r id ing po t en t i a l r ~ . E : t l 3 ]

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3.59" 103In rN,~~= _ 4.92 + T [10b]whe re r~ , i s g iven i n Pa -1 /2 and T i n ke lv in .Ins t ead o f us ing t he se t o f equa t i ons o f type Eq . [9] wi thpa rame te r va lue s g iven by Eq . [10] fo r t he ca l cu l a t i on o fthe phase bounda r i e s , a m ore conven i en t ana ly t i c a l de sc r ip -t i on r e l a t i ng t he t o t a l occu pancy o f t he n i t rogen sub l a tt i c e,C2YN.. 1 ~ k 6Y N , J , to the ni t r iding potent ia l , r~, i s desi red.k- AII t was found t ha t t he fo l l owing equa t i ons p rov ide an ade -qua t e de sc r ip t ion o f t he se t o f equa t i ons o f t ype Eq . [9]us ing t he va lue s de t e rmined fo r W f ~ , J R T and W ~ , / R T (Eq.[ 10a]) for spec i f ic Y s, ranges:

0 .2 6 < YN,~ < 0.3 7: In ( r____N_sor N , e /= -3 .8 4 - 30 .76y s .~ + 82 .87 s.~ [ l l a ]

0 .1 6 < YN.~ < 0 .2 6 : In ( r__~_No\ rN,~,/= -8 .6 1 + 5 .03 yN , + 15 .60 N,

where r~, i s s t i l l g iven by Eq. [10b] . Note tha t Eq. [11] ,in par t icular Eq. [1 lb] , i s obta ined by severe ext rapola t ionof Eq. [9] using the va lues o f Eq. [10], because Eq. [10]holds for the compo si t ion range 0.36 < YN, < 0.50.

I l L E Q U I L I B R I U M B E T W E E N F E - N P H A S E S ;C A L C U L A T I O N O F P H A S E B O U N D A R I ES I N T H EF E - N S Y S T E MEqui l i b r i um be tween two phase s i s e s t ab l i shed i f t he

chemica l po t en t i a ls o f e ach o f t he comp os ing e l emen t s a rethe same in bo th phase s . Hence , fo r equ i l i b r i um be tweence-Fe[N] and y'-Fe4Nl_x,/~ ,~ = /~ ,y . an d /XFo,~ = /XF~,~, [12]

If , as a funct ion of composi t ion and tempera ture for bothphases, the Gibbs f ree energy and thus the chemical poten-t i al s o f n i t rogen and i ron a re kn own, t hen t he phase bound-aries ~/c~ + y' an d c~ + y ' / y ' can be calculated straightfor-wa rdly by appl ica t ion of Eq. [12]. Th e chem ical potent ia l ofdissolved ni t rogen (or v i a Eq. [1] the corresponding ni t r idingpotent ia l ) as a funct ion of composi t ion and tempera ture wasder ived in Sect ion I I for each of the three phases ot -Fe[N],T '-FeaNI_~, and &Fe2Nj_ The va lues for G ~,~ (G~,~ = RTo G Nrf3 o = a, y' , e) are deter-n rN~ + o - - 3GH ]2, wh ere smined on the basis of the exper imenta l va lues for rN~ (sec-t ion I I ) . Then, the chemical potent ia ls of i ron, /~o~, can beob ta ined f rom

aGs = -- IZFo,, + Y I-~. ,cwhere G~ i s the G ibbs f r ee ene rgy fo r an amo unt o f phases (= a , Y ', e ) co r re spond ing wi th a / c mol F e a toms and ymol N a toms , and a / c deno te s t he num ber o f Fe s i t e s wi threspect to the number of interst i t ia l s i tes avai lable for N

900 - b 0.02IcN (wt %)

0.04 0.06 0.08I I I 0 . 1 0

800 - O~

[..,7 0 0 -

600 -

50 0 -I /m *

i/ x ,

Ax

~ A x

~ + u

Dijkstra [33]M Paranjpe et a1.[34]x Astr rm [35][] Burdese [36]9 Fast, Verrijp [37]o Corney, Turkdogan [28]tx Rawlings, Tambini [38]9 Nacken, Rahm ann [39]o Wded t, cited in [21]9 Imai et al.[40]9 Abiko, Imai [41].......... Ku nze [17 ].. . . . Frisk [18]present work

I I I0 . 0 0 . 1 0 . 2 0 . 3 0 . 4CN ( a t . %)

F i g . 2 - - P a r t o f t h e F e - N p h a s e d i a g r am , t e m p e r a t u r e vs t h e n i t r o g e nc on te n t CN, show ing the oda + 3~ pha s e bounda r y : t he od a + ~ ph a seb o u n d a r y a s c a l c u la t e d i n t h e p r e s e n t w o r k ( s o l id l i n e ) a n d t h o s e p r o p o s e din R e f . 17 ( do t t e d l i ne ) a nd R e f . 18 ( da sh - do t l i ne ) , a nd t he c o r r e spond inge xpe r im e n ta l da t a .

a toms ( e . g . , a / c = 1 /3 fo r a -Fe ) . The on ly unknow ns a rethe va lues fo r G~e~.. No exper im enta l da ta for the di rec teva lua tion of G~e,~, and G~e.~wi th r e spec t t o some re fe rence( e . g . , G~e,~) are avai lable . For this reason, in previous ca l -cula t ions o f the Fe-N phase diagram , ~-2~ exper im enta lcompos i t i on - t empe ra tu re da t a o f t he Fe -N phase d i ag ramwere used i n o rde r t o eva lua t e (by f i t t i ng ) t he unknownpa rame te r s i n t he de sc r ip ti on o f t he G ibbs f r ee ene rgy .Then , depend ing on t he number o f compos i t i on - t empe ra -tu re da t a used , a com par i son o f t he ca l cu l a t ed and t he ex -pe r imen ta l l y a sse ssed phase d i ag rams may lose i t spo t en t i a l l y v ind i ca t i ng s ign i f ic ance and a ( seeming ly ) co r -rec t Fe -N phase d i ag ram can be ca l cu l a t ed , a l t hough i t sunde r ly ing t he rmodynamic de sc r ip t i on i s wrong . In t hepre sen t work , ano the r rou t e i s fo l l owed in which use o fexpe r imen ta l compos i t i on - t empe ra tu re da t a o f t he Fe -Nphase d i ag ram i s c i r cumven ted . H e re , t he n i t r id ing po t en t i a l( c f Eq. [1]) hold ing for equ i l ibr ium betw een a NH 3/H 2 mix -tu re and two coex i s t i ng i ron-n i t rogen phase s was used . Inthe fo l l owing , t he se n i t r i d ing po t en t i a ls w i l l be d eno t ed a sphase -bounda ry n i t r id ing po t en t i al s rN.io, wi th i a nd j a s t hecoex i s t ing phase s . The r N , i o ' s a r e expe r imen ta l l y we l l e s -tabl i shed an d are p resented in a s o-ca l led Leh rer diagram , 23~dep ic t ing t he n i t r id ing-po t en ti a l r anges o f t he Fe -N phase sin a p lo t o f the com pos i t i on o f t he amm onia /hyd rogen mix-ture v s t empe ra tu re (F igure I ) . The de sc r ip ti on o f t he phasebounda r i e s c an be ob t a ined d i r ec t l y by subs t i tu t i on o f t he

1066~ VOL UM E 27A, APRIL 1996 METALLURGICAL AND MATERIALS TRANSACTIONS A


5/9

cN (wt %) cN (wt %)5.4 5.6 5.8 6.0 5.885 5.890 5.895 5.900J t 1 I I I IEg + ' ~ [] Q- - - - - 4 - - 8 00 -- - - - - - - - - - x - - - - - - - - - x ~/+E

9 00 7 + y ' ~ ' ~ 7 y + e9 "~ [] xx 9 750 -9 (~ .~/ x ,Ls x

800 - ~ 7009 9 0 X 9 ~ rn

9 x700 - 6 5 0 -

+ H~igg 5]x Eisenhut, Kaupp [42] ~ 9 oLehrer [43]o B r u n a u e r et a l [27] ~1x Guillaud, Creveaux [44] 6 0 0 -9 Paranjpe et al. [34]6 0 0 o Burdese [36] I9 Nauman n, Langenscheid [45]9 Grabke [30]tx Wriedt [46] 5 5 0 -

Somers, Mittemeil.'er 47,48]r T r - I I I !18 . 5 19 . 0 19 . 5 20 . 0 20 . 5 19 . 9 5 19 . 9 6 19 . 9 7 19 . 9 8 19 . 9 9 20 . 00

CN (a t .%) CN (a t .%)(a) (b)

F i g . 3 - - ( a ) a nd ( b ) P a r t o f t he F e - N pha s e d i a g r a m , t e mpe r a t u r e T v s the ni t roge n content oN, sho win g the ~-Fe4N~_~ hom oge ne i t y r ange : the u + 3, '/3a nd ~ / ~ + e pha s e bounda r i e s a s c a l c u l a t e d i n t he p r e s e n t w or k ( bo l d l i ne s ) a nd t he c o r r e s pond i ng e xpe r i me n t a l da t a. E n l a r ge m e n t o f 7 ' - pha s e fi e l d i n( b ) s how s t ha t u s i ng e i t he r E q . [ 14a ] ( s o l i d l ine ) o r E q . [ 14b] ( da s he d l i ne ) doe s no t ha ve a s i gn i f i c a n t e f f e c t on t he 3M '~ + e pha s e bou nda r y .

r N , i / / s i n t he de sc r ip t i ons o f t he absorp t i on i so the rms fo reach phase , a s de r ived i n Sec t i on I I .A . C o e x i s t in g a - F e a n d 3 - F e 4 N l_ x i n E qu i l ib r i u m w i t hN H 3 / H2 M i x t u r e s

Using t he o r ig ina l da t a o f Re fe rence 23 , t he add i t iona lda t a o f the com pi l a t ion p rov ided i n Re fe rence 21" and t he*I n t he c ompi l a t i on o f R e/ '. 21 a l s o , t he da t a o f R e s 23 a pp e a r t o ha vebe e n i nc o r po r a t e d . H ow e ve r , i n s t e a d o f u s i ng t he o r i g i na l e xpe r i me n t a lda t a , t he " da t a po i n t s " g i ve n i n R e f . 21 w e r e de r i ve d f r om a ( f i t te d ) l ine .

da t a o f Re fe rences 24 and 25 , t he t empe ra tu re dependenceof t he phase -bo unda ry n i t r i d ing po t en t i a l fo r coex i s t ing a -Fe a nd 3"-Fe4Nl_x, ry ,~ /v , , can be r ep re sen t ed by t he fo l l ow-ing re la t ion obta ined by l inear regression (Figure 1) :4555In ry ,~ /? = T 12.88 [13]wi th rN,~/~, in P a -1/2 and T in K elvin. Sub st i tut ion o f r~ inEq. [4] by rN, , / r , , as given by Eq. [13] , y ie lds the a / a +3" phase bounda ry . The r e su l t i ng phase bounda ry i s g ivenin F igure 2 by t he so l i d l i ne and can be compared i n t h i sf igure wi th the exp er imen ta l da ta for the a /o~ + 3" phasebound a ry a s we l l a s t he ca l cu l a t ed c e / a + 3" phase bound-a r i es g iven i n r ecen t eva lua ti ons o f t he Fe -N phase d i a -gram. [tTJs] The agree me nt o f the present descr ipt ion for the

phase bounda ry and t he expe r imen ta l da t a i s good , e spe -c i a l l y wi th t he da t a o f Re fe rence 37 g iven fo r t he en t i r et empe ra tu re r ange and t he da t a o f Re fe rences 39 an d 41which a re ava i l ab l e on ly fo r r e l a t i ve ly l ow t empe ra tu re s .Only t he da t a o f Re fe rence 35 i n gene ra l and t he da t a o fRe fe rence 40 a t l ow t empe ra tu re s dev i a t e s i gn i f i c an t l y ;t he se sugges t a cons ide rab ly h ighe r so lub i l i t y o f n i t rogenin a t han p red i c t ed he re . In t h i s r e spect , i t i s r emarked t ha tt h e e x p e r i m e n t a l l y d e t e r m i n e d n i t r o g e n c o n t e n t s f o r t h ea / a + y ' phase bou nda ry t end to be t oo h igh due t o theun-no t i ced p re senc e o f f i ne ly d i spe r sed y '-Fe4NI_.~ o ra "-Fe~rN2 prec ipi ta tes in a -F e . t371 Indeed , i t h as been show nin Referen ce 37 tha t such a sy stem at ic e rror i s l ike ly tohave i n f luenced cons ide rab ly t he da t a o f Re fe rence 35 . A l soin Re fe rence 21 , o n t he ba s i s o f an eva lua t i on o f a ll da t afo r t he a / a + y ' phase boun da ry , the da t a o f Re fe rence 37were r ecom men ded a s mo s t re l i ab le (T > 573 K) .The p re sen t c a l cu l a t i on o f t he a / a + y ' p h a s e b o u n d a r ydoes no t use exp l i c i t l y phase -bounda ry da t a a s i n Re fe r -ences 14 t h rough 20 ( r e fe r to p reced ing d i scuss ion) . In t heca l cu l a ti ons p re sen t ed i n Re fe rences 14 t h rough 18 , equ i-l i b r ium was cons ide red be tw een a -Fe [N] and a phase wi ththe stoichiom etr ic com posi t ion FeaN or Fe4.1N (Fe4.15N,Fe4.3N). Because the chemical potent ia l of ni t rogen in y 'phase i s ve ry sens i t i ve t o sma l l va r i a t i ons i n t he n i t rogencon ten t , t he r e su l t s ob t a ined fo r t he a / a + 3 1 ' phase bound-a ry i n Re fe rences 14 t h rough 18 on t he bas i s o f t he se hy-

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 27A, APRIL 1996 ~106 7


6/9

6tc N (wt %)

7[ 8I

900 -

800 -

700 -

600

/ I " oi

a -~ 11 u

t~ Eisenhut, Kaupp [42]9 Lehrer [23]o Brunauer et al. [27]9 Paranjpe et al. [34]n Burdese [29]Naumaan, Langenscheid [45].......... Kunze [17]..... Frisk [18]- - , - - - present work

#A ,t,:ti

15 20 25 30c N (at.%)Fig. 4~Part of the Fe-N phase diagram, temperature T vs the nitrogencontent cN, show ing the 3" + e/e phase boundary: the ~/ + e/e phaseboundary as calculated in the present work (bold solid and bold dashedlines for which Eqs. [14a] and [14b] are used, respectively) and asproposed in Ref. 17 (dotted line) and in Ref. 18 (dash-dot line), and thecorresponding experimental data.

pothet ica l equi l ibr ia a re only approximate . Fur ther , inReference 12, i t was shown tha t ignoring the occurrence oflong-range order ing of N a toms in 3" phase , as was donein References 19 and 20, led to an incorrec t descr ipt ion ofthe thermodyn amics of this phase . Never the less, the a / a +y' phase boundary, as obta ined in References 19 and 20,compares favorably wi th the corresponding exper imenta lda ta . This good agreement should be a t t r ibuted to usingexp l ic i t ly phase -bounda ry da t a fo r t he "ca l cu l a t i on" o f thephase bounda ry .Subs ti tution of r N in E q. [6] by rN.~/~., as given by Eq.[13] and using Eq. [7], yields the a + y ' / y ' phase bound-ary. The resul t ing phase boundary i s given in Figure 3(a)and can be compared in this f igure wi th the exper imenta lda ta for this phase boundary. Clear ly , the exper imenta lcomposi t ion- tempera ture da ta reported by di f ferent authorssca t te r enormously. The discrepancies can be ascr ibed toexper imenta l di f f icul t ies in de termining the ni t rogen con-tents in y'-nitride for the o d y ' two-phase equi l ibr ium, asholds especia l ly for the older references. For a discussionof the possible exper imenta l di f f icul t ies , see Reference 49 .Minute changes in the ni t rogen content in 7 ' correspondwith la rge changes o f the correspond ing ni t r iding poten-t ial . Ch anges of the rN,~/r , can be obta ine d w i th a re la t ive ly

high accuracy. Therefore , i t i s be l ieved tha t the presentphase bounda ry ca l cu l a t ed by combin ing n i t rogen-absorp -t ion i sotherms for y ' -ni t r ide and phase-boundary ni t r idingpo ten t i a l s fo r t he ody ' equ i l i b r i um i s much more accura t ethan the exper imenta l composi t ion da ta for this phaseboundary.

B . C o e x i s ti n g y ' - F e 4 N t _ x a n d e -F e EN ~ _ ~ i n E q u i l i b r i u mw i t h N H 3 / H 2 M i x t u r e sUsing the or igina l da ta o f Reference 23, the addi t ionalda ta of the compi la t ion provided in Referen ce 21 (f romReference 30 incorpora ted in Reference 21, only those a t773 K; out l iers in Figure 1), and the da ta of Referen ces 24and 25 , t he t empe ra tu re dependence o f the phase bo unda rynitridin g pote ntial, rN,~,i~, for co exis ting 7'-Fe4N~_~ and e -Fe2NI_~, rN,v,/o is ob tained by least-squa res fi t t ing as f ollow s(Figure 1).

fo r 6 2 3 K < T < 9 0 0 K :~/60,_536 56.8 5 [14a]In rN.r./~ = -9 .6 3 + ~ T

or , wi th comparable accuracy:In rN.~./~ = - + 18,708T 21.46 [14b]

and for T > 870 K:~/14 ,385In rN,~,/~ = - 7 . 2 6 +__ v "T 15.1 6 [14 c]

with rN,v./, in Pa -v2 and T in kelvin. Subs ti tution of r N inEq. [6] by rN,v,/~, as given by Eq. [14] , a l so using Eq. [7] ,yie lds the yTy' + e phase boundary. The resul t i s depic tedin Figure 3(a) and can be compared in this f igure wi th theexper imenta l da ta for this phase boundary. For comparisonof the ca lcula ted phase bound ary wi th the exp er imenta lda ta, the same considera t ions apply as for the a + 3/ /y 'phase boundary. The composi t ion corresponding wi th thecong ruent e quilibrium 3" ~- e at T = 949 K (this temp era-ture fol lows di rec t ly f rom Eq. [14c] by taking the squareroot te rm equal to zero) was ca lcula ted to be 19 .53 a t . pc tN. This ca lcula ted content i s in excel lent agreement wi ththe resul t s reported in References 27 and 38. An evalua t ionin Reference 21 yie lded as most probable composi t ion andtemperature for this congruent reaction 19.5 at . pct N at953 K. Tak ing either Eq. [14a] or Eq. [14b] for r~,~./ , at T< 900 K yie lds a minor di f ference in the ca lcula ted result sfor the y ' /y ' + e phase boundary: a di f ference of only 0 .007at . pc t N a t 523 K (Figure 3(b)) . Apparent ly , the ca lcula tedphase bou ndary i s not sensi t ive to smal l devia t ions of theval ue f or rN,~,/~. He nce , it is an ticip ated that th e Y ' / 7 ' + ephase boundary, as ca lcula ted f rom the exper imenta l ly de-termin ed p hase -bou nda ry nitriding potential rN,r,/~, will bemore accura te than the exper imenta l ly de termined ni t rogencontents for the y ' / y ' + e phase bounda ry .Subs ti tution of rs in Eq. [11] by rN,~./~, as giv en b y Eq .[14] , a l so using Eq. [10b] , y ie lds the y ' + e /e phase bound-ary. The resul t i s depic ted in Figure 4 and can be comparedin this figure with the experimental data for this phase

1068--VOLUME 27A, APRIL 1996 METALLURGICAL AND MATERIALS TRANSACTIONS A


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bounda ry* a s we l l a s wi th t he p rev ious ly ca l cu l a t ed ( c f* T h e exper imental co m p o s i t i o n s p e r t a in in g to t h e y ' + e / e p h as eb o u n d a r y i n t h e tem p e r a tu r e ran g e 5 2 3 K < T < 9 0 0 K can b e d e s c r ib edby ( leas t - squares f i t t ing)YN.~ 5.758 I0 -~ + 6.621 10 4 T - 5.345 lO -7 T 21 YN, ~, wh e r e T i s t h e t em p e r a tu r e i n k e lv in .

d i scuss ion i n the beg inn ing o f t h is sec t i on) y ' + e / e phasebounda r i e s , a s g iven in Re fe rences 17 and 18. As comparedto t he p rev ious ly ca lcu l a t ed 7 ' + e / e phase bounda r i e s i nRe fe rences 14 t h rough 20 , t he one ob t a ined he re ag ree smu ch be t t e r wi th t he ava i l ab l e expe r imen ta l da t a i n t he t em-pe ra tu re range 600 t h ro ugh 800 K. Fu r the rmore , i n con tra s twi th t he p rev ious ca l cu l a t ions , expe r imen ta l da t a f rom thephase d i ag ram were no t used i n t he p re sen t p red i c t i on o fthe phase d i ag ram. At h ighe r t empe ra tu re s , t he ca l cu l a t edy ' + e / e phase bound a ry dev i at e s s ign i f i c an t l y f rom theexpe r imen ta l da t a fo r t he y ' + e / e phase bounda ry , r e su lt -i ng i n a c a l cu l a t ed compos i t i on fo r t he congruen t equ i l i b -r ium 7 ' r e of 21.2 a t. pc t N, w hich i s about 1 .7 a t. pc t Ntoo h igh . In t h i s r e spec t , t he p re sen t r e su l t on ly seems l e ssgood than t he r e su l t s o f Re fe rences 14 th rough 20 : i t shou ldbe r ecogn ized t ha t i n t he se p rev ious ca l cu l a t i ons , t hecompo s i t ion and ' t empe ra tu re o f t he congruen t equ i l i b r iumy ' ~ e we re f i xed a t the i r co r rec t va lue s a p r i o r i .The d i sc repancy be tween t he ca l cu l a ted 7 ' + e / e phasebound a ry i n the p re sen t work and t he expe r imen ta l da t a a tt empe ra tu re s h ighe r t han 800 K p robab ly o r ig ina t e s f romthe rest r ic t ing adopt ion tha t W P ] R T a n d W ; , ] R T are con-s t an t. Ad op t ing W ~ , J R T a n d W ~ , e / R T as constants led to agood f i t o f t he GB W mod e l t o the expe r imen ta l absorp ti on-i so the rm da t a i n t he t empe ra tu re r ange 673 t o 723 K (Re f -e rence 13) and , i ndeed , t he y ' + e / e phase bound a ry isve ry we l l de sc r ibed i n t h i s t empe ra tu re r ange . No re l i ab l eabsorp t i on- iso the rm da t a ex i s t fo r t empe ra tu re s above abou t723 K. As shown in Re fe rence 13 , t h i s i s due t o t he oc -currence o f a s ta t ionary sta te , ra ther than equ i l ibr ium, a t thegas/G-phase interface . Therefo re , i t i s impossible to pro videa m ore de t a i l ed de sc r ip t i on o f t he t empe ra tu re dependenceof t he ex change ene rg i e s , a l t hough i t i s r e cogn ized t ha t t hepred i c t ed phase bounda ry s t rong ly depends on t h i s t empe r -a tu re dependence . Fo r exam ple , i f W ~.~ and W ; , , are t akenas cons t an t s , wh ich can be ob t a ined f rom f i t t i ng t he sameGBW mode l t o t he absorp t i on- i so the rm da t a i n t he t em-pera ture range 673 to 723 K (Reference 13) , the ca lcula ted3" + e / e phase bound a ry a t t he h ighe r tempe ra tu re ss t rong ly dev i a te s f rom the expe r imen ta l da t a i n t he oppos i t edi rec t ion (i .e . , i t i s s i tua ted a t too low ni t rogen contents) .Therefore , i t i s suggested tha t W ~ , ] R T a n d W N . ] R T de-sc r ibed wi th t he fo rm a + b / T prov ide a t empe ra tu re de -pendence i n -be tween t he two cons ide red i n Re fe rence 13and may p rov ide a de sc r ip t i on o f the y ' + e / e phase bound-a ry t ha t i s i n be t t e r ag reem ent wi th t he exp e r imen ta l phase -boun da ry da t a t han t he one ca l cu l a ted he re.Tak ing e i ther Eq. [14a] o r Eq. [14b] fo r rN.r,/~,bo th va l i dfor 623 K < T < 900 K , yie lds dist inc t ly di f feren t 3" +e / e phase bounda r i e s a t t empe ra tu re s be low abou t 650 K:the d i f f e rence i n n i t rogen con t en t amount s t o abou t 1 a t .pc t N i f the range o f appl ica t ions o f Eqs. [14a] an d [14b]is extended to 523 K (Figure 4) . Evident ly , the ca lcula tedy ' + e / e phase bounda ry , un l i ke t he ca l cu la t ed y ' / y ' + ephase bou nda ry i n t h i s t empe ra tu re r ange ( compare F igure s

3(b ) and 4 and re fe r t o p rev ious d i scuss ion) , i s ve ry sen-si t ive to smal l chan ges in the va lu e fo r rN.~,/E . This impl iestha t a sma l l , seeming ly i ns ign i fi c an t , sys t ema t i c i naccuracyin the descr ipt ion of rr~.~./~ or in the descr ipt ion of th e ab-so rp t i on i so the rm c lose t o t he phase bounda ry unde r con-sidera t ion can cause a s igni f icant e rror in the ca lcula tedcompos i t i on o f e i n equ i l i b r i um wi th y ' . In t h i s r e spec t , i ti s no t ed t ha t in t he ca l cu l a ti on o f t he y ' + e / e phase bound-a ry , t he r e l evan t pa r t o f t he n i t rogen-absorp t i on i so the rmsfor e i s t ha t a t l ow n i t rogen con t en t , whe re t he number o fdata i s l imi ted and thus the f i t re l ies la rge ly on the da ta a th ighe r n i t rogen con t en t s .C . C o e x i st i ng a - F e a n d E - F e 2 N _ z i n Equ i l i b r i um wi thN H 3 / I - / 2 Mixture s

For the tempera ture range per ta ining to the Leh rer diagram(Figure 1) , no equi l ibr ium can occur be tween a gas mixtureof am mon ia and hydro gen (o r, equ iva l en tl y , pu re n i t rogengas w i th the pressure correspon ding wi th the par t ia l pressureof t he amm onia /hydrogen mix tu re ) and coex i s ti ng so l i dphases a-F e and e-Fe2N~_ . A possible equi l ibr ium of the aand e phases impl ies tha t the phase-boundary ni t r iding po-ten tial s rN.~/~, an d rN.v,/Eattain a certain, identical value at acer ta in tempera ture : a t r iple point where a , 3", and e coexist .Equat ing Eqs. [13] and [14a] yie lds for the tempera ture ofthe t r iple point 295.4 K , which gives, wi th Eq. [11], for thecom pos it ion of e-nitride at the triple po int YN,e = 0.341;equat ing Eqs. [13] and [14b] yie lds for the tempera ture ofthe t r iple point 448.6 K, which gives, wi th Eq. [11] , for thecom posi t ion of e -ni t r ide a t the t r iple point YNx = 0.288. BothEqs. [14a] and [14b] are equ ally justif ied least-squ ares fi tsto the sam e exper im enta l data. T he dist inc t predic t ions forthe t r iple point on ext rapola t ion to low tempera tures are ther e s u lt o f t h e a d o p t e d e m p i r ic a l f u n c t i o n a l d e p e n d e n c e o frN.r./e on 1 / T . There fo re , no conc lus ion can be d rawn re -ga rd ing t he t empe ra tu re o f an a / y ' / e t r i p l e po in t on t hebas i s o f t he p re sen t da t a .Recen t ly , t he obse rva t i on t ha t 7 ' -n i t r i de d id no t appea ron annea l i ng an e -n i t r i de l aye r (p roduced by 1 MeV im-p l an t a t ion o f N + i n to i ron and , consequen t ly , bu r i ed i n aferr i te subst ra te*) a t T < 573 K w as taken as an exper i -

*In general , exper iments on i ron-n i t rogen phases obta ined by ion -beamimplanta t ion canno t be re la ted eas i ly to the equi l ibr ium condi t ions per t,a in ingto t h e ( co m m o n ) Fe - N p h a s e d i ag r am . E q u i l i br iu m s h o u ld b e e s t ab l i s h edb e tween a h o m o g en eo u s Fe - N p h as e an d an am m o n ia /h y d r o g en g a s m ix tu r eor , equivalen t ly , n i t rogen gas o f cor respondin g h igh par t ia l p ressure .Without im pos ing such h igh (v ir tual) par t ia l p ressures of n i t rogen ,ap p r o ach in g th e r m o d y n am ic eq u i l i b r iu m f o r a s - p r o d u ced Fe - N p h as e sinvar iab ly leads to a decom pos i t ion in to N z and fer r i te wi th a low n i t rogencontent (or aus ten i te a t h igher temperature) , p rovided N atoms canrecombine a t favorable s i tes .menta l i nd i ca t i on tha t , i n t he usua l Fe -N ph ase d i ag ram a tt empe ra tu re s l ower t han 573 K , the y ' phase f i e ld wou ldvanish.lS0.5~ This conc lusion was fur ther s ubstant ia ted b yexpe r imen t s wi th two-phase 6 /7 ' sample s whe re t he 3"phase cou ld be t ra nsfo rme d into G-nit -r ide conta ining abo ut20 a t . pc t N ( the same composi t ion as the parent 7 ' -ni t r ide)a t t empe ra tu re s a s l ow a s 423 K, p rov ided a beam o f Neions t r ave r sed t he sample dur ing t he t r ansfo rma t ion . An-nea l i ng t he sample s i n which y ' phase had been t r ans-fo rmed in to e phase a t and above 423 K l ed t o t hereappearance of y ' -ni t r ide . tS~ From this interest ing obser-

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v a t io n o f a " r e v e r s i b l e " 3 / ~ e t ra n s f o rm a t i o n, t h e c o n c lu -s ion was d rawn tha t t he y ' phase i s t he rmodynamica l l yuns t ab l e a t tempe ra tu re s be low 423 K. Th i s t emp e ra tu re i si n -be tween t he tw o e s t ima te s fo r t he t r ip l e po in t c a l cu l a t edprev ious ly .*** * W i th r eg a r d t o t h e r ev e r s ib l e y ' ~ - e t r an s f o r m a t io n , t h e wo r kin t r o d u ced in to t h e s am p le b y th e b eam o f Ne io n s d u r in g an n ea l in gin t r o d u ces d i s p l acem en t s o f b o th i r o n a to m s an d n i t r o g en a to m s , wh ich ,i f t h ey we r e d u e t o t h e r m a l a c t i v a ti o n , wo u ld r eq u i r e a h ig h e r t em p e r a tu r e .T h e p o s s ib l e i n t r o d u c t ion o f s t a ck in g f au l ts i n t h e i r o n s u b la tt i c e d u e t oio n b o m b ar d m en t m ay b e l o ca l ly a s s o c i a t ed wi th t h e t r an s f o r m a t io n o f

th e f cc s u b l a t t i c e o f i r o n a to m s to t h e h cp s u b la t t ic e o f i r o n a to m s . T h en i t r o g en a to m s in y ' - n i t r i d e s h o w a lm o s t p e r f ec t l o n g - r an g e o r d e r in g o nth e i r o w n s u b la t t i c e ,m J wh e r ea s t h e n i t r o g en a to m s in e - n i t r i d e a r e n o t s os t r o n g ly o r d e r ed 5~31 The s t rong order ing o f n i t rogen a tom s in y ' m ay bed i s tu r b ed b y io n b o m b ar d m en t . B o th co n s eq u e n ces o f Ne ~ b o m b ar d m en t ,v iz . t h e i n t r o d u c t io n o f s t a ck in g f au l t s an d th e d i s o r d e r in g o f t h e n i t r o g ena to m s , m ay f av o r t h e f o r m a t io n o f e - n i t r i d e fr o m y ' - n i t ri d e .

I V . C O N C L U S I O N SExpe r imen ta l n i t rogen-absorp t i on i so the rms o f t he a -Fe[N], y '-Fe4Nl_x, and e-Fe2N~_z phases were descr ibed ac-cura t e ly by adop t ing t he rmodynamic mode l s fo r t he se

phase s accord ing t o a r egu l a r i n t e rs t i ti a l so lu t ion , t he W Sapproach , and a GBW approach , r e spec t i ve ly . The o d a +y ' , a + y ' / y ' , y ' / y ' + e , and y ' + e / e phase bounda r i e swere ca l cu l a ted by subs t i t u ti ng t he n i t r i d ing po t en t ia l s pe r -t a in ing t o t he a / y ' and y ' / e two-phase equ i l i b r i a i n t he t he -o re t i c a l de sc r ip t i ons o f t he absorp t i on i so the rms . Theca l cu l a ted phase bounda r i e s ag ree ve ry w e l l wi th the mo s tre l iable exper imenta l da ta . In par t icular , the ca lcula ted y '+ e / e phase boun da ry p rov ides a ma jo r improvem ent a scomp ared to ea r li e r r e su lt s . The y ' + e / e phase bounda rywas found to be ve ry sens i ti ve a t r e la t i ve ly l ow t empe ra tu re(


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17. J. Kunze: Nitrogen a nd Carbon in I ron and Steels, Thermodynamics ,Akademie Verlag , Berl in , 1990.18. K. Frisk: C A L P H A D , 1991, vol. 15 (1), pp. 79-106.19. H. Du: J. Phase Equil ibr ia , 1993, vol. 14, pp. 682-93.20 . A.F. Gui l lermet and H. Du: Z. Metallkd., 1994, vol. 85, pp. 154-63.21. H.A. Wriedt, N.A. Go kcen, and R.H. Nafziger: Bull , Alloy PhaseDiagrams, 1987, vol. 8 (4), pp. 355-77.22. W.S. Gorsky: Z. Phys . , 1928, vol. 50, p. 64; W.L. Bragg and E.J.Wil l iams: Proc. R . Soc . London, 1934, vol. A145, p . 699; W.L. B raggand E.J . Wil l iams: Proc. R . Soc . London, 1935, vol. A151, p. 540;W.L. Bragg and E.J . Wil l iams: P r o c . R . S o c . L o n d on , 1935, vol.A152, p. 231.23. E. Lehrer: Z. Elektrochem., 1930, vol. 36 (6), pp. 383-92.24 . Z. Przyleeki and L. Maldzinski : Carbides , Ni tr ides and Bor ides , Proc.4th Int. Conf., Politech nika Pozn anska , 1987, pp. 153-62.25. L. Maldzinski: Ph.D. Thesis, Politechn ika Poznanska, Poland, 1989(in Polish).26. P.H. Em met t , S.B. Hendricks, and S. Brunauer: J . Am. C h em . So c . ,1930, vol. 52, pp. 1456-64.27 . S. Brunauer, M.E. Jefferson , P.H. Emmet t , and S.B. Hendricks: J .Am. C h em . So c . , 1931, vol. 53, pp. 1778-86.28. N .S. Corne y and E.T. Turkdogan: J. Iron Steel Inst., 1955, vol. 180,pp. 344-48.29. A. Burdese: Ann. Chim., 1959, vol. 49, pp. 1873-84.30. H.J. Grabke: Ber . Bunsengesell . Phys . Chem., 196 9, vol. 73 (6), pp.596-601.31 . H.A. Wile&, N.A. Gokcen, and R.H. Nafziger: B in a r y A l lo y P h a s eDiagrams, ASM, Materials Park, OH, 1990, vol. 2, pp. 1728-30.32. H .H. Podgurski an d F.N. Davis: Acta Metall . , 1981, vol. 29, pp. 1-9.33. L.J. Dijkstra: Trans . AIME, 1949, vol. 185, pp. 252-60.34. V.G. Paranjpe, M. Cohen, M.B. Bever, and C.F. Floe: T r a n s . A I M E,1950, vol. 188, pp. 261-67.3 5 . H .U . / ~ s t r rm: Ar k iv Fys i k , 1954, vol. 8 (49), pp. 495-502.36. A. Burdese: Metall. I tal., 1955, vol. 8, pp. 357-61.

37. J.D. F ast and M.B. Ve rrijp: d. Iron Steel Inst., 1955, vol. 180, pp.337-43.38. R. Rawl ings and D. Tambini : J. Iron Steel Inst., 1956, vol. 184 , pp.302-08.39. M. Nacken and J . Rahm ann: Arc h . Eisenhi i t tenwes . , 1962, vol. 33 (2),pp. 131-40.40 . Y. Imai , T. Masumoto , and M. Sakamoto: Sci . Rep. Res . Ins t . , TohokuUniv. , Ser . A , 1968, vol. A20 (1), pp. 1-13.41 . K. Abiko and Y. Imai : Trans . Jpn . In s t . Met . , 1977, vol. 18, pp. 113-24.42 . O . Eisenhu t and E. Kaupp: Z. Elektrochem., 1930, vol. 36 (6), pp.392-404.43. E. Lehrer: Z. Elektrochem., 1930, vol. 36 (7), pp. 460-73.44 . C. G ui l laud and H. Creveaux: C o r o t . Re n d . Aca d . Sc i . P a r i s , 1946,vol. 222, pp. 1170-72.45. F.K. Naumann and G. Langenscheid : Arch . Eisenhi i t tenwes . , 1965,vol. 36 (9), pp. 677-82.46. H.A. Wriedt: T r a n s . A I M E, 1969, vol. 243, pp. 43-46.47 . M.A.J. Somers and E.J. Mi t temei jer: Metall . Trans . A , 1990, vol. 21A,pp. 189-204.48. M.A.J. So me rs and E.J. Mittemeijer: MetalL T rans . A , 1990, vol. 21A,pp. 901-12.49. M.A.J. S omers, N.M . van der Pers, D. Schalkoord, and E.J.Mittemeijer: Metall . T rans . A , 1989, vol. 20A, pp. 1533-39.50 . A.M. Vredenberg , C.M. Prrez-M art in , J .S. Custer , D.O. Boerm a, L.de Wit, F.W. Saris, N.M. van der Pers, Th.H. de Keijser, and E.J.Mittemeijer: J . Mater . Res . , 1992, vol. 7 (10), pp. 2689-2712.51. L. de Wit, Th. Weber, J.S. Custer, and F.W. Saris: Phys . R ev. Let t. ,1994, vol. 72, pp. 3835-38.52. H .H. Podgurski and H.E. Kne chtel: T r a n s . A I M E, 1969, vol. 245, pp.1595-1602.53. H.J. Grabke: Ber . Bunsengesell . Phys . Chem., 1968, vol. 72 (4), pp.533-41.

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