Investigation of Methods for Calculation of Interdiffusion Coefficients of Iron and Nickel Powder Mixtures

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1 Investgaton o Methods or Calculaton o Interduson Coecents o Iron and Nckel Powder Mxtures F.NAZEMI Materal Eng.Dept. Isahan Unversty o Technology Isahan IRAN Faranaknazem@Gmal.Com Abstract. In ths research, new methods were devsed and nvestgated or calculaton o nterduson o ron and nckel powder mxtures n porous meda. We consder that two partcles s lke thn lm n duson couples and we use SEM and EDAX analyss and two mathematcal methods to calculatng Interduson Coecent. In these samples ater metallography the observaton wth SEM show that mcrostructure conssts o errte and nckel-rch regons. Duson prole was establshed by EDAX analyss rom center o gran rch o nckel up to the out o ts boundary and wth an expermental method and sphercal equaton o ond Fck s law o duson, we obtan acceptable results or nterduson coecent. We dd not use other addtonal element to produce samples and our sample have 4% nckel and.8% Mcrowax n pure ron powder (WPL) and ater mxng and compacton snterng was carred out n a mesh-belt conveyor urnace n ºC and 3 mn n control endogas atmosphere. The green densty o our sample s 6.8 g/cm 3. Keywords: Interduson Coecents, Powder, Nckel, Iron Introducton Alloys based on mxture o Fe and N powders are common throughout powder metallurgy (P/M). Ths alloys may seem smple, consderng that the two elements are close Fg. : Fe -N bnary phase dagram together n perodc table and are smlar chemcally, and n terms o electronc structure and atomc radus. However, the behavor o these alloys s complex. As shown n the Fe- N phase dagram n Fgure, the lqudus and soldus temperatures are hgh, wth a narrow soldcaton range. The ace-centered cubc crystal structure o ron (γ or austente) s stablzed by alloyng wth nckel (the γ regon expands wth ncreasng nckel concentraton). Snterng technques have been exploted or several years n the producton o Fe-N alloys. In mxed elemental powder snterng, there are undamentally three events- partcle adheson, denscaton, and homogenzaton. Adheson occurs by surace duson, typcally durng heatng. Concomtant bondng wthout denscaton provdes handlng strength n the powder mass. At hgher temperatures, denscaton processes become actve, leadng to pore elmnaton va gran boundary duson. However, as hgh sntered denstes are acheved the mcrostructure s not homogeneous, but conssts o N-rch slands n the Fe-C steel matrx. Durng the snterng ISSN: 79-46X 36 ISBN:

2 o mxed Fe-N powders, the adheson, denscaton and homogenzaton events are actors. In the early stage o snterng, chemcal gradents assocated wth mxed N and Fe powders mprove duson luxes over those assocated wth surace energy whch normally drves sngle-phase snterng. Thus ntal snterng can be mproved sgncantly by the addton o N. However, ths chemcal gradent enhancement decreases wth ncreasng temperature as the concentraton gradents are elmnated. Also, N enlarges the austente zone and lowers the errte-to-austente transormaton temperature. Snce lattce dusvty n acecentered cubc Fe s much lower than that the body-centered cubc Fe, the phase transormaton lowers the snterng rate. The concentraton o N n Fe ncreases durng snterng, nducng N-rch areas to transorm nto austente earler than would occur wth a low N content. The result s slower hgh temperature denscaton due to the reduced duson rate. Also, when Fe goes through the alpha-to-gamma transormaton, there s a sgncant ncrease n gran sze. Ths result n a decrease n annhlaton stes or vacances and substantal decrease n the snterng rate, whch s senstve to gran boundary area. Thus the addton o N powder to Fe powder enhances early stage snterng but retards later stage snterng. The coecent o duson Fe s much hgher than those o N, leadng to possble pore creaton durng nterduson. For example, rasng the snterng temperature rom C to 5 C ncreases the nterduson coecent o Fe nto N by a actor o our, whle that o N duson nto Fe ncreases by only two and hal tmes. The derence n dusvty s another actor that nluences denscaton and homogenzaton n mxed Fe-N powder snterng. Thus, t s dcult and costly to obtan a ully homogenzed Fe-N alloy based on the snterng o mxed elemental powder the N content s hgh. 5 Ths study measures the nterduson coecent o mxture o Fe-N powders that snter n C and 3 mn tme, n ths study we assume that the partcles o gven type are sphercal and o the same sze 6, we can drve a controlled by several smple model that partcle o N surrounded by Fe and durng snterng gradent o concentraton causes the nterduson o these partcles so ater snterng we have grans N-rch areas. By usng SEM and EDAX analyss and two mathematcal methods a consderable good result near sold partcle obtaned. Expermental Procedure: In ths research, we use N and Fe powder to produce expermental samples ater mxng, compacton and snterng, cylndrcal samples prepared or metallugraphy and ths process was perormed by optcal and ondary electron mcroscope. 3 Result and Dscusson: Metallography ndcates that these samples ncluded o errte, errte rch o nckel, mnor pearllte and porosty. Fgure () show these regons. Also, EDAX analyses show us concentraton gradent o Nckel rom errte rch zone to Nckel poor zone. Fgure : Mcrostructure o Fe-4%Nckel by ondry electron mcroscope Brght zone: Ferrte rch o Nckle, Gray zone: α-iron, mnor pearllte, Dark zone: porosty ISSN: 79-46X 36 ISBN:

3 (4) d=6 μm () d=, Center o Brght Regon The results o some other analyss rom these samples around the gran N rch show the same varaton, wth mathematcal Eq., Eq. and least square method and some lnear condton we assume two partcles lke thn lm so duson could perorm n one dmenson and two derent negatve and postve drectons. c( x, t) bc Dt x exp. () (5)d=8 μm () d= μm ln c( x, t) ln bc x. () Dt d (6) d= μm (3) d=4 μm Fgure 3: The results o EDAX analyss (Nckel contents: ()=9.5wt%, ()=8.54wt%, (3)=3.54wt%, (4)=6.74wt%, (5)=.wt%, (6)=.459wt%) 3- Calculaton o nterduson coecent Lnear Duson at one coordnaton 3 : Table and show the calculatons and the results o ths method. Table : Calculatons o the expermental data or rst method dd=x [μm] Dstance rom assumng orgnal C=the results o EDAX analyss LnC= Y XY XX Table : Result o the expermental data or rst method n ( x ) ( x ) * -4 a [( n x y ) x y ] -.88* 8 y x x x b ( y ) Y=ax+ b, a= Not requred D , t=8, cm Ater rectyng the Data D cm Fg. 4 shows the results o LnC(X,t) accordng X, by reactyng these data, the slope o ths dagram s better show o. Rectyng take places by contnung the rst lne passng rom rst data untl cuttng the horzontal lne at -35 (μm). By addng ths content to all data, the lne passng rom ond data ntert the horzontal lne at zero. The ISSN: 79-46X 363 ISBN:

4 orgnal era o duson can obtan accordng to ths rectyng. LnC(X,t) Beore rectng Dstance X (μm) Ater rectyng Fg.4: Dagram o Logarthm o concentraton data accordng to square dstance 3- Calculaton o nterduson coecent at sphercal coordnaton 4 : By the separatng varatons on sphercal coordnaton also we could calculate nterduson coecent o ths mxture. The ond Fck s law on sphercal coordnaton at varable condtons s lke below: Eq. 3 n c c D. (3) t x r r Ater soluton o ths equaton we could understand the relatve varaton o concentraton wth sutable lnear condton a, b and c that are lke below: a) Duson rom out to nsde the sphere o N to Fe r r, c, t c c, r r, t b) Duson rom nsde to out the sphere o N to Fe c c, r r, t c c, r r, t c) In total condton c c c c, r r, t, r r, t In ths lnear condton C, C, C are ntal, nal and average o concentraton and r s the average radus o Nckel partcles and wth orcng ths lnear condton the soluton o Fck s equaton s as below: Eq. 4 c c c c 6 exp Dt.(4) r In ths equaton the expermental tme s too long wth assumeng the rst seral sentence, the result o calculaton o equaton s lke below: Eq. 5 and we could calculate D wth Eq.6 c c c c c c ln c c 6 exp Dt r 6 ln ln Dt r. (5). (6) The result o D can obtan by puttng data rom EDAX analyss and assumng tme 4 equal 3 mn and radus equal cm as ollow: ln(.39.)/(.99.).4977 ln D36/ D Summary cm 8 - By usng the method o o calculaton o nterduson coecent Lnear Duson at one coordnaton we can obtan D cm - Ater rectyng data the nterduson coecent obtan ISSN: 79-46X 364 ISBN:

5 D cm 3- By usng Calculaton o nterduson coecent at sphercal coordnaton o mxture o Fe-4%N powders that snter n C and 3 mn we can obtan D.334 cm Reerences [] R. M. German, Powder Metallurgy o Iron and Steel, 998, Wley- Interscence, New York, NY. [] L.J. Swartzendruber, V.P. Itkn, and C.B. Alcock, Alloy Phase Dagrams, Volume 3 o the ASM Handbook. 99 [3] P.Shewmon, Duson n Solds, ed. 989, Warrendale, PA: The Mnerals, Metals, Materals Socety. [4] A. Sadjad, Duson n Solds, Iran Un.o Sc.and Tech., 997 [5] H.Zhang, M.German.Randall Snterng MIM Fe N Alloys, The Internatonal Journal o Powder Metallurgy Vol 38, NO., [6] P.Marsh., J.V.Wood, J.R.Moon, Duson between hgh speed steel and ron powders, Powder Metallurgy,Vol.44 No.3 ISSN: 79-46X 365 ISBN: