In this paper, the possible reasons for the high thermal vacancy concentration and the low migration barriers for the Fe atom diffusion in the DO3 structure Fe3Si have been discussed

张永刚

陈永冲

魏炳忱

English

Institute Of Mechanics,Chinese Academy of Sciences

第 20 卷第 2 期 原　子　与　分　子　物　理　学　报 Vol. 20 , №. 22003 年 4 月 CHINESE JOURNAL OF ATOMIC AND MOL ECULAR PHYSICS Apr. , 2003Article ID : 100020364(2003) 0220143206Diffusion mechanisms in the Fe3Si alloysΞCHEN Yong2chong1 , ZHAN G Yong2gang1 , WEI Bing2chen2 , CHEN Chang2qi1(1. School of Materials Science & Engineering , Beijing University of Aeronautics and Astronautics , Beijing 100083 ,P. R. of China ;2. National Microgravity Laboratory , Institute of Mechanics , Chinese Academy of Science , Beijing 100080 ,P. R. of China)Abstract : In this paper , the possible reasons for the high thermal vacancy concentration and the low migration barriersfor the Fe atom diffusion in the stoichiometric D03 structure Fe3 Si have been discussed. The high thermal vacancyconcentration was attributed to the compression of Fe - Fe atomic pairs and the tension of Fe - Si atomic pairs in Fe75Si25 . The deformations (compression or tension) of the atompairs increase the interatomic potentials and thus decreasethe enthalpies of vacancy formation. The low migration barriers for the Fe atom diffusion in Fe75 Si25 were related to thesymmetric property of the triangular barriers. Additionally , it was considered that the Si atoms in Fe3 Si could probablymigrate via nearest2neighbour jumps without disturbing the long2range order of atomic arrangements , provided thatduring the diffusion process the residence time on the antistructure sites is very short .Keywords :Self2diffusion ; D03 - Fe3 Si alloys ; Thermal vacancy ; Migration barriersCLC number : O436. 1 　　　Document code :A1 　IntroductionWith the only exception that the small impurity orminority atoms can move by the interstitial mechanism ,it is mostly the vacancy that is held responsible for thediffusion of atoms in the ordered alloys[1 ] . It wasgenerally considered that the minority atoms in theordered alloys , such as the Si atoms in Fe3Si , cannotmigrate randomly via the nearest2neighbour ( NN )jumps , because this mechanism may generate more andmore antisite defects and hence the order of alloy wouldbe destroyed[2 ,3 ] . In this case , diffusion of the Si atomcan only take place via direct jumps to further distantsites on sublattices with Si atoms , or via mechanismsinvolving more than one elementary jump process , e. g.the six2jump cycle mechanism[4 , 5 ] .In our opinions[6 ] , however , it is probable , notonly possible , that the Si atoms migrate via NN jumps inFe3Si without disturbing the long2range order , andinvolving no unique jump process. Since the residencetime of the Si atoms on the antistructure sites could be soshort that there are a very few of Si atoms on the‘wrong ’ sublattices measured at any time.Furthermore , the majority atoms Fe can also migrate tothe antistructure sites via NN jumps , although there areNN sites belonging to the Fe atoms.But the theoretical problems of atomic diffusion inthe Fe3Si alloys are far from solved. MÊssbauerspectroscopy experiments by Sepiol and Vogl have shownthat diffusion of the Fe atoms in Fe75Si25 is astonishinglymuch faster than that of Fe diffusion in Fe2rich Fe3Si ,or in pure BCC iron[7～9 ] . In other words , the less theFe content of Fe3Si is , the faster the diffusion of Featoms would be. By contrast , self2diffusivity of Si is aΞ Received date :2002209202Foundation item :Project supported by the Nature Science Foundation under the contract Number 50071001.Biography :CHEN Yong2chong (1975 - ) , male , Dayu county Jiangxi Province Doctorate Major in Materials Science. Tel :010 - 82314488 ; E2mail :matscichen @sina. com. cn.great deal slower and much less sensitive to the Sicontent. Herein we try to analyze the diffusionmechanisms to explain the interesting results of previousexperiments.2 　Thermal formation of vacanciesinFe3SiThermal vacancies and the effective vacancyformation anthalpies of Fe3Si with the D03 structure havebeen investigated by the positron2lifetime spectroscopymethod[10 ] . High vacancy concentration was deduced forthe stoichiometric alloy Fe75 Si25 from the trapping ofpositrons. At about 750 K the trapping rate in Fe75Si25reaches saturation , while at which temperature the off2stoichiometric alloy Fe79Si21 contains nearly no vacancies( Fig. 1) , although an extrapolation of the vacancyconcentration of Fe79Si21 also yields in the percent rangenear the melting temperature[10 ,11 ] .Generally , the vacancy concentrations in alloys arehigher than the vacancy concentrations in puremetals[12 ] , yet how can we understand the sensitiverelationship between the vacancy concentrations and thealloy compositions for the Fe3Si alloys ?As Shown in Fig. 2 , the D03 structure is an orderedBCC structure with three different sublatticesα, βandγ. In Fe75 Si25 , the Fe atoms are located on twodifferent sites α and γ, and the Si atoms on β. It isshown that the cluster of one Fe atom on γ site witheight nearest2neighbour Fe atoms onαis enclosed in thenet of Si atoms on β ( Fig. 3) . Since the equilibriumbonding distance r1 , r2 of Fe - Fe and Fe - Siatompairs respectively are not equal , the enclosedstructure may result in the deformation in the wholecrystal lattice. The deformed interatomic distance R1 ,R2 of Fe - Fe and Fe - Si atompairs respectively shouldsatisfy the geometrical restrictionR1 = R2 = r (1)For values of | r1 - r2 | ν r1 , the elastic deformationenergy Δε1 of the Fe - Fe atompairs can beapproximately given byΔε1 = k1( r - r1) 22 (2)and the elastic deformation energy Δε2 of the Fe - SiatompairsΔε2 = k2( r - r2) 22 (3)441 　 原　子　与　分　子　物　理　学　报 　 2003 年　where k1 (or k2) is the force constant of the Fe - Fe (orFe - Si) atompairs[13 ] .Considering the quantity ratio of Fe - Fe and Fe -Si atompairs is 1∶1 in Fe75 Si25 , the real interatomicdistance r0 can be given by the harmonic deformationfunctionr0 = r5 (Δε1 + Δε2)5 r = 0i. e.r0 =k1 r1 + k2 r2k1 + k2(4)Substituting in Eq. (2) and (3) shows thatΔE1 = k1( r1 - r0) 22 (5)andΔE2 = k2( r2 - r0) 22 (6)where ΔE1 , ΔE2 are the deformation energy of Fe - Feand Fe - Si atompairs , respectively , resulting from theharmonic deformation of atompairs in Fe3Si matrix withfull order (Fig. 4) .The deformation energiesΔE1 and ΔE2 increase thepotential energies of Fe and Si atoms and thus attributeto the easier formation of vacancies in Fe75Si25 . If the Fecontent increases in Fe3Si , the enclosed structure ofFe75Si25 matrix would be destroyed and the averagedeformation energies in the whole crystal would decreaseto the local lattice2distortion energies. Therefore ,thermal vacancies in Fe3Si also decrease.3 　Self2diffusion in Fe3SiFor Fe75 Si25 , the resulting value from high2temperature 57 Fe MÊssbauer spectroscopy of the Fe self2diffusivity is strikingly high ; it amounts to 5 ×10 - 13 m2s- 1already at 993 K, but a factor of 5 to 10 lower forthe off2stoichiometric alloy Fe80Si20[10 ] . Radiotracerinvestigation by Gude and Meher[14 ] also indicates thatFe diffusion in Fe3Si is strongly dependent on thecomposition; with increasing Fe content the Fediffusivity decreases rapidly. But diffusion of Si(simulated by 71 Ge) is much less affected by thecomposition ( Fig. 5 ) , i. e. the diffusion of bothcomponents is obviously not‘coupled’[15 ] .●Fe75Si24 :■Fe79Si21 :▲Fe82Si18 :59Fe ; 　○Fe76Si24 :□Fe79Si21 :△Fe82Si18 :71 Ge 　∀ Fe76Si24 :31SiUpon deviation from the stoichiometric compositionto the iron rich side , maybe the thermal vacancyconcentration decreasing account for the decrease of theself2diffusivity of Fe in Fe3Si. However , it fails toexplain the ‘decoupled’diffusion of the Si atoms.Furthermore , MÊssbauer experiments imply that in theoff2stoichiometric alloy Fe80Si20 or Fe82Si18 , there are541　第 20 卷第 2 期　　 CHEN Yong2chong , et al :Diffusion mechanisms in the Fe3 Si alloys 　significantly more jumps between theαandβsites thanjumps between theαandγ sites[7 ,16 ] .So it remains herein an open problem for discussionthat why the Fe atoms jumping to the antistructure sitesin Fe3Si becomes dominating when leaving stoichiometryversus the Fe - rich side.As we know , for an atom diffusion in the BCCstructure via an NN jump there are two barriers oftriangular shape to overcome ; while for an NN jump inthe FCC structure the gate is the four atoms at thehalfway point (Fig. 6) [17 ] . In a successful jump , whenthe atom moves from the average position by thermalactivation , its potential energy Φ ( r0 ) increases to amaximum Φ ( r0 ) + ΔΦ at the barrier and thendecreases. This maximum is the least height for a certainpath which defines the saddle point of the function Φ( r) and the height of the potential barrier ΔΦ. In thepure BCC (or FCC) structure , the potential energyfunction Φ( r) described by this potential2barrier modelis perfectly symmetric (Fig. 6 (b) , (d) ) .For the ordered alloys , the geometric characteristicsof the potential function of atom migrations via NNjumps are much complicate. In the Fe3Si alloy with fullorder , when the Fe atom jumps from the α to the γsublattice it has to overcome the first barrier of triangularshape consisting of three Si atoms and the second ofthree Fe atoms (Fig. 7) .This jumping path , symmetric in geometry , could bereferred to as‘rapid passage’for the Fe atoms diffusionin Fe75Si25 . In Fe75Si25 , each Si atom relates to 24 rapidpassages for the Fe atoms jumping between theαandγsites , i. e. theβ sublattice or the Si atoms net providesthe triangular2barriers as the rapid passages for Fediffusion. In Fe76 Si24 , however , there are 4 to 12percent of the rapid passages substituted by the highermigration barriers of triangular shape with only one ortwo Si atoms (Fig. 8 (a) (b) ) . In Fe80Si20 , 20 to 60641 　 原　子　与　分　子　物　理　学　报 　 2003 年　percent of the rapid passages are destroyed. In otherwords , the migration barriers for Fe diffusion in Fe3Siare much sensitive to the Fe content. If the potentialbarriers with one or two Si atoms are higher than thatwith six Fe atoms for the Fe atom jumps between theαandβsublattice , Fe diffusion in Fe80 Si20 may prefer totheα- βmodel rather than theα- γmodel , as provedby the results of MÊssbauer experiments[7 ] .By contrast , the barriers for the Si atoms diffusionin Fe80 Si20 are less affected by the change ofcomposition. Yet the potential energy of the Si atoms onαsites is higher according to the change of NN atomsaround the α sites. This change would increase theresidence time of the Si atoms on α sites and thuscontribute to the Si atoms taking effective jumps , i. e. itshauld contribute to the self2diffusivity of Si in Fe20Si80[6 ] . Therefore , when the D03 order decreases the Siself2diffusivity would be less affected or even accelerated ,though the thermal vacancies decrease a lot (Fig. 5) .4 　SummaryGeometric discussions on the atompairs andmigration barriers indicate that the potential energybarriers for the Fe atoms diffusion in Fe3Si , as well asthe thermal vacancy concentrations , are closely sensitiveto change of the composition. So the low migrationbarriers should also attribute to the extremely highdiffusion coefficient of Fe in Fe75Si25 .The minority Si in Fe3Si could probably migrate viaNN jumps only if the residence time on the antistructuresites is very short . In the off2stoichiometric Fe3Si alloysthe longer residence time of Si onαsites contribute to itstaking effective jumps. Therefore the self2diffusivity ofSi in Fe3Si is much less affected or even accelerated whenleaving stoichiometry versus the iron rich side. Thediscussions explain the results of previous experiments.References[1 ] Tuijn C. On the history of models for solid2state diffusion[J ]. Defect and Diffusion Forum , 1997 , 143～147 : 11～18.[2 ] Elock E W , McCombie C W. Vacancy diffusion in binaryordered alloys [J ]. Phys. Rev. , 1958 , 109 :605～606.[3 ] Bakker H , Lo Cascio D M R. Diffusion in intermetallicscompounds2underlying aspects [ J ]. Defect and DiffusionForum , 1993 , 95 - 98 : 803～822.[4 ] Belova I V , Ivory M E , Murch G E. Diffusion in a model ofan ordered alloy [J ]. Philos. Mag. 1995 , A72 (4) : 871～880.[5 ] Drautz R. F¾hnle M , The six2jump diffusion cycles in B2compounds revisited [J ]. Acta Mater. , 1999 , 47 (8) : 2741　第 20 卷第 2 期　　 CHEN Yong2chong , et al :Diffusion mechanisms in the Fe3 Si alloys 　437～2 447.[6 ] Chen Y C , Zhang Y G, Chen C Q. The residence time forunderstanding diffusion in the ordered alloys [J ]. ChinesePhys. Lett . (has been submitted) .[7 ] Sepiol B , Vogl G. Atomistic determination of diffusionmechanism on an ordered lattice [J ]. Phys. Rev. Lett . ,1993 , 71 (5) : 731～734.[8 ] Sepiol B. MÊssbauer spectroscopy in diffusion studies [J ].Defect and Diffusion Forum , 1995 , 125～126 : 1～18.[9 ] Sepiol B , Vogl G. Diffusion in ordered Fe - Si alloys [J ].Hyperfine Interactions , 1995 , 59 : 149～159.[10 ] Kümmerle E A , Badura K, Sepiol B , Meher H , Schaefer H∃ E. Thermal formation of vacancies in Fe3 Si [J ]. Phys.Rev. 1995 , B52 (10) : R6947～R6950.[11 ] Vogl G. Diffusion in intermetallic phases2historical facts andnew results [J ]. Defect and Diffusion Forum , 1997 , 143～147 : 223～238.[12 ] Kraftmakher Y. Equilibrium vacancies and thermophysicalproperties of metals [J ]. Physics Reports , 1998 , 299 : 79～188.[13 ] Howe J M. Interfaces in materials [ M]. (New York : JohnWiley & Sons Inc. ) Chps. 1 , 1997.[ 14 ] Gude A , Mehrer H. Diffusion in the D03 - typeintermetallic phase Fe3 Si [J ]. Philos. Mag. 1997 , A76(1) : 1～29.[15 ] Mehrer H , Eggersmann M , Gude A , Salamon M , SepiolB. Diffusion in intermetallic phases of the Fe - Al and Fe -Si systems [J ]. Mat. Sci. Eng. 1997 , A239～240 : 889～898.[ 16 ] Gude A , Sepiol B , vogl G, Mehrer H. Diffusion in theintermetallic Phase Fe3 Si studied by Tracer and MÊssbauertechniques [J ]. Defect and Diffusion Forum , 1997 , 143～147 : 351～358.[17 ] Philibert J . Atom movements : diffusion and mass transportin solids [ M ]. ( France : Les ∗ditions de Physique) Chps.1 , 1991.(continued from page 142)Multiphoton ionization dissociation mechanism of 22ButanoneGUO Wen2yue1 , HU Song2qing1 , Fang Li2 , ZHAN GBing2 , ZHAN G Shu2Dong2 , CAI Ji2ye2(1. Applied Physics Department , University of Petroleum , Dongying , 257061 ,P. R. of China ;2. Anhui Institute of Optics and Fine Mechanics , The Chinese Academy of Sciences , Hefei 230031 ,P. R. of China)Abstract : Multiphoton ionization dissociation ( MPID) mechanism has been studied on 2 - butanone moleculeresonated via ( no , 3 d) state by 3 photons. The main MPID products are C2 H3O + and CH3CH+2 , the intensity ofC2 H3O + is 1～4 times larger than that of CH3CH+2 , and some mionr ions C2 H+2 , C2 H+3 and CH+3 are also observed inthe whole experimentally spectral region , where as no parent ion is observed. The mass2selected resonance2enhancedmultiphoton ionization dissociation spectra take a similar feature , but the laser power indexes of the fragmental ions aredifferent from each other. Based on the experimental results , the multiphoton ionization dissociation mechanism ismade out to accord with“molecular ion ladder model”. The producing mechanism of the main ions has been discussedin detail according to“ladder switching”.Keywords : 22butanone ; Multiphoton ionization dissociation ; Ladder switching ; Time2of2fight mass spectrum841 　 原　子　与　分　子　物　理　学　报 　 2003 年　

Diffusion mechanisms in the Fe3ASi

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Diffusion mechanisms in the Fe3ASi

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Institute Of Mechanics,Chinese Academy of Sciences