MechanicaHy driven alloying and grain size changes in nanocrystalline Fe-Cu powders

Transcription

1 MechancaHy drven alloyng and gran sze changes n nanocrystallne Fe-Cu powders J. ckert, J. C. Holzer, C.. Krll III, and W. L. Johnson Calforna Insttute of Technology, W; M. Keck Laboratory of ngneerng Materals , Pasadena, Calforna 9112 (Receved 24 March 1992; accepted for publcaton 21 September 1992) Hghly supersaturated nanocrystallne Fe,Culcc-X alloys (lo<n<9) have been prepared by mechancal alloyng of elemental crystallne powders. The development of the mcrostructure s nvestgated by x-ray dffracton, dfferental scannng calormetry, and transmsson electron mcroscopy. The results are compared wth data for ball-mlled elemental Fe and Cu powders, samples prepared by nert gas condensaton, and sputtered flms. The deformaton durng mllng reduces the gran sze of the alloys to 6-2 nm. The fnal gran sze of the powders depends on the composton of the materal. Sngle-phase fee alloys wth x<6 and sngle-phase bee alloys wth ~8 are formed even though the Fe-Cu system exhbts vanshngly small sold solubltes under equlbrum condtons. For 6O<x<8, fee and bee sold solutons coexst. The alloy formaton s dscussed wth respect to the thermodynamc condtons of the materal. The role of the large volume fracton of gran boundares between the nanometer-szed crystals, as well as the ntluence of nternal strans and stored enthalpes ntroduced by ball mllng, s crtcally assessed. I. INTRODUCTION The synthess of metastable phases by mechancal alloyng/ball mllng has been studed extensvely n recent years snce t has been shown that ths technque s a versatle tool for producng materals far from thermodynamc equlbrum. Much work has been performed on the formaton of metastable amorphous, quascrystallne, and crystallne phases for systems wth a negatve enthalpy of mxng.ls4 For such materals, the phase formaton has been explaned by both thermodynamc and knetc arguments. However, mechancal alloyng of systems wth a postve enthalpy of mxng s far from beng well understood. Sold solutons n mmscble systems, such as Fe- CU,~- Fe-Ag, Ag-Cu, Cu-V,* CU-W,~ and CuTa, have been prepared by mechancal alloyng. The formaton of these sold solutons s n apparent contrast to what one would expect from the equlbrum phase dagram of these systems. Recently, t has been shown that nanocrystallne metals and alloys wth large excess enthalpes can be obtaned by mechancal attrton. - It has therefore been suggested that the mechancally stored enthalpy caused by nternal strans and the large gran boundary fracton due to the small crystal sze n these materals can serve as a drvng force for alloy formaton.7 16 Transmsson electron mcroscopy revealed that by ball mllng, the nanocrystallne structure wth random orentaton of ndvdual grans evolves from dslocaton cell structures wthn shear bands.t2 By further deformaton, the dslocaton cells/lowangle gran boundares vansh, leadng fnally to a fully nanocrystallne powder wth a completely random orentaton of neghborng grans separated by hgh-angle gran boundares.12 Thus, the detals of generaton and moton of dslocatons under mechancal attrton, as well as ther annhlaton by recovery and recrystallzaton, seem to play a crucal role n the formaton and the propertes of ballmlled nanocrystallne materals. In ths work, we nvestgate alloy formaton n bnary FeXCuloo-X mxtures ( 1~~~9). Mechancal alloyng leads to nanocrystallne sold solutons wth drastcally extended solubltes. The results are compared wth data for ball-mlled elemental powders and samples prepared by lqud quenchng and evaporaton technques. The alloyng process s dscussed wth respect to the large nterfacal area between the small crystals, the mechancally nduced strans, and the excess enthalpes produced by mllng. The gran sze of the alloys depends on the overall composton of the materal. For ths, a model based on the deformaton mechansm durng ball mllng, ncludng soluton hardenng durng alloyng, s nferred, and the nfluence of gran boundares and chemcal nhomogenetes on the deformaton characterstc s crtcally assessed. II. XPRIMNTAL MTHODS lemental Fe and Cu powders wth a purty of 99.9% or better and a partcle sze of ~1 pm were used. The powders were mxed to gve the desred average composton and sealed n a val under an argon atmosphere. The ball mllng was performed n a standard Spex 8 laboratory mll usng hardened steel balls and val wth a ballto-powder weght rato of 4:l. The val temperature was kept constant durng the experments by ar coolng. After dfferent mllng tmes, the mechancal attrton was nterrupted and a small quantty of powder was removed for further characterzaton. All the handlng was done under an argon atmosphere to avod oxdaton. The x-ray dffracton patterns were taken wth a Norelco dffractometer usng N-fltered Cu Ka radaton (J+==O.142 nm). For transmsson electron mcroscopy (TM) (Phlps M 43 mcroscope operated at 3 kv), 2794 J. Appl. Phys. 73 (S), 1 March /93/ $ Amercan Insttute of Physcs 2794

2 the powders were mxed wth epoxy, and 2--nm-thck sectons were prepared by damond-knfe mcrotomy. Chemcal analyss of the powders was done by wavelengthdspersve x-ray analyss (WDX) usng a JOL Superprobe 733 operated at 1 kv. The WDX analyss revealed only slght changes n the overall composton of the powders due to wear debrs from the mllng tools: less than 2 at. % addtonal Fe was found even after 24 h of mllng for all compostons. Thermal analyss was performed n a dfferental scannng calormeter (Perkn-lmer DSC 4) at a heatng rate of 2 Wmn under flowng argon. After each scan, a subsequent scan was carred out wthout changng the sample confguraton and used as a baselne (degrees) Ill. RSULTS A. Progress of phase formaton and development of mcrostructure The x-ray dffracton patterns for Fe3Cu7, Fe7Cu3, and Fe9eCulo p owders after dfferent mllng tmes are shown n Fgs. 1 (a) - 1 (c). For Fe3Cu7, the ntally sharp dffracton lnes of elemental Cu and Fe broaden sgnfcantly durng mllng and are reduced n ntensty. After 8 h, the Fe peaks have completely dsappeared and only fee peaks reman [Fg. 1 (a)]. A smlar development s observed for FegoCulc. The fee Cu peaks dsappear completely after 8 h and only bee peaks are vsble after 24 h of mllng [Fg. 1 (c)l. As the ntensty of the elemental x-ray lnes s reduced, the dffracton lnes of the sold solutons are dsplaced compared to the Bragg peaks of pure Cu and Fe, thus ndcatng true alloyng (see below). For Fe7Cu3, the x-ray lnes of Fe and Cu also broaden and decrease n ntensty wth mllng, but both sets of fee and bee dffracton lnes reman clearly vsble, even after extended mllng [Fg. 1 (b)]. Therefore, a two-phase mxture of fee and bee sold alloys forms n ths case rather than a homogeneous sold soluton. The mcrostructure of the mechancally alloyed powders was nvestgated by TM. For ~6 and x)8, the selected-area dffracton (SAD) patterns exhbt only the characterstc Debye-Scherrer rngs of fee and bee structures, respectvely. Ths confrms the nterpretaton of the x-ray results n terms of sngle-phase alloys. Fgure 2 shows (111) fee and (11) bee dark-feld mages and the correspondng SAD patterns for fee FeCu~ and bee Fe9,CuIo powders after 24 h of mllng, respectvely. The TM mages reveal a very fne-graned mcrostructure of ndvdual crystals whch are separated by hgh-angle gran boundares (the larger areas vsble n Fg. 2 are composed of several ndvdual grans). The progress of alloyng s llustrated n Fg. 3, whch shows the change of the fee and bee lattce parameters for FesoCu7 and F~cCuIO, respectvely, as a functon of mllng tme. The lattce parameters were calculated usng Cohen s method and the extrapolaton functon cos2 / sn 8. Between 2 and 8 h, both the fee and bee lattce parameters ncrease strongly and approach a saturaton value wth longer processng. Ths ndcates that alloyng takes place manly wthn the frst 8 h, reachng a steady L I I I I I I (degrees) I I I I I I (degrees) FIG. 1. X-ray dffracton patterns for (a) F~,&u,~, (b) Fe,&u,,, and (c) Fe,&u,, after dfferent mllng tmes are shown. state after 24 h. Ths s consstent wth the results shown n Fg. 1: the x-ray peaks of unreacted elemental Fe and Cu are no longer vsble after 8 h of mllng. The x-ray dffracton data as a functon of mllng tme were used to gan further nsght nto the refnement of the mcrostructure and the ncrease of atomc-level stran durng mechancal alloyng. The ntally sharp dffracton lnes of fee Cu and bee Fe broaden sgnfcantly durng mllng, as mentoned above (Fg. 1). Ths s due to two effecks: fnte sze broadenng and atomc-level stran broadenng. To separate these two effects we analyzed the full wdth at half maxmum (FWHM) of the Bragg peaks as a functon of the dffracton angle. The sze broadenng profle was approxmated by a Cauchy functon and the stran broadenng profle by a Gaussan functon.18 The functonal relatonshp between the observed peak FWHM and 279 J. Appl. Phys., Vol. 73, No. 6, 1 March 1993 ckert eta/. 279

3 32 -. w * z / / tj / 2 c! / P- //y----m a $.382 -! I & $ I jg ,f 3 l FesoQvo WC) a 8 n FegoW o (bee) IO Mllng Tme (h) FlG. 3. Lattce parameters for Fe&u,, and Fe9&u,, versus mllng tme are shown. tween the volume-average gran sze d and the rms atomclevel stran (e) * s * FIG. 2. Dark-feld TM mages and correspondng selected area dffracton patterns for (a) FeSOCuSO and (b) Fe&u,, after 24 h of mllng are shown. the sze and stran FWHMs can then be calculated from the convoluton of a Cauchy and a Gaussan functon. Convertng the dffracton angle 2 to the recprocal space varable s=2 sn /l, one can show * that the peak broadenng (SS)szc due to sze effects s ndependent of s, whle the stran broadenng (Ss),tran s proportonal to s. Thus, the dependence of the measured peak wdth (6s)b on.y, determned after Ka2 ntensty and nstrumental broadenng correctons, enables the broadenng contrbutons of sze and stran effects to be separated. Furthermore, by substtutng the functonal dependence of (SS)sze and (6s) stran on s nto an approxmaton for a Cauchy/ Gaussan convoluton, one fnds that the relatonshp be- l/(ss>,~=d-6.2(e2)d[s/(ss),12. (1) By performng a least-squares ft to l/(&)e plotted aganst [~/(&)a]~ for all the measured peaks of a sample, we are abie to determne d and ( e2> 1 2. Fgure 4 shows the reducton of gran sze and the ncrease n rms atomc-level stran wth ncreasng mllng tme for FeJOCu,u and FegOCul, as typcal examples. In the early stages of mllng, the gran sze decreases rapdly to less than 2 nm and approaches a steady-state value of about 12 nm for Fe&u,, and 1 nm for Fe,,C!u,, after 24 h of mllng. Smultaneously, the rms atomc-level stran ncreases to a maxmum value of about.3% for Fe&&, and.8% for Fe9&ut,, after 8 h of mllng. Wth extended processng, the stran decreases agan and approaches a steady-state value for long mllng tmes/small gran szes. The observed stran values are comparable to the values found for other ball-mlled metals and alloys.7- In partcular, a maxmum n the rms stran has also been reported for ball-mlled elemental Ru and the &Cl-type compound AlRu. t Further nformaton on the progress of alloyng can be obtaned by dfferental scannng calormetry (DSC). Fgure shows the DSC traces after dfferent mllng tmes for Fe&J.t,, as a typcal example. Mllng for 2 h results n a broad exothermc reacton that starts at about 37 K and s almost completed at 87 K. Wth ncreasng mllng tme, two exothermc maxma at - 68 K and - 7 K become more pronounced. X-ray dffracton of samples heated above the frst maxmum reveals that phase separaton occurs durng ths exotherm. Smultaneously, the gran szes of Fe and Cu ncrease to about 2 nm, and the stran drops to about.1% Durng heatng to 87 K, further gran 2796 J. Appl. Phys., Vol. 73, No. 6, 1 March 1993 ckert et al. 2796

4 3 (a) b.4 6-8h 24 h.2 : Temperature (K) o Mllng Tme (h) Mllng Tme (h) FIG. 4. Average gran sze (flled symbols) and atomc-level stran (open symbols) for (a) Fe&u,, and (b) Fe&k,, versus mllng tme are shown. growth and stran release occurs. Smlar results have been observed for all compostons (for further detals see Ref. 19). Integratng the DSC traces from 32 to 87 K yelds an estmate for the total stored enthalpy ntroduced durng mllng. The stored enthalpy as a functon of mllng tme s shown n Fg. 6 for Fe-&u,, and Fe,&uto as typcal examples. It ncreases to a maxmum value of about 8. kj/ mol for Fe,eC!u7c and.8 kj/mol for Fe,,Cu,, after 8 h of mllng. Further mllng/refnement of the mcrostructure results n a decrease of the heat release for both compostons. Smlar results have been reported for other ballmlled nanocrystallne powders.11t T ;2- FIG.. DSC scans for Fe,,@+, after dfferent mllng tmes (heatng rate 2 K/mn) are shown. B. Formaton ranges of fee and bee sold solutons and compostonal dependence of gran sze and lattce The x-ray dffracton and TM nvestgatons reveal that mechancal alloyng results n a drastcally enhanced mutual solublty for. the Fe-Cu system (Fgs. 1 and 2). Ths s llustrated n Fg. 7, whch shows the compostonal dependence of the atomc volume n terms of the Wgner- Setz cell volume for fee and bee sold solutons n 24 h mlled samples. For ~~6, the atomc volume ncreases contnuously from the value of pure Cu wth ncreasng Fe content. For Fe-rch samples (x>8), the atomc volume ncreases wth ncreasng Cu content. Ths demonstrates that true alloyng takes place for Cu-rch and Fe-rch powders, respectvely. In the two-phase regon from 6 to 8 at.% Fe, the atomc volume of the fee phase decreases wth the ncreasng overall Fe content. The data suggest that about 1-3 at.% Fe s dssolved n the fee phase n ths regme. On the other hand, the atomc volume of the bee phase ncreases n the two-phase regon wth the ncreasng overall Cu content, ndcatng that even more than 2 at.% Cu s dssolved n the bee phase. Our measured Wgner-Setz cell volumes exhbt a smlar compostonal dependence as the data reported for other mechancally alloyed powders,-6 but are n general smaller for x>2. On the other hand, for fee sold solutons, our atomc values are larger than the values for Sam; ples obtaned by lqud quenchng2 and evaporated alloys For bee sold solutons, the data reported for the other preparaton technques exceed our measured values. Comparson of the data suggests that the atomc volume and the formaton ranges of the alloys are very senstve to expermental condtons, even for samples produced by the same preparaton technque. The ncrease n the bee atomc volume wth ncreasng Cu content has been clamed to ndcate a tendency to nstablty of the bee phase upon alloyng that could trgger the phase transton from the bee to the fee structure.22 However, the drastc volume expanson reported by Chen et al. for sputtered bee alloys 2797 J. Appl. Phys., Vol. 73, No. 6, 1 March 1993 ckert et all 2797

5 z tu c, 4 4 $, G 2 I I I I I 16 %...,,?%., / -.m.,,. -%_._l --._../ ~ ~ * / * a!!, I --._. ; & a ; I P $ e Fe3oWo mow t!i MOW FegoW o, I I I I II z 3 Y s 2 ul $ 6 b IFexCu1-x( 1 e *,/I* I,I - I I b I 3: - I, I, r/e fee I 8 f \ : * \A (a), +, y o,@ fee f b,. b+cc YP \ j bee IL,; \ I I I Mllng Tme (h) Fe Content (at.%) FIG. 6. Stored enthalpy n Fe&u,, and Fe&u,,-, versus mllng tme s shown. n the two-phase regon has not been observed n our samples or by any other nvestgators (Fg. 7). As mentoned above, an estmate of the postve enthalpy of mxng for Fe-Cu alloys can be obtaned by measurng the heat release durng heatng n the DSC. The maxmum total stored enthalpes after 8 h of mllng and the resdual stored enthalpes after 24 h of mllng for var- z c 1 al?? IL 12.4 I I I I z 12.2 b z 2 12.a s Y.- f CD ll c B. 4 6 Fe Content. : A : fee + bee bee (at.%) 8 1 FIG. 7. Shown s the compostonal dependence of the Wgner-Setz cell volume for FeXCuloo-X alloys: (, ) ths work after 24 h of mllng (A, A) mechancal alloyng (Refs. -6), (H, Da) lqud quenchng (Ref. 2), (+, ) evaporaton (Ref. 21), (B, Cl) evaporaton (Ref. 22). Flled symbols refer to fee alloys and open symbols to bee alloys Fe Content (at.%) FIG. 8. (a) The maxmum total stored enthalpy after 8 h of mllng (flled symbols) and the resdual total stored enthalpy after 24 h of mllng (open symbols) n FeXCulm-X powders are shown and compared wth the postve enthalpy of mxng (dashed lne) calculated usng Medema s model (Ref. 23). (b) Free energes at 3 K for the fee and the bee phase calculated from thermodynamc data usng the CALPHAD method (Ref. 24) are shown. ous Fe,Cu,,,,-, powders are shown n Fg. 8 (a). The measured enthalpes depend on the overall composton of the samples. Large enthalpes of up to 14 kj/mol for Fe6&u4, are- stored n the materal. In partcular, our maxmum value of 11.9* 1.3 kj/mol for Fe.&&, agrees wth the value reported by Yavar for the same alloy. (1.8 kj/ mol).6 The dashed lne n Fg. 8 (a) refers to the postve enthalpy of mxng Unx calculated usng Medema s mode1.23 The measured enthalpes reach or even exceed the AHmx values, ndcatng that mechancal alloyng can n fact store enough enthalpy n the materal to overcome the postve enthalpy of mxng n ths system. The measured formaton ranges of fee and bee alloys 2798 J. &PI. Phye., Vol. 73, No. 6, 1 March 1993 ckert et al. 2798

6 2 I I I!! 1 II I I I I II Fe Content (at.%) Fe Content (at.%) FIG. 9. Shown s the average gran sze obtaned by ball mllng for Fe.$u,m-, powders after 24 h of mllng versus the Fe content. FIG. 1. Atomc-level stran for FexCu,m-x powders s shown after 8 h (crcles) and 24 h (trangles) of mllng versus the Fe content. dffer from the ranges one would expect from the free energy curves at 3 K for metastable fee and bee sold solutons calculated from thermodynamc data usng the CALPHAD method24 [Fg. 8(b)]. We found sngle-phase fee alloys n the concentraton range 3~~~6, although the bee phase has a lower calculated free energy than the fee phase for x)3. For Fe-rch compostons (x> 8)) the measured enthalpes agree reasonably well wth the calculated curves, but accordng to the calculated free energy of the bee phase, one would expect an even larger extenson of the bee phase feld. In addton, the observed two-phase regon between 6 and 8 at,% Fe dsagrees wth the calculated free energy curves. Ths suggests that the mechancally alloyed powders cannot be descrbed by a metastable equlbrum accordng to the calculated free energy curves. It s not yet clear why a two-phase mxture rather than sngle-phase alloys form for 6~~~8, for the measured enthalpy release n ths regon would be suffcent for complete alloyng, accordng to the thermodynamc calculatons. Further experments are under way to clarfy these effects. Independent of the overall composton, the refnement of the mcrostructure durng mllng s qualtatvely the same for all samples nvestgated. The fnal gran szes determned from x-ray dffracton and TM vary between 6 and 2 nm, smlar to the gran szes reported for other ball-mlled metals and alloys7-1 and to data reported for Fe-Cu alloys prepared by mechancal alloyng 6 and nert gas condensaton.2 The ultmate gran sze depends on the composton of the materal. Ths s llustrated n Fg. 9, showng the fnal average gran sze for FeXC!ulcO-, powders after 24 h of mllng. Whereas the gran sze s reduced to only 2 nm for pure Cu, t decreases to values below 1 nm for Fe-rch fee sold solutons. On the other hand, a slght ncrease of the average gran sze wth ncreasng Cu content s observed for bee alloys. In the two-phase regon between 6 and 8 at.% Fe, the data ndcate a decrease n gran sze wth ncreasng Fe content n the fee phase, and wth ncreasng Cu content n the bee phase. The observed compostonal dependence of the gran sze demonstrates that the alloy composton strongly affects the fnal gran sze. = The compostonal dependence of the maxmum atomc-level stran after 8 h of mllng and the resdual stran after mllng for 24 h are shown n Fg. 1. The maxmum rms stran ncreases sgnfcantly wth ncreasng Fe content for fee sold solutons. For bee alloys, the stran decreases wth ncreasng Cu content. However, the resdual stran after 24 h mllng seems to be ndependent of composton: all fee sold solutons exhbt a stran level of about.2%, whle for bee alloys the resdual stran s about.%. These values are typcal for ball-mlled elemental Cu and Fe powders, respectvely.t2- It s nterestng to note that no sgnfcant stran release after extended mllng s observed for fee sold solutons n the two-phase regon. IV. DISCUSSION A. Mechansm of alloyng and formaton ranges of fee and bee alloys Durng mllng, the gran sze of the elemental Fe and Cu powders decreases to the nanometer scale. Smultaneously, the lattce stran s enhanced. Our results ndcate that alloy formaton occurs when the Fe and Cu gran szes are n the range of 1-2 nm and that the resultng fee and bee alloys have smlar fnal gran szes. It has been suggested that the enthalpy stored n the large gran boundary area could serve as a drvng force for alloyng.7. 6 However, the alloy phases are also nanocrystallne. Thus, only the chemcal component of the nterfacal energy can serve as a drvng force for alloyng. An estmate of the possble reducton of the nterfacal energy due to alloyng yelds a 2799 J. Appl. Phys., Vol. 73, No. 6, 1 March 1993 ckert et a/.,2799

7 value of about 1.7 kj/mol for Fe&ue.6 The stored en- stran values s lkely to be small. The fracton of gran thalpy caused by the heavy deformaton of the powders can boundares ncreases contnuously wth decreasng gran be as large as 2 kj/mol. Thus, the contrbutons of alloy- sze and cannot, therefore, explan the observed maxmum ng at the nterface and mechancal deformaton- yeld a and subsequent decrease of the rms stran. However, metotal stored enthalpy of about 3.7 kj/mol, whch s roughly chancal deformaton could account for ths behavor. In three tmes too small to overcome the calculated postve the early stages of mllng, the dslocaton densty ncreases enthalpy of mxng of 12 kj/mol for FeCu4.23 Such a rapdly due to severe plastc deformaton. A saturaton and value could explan alloy formaton for samples wth only subsequent decrease of the rms stran wth ncreasng mllabout 1 at.% Fe n Cu or Cu n Fe [Fg. 8(a)]. However, ng tme/decreasng gran sze has also been reported for the stress felds of dslocatons also rase the free energy of Ru and AlRu and attrbuted to a reducton n the dslocathe elemental powder mxture and can, therefore, serve as ton densty by the annhlaton at gran boundares for a drvng force for alloyng.% The stress actng on a solute very small gran szes. These consderatons suggest that atom located at a dstance r from a dslocaton core s gven the man contrbuton to the lattce stran s the dslocaton by densty. cr=-gb(l+u)sn/3~(1---v)r, (2) where G s the shear modulus, b the Burgers vector, u the Posson rato of the host metal, and 8 the angle about the glde plane.% The effect of stress upon the chemcal potental p of a solute atom s gven by A/L= -av,, (3) where V, s the molar volume of the solute atom.* Thus, tensle stresses, as typcal for hgh dslocaton denstes,* reduce the chemcal potental and lead to an enhanced solublty. The solublty enhancement X/X, s gven by x/xo=exp( -&/RT) =exp( -ov,/rt), where x s the equlbrum solublty, R s the gas constant, and T s the temperature.29 For a typcal dslocaton densty of lo * cm- (Ref. 1 ), t follows that there s approxmately one dslocaton wthn a gran of 1 run dameter. For a temperature of 4 K and a gran sze of 1 run (r= run), ths yelds a solublty enhancement of x/x -3.4 for Fe n Cu and of.8 for Cu n Fe, respectvely. The solublty enhancement depends strongly on r -.e., a stackng fault wth a typcal wdth of 3 nm (Ref. 28) reduces the average r, resultng n an even larger solublty enhancement of x/x=2 for Fe n Cu. Ths suggests that the hgh dslocaton densty n ball-mlled powders -I causes a drastc ncrease n the mutual solublty. Together wth the excess enthalpy of gran boundares, ths shows that the drvng force for alloyng, even for concentrated Fe-Cu mxtures, can n fact be provded by mllng. Further support for the mportant role of the hgh dslocaton densty on the alloyng process can be derved from the dependence of the rms atomc-level stran on mllng tme. As shown n Fg. 4, the rms stran ncreases to a maxmum after 8 h of mllng and decreases wth longer mllng/further refnement of the mcrostructure. Furthermore, the stored enthalpy also exhbts a maxmum after 8 h mllng. (Fg. 6). Concomtantly, the lattce parameter and the gran sze have almost reached ther steady-state values (Fgs. 3 and 4)) ndcatng that most of the alloyng has already occurred at ths mllng tme. In general, lattce stran may arse from the sze msmatch of the consttuents, from an ncreasng gran boundary fracton,3 or from mechancal deformaton.* Snce the sze msmatch of Fe and Cu s only 1.%, ths contrbuton to the measured B. Formaton ranges of fee and bee sold solutons The change of the lattce parameter and the atomc volume wth mllng tme and composton clearly shows that true alloyng occurs durng mllng (Fgs. 3 and 7). The expanson of the bee lattce parameter wth the ncreasng Cu content can be explaned by the ncreasng fracton of the larger Cu atoms and ncreasng lattce stran. On the other hand, the expanson of the fee lattce wth the ncreasng amount of smaller Fe atoms can be attrbuted to elastc stran and magnetovolume effects. The formaton ranges of the sold solutons agree well wth the ranges reported by Uensh et al. for mechancally alloyed powders and wth the ranges found for evaporated samples.22 The observed compostonal dependence of the atomc volume n the two-phase regon s not yet well understood. Our results show that for 6~~~8, the atomc volume of the fee phase decreases wth the ncreasng overall Fe content, ndcatng that the fee phase s depleted n Fe compared to the overall composton. On the other hand, the atomc volume of the bee phase s even larger than for sngle-phase bee alloys (x28), ndcatng an enhanced Cu solublty n the two-phase regon. Apparently, the presence of a second phase strongly alfects the solublty n Fe-Cu alloys. The expermentally observed formaton ranges of the sngle-phase alloys are qute dfferent from what one would expect gven the calculated free energy curves for ths system [Fg. 8(b)]. Ths suggests that no metastable equlbrum s acheved durng mllng, whch s supported by the compostonal dependence of the atomc volume n the two-phase regon. For a metastable equlbrum between homogeneous fee and bee sold solutons, one would expect two phases wth txed compostons n the two-phase regon, and only the relatve amounts of both phases should vary wth composton. Presumably, the heavly deformed powders have a hgher free energy than under metastable equlbrum condtons, resultng n dfferent formaton ranges than expected from the calculated free energy curves [Fg. 8(b)]. Other possble explanatons that could account for the dfference between the measured and the calculated formaton ranges are magnetc effects upon alloyng n these hghly supersaturated alloys and addtonal contrbutons due to the gran boundary energy n nanocrystallne materals. These effects are not ncluded n the 28 J. Appl. Phys., Vol. 73, No. 6, 1 March 1993 ckert et a/. 28

8 thermodynamc calculatons. They could alter the calcu- dependence of l/d s even stronger than the x2/3 depenlated free energy curves for the fee and bee phases, result- dence typcal for sold soluton hardenng caused by the ng n dfferent metastable formaton ranges of the super- dslocaton frcton n conventonal hghly concentrated alsaturated sold solutons. loys? However, ths explanaton holds only for sngle-phase C. Compostonal dependence of gran sze and fee alloys wth ~~6. The compostonal dependence of the stran gran sze for the bee phase cannot be explaned by a so- Ball mllng reduces the gran sze of the powders to the nanometer scale. The fnal gran szes are comparable to the gran szes reported for mechancally alloyed Fe- Cu 16 and other ball-mlled metals and alloys7- as well as to data reported for samples prepared by nert gas condensaton.= The mechansm for producng nanocrystallne powders by ball mllng s governed by the severe plastc deformaton ntroduced durng mllng. l-l3 The gran sze saturates at a steady-state value and no further refmement occurs. For pure metals, we have suggested that the ultmate gran sze achevable by mllng s determned by the mnmum gran sze that can sustan a dslocaton pleup wthn a gran and by the rate of recovery durng mllng. l An estmate of the mnmum dslocaton separaton n a pleup L s obtaned from the equlbrum between the repulsve force between dslocatons and the externally appled force: L=3Gb/?r( 1 -u)h, () wth shear modulus G, Burgers vector b, Posson rato u, and hardness of the materal Lz.~I Ths gves a lower bound for the gran sze of pure metals and reveals that a small gran sze tself provdes a lmt for further plastc deformaton va dslocaton moton and, therefore, for further gran sze refnement by mllng (for detals see Ref. 1). Fgure 9 shows that the fnal gran sze of the fee Fe-Cu alloys decreases consderably wth the ncreasng Fe content. Ths can be explaned by consderng the soluton hardenng effects upon alloyng. In general, the addtons of a second element to a pure metal ncrease the strength and the hardness of the materal2* resultng n a smaller L than for a pure metal and, therefore, n a smaller fnal gran sze obtaned by mllng. For ~~6, the compostonal dependence of the gran sze d can be ftted best by a relaton of the type d=l/(a+bx), (6) as shown by the dashed lne n Fg. 9. Ths lnear compostonal dependence for t/d s characterstc of dslocaton lockng mechansms where dslocatons are ether chemcally locked by segregated solute atoms at stackng faults n the fee lattce3 or by elastc lockng due to the atomc sze msmatch of the consttuents.33 Snce the dfference n the atomc szes of Cu and Fe atoms s only 1.%, the lockng effect due to the sze msmatch s very small. Therefore, the major contrbuton to the solute hardenng s lkely to be due to segregaton of Fe atoms at stackng faults n the fee lattce. The dslocatons become mmoble due to the decoraton wth solute atoms and no further plastc deformaton by dslocaton moton can occur. Hence, the gran sze reaches a steady-state value. It s nterestng to note that the observed lnear compostonal luton hardenng model. As the Cu content n the bee phase ncreases, sold soluton hardenng would predct a decrease n gran sze, as descrbed above for the fee phase. Possble explanatons for the compostonal dependence of the gran sze for the bee phase nclude the stablzaton and lockng of normally unstable stackng faults n the bee lattce of nanocrystallne powders19 (whch would reduce the number of moble dslocatons) or a change n the dslocaton densty by a change of the annhlaton behavor at gran boundares. For samples n the two-phase regon, addtonal contrbutons due to the nhomogenety of the materal consstng of grans wth dfferent lattces and compostons mght also affect the dslocaton formaton and annhlaton characterstcs. It s well known that gran boundares can act as sources and snks for dslocatons.r Therefore, the formaton of addtonal secondary gran boundary dslocatons36 at fcc/bcc nterfaces could strongly affect the deformaton behavor and, therefore, the fnal gran sze of the powders. Furthermore, Fe-Cu s a system wth a tendency for nter-facal segregaton.37 Hence, t s possble that the gran boundary regons are enrched n Cu or Fe n comparson to the bulk of a gran, Ths mght affect the formaton and annhlaton of dslocatons at the gran boundares, snce the mage stresses actng on dslocatons near the nterface between two grans strongly depend on the nature of the grans and the mechancal propertes of the phases n contact.3 Hence, compostonal varatons from the gran nteror to the gran boundary due to segregaton effects could affect the behavor of the gran boundares as sources and snks for dslocatons. Further experments are necessary to gan more nsght nto these processes for an understandng of the gran sze changes for x26. Mechancal alloyng/ball mllng enhances the lattce stran consderably. As shown n Fg. 1, the maxmum rms atomc-level stran n the sold solutons after 8 h of mllng depends on composton and ncreases wth the ncreasng Fe content. It has been argued above that the stran s caused manly by the dslocaton densty ntro- duced durng mllng, whch, as we suggested, s closely related to the ultmate gran sze. The compostonal dependence of the stran correlates well wth the measured gran szes (Fg. 9): the hgher the rms stran, the smaller the gran sze. The decrease of the rms stran after 24 h of mllng s lkely due to the annhlaton of dslocatons at gran boundares for very small gran szes by dynamc recovery.,12 Ths agrees wth the fndng that the stored enthalpy of the powders-whch s manly assocated wth the dslocaton densty-decreases for long mllng tmes/ very small gran szes (Fgs. 6 and 8). It s nterestng to note that the resdual stran after extended mllng s nearly ndependent of composton and reaches values that are 281 J. Appl. Phys., Vol. 73, No. 6, 1 March 1993 ckert et al. 281

9 typcal for ball-mlled pure metals (Fg. 1). Ths proves that the sze msmatch of Cu and Fe atoms does not play a sgnfcant role for fully alloyed homogeneous powders, snce f t were, one would expect a compostonal dependence of the resdual stran on the Fe and Cu content of the samples3* The fact that no sgnfcant stran release s detected for fee alloys n the two-phase regon suggests that the harder bee phase n these powders could at least partally prevent dslocaton annhlaton at gran boundares, smlar to what s known for conventonal polycrystallne materals consstng of soft and hard regons.3 V. CONCLUSIONS We have shown that mechancal alloyng of bnary Fe-Cu powder mxtures leads to the formaton of nanocrystallne sngle-phase fee sold solutons wth up to 6 at.% Fe n Cu and sngle-phase bee sold solutons wth up to 2 at.% Cu n Fe. Between 6 and 8 at.% Fe, both phases coexst. The alloy formaton can be explaned by an enhanced solublty due to the hgh dslocaton densty durng the ntal stages of mllng of the nanocrystallne powders. The enthalpy stored n the gran boundares may also assst the alloyng, but ths effect alone cannot account for the drastc solublty extenson. The ultmate gran sze of the powders vares between 6 and 2 nm and scales wth the overall composton of the materal. Ths has been explaned by the underlyng mechansm of plastc deformaton va dslocaton moton, ncludng solute hardenng effects durng mllng and the nfluence of gran boundares on the deformaton characterstcs. The results reveal that the detals of dslocaton formaton and moton are essental for understandng the alloyng process and the characterstcs of mechancally alloyed nanocrystallne powders. Further nvestgatons, such as thermal analyss, TM, MSssbauer studes and measurements of magnetc propertes, are under way to gan a better nsght nto the detals of the phase formaton and stablty of these materals.39 ACKNOWLDGMNTS Ths work was supported by the U.S. Department of nergy (DO Contract No. DFGO386R4242). Specal thanks are gven to P. Carpenter and C. Garland for techncal assstance, and to Y. R. Abe, R. Brrnger, and B. Fultz for-stmulatng dscussons and effectve cooperaton. W. L. Johnson, Prog. Mater. Sc. 3, 81 ( 1986). 2L. Schultz, Mater. Sc. ng. 97, 1 (1988). J. ckert, L. Schultz, and K. Urban, Appl. Phys. Lett., 117 (1988). 4. Ivanov, T. Grgoreva, G. Golubkova, V. Boldyrev, A. B. Fasman, S. D. Mkhalenko, and. T. Kalnna, Mater. Lett. 7, 1 (1988). K. Uensh, K. F. Kobayash, S. Nasu, H. Hatano, K. N. Ishhara, and P. H. Shngu, Z. Metallk 83, 132 (1992). A. R. Yavar, P. J. Des&, and T. Benameur, Phys. Rev. Lett ( 1992). P. H. Shmgu, K. N. Ishhara, K. Uensh, J. Kuyama, and S. Nasu, n Sold State Powder -Processng, edted by A. H. Clauer and J. J. de Barbadllo (The Mnerals, Metals and Materals Socety, Cncnatt, OH, 199), p. 21. T. Fukunaga, M. Mor, K. Inou, and U. Mzutan, Mater. Sc. ng. A 134, 863 (1991).. Gaffet, C. Louson, M. Harmen, and F. Faudet, Mater. Sc. ng. A 134, 141 (1991). T. Fukunaga, K. Nakamura, K. Suzuk, and U. Mzutan, J. Non-Cryst. Solds 117/118, 7 (199). Hellstern, H. J. Fecht, Z. Fu, and W. L. Johnson, J. Appl. Phys. 6, 3 ( 1989). H. J. Fecht,. Hellstem, Z. Fu, and W. L. Johnson, Adv. Powder Metall. 1, 11 (1989). I3 J. S. C. Jang and C. C. Koch, Ser. Metall. Mater. 24, 199 (199). 14J. ckert, J. C. Holzer, C.. Krll HI, and W. L. Johnson, Mater. Sc. Forum 88-9, ( 1992). J. ckert, J. C. Holzer, C.. Krll III, and W. L. Johnson, J. Mater. Res. 7, 171 (1992). 16T. D. Shen, K. Y. Wang, M. X. Quan, and J. T. Wang, Mater. Sc. Forum 88-9, 391 (1992). 17B. D. Cullty, lements of X-ray D@acton, 2nd ed. (Addson-Wesley, Readng, MA, 1978), p H. P. Klug and L. Alexander, X-ray Dffracton Procedures for Polycrystallne and Amorphous Materals, 2nd ed. (Wley, New York, 1974), p J. ckert, R. Brrnger, J. C. Holzer, C.. Krll III, and W. L. Johnson, n Structure and Properfes of Interfaces n Mater&, edted by W. T. Clark, U. Dahmen, and C L. Brant (Mater. Res. Sot., Pttsburgh, PA, 1992), Vol. 238, p ao W. Klement, Jr., Trans. AIM 233, 118 (196). K. Sumyama, T. Yoshtake, and Y. Nakamura, J. Phys. Sot. Jpn. 3, 316 (1984). 22C. L. Chen, S. H. Lou, D. Kofalt, W. Yu, T. gam, and T. R. McGure, Phys. Rev. B 33, 3247 (1986). 23A. K. Nessen, F. R. de Boer, R. Boom, P. F. de ChLtel, W. C. M. Mattens, and A. R. Medema, CALPHAD 7, 1 (1983). 24 L. Kaufman, CALPHAD 2, 117 ( 1978 ). =U. Herr, J. Jng, U. Gonser, and H. Gleter, Sold State Commun. 76, 197 (199). 26J. C. M. L, R. Oran, and L. S. Darken, Z. Phys. Chem. Neue Folge 49, 271 (1966). 27D. Hull and D. J. Bacon, Introducton to Dslocatons (Pergamon, Oxford, 1984), p. 88. s8 P. Haasen, PhysZcaZ Metallzqy, 2nd ed. (Cambrdge Unversty Press, Cambrdge, 1986), p D. A. Porter and K.. asterlng, Phase Transformatons n Metals and Alloys (Van Nostrand Renhold, London, 1981), p R. C. Cammarata and R. K. by, J. Mater. Res. 6, 888 (1991). T. G. Neh and J. Wadsworth, Ser. Metall. Mater. 2, 9 (1991). 32H. Suzuk and C. S. Barrett, Acta Metall. 6, 16 (198). 33A. H. Cottrell, C. S. Hunter, and F. R. N. Nabarro, Phlos. Map. 44, 164 (193). 34R. Labusch, Phys. Status Sold 41, 69 (197); Acta Metall. 2, 917 (1972). J. P. Hrth, Metall. Trans. 3, 347 (1972). 36R. Hook and J. P. Hrth, Acta Metall. 1, 199 (1967). 37. D. Hondros and M. P. Sea.h, n PhyscaZ MetaZZuqy, edted by R. W. Cahn and P. Haasen, 3rd ed. (lsever Scence B. V., Amsterdam, 1983), p T. gam and Y. Waseda, J. Non-@&. Solds 64, 113 (1984). H. Ouyang, J. ckert, and B. Fultz (to be publshed). 282 J. Appl., Phys,, Vol. 73, No. 6, 1 March 1993 ckert ef a/. 282