Formation of CuxAu1-x phases by cold homogenization of Au/Cu nanocrystalline thin films

1491 Fo ma ion o CuxAu1−x phases by cold homogeniza ion o Au/Cu nanoc ys alline hin ilms Alona Tynko a1,2, Gabo L. Ka ona2, Gabo A. Lange 2, Se gey I. Sido enko1, S e lana M. Voloshko1 and Dezso L. Beke*2 Full Resea ch Pape Open Access Add ess: 1Na ional Technical Uni e si y o Uk aine “Kie Poly echnic Ins i u e”, 37 P ospec Pe emogy, 03056 Kie , Uk aine and 2Depa men o Solid S a e Physics, Uni e si y o Deb ecen, P.O. Box 2, 4010 Deb ecen, Hunga y Email: Dezso L. Beke* - [email p o ec ed] * Co esponding au ho Keywo ds: Cu/Au; g ain bounda y di usion; nano ilms o in e me allic compounds; seconda y neu al mass spec ome y (SNMS); solid s a e eac ion Beils ein J. Nano echnol. 2014, 5, 1491–1500. doi:10.3762/bjnano.5.162 Recei ed: 10 Ap il 2014 Accep ed: 20 Augus 2014 Published: 10 Sep embe 2014 Associa e Edi o : P. Leide e © 2014 Tynko a e al; licensee Beils ein-Ins i u . License and e ms: see end o documen . Abs ac I is shown, by using dep h p o iling wi h a seconda y neu al mass spec ome e and s uc u e in es iga ions by XRD and TEM, ha a low empe a u es, a which he bulk di usion is ozen, a comple e homogeniza ion can ake place in he Cu/Au hin ilm sys em, which leads o o ma ion o in e me allic phases. Di e en compounds can be o med depending on he ini ial hickness a io. The p ocess s a s wi h g ain bounda y in e di usion, which is ollowed by a o ma ion o eac ion laye s a he g ain bound- a ies ha leads o he mo ion o he newly o med in e aces pe pendicula o he g ain bounda y plane. Finally, he homogeniza- ion inishes when all he pu e componen s ha e been consumed. The p ocess is asymme ic: I is as e in he Au laye . In Au(25nm)/Cu(50nm) samples he inal s a e is he o de ed AuCu3 phase. Dec ease o he ilm hicknesses, as expec ed, esul s in he accele a ion o he p ocess. I is also illus a ed ha changing he hickness a io ei he a mix u e o Cu- ich AuCu and AuCu3 phases (in Au(25nm)/Cu(25nm) sample), o a mix u e o diso de ed Cu- as well as Au- ich solid solu ions (in Au(25nm)/Cu(12nm) sample) can be p oduced. By using a simple model he in e ace eloci y in bo h he Cu and Au laye s we e es ima ed om he linea inc ease o he a e age composi ion and i s alue is abou wo o de s o magni ude la ge in Au (ca. 10−11 m/s) han in Cu (ca. 10−13 m/s). 1491 In oduc ion Solid-s a e eac ions in nanos uc u ed hin ilm sys ems a e in e es ing and challenging no only om he poin o iew o pu e undamen al esea ch, bu a e also impo an o echno- logical applica ions. Examples o he la e a e he me alliza- ion o in eg a ed ci cui s ( he o ma ion o a nanome ic NiSi laye on he Si subs a e [1,2]), o he p oduc ion o hin chemi- cally o de ed FeP ilms o pe pendicula magne ic da a eco ding [3,4]. Rega ding he basic unde s anding o such eac- Beils ein J. Nano echnol. 2014, 5, 1491–1500. 1492 ions he ques ions abou he con ibu ions o a as mass ans- po along di e en g ain bounda ies (GBs, i.e., sho ci cui s) can be men ioned; hey can ha e an impo an e ec on he en i e in e mixing p ocess in nanoc ys alline bi- o mul ilaye s. In addi ion he GB di usion coe icien s can co e a ange o se e al o de s o magni ude, depending on he ype o GB s uc- u e (low o high angle GBs [5], iple junc ions [6]). Fu he - mo e i can be obse ed a e y low empe a u es ha he mo phology o he o ma ion and he g ow h o he new phase(s) can be di e en om he usual plana g ow h o a eac- ion laye [7-9]: The new phase(s) can be o med a g ain bounda ies, GBs, and can g ow u he by he mo ion o he new in e aces pe pendicula o he o iginal GB plane [10]. The e a e examples in he li e a u e, in which he so-called “cold homogeniza ion” was obse ed: Al hough he bulk di u- sion p ocesses we e p ac ically ozen in bina y nanoc ys alline couples e en a comple e in e mixing o componen s leading o ull homogeniza ion was ound [11-15]. Two easons we e men ioned as possible explana ion o his phenomenon: i) di usion-induced g ain bounda y mo ion (DIGM) and/o di usion-induced e-c ys alliza ion (DIR), and ii) g ain bounda y mo ion du ing usual e-c ys alliza ion [11,12]. In he la e he alloying is he consequence o he alloyed zones le behind by e-c ys alliza ion du ing di usion in e mixing and as a esul o g ain g ow h he g ain size should be inc eased. On he o he hand du ing DIGM he composi ion behind he mo ing bounda y can be abou se e al en h o an a omic ac- ion, i.e., he homogeniza ion o a hin ilm wi h small g ain size is also possible by his mechanism. Du ing DIR, which is ano he mani es a ion o he s ess elaxa ion caused by he ini ial inequali y o he GB di usion luxes o he wo compo- nen s, new g ains a e o med, wi h a composi ion mo e discon- inuously di e en om he su ounding g ains as compa ed o DIGM. In addi ion, i is di icul o make a dis inc ion be ween DIR and DIGM expe imen ally [16]. DIR has mainly been in es iga ed in bina y sys ems wi h a wide mu ual solubili y ange abo e ei he he miscibili y gap o he c i ical empe a u e o o de ing (e.g., in Cu/Pd [16], Au/Cu [15], Ag/Pd [7], Ni/Cu [17-19], NiPd [20]). Less wo ks ha e been de o ed o sys ems wi h eac- i e di usion [21]. Fo ins ance in he Cu/Pd sys em [8,22] no eac ion laye s we e de ec ed a he o iginal in e ace (see he ansmission elec on mic oscopy (TEM) image in Figu e 9b o [8]) a 200 °C, bu he selec ed-a ea di ac ion pa e ns in TEM indica ed he p esence o he PdCu phase. A e hea ea men s a 260 °C, an ex ensi e in e mixing had aken place, accompa- nied by g ain bounda y mig a ion, g ain g ow h, and o ma ion o CuPd and Cu3Pd phases. Simila esul s we e ob ained in Cu/Pd [23] Ni2Si/Si [24] and Fe/P [9] sys ems. In [10] hese esul s we e summa ized and an in e p e a ion based on he g ain bounda y di usion induced eac ion laye o ma ion, GBDIREAC, was o e ed. Thus, i was p o en ha in bina y sys ems wi h in e me allic laye s no only a homogeniza ion (by o ma ion o solid solu ions) bu o ma ion o compounds is also possible. In addi ion he mo phology o he g owing phases in such hin ilm couples can be di e en om he plana g ow h mode: Ins ead o nuclea ion and g ow h o he eac ion laye a he ini ial in e ace, he eac ion akes place in he GBs and he amoun o he p oduc phase g ows by he mo ion o he o med new in e aces pe pendicula o he GBs. Thus, he en i e laye o he pu e pa en ilms can be consumed by in e - ace di usion d i en in e ace mo ion and a ully homogeneous p oduc laye can be ob ained. Fu he mo e, in he i s s age o such a p ocess, assuming ha he in e ace eloci y is cons an , he a e age composi ion in he cen e o he ilms should linea ly inc ease wi h ime (by g adually consuming he ini ial ma e ial o he g ains) and he slope o his unc ion is p opo - ional o in e ace eloci y [24-26]. In his s udy, simila p ocesses a e in es iga ed in Au/Cu sys em a low empe a u es. No e ha in [7] his sys em was in es iga ed in de ail abo e he o de ing empe a u e and compa a i e measu emen s we e ca ied ou only a 230 and 350 °C (below he o de ing empe a u e). I was ob ained ha a highe empe a u es he phase o ma ion kine ics was e y simila o he one ob ained in Ag/Au sys em, when only diso - de ed phases we e o med. I was also concluded ha in he Au/Cu sys em he main d i ing o ce was he chemical in e - mixing and he d i ing o ce o o de ing ga e only a mino con ibu ion, i.e., he s uc u al ans o ma ion was simila below and abo e he o de ing empe a u e. The ini ial sha p plana in e ace s ill exis ed in he hea - ea ed samples and, simila ly o he esul s o [8] in Cu/Pd, he ea ly s ages in Cu/Au could no be unde s ood as a plana laye eac ion. I was also obse ed ha new g ains we e o med in he eac ion zone (DIR). While in [7] he main phenomenon was he elaxa ion o misma ch s ess (accumula ed mainly by bulk di usion abo e he o de ing empe a u e), in his pape we will concen a e on p ocesses a low empe a u es, a which he bulk di usion is comple ely ozen. Resul s The concen a ion p o iles o Au(25nm)/Cu(50nm) samples annealed a di e en empe a u es a e shown in Figu e 1. The p esence o he smea ed in e ace in he as-deposi ed sample can be explained by some ini ial su ace oughness, di usion du ing he sample p epa a ion o ins umen al e ec s o he spu e dep h p o iling [27,28]. I can be clea ly seen ha , du ing hea ea men s he Cu pene a ion in o he Au laye is mo e in ensi e han he Au pene a ion in o he Cu laye . Beils ein J. Nano echnol. 2014, 5, 1491–1500. 1493 Figu e 1: Concen a ion p o iles o Au(25nm)/Cu(50nm) sys em a) as deposi ed sample and annealed b) a 160 °C o 1 h and c) 3 h, (d) 180 °C o 5 h, (e) 200 °C o 10 h, ( ) 330 °C o 4 h. Du ing annealing a 160 °C o 3 h, on he Au-side a signi ican in e mixing occu s wi h Cu concen a ion up o 20 a om %, while on he Cu-side he concen a ion o Au a oms eaches only 7 a om % (Figu e 1c). I can also be seen (see, e.g., Figu e 1b and Figu e 1c) ha he e a e no pla eaus on he composi e p o iles (as indica ions o o ma ion o compound laye s wi h plana in e aces in dep h p o iles aken, e.g., by SNMS) a sho e imes, bu he e is a ela i ely high a e age composi ion o Cu inside he Au laye (Figu e 1b) as well as o he Au composi ion inside he Cu laye (Figu e 1d). In addi ion he e is a minimum o he Cu p o ile inside he Au laye . These a e he consequences o he GB mass anspo along he GBs. The comple e illing-up o g ain bounda ies, e.g., in Au would lead o a maximum a e age composi ion o abou 7 a om % (since, wi h δ = 0.5 nm g ain bounda y hickness, 2δ/d is 0.066), and abou 10% would be expec ed o his alue in he Cu ilms, using he es ima ed a e age GB olume ac ion calcula ed om he g ain sizes (dAu = 15 nm, dCu = 10 nm, see below). In Beils ein J. Nano echnol. 2014, 5, 1491–1500. 1494 Figu e 2: XRD θ–2θ pa e ns o Au(25nm)/Cu(50nm) samples a) as deposi ed, b) annealed a 180 °C o 5 h, c) o 10 h and d) a 200 °C o 44 h. Figu e 1e he o e all composi ion o he di using elemen s on bo h sides is a he high and canno be simply explained by a illing-up o g ain bounda ies only, because he alues ob ained a e la ge han he one co esponding o he a e age alue es i- ma ed om he olume ac ion o he g ain bounda y a ea a he obse ed g ain sizes. I is no ewo hy ha he appea ance o some Cu a oms a he opmos su ace and he de elopmen o a minimum can be obse ed in he cen e o he Au laye (Figu e 1c). I can be explained by he seg ega ion o Cu [29] and/o by he coexis- ence o as and slow di usion bounda ies (bimodal GB ne wo k) [25]. I was shown in [25] ha in he la e case he GB di usion s a s along GBs wi h he la ges di usi i ies and he e is only sho pene a ion along GBs wi h small di usi i y alues. A longe annealing imes he GB pene a ion leng h is la ge han he hickness o he ilm and he anspo ed a oms sp ead ou on he ee su ace o ming a new sou ce o di u- sion along he s ill no illed GBs wi h smalle di usi i ies. As a esul a minimum in he a e age composi ion p o ile de elops inside he ilm, close o he ee su ace. Thus in ou case he minimum o he Cu composi ion in he Au laye (Figu e 1c) can also be a consequence o he bimodal GB s uc u e. A comple e homogeniza ion o he sys em akes place bo h a low empe a- u es o longe annealing imes (Figu e 1e) and/o a highe empe a u es (Figu e 1 ). We would like o emphasize ha we did no obse e a eac ion laye a he o iginal in e ace in ou dep h p o iles. This indi- ca es ha ins ead o nuclea ion o he p oduc laye a he o ig- inal in e ace, he new phase(s) o med in he whole olume o he ilms. In addi ion he compound phases ha e been o med wi hou he pa icipa ion o olume di usion (acco ding o bulk di usion da a he bulk di usion pene a ion leng h is abou 2.8 × 10−11 m in pu e Cu a 250 °C o 30 min [30]). F om Figu e 1 i is clea ly seen ha he a e age composi ions on bo h sides g adually le eled o and he esul is he o ma ion o an almos homogeneous laye wi h abou 75 a om % o Cu and 25 a om % o Au composi ion. The XRD pa e ns o as deposi ed and annealed samples a e shown in Figu e 2. The weak e lec ion a 23.7°, belonging o a supe la ice s uc u e, indica es ha he AuCu3 phase ha is o med du ing he homogeniza ion p ocess (Figu e 2d) is pa ially o de ed. This is in ag eemen wi h SNMS da a, indi- ca ing he p esence o a sligh ly Cu ich AuCu3 phase. Beils ein J. Nano echnol. 2014, 5, 1491–1500. 1495 Figu e 3: Concen a ion p o iles o Au(10nm)/Cu(25nm) sys em a) as deposi ed and b) annealed a 180 °C o 5 h samples. The es ima ed g ain sizes, d ( om he ull wid h a hal maximum o he (111) peaks o Au and Cu by using he Debye–Sche e o mula [31,32]), a e 15 nm o Au c ys als and 10 nm in he case o Cu. A e annealing a 180 °C o 5 h hey dec ease o d = 9 nm and d = 2 nm o Au and Cu, espec - i ely (Figu e 2b). The g ain size o he newly o med AuCu3 phase (a e 10 h o hea ea men a 180 °C) was es ima ed om he (111) peaks and 6 nm was ob ained (Figu e 2c). Rega ding he eliabili y o he g ain sizes es ima ed i is wo hy o men ion ha calcula ions based on he Debye–Sche e o mula p o ide unde es ima ed alues o d [32], because o he ac ha besides ins umen al e ec s and g ain size o he ac o s (like inhomogeneous s ain and c ys al la ice impe ec- ions) also con ibu e o he wid h o a di ac ion peak. In o de o in es iga e he e ec o he indi idual hicknesses o he ilms, samples wi h hicknesses o 10 and 25 nm o Au and Cu, espec i ely, we e also annealed unde he same condi ions. The concen a ion p o iles a e shown in Figu e 3. I can be seen ha he p ocess is qui e simila o he samples wi h ilm hicknesses 25 and 50 nm (compa e Figu e 3b o Figu e 1d) bu he di usion p ocesses de elop as e . Thus, al eady a e 5 h o annealing a 180 °C he AuCu3 phase has been o med. The XRD pa e ns shown in Figu e 4 also illus- a e he o ma ion o his AuCu3 phase. I is di icul o iden- i y whe he i is o de ed o diso de ed: The expec ed posi ions o he supe -la ice e lec ions (100) and (110) a e indica ed oo. In o de o in es iga e he e ec o he o e all composi ion (i.e., he e ec o he hickness a io), measu emen s on samples Au(25nm)/Cu(25nm) and Au(25nm)/Cu(12nm) ha e also been ca ied ou . I can be seen in Figu e 5 ha al eady a e 5 h a 180 °C a homogeneous laye (o abou he same hickness as he hickness o he o iginal Au laye ) has been o med wi h a Figu e 4: XRD θ–2θ pa e ns o Au(10nm)/Cu(25nm) annealed samples. 50/50 composi ion in he opmos laye in he place o gold. On he o he hand, he e is a conside able inc ease (up o abou 10%) o he Au composi ion in he cen e o he Cu laye . Beils ein J. Nano echnol. 2014, 5, 1491–1500. 1496 Figu e 5: Concen a ion p o iles o Au(25nm)/Cu(25nm) sys em a) as deposi ed sample and b) annealed samples. Figu e 6 shows he θ–2θ XRD pa e ns o Au(25nm)/Cu(25nm) annealed samples. I can be seen ha e lec ions o bo h AuCu and AuCu3 diso de ed phases can be obse ed al eady a e annealing a 180 °C a e 5 h. These esul s a e in line wi h he p o iles shown in Figu e 5b: A longe annealing imes he a e age composi ion o he Au inside he Cu ilm g adually inc eases and a 200 °C a e 20 h he sys em seems o be a mix- u e o Cu- ich AuCu and AuCu3 phases. In addi ion, Figu e 7 illus a es ha wi h a p ope choice o he ilm a io one can a i e a a mix u e o Cu- and Au- ich AuCu solid solu ions. The XRD pa e ns shown in Figu e 8 con i m his: Re lec ions o he diso de ed AuCu solid solu ions can be iden i ied. The e ical lines co espond o Au1.5xCux and AuxCu1.5x solid solu- ions. Figu e 9 shows b igh ield ( op iew) TEM images and selec ed a ea elec on di ac ion pa e ns o as deposi ed and hea ea ed ( o 1 h a 160 °C) Au(10nm)/Cu(15nm) bilaye s, espec i ely. Fo TEM in es iga ions he specimens we e p epa ed by subsequen magne on spu e ing on monoc ys- alline sodium chlo ide subs a es a oom empe a u e. A e he hea ea men he subs a e was dissol ed and he sel - suppo ing ilm was used in TEM in es iga ions. I can be seen ha he e is no de ec able change in he g ain size a e he hea ea men , which is abou 10 nm. The di ac ion pa e n o as deposi ed sample shows clea e lec ions om Au (Figu e 9b) and a e annealing addi ional di ac ion peaks a e ound ha co espond o he o de ed Au3Cu phase (Figu e 9d). In addi ion, he a ow in Figu e 9c indica es a egion o he o ma ion o he eac ed laye a ound a g ain bounda y; he indica ed e lec ions pe ain o his phase. Figu e 6: XRD θ–2θ pa e ns o Au(25nm)/Cu(25nm) annealed samples. Beils ein J. Nano echnol. 2014, 5, 1491–1500. 1497 Figu e 7: Concen a ion p o iles o Au(25nm)/Cu(12nm) sys em a) as deposi ed sample and b) annealed samples. Figu e 8: XRD θ–2θ pa e ns o Au(25nm)/Cu(12nm) annealed samples. Figu e 9: B igh ield ( op iew) TEM images o Au(10nm)/Cu(15nm) bilaye a) as deposi ed and c) a e 1 h o hea ea men a 160 °C. The a ow indica es he a ea o o ma ion o a new phase. Selec ed a ea elec on di ac ion pa e ns o Au(10nm)/Cu(15nm) bilaye b) as deposi ed and d) a e 1 h o hea ea men a 160 °C. Discussion Ou esul s indica e a special way o nuclea ion and g ow h o homogeneous eac ion p oduc s in AuCu sys em. In acco dance wi h he esul s o [7] in he same sys em he obse a ions canno be unde s ood as a plana laye eac ion: No con inuous eac ion laye o ma ion was obse ed a he o iginal in e ace. Ins ead homogeniza ion o he ini ial pu e laye s can be cha ac- e ized wi h a g adual inc ease o he composi ion in he cen e o he laye s. Fu he mo e, we can conclude ha all hese Beils ein J. Nano echnol. 2014, 5, 1491–1500. 1498 Figu e 10: Dependence o he a e age concen a ion o elemen s on he annealing ime a 150 °C in a) Au(25nm)/Cu(50nm), b) Au(25nm)/Cu(25nm) and c) Au(25nm)/Cu(12nm) sys ems. phenomena should be he esul o g ain bounda y anspo as a as he bulk di usion is negligible a such low empe a u es. Thus he GB di usion ini ia es he nuclea ion o he eac ion p oduc and sweeps he GBs pe pendicula o he o iginal su ace and as a esul , an alloyed zone emains behind he mo ing GBs. The ob ained g ain sizes a o his in e p e a ion in con as o he g ain bounda y mo ion du ing usual e-c ys al- liza ion [11,12]. In he la e case, a g ain g ow h should be obse ed a he same ime as he homogeniza ion. Bu ou esul s, bo h ob ained om XRD and TEM in es iga ions, show ha he a e age g ain size ei he emained he same o e en dec eased a e he hea ea men s. Thus, he o e all cold homogeniza ion akes place h ough g ain bounda y di usion induced g ain bounda y mo ion and a solid s a e eac ion con olled by he in e ace di usion along he newly o med in e aces. The XRD and TEM esul s con i med he conclu- sions d awn om he SNMS dep h p o iles: Indeed he o ma- ion o eac ion laye s ook place, and a e longe annealing imes e en he supe la ice e lec ions o he o med AuCu3 phase could be de ec ed, indica ing he o de ing o his phase. I is no ewo hy ha he abo e p ocesses a e in e ace/g ain bounda y di usion con olled: A e he o ma ion o he new phase in he GBs, he p ocess akes place h ough he a omic anspo along he mo ing GB (like in he classical DIGM, when a solid solu ion is le behind) o along he in e aces o he new o de ed phase (in his case he o iginal GB is eplaced by wo new in e aces). In he la e case i is an in e es ing and open ques ion whe he bo h in e aces mo e o dominan ly only one o hese shi s: Di ec in si u TEM in es iga ions can help o cla i y his poin . Ne e heless, by using he esul s o [24,26] we can es ima e he eloci y o he in e aces mo ing pe pendicula o he ini ial g ain bounda y. Acco ding o his model one can assume ha in hin ilms he g ain size, d, is usually less han he ilm hick- ness, H. I is plausible o assume a sphe ical g ain s uc u e (2R0 = d) wi h a δ/2 hick sphe ical shell a he beginning (a = 0), which g ows wi h ime by , whe e is he cons an in e ace eloci y. Then he in e nal shell, in which he ini ial composi ion is c0, has he adius Assuming ha he in e ace shi s a s only a e , e.g., Au GBs ha e been illed up o he equilib ium Cu composi ion o he g owing phase, ce, hen he a e age concen a ion, c, in he middle o he ilm can be gi en as (1) which, neglec ing e ms (δ + 2 )/d on he hi d powe , has he o m, wi h ce (in Au) = 0.5, ce (in Cu) = 0.25 and c0 = 0: (2) A sho imes, he las e m in he las b acke o Equa ion 2 can be neglec ed leading o a linea ela ion. Figu e 10 shows he a e age composi ion inside he gold and coppe laye s as he unc ion o he annealing ime ob ained a e hea ea men s a 150 °C: The i s pa is linea ( he sa u a ion a longe alues Beils ein J. Nano echnol. 2014, 5, 1491–1500. 1499 Table 1: Calcula ed alues o he eloci y o mo ing in e aces. Au(25nm)/Cu(50nm) Au(25nm)/Cu(25nm) Au(25nm)/Cu(12nm) in he Au laye 7 × 10−12 m/s 1.4 × 10−11 m/s 3 × 10−11 m/s in he Cu laye 6 × 10−14 m/s 2 × 10−13 m/s 5 × 10−13 m/s is due o ini e size e ec s). F om he linea ini ial pa he alues o he in e ace eloci y can be ob ained (Table 1). I can be seen ha he in e ace eloci y is abou wo o de s o magni ude highe in Au han in Cu: This is plausible i we ake in o accoun a simila endency in he g ain bounda y sel -di u- sion coe icien s. In addi ion, ou esul s o e an explana ion o he linea g ow h kine ics in his egime: I he on eloci y is cons an , he amoun o he p oduc phase should g ow linea ly wi h ime and he ac i a ion ene gy ob ained om his pa should be close o he ac i a ion ene gy o GB/in e ace di usion [24,26]. Conclusion I is shown ha a low empe a u es, a which he bulk di u- sion is ozen, an almos comple e homogeniza ion can ake place in he Cu/Au hin ilm sys em, leading o he o ma ion o in e me allic phases. I is illus a ed ha he p ocess is based on g ain bounda y di usion induced g ain bounda y mo ion and eac ion laye o ma ion, he p ocess s a s by g ain bounda y in e di usion and a e he illing-up o g ain bounda ies he eac ion s a s he e. A e he o ma ion o he eac ion zone (solid solu ion o o de ed phase) he a omic anspo along he o iginal GB, o along he newly o med in e aces pe pendic- ula o he g ain bounda y plane, esul s in he g ow h o he eac ed ma e ial. Finally, he homogeniza ion inishes when all he pu e componen s ha e been consumed. The ini ial pa , in acco dance wi h he well-known ule o humb decla ing ha he di usion is as e in he componen wi h lowe mel ing poin , is asymme ic: The p ocess is as e in he Au laye . In Au(25nm)/Cu(50nm) samples, acco ding o Figu e 1 and Figu e 2d, he inal s a e is he o de ed AuCu3 phase. Dec easing he ilm hicknesses (see he esul s ob ained in Au(10nm)/Cu(25nm) and shown in Figu e 3b and Figu e 4) esul s, as expec ed, in he accele a ion o he p ocess. I is illus a ed ha by changing he hickness a io ei he a mix- u e o Cu- ich AuCu diso de ed and AuCu3 phases (see Figu e 5b and Figu e 6 o Au(25nm)/Cu(25nm) sample), o a mix u e o diso de ed Cu- as well as Au- ich solid solu ions (see Figu e 7 and Figu e 8) can be p oduced. By using a simple model, we we e able o es ima e he in e - ace eloci y in bo h he Cu and Au laye s om he linea inc ease o he a e age composi ion and, again in acco dance wi h he abo e ule o humb, i s alue is abou wo o de s o magni ude la ge in Au (o he o de o 10−11 m/s) han in Cu (o he o de o 10−13 m/s). Expe imen al Au/Cu nanoc ys alline hin ilms we e p epa ed by DC magne on spu e ing on o (001)-o ien ed Si wa e s wi h na i e SiO2 laye . The ollowing bilaye samples we e deposi ed: Au(25nm)/Cu(50nm), Au(25nm)/Cu(25nm), Au(25nm)/ Cu(12nm), Au(10nm)/Cu(25nm) and Au(10nm)/Cu(15nm). Du ing he deposi ion o me al laye s he Si subs a e was kep a oom empe a u e and he A base p essu e was se a 0.5 Pa. The a es o he deposi ion o Au and Cu laye s we e 0.85 nm/s and 0.5 nm/s, espec i ely. The samples we e annealed unde acuum (1 × 10−4 Pa) a empe a u es anging om 160 o 330 °C. The e olu ion o he in e mixing p ocess was s udied o e a ime be ween 0.5 and 44 h. The concen a ion p o iles we e measu ed by using a seconda y neu al mass spec ome e (SPECS INA-X), ha wo ks wi h noble gas plasma and he bomba ding ion cu en has an ex emely high la e al homogenei y. The low bomba ding ene - gies (o he o de o 100 eV) and he homogeneous plasma p o ile esul in an ou s anding dep h esolu ion (smalle 2 nm). De ails o he SNMS de ice and he p o ile e alua ion can be ound elsewhe e [27,28]. The c ys alline s uc u e was examined by means o X- ay di ac ion in θ–2θ scanning geome y while using Cu Kα adia- ion (Rigaku Ul ima IV di ac ome e ) and by ansmission elec on mic oscopy (TEM, JEOL 2000FX-II). Acknowledgemen s The esea ch was suppo ed by he TÁMOP-4.2.2.A-11/1/ KONV-2012-0036 p ojec , implemen ed h ough he New Hunga y De elopmen Plan co- inanced by he Eu opean Social Fund, and he Eu opean Regional De elopmen Fund. The au ho s g a e ully acknowledge he suppo o he Hunga ian Scien i ic Resea ch Fund (OTKA) h ough G an NF 101329.