Calculaton Of The Interdffuson Coeffcent In The Cu Zn Dffuson Couple Adhurm Hoxha a and Henrch Oettel b and Detrch Heger b a Polytechnc Unversty of Trana b TU Bergakademe Freberg, Insttut für Werkstoffwssenschaft Abstract. A quanttatve analyss of multphase dffuson n Cu-Zn dffuson couple s presented. The analyss s based n usng the concentraton profles provded by electron mcro-beam analyzer. From the dependence of the square of phase thckness from annealng tme, the growth constant for each phase n each annealng temperature can be calculated. Knowng the growth constant of γ and ε phases one can calculate the actvaton energy and the dffuson coeffcent of the above mentoned ntermetallc phases. Keywords: Dffuson, Interdffuson coeffcent, Actvaton energy; Plattng technque, Optcal mcroscopy; Electron mcro-beam analyzer. PACS: 66.3.-h; 66.3.Ny; 66.3.Xj; 67.8.dj; 68.35.Fx INTRODUCTION Dffuson between two metallc speces s now a well recognzed phenomenon and t s often accompaned by the formaton of one or several ntermetallc compounds. Ths phenomenon s generally descrbed under the headng multphase dffuson, whch emphaszes the dffuson part of the whole process [1,4]. In a typcal case pure metal A s bonded to pure metal B and dffuson s permtted at hgh temperature. Although both A and B atoms move, only one concentraton profle, say of A, s establshed (the profle of B contans no new nformaton). The resultng dffuson coeffcent whch s extracted from the profle s termed the nterdffuson coeffcent [1,7,4]. In ths work we have consdered the dffuson n the nfnte Cu Zn couple produced by the plattng technque. They were used four dfferent annealng temperatures rangng from o C to 38 o C. For each temperature they were used sx dfferent annealng tmes, rangng from 1 hour to 32 hours. The concentraton profles were determned by the use of the electron mcro-beam analyzer. From the optcal mcroscopy and the concentraton profles one can detect the presence of, and phases accordng to the Cu Zn phase dagram. Usng the above mentoned concentraton profles we were able to do calculatons only for γ and ε phases. The phase was observed only at very hgh temperature and very long annealng tmes and t shows a reduced thckness. EXPERIMENTAL The base materal was pure Copper and pure Znc. The composton of the base materal was determned by GD OES. To determne the approprate fllng materal for the sample contaner two no annealed samples, were put n the sample contaner by fllng those respectvely wth epoxy and tn. We were nterested n fndng an approprate fllng materal,.e. we dd not want any dffuson to happen durng the fllng process. From the concentraton profles we noted that when the fllng process was carred out usng melted tn, the dffuson process has started. So the temperature reached durng the fllng process (or that of the melted tn) was hgh enough for the dffuson process to start, regardless of the tme used to carry out the fllng process. Usng epoxy as a fllng materal we were able to get a sharp concentraton profle wth no ntermetalc phase presented. From that pont we decded to use epoxy as our fllng materal. One of the dsadvantages of ths fllng materal (wth respect to tn) was that we wll CP123, 7 th Internatonal Conference of the Balkan Physcal Unon, edted by A. Angelopoulos and T. Fldss 29 Amercan Insttute of Physcs 978--7354-74-4/9/$. 591
use the carbon layer, needed for electron conducton durng the measurement n the electron mcro-beam analyzer. However, compared to tn, epoxy can offer very good possbltes for metallographc sample preparaton [2]. The nfnte Cu Zn couple was produced by pressng two peces of pure copper and pure znc approxmately 4cm 2 n sze. To determne the approprate force appled to the above mentoned peces, we tred the forces: 2kN, 3kN and 32kN. From the concentraton profles of such samples (no annealng was appled) one can easly see that the results are almost the same. Therefore we thnk that the force appled to produce our samples (the nfnte couple Cu-Zn) wll have no effect n the dffuson process that we are gong to study. Annealng was carred out n thermal oven model: NABERTHERM Model L5 (3-3 o C). We have used four dfferent annealng temperatures: o C, 3 o C, 35 o C and 38 o C. For each temperature the annealng tmes have been: 1h, 4h, 9h, 16h, h and 32h. After annealng, the samples were cooled very fast n cold water. After the annealng, a layer of less than 1mm n thckness was mechancally cut off from the sample and the sample was put n the sample support by fllng t wth epoxy. After ths process the sample was ready for metallographc preparaton. RESULTS AND DISCUSSIONS Our optcal mcroscope was model NEOPHOT 3, ZesJena. In the followng we wll show the pctures provded for two of our annealng tmes (respectvely 16h and h) for the temperature 38 o C: FIGURE 1. Obtaned pctures from two samples at 38 o C wth dfferent annealng tmes (16h and h). The electron probe mcro-analyzer was model JXA-89. The measurement lne has been perpendcular wth the dffuson nterface. There were used 2 12 measurement ponts,.5 1 m apart. In the followng one can see the concentraton profles n weght percentage for the temperature 38 o C. 592
1 1 5 5 1 2 3 4 1 hour 1 2 3 4 5 4 hours 1 1 5 5 2 4 6 8 9 hours 2 4 6 8 1 16 hours 1 1 5 1 5 2 4 6 8 1 hours 2 4 6 8 1 32 hours FIGURE 2. Concentraton profles at 38 o C. From the two pctures presented below one can see the presence of the expected phases accordng to the Cu-Zn phase dagram. (We have used an optcal mcroscopy pcture and the atomc map for two of our samples). FIGURE 3. Graphcal representaton of the expected phases accordng to the Cu-Zn phase dagram. The thckness of γ and ε phases were measured drectly at the concentraton profles. From the data provded n such manner the dependence of the square of phase thckness from annealng tme was studed. From the graphcal 593
analyss of the expermental results t was observed a devaton from the parabolc law of phase growth 2 ( Δ x = 2k t ) [3,5,6,8]. Ths was observed for the frst two annealng tmes (1h and 4h). It may be explaned as a lack of equlbrum state due to the very short annealng tmes. Anyway, we have reasons to beleve that for very short annealng tmes the man role n the dffuson process s played by the chemcal reactons. At ths stage the phase growth law s a lnear one [3]. By ncreasng the annealng tme, the mass transport or atomc movements s the domnant factor n the dffuson process. The next step was to determne the coeffcent of phase growth for both phases n every used temperature. Ths 2 was done by the use of regresson analyss and the relaton ( Δ x = 2k t ). The results are presented n the followng tables: TABLE a). The coeffcents of phase growth. Temperature (K) k x1-12 (m 2 /s) k x1-12 (m 2 /s) 523.2 622.8 12.4 573.2 1635.6 91.3 623.2 479.8 399.2 653.2 67.5 115.6 The coeffcent of phase growth k determnes the speed of phase growth and therefore s proportonal wth the dffuson coeffcent. From the well known form of dependence of the dffuson coeffcent on temperature D = D exp( Q RT) we get k = k exp( Q RT). After the graphcal analyss of the expermental results the calculated values are: TABLE b). The actvaton energes for both phases. Q (J/mol) Q (J/mol) 5.1x1 4 9.7x1 4 The theoretcal formulas used to calculate the dffuson coeffcents are: 1 (b a) (d c) D γ = k γ and D c b (b a) + (d c) The meanng of the symbols used n the above formulas are: ε = k ε 1 (d c) (f e) e d (d c) + (f e) TABLE c). Symbols used n the above formulas. Symbol a b c d e f The meanng c c c c c c The above mentoned symbols were determned drectly from the concentraton profles n the way that s shown n the followng pcture. FIGURE 4. Gettng the symbols used n our formulas by the concentraton profles. 594
The results are shown n the tables below: TABLE d). The dffuson coeffcents values. T ( o C) D x1-12 (m 2 /s) D x1-12 (m 2 /s) 27.39 69.44 3 1445.87 34.3 35 119.71 4.29 38 1432.97 896.32 SUMMARY AND CONCLUSIONS Durng the study of the dffuson process n the Cu-Zn couple there were noted the presence of fve phases. These are the expected ones accordng the Cu-Zn phase dagram (concernng the temperature range we have used). Durng our expermental work we dd not notce any phase boundary between sold soluton and, respectvely wth Cu and Zn. In the used temperature range the thck enough phases to do calculaton are and phases. For the hgh enough temperatures and the long enough annealng tmes we dd notce the presence of the phase. The absence of ths phase for short annealng tmes s connected to the homogenety of ths phase. By the use of the concentraton profles frstly we study the dependence of the square of phase thckness from the annealng tme. It was shown that the law of phase growth s parabolc. For very short annealng tmes we dd notce a devaton from the parabolc law of phase growth. At ths stage of the process there s no equlbrum state reached yet due to very short annealng tmes. We thnk that the domnant factors at ths stage of the process are the chemcal reactons happenng at the nterface between Cu and Zn atoms. For the Cu-Zn dffuson couple we have calculated the coeffcents of phase growth, ther actvaton energes and correspondng dffuson coeffcents for each of the annealng temperatures used. In the future we wll try to work at hgher temperatures by usng an approprate geometry for the dffuson couple. Ths wll enable us to do calculaton even for phase. REFERENCES 1. J. Phlbert, Dffuson and Mass Transport n Solds, Les Édtons De Physque, Les Uls, France 1991. 2. H. Schumman and H. Oettel, Metallografe, Wley-VCH Verlag GmbH & Co, KgaA, 14 Auflage,. 3. C. P. Chen and Y. A. Chang, Formaton And Growth Of Intermetallc Phases In Bnary Dffuson Couples, Dffuson In Ordered Alloys, EMPMD Monograph Seres. 4. W. Seth, Dffuson n Metalen, Sprnger Verlag, Berln 1995. 5. G. Neumann, Dffuson Mechansms In Metals, Defects And Dffuson Forum, Vols, 66 99 (1989), pp. 43-64. 6. J. Phlbert, Interplay Of Dffuson And Interface Processes In Multphase Dffuson. Defect And Dffuson Forum, Vols, 95-98 (1993), pp. 493-56. 7. B. S. Boksten and L. M. Klnger and S. N. Kholodov, Znk Dffuson Along Indvdual Gran Boundares <11> In Alumnum, Defect and Dffuson Forum, Vols, 66-99 (1989), pp. 849-854. 8. H. Theodor, Dffuson In Metalen, Grundlagen Theore, Vorgänge In Penmetallen Und Legerungen. Sprnger-Verlag, Hedelberg, 1992. 595
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