Hydrodynamic aspects of the amorphous alloy ribbon fabrication M. Imaizumi and M. A. Tenan Citation: Journal of Applied Physics 65, 4010 (1989); doi: 10.1063/1.343322 View online: http://dx.doi.org/10.1063/1.343322 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/65/10?ver=pdfcov Published by the AIP Publishing [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 200.145.3.45 On: Wed, 05 Feb 2014 15:53:30 http://scitation.aip.org/content/aip/journal/jap?ver=pdfcov http://oasc12039.247realmedia.com/RealMedia/ads/click_lx.ads/www.aip.org/pt/adcenter/pdfcover_test/L-37/1479233748/x01/AIP-PT/JAP_Article_DL_0214/aipToCAlerts_Large.png/5532386d4f314a53757a6b4144615953?x http://scitation.aip.org/search?value1=M.+Imaizumi&option1=author http://scitation.aip.org/search?value1=M.+A.+Tenan&option1=author http://scitation.aip.org/content/aip/journal/jap?ver=pdfcov http://dx.doi.org/10.1063/1.343322 http://scitation.aip.org/content/aip/journal/jap/65/10?ver=pdfcov http://scitation.aip.org/content/aip?ver=pdfcov Hydrodynamic aspects of the amorphous alloy ribbon fabrication M. Imaizumi D~partamento de Fisica, UNESP, 17033 Bauru, SP, Brazil M. A. Tenan , I Instituto de Fisica, Universidade Estadual de Campinas, 13081 Campinas, SP, Brazil (Received 7 December 1988; accepted for publication 5 January 1989) Conditions for as-quenched amorphous ribbon fabrication by a single roll-casting method are analyzed from a hydrodynamic standpoint. The analysis is based on the investigation ofthe processing conditions for Fe4oNi4oP 14B6 amorphous ribbons. It is shown that the dependence of ribbon thickness on the ejection pressure for different roll angular velocities and different dimensions of crucible and orifice can be obtained from general considerations on the melt flow regime. I. INTRODUCTION In recent years the possibility of important technologi­ cal applications of amorphous alloy ribbons has aroused great deal Of interest, 1,2 and much attention has been focused on their formation and processing conditions. 3 -6 The at· tempts of mathematically describing the hydrodynamic step of the fabrication process are based on the assumption that the melt is an inviscid fluid which obeys Bernoulli's equa­ tion.5 • 6 However, depending on Reynolds number, energy losses in the flow through an orifice within a pipe or at its end cannot be neglected.7 - 9 While the discrepancies between the­ ory and experiment in the case of Ref. 5 could be attributed to experimental errors, the more refined treatment in Ref. 6 faced difficulties which could not be convincingly resolved. Hence the mathematical development of the melt flow de­ serves to be reexamined. Reformulating the main assumption on the melt flow, we thus study in this paper the role played by hydrodyna­ mics in amorphous ribbon fabrication. The study is based on the investigation of the processing conditions of Fe4oNi4oP 14B6 amorphous ribbons. 10 Our results and those of Ref. 6 are analyzed by taking into account the basic phe­ nomena of fluid discharge through orifices. II. EXPERIMENT A diagram of the apparatus used in our experiment is shown in Fig. 1. It consists of a copper roll (20 cm in diame­ ter) used as a substrate to obtain amorphous ribbons from a master alloy of nominal composition Fe4oNi4oP 14B6' A I-g charge of this master alloy was precisely weighed by an elec­ tronic balance and then placed in a quartz crucible (8 mm o.d. and 7 mm i.d.) having a circular orifice (0.5 mm in diameter) at its bottom. After each run, the crucible was cleaned to maintain the original size. By doing this, the same crucible was used in each series of experiments. For all runs the distance between the orifice and the copper roll surface was held fixed at 1 mm and the quartz tube axis made a constant 10· angle with respect to the vertical direction. The melt temperature measured by an optical pyrometer was de­ termined to be 1100 ·C. All amorphous ribbons were cast in such a way that the resultant width was about 1.5 mm and the resultant thickness ranged from 15 to 30 {lm. To get high-quality continuous amorphous ribbons of different thicknesses two series of runs were performed. In the first series, the gauge pressure of the gas (pure argon) above the melt was varied step by step from 1.0 to 2.5 kgf/cm2, while keeping the roll angular velocity fixed at 3000 rpm. Conver­ sely, in the second series, the angular velocity was changed from 2000 to 3500 rpm at a constant gauge pressure of 1.8 kgf/cm2 [1 kilogram force (kgf) = 9.806 65 N]. In our experiment it was observed that for all runs for which the gauge pressure was greater than 2.3 kgf/cm2 or the angular velocity of roll was less than 1800 rpm, the rib­ bons produced were crystalline. On the other hand, in the cases for which the gauge pressure was less than 1.0 kgf/cm2 or the roll angular velocity was greater than 3500 rpm, the ribbons produced were amorphous but porous. The as-quenched ribbons were examined by x-ray dif­ fraction using CuKa radiation to evaluate the nature of their amorphous structure. III. RESULTS AND DISCUSSION The basic equation for the melt discharge through the orifice at the bottom of the crucible can be written as9 -¥.il---mell r~-- crucible FIG. 1. Apparatus for ribbon fabrication (schematic not on scale). 4010 J. Appl. Phys. 65 (10), 15 May 1989 0021-8979/89/104010-04$02.40 © 1989 American Institute of Physics 4010 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 200.145.3.45 On: Wed, 05 Feb 2014 15:53:30 (1) where Q is the volume flow rate, C is the discharge coeffi­ cient, A2 is the orifice area, p is the melt density, and 6.p is the pressure drop due to melt flow through the orifice. The dimensionless coefficient c in Eq. (1) depends pri­ marilyon (i) the ratio between the orifice area A2 and the crucible inner cross sectional area A I' and (ii) the Reynolds number, NR =..!.e...Q, (2) 1T f-L d l for the melt flow in the crucible. In Eq. (2), f-L is the melt viscosity and d 1 is the crucible inner diameter. It is an experimental factS that the discharge coefficient is much smaller than unity for very low Reynolds numbers and increases with increasing N R until it reaches a maxi­ mum value. A further increase in the Reynolds number re­ sults in a decrease in c, and finally the coefficient becomes nearly constant for large NR • The computed values of c for the melt discharge in our experiment when plotted together with those from Ref. 6 display this general trend (see Fig. 2). If we combine Eq. (I) with Eq. (2), we get the relation (3) which shows that for a given liquid alloy at a fixed tempera­ ture and for given values of crucible and orifice dimensions, the ratio NR /c is determined by the pressure drop 6.p. Since the discharge coefficient is a function of N Rand A2/ A I' Eq. (3) indicates that the pressure difference I1p determines the Reynolds number and consequently the flow regime for cho­ sen values of the melt temperature and the sizes of crucible and orifice. For the conditions of our experiment the pressure drop 6.p in Eq. (3) can be taken as the ejection pressure measured above the atmospheric pressure (gauge pressure), while for the experimental conditions given in Ref. 6 6.p can be consid­ ered as the sum of the gauge pressure with the hydrostatic pressure difference due to a melt column of height H = 1.64 cm and a density p = 7.7 glcm3 • In fact, the hydrostatic pressure difference in the case of our experiment (H = 0.70 cm and p = 7.8 g/cm3) is approximately three orders of magnitude smaller than the applied gauge pressure. The pressure drop across a surface with a curvature radius of about the orifice dimension is negligible for both experi­ ments, even for a surface tension value as high as 500 dyn/ cm. Finally, it can be shown that the pressure drop due to flow in the crucible gives a vanishing contribution for a melt viscosity f-L - 2.25 cP (Ref. 11) and a Reynolds number be­ low 4000. 12 To evaluate the flow rate Q we equate the amount of melt ejected from the orifice per unit time to that of the solid ribbon produced on the roll surface per unit time. Hence we write Q = OJri€, (4) where OJ and r are the angular velocity and the radius of the roll, respectively, i is the width of the ribbon, and € is its 4011 J. Appl. Phys., Vol. 65, No. 10, 15 May 1989 ... I.° t " ~ ~" (al ... w o u ~ 0 .. 5 a: .. :t: U VI C (bl I I 0.0 L._--'-__ --L.._---' __ .....L. __ '--_--' 500 1500 2500 3500 REYNOLDS NUMBER FIG. 2. Discharge coefficient as a function of Reynolds number. (a) Our experiment (area ratio: Sx 10-3 ) and (b) Ref. 6 (area ratio: 2X 10- 2 ). thickness. In writing Eq. (4) we have assumed the equality between the densities of the amorphous solid and the liquid melt.6 Figures 2 and 3 show respectively the discharge coeffi­ cient c and the ratioNR/c as functions of the Reynolds num­ ber. The points in the figures have been evaluated from our experimental data and those of Ref. 6. To evaluate NR we have considered Eqs. (2) and (4); the values for c have been evaluated with the help ofEqs. ( 1 ) and (4); Eq. (3) has been used for computing N R /c. The points with bars in Figs. 2 and 3 represent average values obtained from data for differ­ ent roll angular velocities at a fixed pressure drop 6.p. The dispersion (rms deviation) represented by bars in the figures does not exceed 3.6% and 7.5% in the case of our experi­ ment and of Ref. 6, respectively. It is evident from Figs. 2 and 3 that our results and those of Ref. 6 are complementary in the sense that they concern to essentially different flow regimes as determined by Reynolds numbers below and above 2300. 12 1500 N" °1000 ;.:, (" 5500 4500 2500 5ooL--'--~----'-~---'--~ 1500 500 1500 2500 3500 REYNOLDS NUMBER FIG. 3. Ratio NR/c, Eq. (3), as a function of Reynolds number. (a) Our experiment and (b) Ref. 6. M. Imaizumi and M. A. Tenan 4011 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 200.145.3.45 On: Wed, 05 Feb 2014 15:53:30 As pointed out above, the pressure drop /:l.p determines the Reynolds number for given values of melt density and viscosity and of crucible and orifice sizes. This result implies that NRlc vs NR curves for different A21A J ratios play an important role in determining the conditions for amorphous ribbon fabrication: the knowledge of the quantities p and J.l, and the choice of (i) the crucible and orifice dimensions and (ii) the pressure difference I:l.p will determine, via Eq. (3) and the appropriate NR/c vs NR curve, the corresponding Reynolds number. Since the ribbon width is essentially con­ trolled by the orifice size,5 the values of NR , I (for a given orifice area A 2 ), and the roll radius r will be sufficient in predicting through Eqs. (2) and (4) the ribbon thickness for each value of the roll angular velocity. This procedure has been adopted in obtaining Figs. 4 and 5 from the curves in Fig. 3 and the other experimental data. The diagrams in Figs. 4 and 5 show the predicted ribbon thickness as a function of gauge pressure for different roll angular velocities. The dashed horizontal lines in the figures represent the limits of thickness at which an amorphous rib­ bon can be cast continuously without porousness. The limits have been taken empirically as being 15 /-tm < € < 35 /-tm in the case of our experiment and 20 J.lm < € < 60 J.lm in the case of Ref. 6. For comparison, experimental points for a fixed roll an­ gular velocity are also shown in Figs. 4 and 5. In all the cases the discrepancies between experimental and predicted thick-. nesses do not exceed 2/-tm, a value not too far from the ± 1- /-tm variation of thickness measured along ribbons. Hence, diagrams like those in Figs. 4 and 5 will be very helpful in determining the conditions for casting amorphous ribbons with desired thickness and width. 35 ------------- §. en en UJ Z 30 " 25 u :J: f- Z a III III ii: 20 1.2 1.6 2.0 2.4 GAUGE PRESSURE (kQflcm2) FIG. 4. Ribbon thickness as a function of the ejection gauge pressure for different values of the roll angular velocity /iJ. The symbols 0 represent our experimental data for /iJ = 3000 rpm. 4012 J. Appl. Phys., Vol. 65, No. 10, 15 May 1989 .§. VI VI lLJ Z 60 50 ~ 40 J: ~ Z o CD CD a:: 30 20 0.0 0.3 0.7 1.1 GAUGE PRESSURE (kgf/cm 2) FIG. 5. Ribbon thickness as a function of the ejection gauge pressure for different values of the roll angular velocity /iJ. The symbols 0 represent the experimental data of Ref. 6 for /iJ = 2000 rpm. IV. CONCLUSION The basic outcome of the analysis presented here is that the flow regime of the melt in the crucible plays a fundamen­ tal role in determining the conditions for ribbon fabrication by the single roll-casting method. As we have seen, the knowledge of general curves of the ratio N R / c vs N R' for different orifice/crucible area ratios, allows us to obtain the ribbon thickness from diagrams of thickness versus gauge pressure for a given choice of the parameters which deter­ mine the flow regime. We believe that our analysis would be useful to design new apparatuses which might optimize the processing con­ ditions for fabrication of amorphous ribbons with prescribed dimensions. ACKNOWLEDGMENTS We would like to thank Dr. M. Shukla, Dr. S. Gama, and Dr. B. Laks for critically reading the manuscript. One of us (M.I.) also wishes to thank Dr. R. S. Turtelli for assis­ tance with the experimental work. ID. Raskin and C. H. Smith, in Amorphous Metallic Alloys, edited by F. E. Luborsky (Butterworths, London, 1983), Chap. 20; T. Hosokawa, T. Sa­ saki, and H. Nose, IEEE Trans. Magn. MAG-23, 316 (1987) (abstract); K. Kakuno, Y. Ohshima and T. Yamada, IEEE Trans. Magn. MAG-23, 316 (1987) (abstract); H. J. de Wit, C. H. M. Witmer, and F. W. A. Dime, IEEE Trans. Magn. MAG-23, 2123 (1987); A. T. Rezende, R. S. Turtelli, and F. P. Missell, IEEE Trans. Magn. MAG-23, 2128 (1987); Y.-H. Lee, IEEE Trans. Magn. MAG-23, 2131 (1987); A. Mitra M. Imaizumi and M. A. 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