Communications

12 downloads 0 Views 2MB Size Report
On the basis of the pro- ...... ment, Nagoya Aerospace Systems, Mitsubishi Heavy Industries, Ltd., .... The specimen was prepared with a diamond cut- ..... the fabrication process. p. 2040. Summarizing the results, the tensile strength of the Cu/ ...
Communications Partial Fe-Ti Alloy Phase Diagrams at High Pressure TOSHIMI YAMANE, KOJI HISAYUKI, RIYUICHIRO NAKAO, YORITOSHI MINAMINO, HIDEKI ARAKI, and KEIICHI HIRAO Recently, high pressure treatments such as hot isostatic pressing have become more familiar in industrial processes. The high pressure induces changes of both the phase equilibrium and the kinetics of the phase transformation in alloys. The iron-rich phase diagrams under high pressure have been previously reported in the Fe-Mo,[1] Fe-W,[2] Fe-Cr,[3] FeV,[4] and Fe-Si[5] systems, which have the g loop in the ironrich side at the ordinary pressure.[6] These systems exhibit the astonishing changes in phase equilibrium under high pressure: the g loop expands under high pressure, and especially the g loop type phase diagrams of Fe-Mo and Fe-W systems transform to the g shrink type phase diagram at higher pressures. So, it is very interesting to investigate the effect of high pressure on phase equilibrium in the g loop phase diagram of the Fe-Ti system, which is practically important for hydrogen storage alloys, titanium clad steels, and so on. Therefore, the authors have established the ironrich Fe-Ti phase diagrams at the high pressure up to 2.7 GPa. The ingots of pure iron, pure titanium, and Fe-Ti alloys were prepared from 99.9 mass pct purity electrolysis iron and 99.85 mass pct purity titanium by arc melting in argon gas. These ingots were annealed at 1373 to 1573 K for 28.8 ks for homogenization in argon gas. The chemical compositions of the ingots were 99.9 mass pct Fe, Fe-2.13 at. pct Ti (quenched a Fe phase), Fe-4.31 at. pct Ti (quenched a Fe phase), Fe-7.86 at. pct Ti (quenched a Fe phase), a Fe-30 at. pct Ti (Fe2Ti phase), Fe-81.4 at. pct Ti (quenched b Ti phase), Fe-90.2 at. pct Ti (quenched b Ti phase), 99.85 mass pct Ti, and so on. The ingots of pure iron and titanium were cut into discs, 2.5 mm in thickness and 4 mm in diameter. The surfaces of the discs were metallographically polished by 0.05-mm alumina, and then the diffusion couples were immediately assembled with discs of pure iron and pure titanium. These diffusion couples were annealed at the pressures of 0, 2.3, and 2.7 GPa at 973 to 1643 K and for 3.6 to 432 ks. The method for annealing of the diffusion couples has been reported elsewhere.[1,2] The annealed diffusion couples were cold mounted in resin and were cut to expose a section parallel to the diffusion direction. The section was metallogrphically polished. The concentrations of titanium and iron on the polished sections in these diffusion couples were measured by an electron probe microanalyzer. The Ti Ka and Fe Ka X-ray intensities TOSHIMI YAMANE, Professor, and KOJI HISAYUKI, Graduate Student, are with the Department of Mechanical Engineering, Hiroshima Institute of Technology, Hiroshima 731-5193, Japan. RIYUICHIRO NAKAO, Graduate Student, HIDEKI ARAKI, Associate Professor, and KEIICHI HIRAO, Technical Officer, Department of Materials Science and Engineering, and YORITOSHI MINAMINO, Professor, Department of Adaptive Machine Systems, are with Osaka University, Osaka 565-0871, Japan. Manuscript submitted May 13, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 1—Iron concentration profiles as a function of Boltzmann parameter X/t1/2 in Fe/Ti react diffusion couples annealed at 1173 K and 2.3 GPa for 14.4, 28.8, and 57.6 ks.

Fig. 2—Titanium concentration profiles in Fe/Ti react diffusion couples annealed at 1373 K for 14.4 ks at 0, 2.3, and 2.7 GPa.

were converted to the concentrations of titanium and iron with the aid of prepared alloy standards. Figure 1 shows the diffusion profiles of iron concentrations in the diffusion couples annealed at 1173 K and 2.3 GPa for the various diffusion times of 14.4, 28.8, and 57.6 ks against the Boltzmann parameter, X/t1/2, where X is the distance from Matano interface and t the diffusion time. As a result of react diffusion, the b Ti, Fe2Ti, FeTi, g Fe, and a Fe phases appear in the react diffusion zones. All of the diffusion profiles are on the same curve against the Boltzmann parameter. This means that the diffusion phenomena are kept in partial equilibrium and the phase interface concentrations in the diffusion zones should be equal to the equilibrium concentrations in the Fe-Ti phase diagram. Therefore, the react diffusion couple method enables us to clarify equilibrium for constructing the phase diagrams. Namely, the phase diagrams can be established from the interface concentrations between the adjacent phases in the diffusion zone. Figures 2 and 3 show, as an example, the diffusion profiles of titanium concentrations in the iron-rich part of the diffusion couples annealed at 1373 K for 14.4 ks under 0, 2.3, and 2.7 GPa, and those annealed at 1323, 1273, and 1223 K for 28.8 ks under 2.7 GPa, respectively. From the interface concentrations, the iron-rich Fe-Ti phase diagrams are assessed as shown in Figures 4 through 6. As shown in Figures 2 and 3, the diffusion distance in the a Fe phase is VOLUME 30A, NOVEMBER 1999—3009

Fig. 3—Titanium concentration profiles in Fe/Ti react diffusion couples annealed at 1323, 1273, and 1223 K for 28.8 ks under 2.7 GPa.

Fig. 5—Iron-rich Fe-Ti phase diagram at 2.3 GPa.

Fig. 4—Iron-rich Fe-Ti phase diagram at 0 GPa.

long and the titanium concentration varies gently, while the diffusion distance in the g Fe region is quite short and its concentration gradients are considerably steep, because titanium diffuses fairly faster in the a Fe phase than the g phase. Therefore, the concentrations at the a/(a 1 g) and a/(a 1 Fe2Ti) are not distinct, because the diffusion distances in the g Fe region are about 4 mm, which is near the resolution area (about 1 or 2 mm in diameter) for the concentration measurement by electron probe microanalysis. Therefore, The Cg/(a 1 g)’s are drawn by the bars in the phase diagrams. Both interface concentrations increase with increasing pressures. As shown in Figure 3, the a and g Fe phases are observed in the diffusion zones and interface concentrations are almost equal at both 1324 and 1273 K under the same pressure of 2.7 GPa. However, it is noticed that the a Fe disappears in the diffusion zone at 1223 K and 2.7 GPa, and thereby, the g Fe region phase is adjacent to the Fe2Ti phase. From these diffusion files, the concentrations at the g/(g 1 Fe2Ti) interface, Cg/(g 1 Fe2Ti) are determined. 3010—VOLUME 30A, NOVEMBER 1999

Fig. 6—Iron-rich Fe-Ti phase diagram at 2.7 GPa.

The a Fe phase is in equilibrium with the g Fe phase, which forms the g loop, the experimental Ca/(a 1 g)’s, and also the Fe2Ti phase at 0 GPa, as shown in Figure 4. The METALLURGICAL AND MATERIALS TRANSACTIONS A

experimental Ca/(a 1 g)’s and Cg/(a 1 g)’s are in good agreement with the Fe-Ti phase diagram of Massalski.[6] The Ca/(a1Fe2Ti)’s are shown in Figure 4 with the previous data by Massalski, Tuji,[7] and Ko and Nishizawa.[8] These experimental values are in good agreement with each other above about 1300 K, while they are scattered at lower temperatures. Generally speaking, the scattering of experimental data in phase equilibrium at low temperatures is due to the insufficient annealing, fine structures of alloys for concentration measurements, and so on. At the high pressures of 2.3 and 2.7 GPa, the g loop expands to higher titanium concentration with increasing pressures, while the Ca/(a 1 Fe2Ti)’s slightly shift to lower titanium concentration. As a result, a eutectoid reaction a → g 1 Fe2Ti and a peritectoid reaction g 1 Fe2Ti → a appear. At high pressures over 2.3 GPa, the g phase can be equilibrium with the Fe2Ti phase near 1150 K. These changes in the iron-rich binary phase diagrams at high pressure are observed in the Fe-Mo and Fe-W systems.[1,2] REFERENCES 1. Y. Minamino, T. Yamane, H. Araki, H. Hiraki, and Y. Miyamoto: J. Iron Steel Inst. Jpn., 1988, vol. 74, pp. 733-40. 2. T. Yamane, Y.S. Kang, Y. Minamino, H. Araki, A. Hiraki, and Y. Miyamoto: Z. Metallkd., 1995, vol. 86, pp. 453-56. 3. Y. Minamono, A. Araki, T. Yamane, H. Deguchi, A. Hiraki, S. Saji, and Y. Miyamoto: J. High Temp. Soc. Jpn., 1992, vol. 18, pp. 356-64. 4. R.E. Hanneman, R.E. Ogilvle, and H.G. Gatos: Trans. AIME, 1965, vol. 233, pp. 685-91. 5. L. Tanner and S.A. Kulin: Acta Metall., 1961, vol. 9, pp. 685-91. 6. Binary Alloy Phase Diagrams, 2nd ed., T.B. Massalski, ed., ASM INTERNATIONAL, Materials Park, OH, 1990, vol. 2, pp. 1783-86. 7. S. Tuji: J. Jpn. Inst. Met., 1976, vol. 40, pp. 844-51. 8. M. Ko and T. Nishizawa: J. Jpn. Inst. Met., 1979, vol. 43, pp. 118-26. 9. E.Y. Tonkov: Phase Diagrams of Elements, Nauka, Moscow, 1979, pp. 115-17.

Discussion of “Dendrite Growth Processes of Silicon and Germanium from Highly Undercooled Melts”* D. LI and D.M. HERLACH Aoyama et al.[1] used electromagnetic levitation (EML) with a laser preheating[2] and photodiode method[3] to investigate the solidification behavior of undercooled Ge and Si. The authors of Reference 1, referred to hereafter as the authors, have taken account of the emissivity change during melting and solidification for temperature calibrations and measured the growth velocity as a function of undercooling DT. The authors have not observed the faceted to nonfaceted transition in microstructure evolution with increasing undercooling, which has been revealed previously. Using Ge as *T. AOYAMA, Y. TAKAMURA, and K. KURIBAYASHI: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 1333-39. D. LI, NASA/NRC Resident Research Associate, is with the Drop Facilities/SD47, NASA/MSFC, Huntsville, AL 35812. D.M. HERLACH, Professor, is with Institute of Space Simulation, DLR, D-51170 Cologne, Germany. Discussion submitted May 21, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A

an example, we would like to comment on their main results and will show that deep undercooling can be achieved and that the preceding transition does, indeed, exist. There have been numerous studies on the large undercooling of semiconductors under conditions of slow cooling[4–17] and rapid quenching.[18,19] With regard to the former, a fairly complete list of experimental studies on undercooling Ge is summarized in Table I with respect to the maximum DT. First, it is seen from the listing that there has been a large range of reported maximum undercooling for this material due to different processing techniques and the difficulty of doing an experiment where all heterogeneities have been removed or deactivated. In the well-known classic article by Turnbull and Cech,[6] Ge was undercooled by 235 K using a microscope stage method. More impressively, the degree of undercooling was reported to be up to 214 K[4,5] for 150-g Ge samples processed in an open vertical cylindrical furnace without using vacuum or protective gas. In the 1980s, Ge droplets were successfully undercooled by up to 415 K[13,14] in a B2O3 flux in a clean environment. It may be argued that deep undercooling occurred only in very small droplets of less than 1 mm in diameter. However, studies[20] in other systems have verified that both melt fluxing and containerless processing can also lead bulk millimeter size specimens to a substantial degree of undercooling comparable with that in small droplets. The results in the last row of Table I might be partially caused by a melting point depression for the Ge nanoparticles due to the Gibbs– Thomson effect. However, the sample diameter ranging from hundreds of microns to a few millimeters should not be a crucial factor in determining the maximum undercooling obtained using state-of-the-art denucleation techniques. The maximum DT attained in the EML of Reference 1 is 180 K (derived from their Figure 4(b)), which is the smallest value given in Table I. The discrepancy between Reference 1 and the others cannot be simply imputed to the temperature errors, as concluded by Aoyama et al.,[1] who did not refer to the closely relevant articles. Second, it is seen from Table I that thermocouples were used in most of the experiments that have nothing to do with the emissivity change. As for the levitation processing, our EML approach[15,16] differs from that of Aoyama et al.[1] in preheating and temperature measurements. In our experiment, Ge samples were preheated by a graphite holder (preheater), which was removed from the coil after the sample was levitated as soon as the electrical conductivity became sufficiently high at elevated temperatures, while the laser heating was used by the authors of Reference 1. Our pyrometer looked through a quartz viewport at the top of the chamber. The advantage for top view is that the EML coil does not block the optical path at all and the pyrometer focuses on the top surface of the sample that is in the liquid state, as the triggered recalescence started from the bottom. Furthermore, a clean environment was established in our work by evacuating the experimental chamber to a pressure of 1024 Pa and then back-filling with high-purity He-20 pct H2 gas through a liquid-nitrogencooled trap (Table I), which is conducive to deep undercooling. There is convincing evidence by several independent experiments applying both melt fluxing[7,8,11–13] and containerless processing[16,21] that sufficiently large undercooling VOLUME 30A, NOVEMBER 1999—3011

Table I. Partial Summary of Experimental Studies on Undercooling and Solidified Microstructure of Ge Maximum DT (K)

Method

Sample Size D (mm)

Prior Vacuum Pressure (Pa)

Protective Gas

Structural Transition

References

180 214 235 250 to 300 280 316 342 415 426 439 to 472

EML, OP SLG, TC HSM, TC SLG, TC BOF, TC PCF, TC BOF, TC BOF, TC EML, OP TEM, TC

5 40 0.015 3 to 5 0.4 to 0.8 0.1 to 0.5 7 to 11 0.3 to 0.5 6 to 8 1025 to 1024

1023 no vacuum 0.7 5 3 1023 0.7 unreported ,0.1 0.7 1024 ,1023

Ar not used He N2 He-20 pct H2 unreported not used He-20 pct H2 He-20 pct H2 not used

no yes unreported yes unreported unreported yes yes yes unreported

1 4, 5 6 7, 8 9 10 11, 12 13, 14 15, 16 10, 17

SLG, soda-lime glass; HSM, hot stage microscope; BOF, boron oxide flux; PCF, potassium chloride flux; TEM, transmission electron microscope; OP, optical pyrometer; TC, thermocouples; and D, diameter. The structural transition here means the faceted (twin dendrites) to nonfaceted (twin-free dendrites) transition. The transition in the second row is caused by recrystallization.[5]

can result in a growth mode transition from faceted to nonfaceted morphology of the as-solidified microstructures in some materials such as Ge. But this transition has not been reproduced by Aoyama et al.[1] Before further discussion here, it should be noted that (a) free growth of an undercooled liquid is dendritic in nature and (b) the so-called faceted to nonfaceted transition has been determined from microstructure examination and not from the relationship between DT and growth velocity. In contrast to the statement of Aoyama et al., the undercooling-growth velocity relation is monotonic and no jump is detected at all in the measuring range of our experiments 60 K , DT # 426 K. Devaud and Turnbull[13] first observed the structural transition from ^211&[22] or ^110&[12] twin dendrites to ^100& twin-free dendrites for Ge, at a critical undercooling DT* of about 300 K. Later, this transition was confirmed,[7,11] but at a different critical DT*, which was found to decrease with the addition of a small amount of impurities. These observations clearly reveal that even small amounts of impurities to pure Ge can change the microstructural development in an essential way. We employed EML to undercool bulk Ge samples and reproducibly observed the transitions from twin dendrites to twinfree dendrites and to refined equiaxed grains.[15] Moreover, the critical undercoolings for microstructural transitions are consistent with the previous report.[13,23] In addition, we performed containerless processing of Ge using an 8.5-m drop tube[16] in order to eliminate a possible stirring effect during EML. Figure 1 illustrates the surface relief morphology of two Ge particles solidified in free fall in the drop tube. Please note that this picture is at the microscopic scale, which is almost identical to that of the upper schematic diagram[24] serving to depict the clear distinction between faceted and nonfaceted structure. On the basis of the pronounced edge faces in Figure 1(a), the sample can be assumed to grow by lateral mechanism at small DT. In contrast, Figure 1(b) presents a microscopically flat, or nonfaceted, surface, which should be induced by a continuous growth in the deeply undercooled droplet of pure Ge. Judging by the common results of fluxing,[7,8,11–14] EML,[15] pulsedlaser quenching,[23] and drop tube experiments, it can be concluded that the transition from lateral to continuous growth in Ge is a general effect of undercooling. While looking at the impurity-rich dendrites at the center of each grain in Figure 6(c) of Reference 1, it became evident 3012—VOLUME 30A, NOVEMBER 1999

Fig. 1—Scanning electron micrographs of (unetched) surface relief of two Ge particles solidified in free fall in an 8.5-m drop tube: (a) jagged and faceted surface and (b) microscopically flat and nonfaceted structure. METALLURGICAL AND MATERIALS TRANSACTIONS A

that some impurities have been drawn into the sample during processing. In the case of the presence of impurities, the dendrite growth velocity markedly deviates from that of pure materials, especially for semiconductors.[25] On the other hand, it has been suggested that the fraction of interfacial sites at which attachment can occur is about 0.01[23,26] for the covalently bonded Ge and Si because their electronic state changes from metallic to semiconducting upon solidification. Evans et al.[23] numerically simulated the relative morphological instability in undercooled Ge and predicted that the growth of faceted materials requires relatively large kinetic undercooling in contrast to what Aoyama et al. have reported. In light of these arguments, the agreement between the measured growth velocities and the calculations of socalled no fitting parameters in Reference 1 might be fortuitous, for instance, due to a conspiring effect of impurity and negligence of the kinetic attachment factor. Certainly, more work is needed in the area of measuring and modeling the dendrite growth in undercooled melts of semiconducting materials. Further measurements[27] of the solidification velocity in highly undercooled semiconductors are underway using a high speed digital camera in an electrostatic levitator, where the preheating and cooling gas are unnecessary and the heating is decoupled with the levitation. In conclusion, the undercooling observed by Aoyama et al.[1] from their EML is considerably less than that of various studies since the early 1950s. This discrepancy may not be simply ascribed to the temperature calibration of the pyrometer, despite the fact that we completely agree with the authors that pyrometric measurements on levitated drops need great care with regard to calibration and the change in the emissivity of semiconductors during melting or freezing. Nevertheless, a number of previous studies have clearly demonstrated the transition from lateral to continuous growth for the achieved undercooling exceeding a threshold. There is, in principle, one possible reason for missing this result: the maximum undercooling obtained in Reference 1 is too small to reach the transition regime.

The experiments were performed while one of the authors (DL) held the Alexander von Humboldt Fellowship. The authors also thank Dr. M.B. Robinson, Mr. T.J. Rathz, and Professor K. Kuribayashi for stimulating discussions and Mr. T. Aoyama for sending us the proof ahead of publication. REFERENCES 1. T. Aoyama, Y. Takamura, and K. Kuribayashi: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 1333-39. 2. J.K.R. Weber, S. Krishnan, R.A. Schiffman, and P.C. Nordine: Adv. Space Res., 1991, vol. 11, pp. 43-52. 3. D.M. Herlach and B. Feuerbacher: Adv. Space Res., 1991, vol. 11, pp. 255-62. 4. G.L.F. Powell: Trans. TMS-AIME, 1967, vol. 239, pp. 1662-63. 5. G.L.F. Powell: Mater. Sci. Eng., 1997, vol. A237, pp. 119-20. 6. D. Turnbull and R.E. Cech: J. Appl. Phys., 1950, vol. 21, pp. 804-10. 7. S.E. Battersby, R.F. Cochrane, and A.M. Mullis: Mater. Sci. Eng., 1997, vols. A226–A228, pp. 443-47. 8. S.E. Battersby, R.F. Cochrane, and A.M. Mullis: J. Mater. Sci., 1999, vol. 34, pp. 2049-56. 9. G. Devaud and D. Turnbull: Appl. Phys. Lett., 1985, vol. 46, pp. 844-45. 10. V.P. Skripov: in Current Topics in Materials Science, Crystal Growth and Materials, E. Kaldis and H.J. Scheel, eds., North-Holland Publishing Co., New York, NY, 1977, vol. 2, pp. 327-78. METALLURGICAL AND MATERIALS TRANSACTIONS A

11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

C.F. Lau and H.W. Kui: Acta Metall., 1991, vol. 39, pp. 323-27. C.F. Lau and H.W. Kui: Acta Metall. Mater., 1994, vol. 42, pp. 3811-16. G. Devaud and D. Turnbull: Acta Metall., 1987, vol. 35, pp. 765-69. D. Turnbull: Mat. Res. Soc. Symp. Proc., 1986, vol. 51, pp. 71-81. D. Li, K. Eckler, and D.M. Herlach: Acta Mater., 1996, vol. 44, pp. 2437-43. D. Li and D.M. Herlach: J. Mater. Sci., 1997, vol. 32, pp. 1437-42. V.N. Skokov, A.A. Dik, V.P. Koverda, and V.P. Skripov: Sov. Phys. Crystallogr., 1985, vol. 30, pp. 236-37. H.A. Davies and J.B. Hull: Scripta Metall., 1973, vol. 7, pp. 637-42. S.R. Stiffler, M.O. Thompson, and P.S. Peercy: Appl. Phys. Lett., 1990, vol. 56, pp. 1025-27. See, for example, D.J. Thoma and J.H. Perepezko: Metall. Trans. A, 1992, vol. 23A, pp. 1347-62. R.F. Cochrane, P.V. Evans, and A.L. Greer: Mater. Sci. Eng., 1988, vol. 98, pp. 99-103. D.R. Hamilton and R.G. Seidensticker: J. Appl. Phys., 1960, vol. 31, pp. 1165-68. P.V. Evans, S. Vitta, R.G. Hamerton, A.L. Greer, and D. Turnbull: Acta Metall. Mater., 1990, vol. 38, pp. 233-42. W. Kurz and D.J. Fisher: Fundamentals of Solidification, 3rd ed., Trans Tech Publications Ltd., Aedermannsdorf, Switzerland, 1989 (reprinted 1992), pp. 37-37. D. Li and D.M. Herlach: Phys. Rev. Lett., 1996, vol. 77, pp. 1801-04. X. Xu, C.P. Grigoropoulos, and R.E. Russo: Appl. Phys. Lett., 1994, vol. 65, pp. 1745-47. M.B. Robinson: NASA/Marshall Space Flight Center, private communication, Huntsville, AL, Mar. 1999.

Authors’ Reply: “Emissivity Change and Adiabatically Solidified Structure during Rapid Solidification in Semiconductor” T. AOYAMA, Y. TAKAMURA, and K. KURIBAYASHI The growth behavior of a semiconductor from an undercooled melt was investigated by us (ATK, hereafter),[1] where we found that the growth velocity (V ) measurement predicted the growth behavior to be thermally controlled in the measured range of undercooling, 36 to 181 K. Li and Herlach (LH) claimed that our results negate the transition from a lateral growth to a continuous growth with increasing undercooling, DT. The critical undercooling for the transition (DT*), however, is estimated by ATK[1] to be about 30 K for Ge by microstructural observation, while the estimation of LH is DT* 5 300 K on the basis of the measured V-DT relationship.[2] Therefore, this discussion should focus on what gives rise to the large difference in DT*. From the following points of view, the consistency of Reference 1 is verified: (1) temperature calibration of pyrometric output caused by difference in emissivity between solid and liquid, (2) determination of a suitable spot for microstructural observation to estimate DT*, and (3) comparison with the previous report.[8–10,14,18,19] The morphological changes were shown in Figures 6 through 8 of ATK.[1] Figures 7(a) and 8(a), respectively, show a twin dendrite for Si and a faceted structure for Ge, both of which demonstrate the stepwise lateral growth at low undercooling. At higher undercooling, dendrites containing no twin planes for Ge and typical ^100& dendrites with the fourfold symmetry for Si are, respectively, observed in Figures 8(b) and 6(c), both of which appear to grow continuously. It should be noted that the morphological VOLUME 30A, NOVEMBER 1999—3013

changes in Figures 7 and 8 were observed by optical microscopy due to a surface relief without attack by any etchant, that is, these morphologies are not caused by any impurities. In this way, the critical undercooling for the transition from edgewise to normal growth is estimated to be about 30 K for Ge by microstructural observation.[1] Based on the aforementioned reason, it is necessary to modify Table I in LH’s discussion with regard to the structural transition. Therefore, experimental studies on the undercooled Ge are summarized again in Table I, particularly for the studies in which specimens with similar diameter are used, because the sample size has a crucial influence on cooling rate and convection, and the morphologies of specimens of very different sizes cannot be indiscriminately compared. The maximum undercooling observed by ATK is 235 K, which has been reported previously[3] and is not referred to in LH’s discussion. All undercoolings in Figure 4(b) of Reference 1 are measured when the solidification is initialized by a trigger at given temperatures and do not include the maximum undercooling measured at spontaneous solidification. Although the purity of Ge used by ATK is higher than 99.999 pct as a guaranteed value, the measured resistivity is larger than 45 V?cm, which is equivalent to 99.999999 pct purity or higher.[4] Table I shows that DT* estimated by LH is much larger than those estimated by the other three studies. One primary factor behind this conflict is the difference in the temperature calibration techniques between LH and ATK, as mentioned in Reference 1. The temperature-time profiles of Ge are shown in Figures 1(a) and (b), which are obtained by calibrating ATK’s raw data in the same way[5,6] as LH; that is, the output of a monocolor pyrometer is corrected by a single emissivity from beginning to end, so that the temperature recorded after recalescence is considered to be the melting point. Figure 1(b) shows the fluctuations measured from the side of the chamber. The upper and lower limits of the fluctuation correspond to the radiation of the solid and liquid phases at the coexistence state, respectively.[1] The temperature difference between the upper and the lower limits is 142 K. In reality, these temperatures must be the same and equal to the melting point. This difference results in the overestimation of the undercooling, and the bulk undercooling shown in Figure 1(a) is evaluated as if it were 330 K. LH measured the temperature of the sample through a quartz view window at the top of the chamber and suggested the advantage of top-view measurement in

Fig. 1—Temperature-time profile of an undercooled Ge. Output of the monocolor pyrometer is corrected by a single emissivity, although this calibration technique is not applicable for semiconductors. (a) Recalescence curve measured from the top of the chamber. (b) Fluctuations measured from the side. The upper and lower limits of the fluctuation correspond to the radiation of the solid and the liquid phases at the coexistence state, respectively.

their discussion. The electromagnetic levitation coil, however, does not block the optical path when measurements are made from the side, as apparently shown in Figures 1, 9, and 10 of Reference 1. Furthermore, it is difficult to keep focusing the pyrometer on the liquid surface from the top or the side even when the triggered recalescence started from the bottom. This is because rapid solidification from the undercooled melt makes the thermal boundary layer thin, the thickness of which can be estimated approximately based on the ratio of the thermal diffusivity to the interface velocity and is of the order of 1 mm at V 5 1 m/s. In fact, Figure 1(a) was obtained by measuring the specimen temperature from the top using ATK’s facility. Comparing Figure 1(a) to 1(b), the temperature after recalescence from a sufficiently undercooled state is apparently measured on the solid surface. ATK measured the radiations of liquid Si and Ge at the coexistence state by separating from the solid,[1,3] while LH did not.[5,7] This measurement, which derives the spectral emissivity of each phase, is essential to infer the true temperature of semiconductors using the pyrometer. The undercooling is overestimated by 142 K without this measurement. Devaud and Turnbull[8] observed the cross sections of Ge droplets and suggested structural transition at critical undercooling, the value of which is almost the same as LH’s result.[2] Much attention, however, should be paid to the microstructural observation of the samples solidified from an

Table I. Partial Summary of Experimental Studies on Solidification from Undercooled Ge DTmax (K)

D (mm)

Purity (Pct)

DT* (K)

Spot of MO

Method for Estimating DT*

References

235 426* 342 300

5 6 to 8 ,7 3 to 5

.99.999 99.999 99.999 99.9999

30 300* 93 170

triggered point cross section surface cross section

MO VM MO VM

1, 3 2, 16 9, 18, 19 14

DTmax: maximum undercooling obtained experimentally. D: sample diameter. DT*: critical undercooling for the transition from lateral to continuous growth. MO: microstructural observation. VM: velocity measurement. *Validity of these values is discussed in this article. 3014—VOLUME 30A, NOVEMBER 1999

METALLURGICAL AND MATERIALS TRANSACTIONS A

undercooled melt, particularly of semiconducting materials. Their large heat of fusion may influence the microstructure after nucleation, even if some experimental modification is added to remove the released latent heat effectively. As ATK discussed in Reference 1, the volume fraction of the solid solidified adiabatically during recalescence, fs , is very small in the case of semiconductors. For Ge, fs 5 0.04 at DT 5 50 K and fs 5 0.25 at DT 5 300 K. Following adiabatic solidification, the remaining liquid with the volume fraction (1 2 fs) begins to solidify at the melting point, growing in a lateral manner. Even if continuous growth occurs at low undercoolings, it may be extremely difficult to find any traces of twin-free dendrites by observing the cross section of the sample. To make matters worse, the scarce traces may have disappeared by remelting, which is driven by the capillarity effect. Actually, Lau and Kui reported DT* 5 93 K by observing the surface structure.[9] Although it may be easier to find the traces on the surface than in the cross section, the most suitable section for observing the adiabatically solidified structure at any given undercooling may be around the first nucleation site. Therefore, ATK observed the surface relief at the point where solidification was initiated by the trigger.[1] Evans et al. estimated the critical interface undercooling for the transition, DT *i , to be 153 K by employing a numerical model for spherical growth, presuming that dendrites first appear in pure Ge for bulk undercoolings greater than 300 K.[10] The interfacial undercooling, DTi , is defined as the undercooling below the equilibium temperature, Te (5Tm 2 DTr), where Tm is the melting temperature and DTr is the curvature undercooling. LH expressed the undercooling equation using the value of DT i* estimated by Evans et al. as follows (Eq. [1] in Reference 6): DT 2 DT *i 5 DTt 1 DTr 1 DTk 1 DTs

[1]

where DTt , DTk , and DTs are the thermal, kinetic, and constitutional undercooling, respectively. The total undercooling, however, is defined as follows by the commonly used dendrite growth theory:[11,12] DT 5 DTt 1 DTr 1 DTk 1 DTs

[2]

Equation [2] shows that Eq. [1] is not valid. The theoretical value predicted using Eq. [1] inflates the undercooling unsubstantially by 153 K. Although the growth velocities measured by LH seem to correspond well with the theoretical prediction by the dendrite growth theory[11,12] modified slightly using Eq. [1],[2] this agreement may be caused by a coincidence between the inflation of the prediction (153 K) and the overestimation of the measurement (142 K). The relationships between the bulk undercooling and the growth velocity for pure Ge measured by ATK,[1] LH,[2,13] and Battersby et al.[14] are made into a graph, as shown in Figure 2. The three studies have a comparatively similar tendency if the set of data measured by LH can be shifted down to the lower undercooling for a given amount of overestimation. This is also supported by the contradiction that the growth velocity of LH (about 0.8 m/s at DT 5 400 K) is much smaller than that predicted by Evans et al. (17.3 m/s at DT 5 400 K),[10] though LH mentioned in their discussion that the critical undercooling is consistent with the prediction of Evans et al. A high growth velocity is necessary to initiate the continuous growth from an atomically roughened interface. METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 2—Relationship between bulk undercooling and growth velocity for pure Ge measured by Aoyama et al.,[1] Li et al.,[2, 13] and Battersby et al.[14]

As pointed out by LH in their discussion, the kinetic undercooling predicted by ATK[1] is lower than that by Evans et al.[10] The prediction of Evans et al. however, was simulated for a concentrated alloy and a dilute one (Figure 7 in Reference 10), while that of ATK was for a pure material. In pure Ge, the contribution of kinetic undercooling to the total undercooling is expected to decrease with increasing undercooling, particularly around the critical undercooling. In conclusion, the structural transition from lateral to continuous growth has already been observed by ATK at DT* 5 30 K.[1] One of the major points of Reference 1 is that the undercoolings in LH’s article[2,5,7,13,15–17] might be overestimated by about 140 K due to experimental error. Measuring the spectral emissivities of the solid and liquid phases is essential to avoiding this overestimation. The most suitable section for observing the adiabatically solidified structure is concluded to be around the first nucleation site in the case of semiconductors. The results of Reference 1 are demonstrated to be consistent by comparing with the previous reports. REFERENCES 1. T. Aoyama, Y. Takamura, and K. Kuribayashi: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 1333-39. 2. D. Li, K. Eckler, and D.M. Herlach: Acta Mater., 1996, vol. 44, pp. 2437-43. 3. T. Aoyama, Y. Takamura, and K. Kuribayashi: Jpn. J. Appl. Phys., 1998, vol. 37, pp. L687-L690. 4. Physics of Semiconductor Devices, S.M. Sze, ed., Wiley Interscience, New York, NY, 1969. 5. D. Li and D.M. Herlach: J. Mater. Sci., 1997, vol. 32, pp. 1437-42. 6. M. Przyborowski, T. Hibiya, M. Eguchi, and I. Egry: J. Cryst. Growth, 1995, vol. 151, pp. 60-65. 7. D. Li and D.M. Herlach: Europhys. Lett., 1996, vol. 34, pp. 423-28. 8. G. Devaud and D. Turnbull: Acta Metall., 1987, vol. 35, pp. 765-69. 9. C.F. Lau and H.W. Kui: Acta Metall. Mater., 1993, vol. 41, pp. 1999-2005. 10. P.V. Evans, Satish Vitta, R.G. Hamerton, A.L. Greer, and D. Turnbull: Acta Metall. Mater., 1990, vol. 38, pp. 233-42. 11. W.J. Boettinger, S.R. Coriell, and R. Trivedi: in Rapid Solidification Processing—Principles and Technologies IV, R. Mehrabian and P.A. Parrish, eds., Claitor’s, Baton Rouge, LA, 1988, pp. 13-25. 12. J. Lipton, W. Kurz, and R. Trivedi: Acta Metall., 1987, vol. 35, pp. 957-64. 13. D. Li and D.M. Herlach: Phys. Rev. Lett., 1996, vol. 77, pp.1801-04. VOLUME 30A, NOVEMBER 1999—3015

14. S.E. Battersby, R.F. Cochrane, and A.M. Mullis: J. Mater. Sci., 1999, vol. 34, pp. 2049-56. 15. D. Li, K. Eckler, and D.M. Herlach: Europhys. Lett., 1995, vol. 32, pp. 223-27. 16. D. Li, K. Eckler, and D.M. Herlach: J. Cryst. Growth, 1996, vol. 160, pp. 59-65. 17. D. Li, T. Volkmann, K. Eckler, and D.M. Herlach: J. Cryst. Growth, 1995, vol. 152, pp. 101-04. 18. C.F. Lau and H.W. Kui: Acta Metall. Mater., 1991, vol. 39, pp. 323-27. 19. C.F. Lau and H.W. Kui: Acta Metall. Mater., 1994, vol. 42, pp. 3811-16.

Approximate Models of Microsegregation with Coarsening V. R. VOLLER and C. BECKERMANN Microsegregation refers to the processes of solute rejection and redistribution at the scale of the dendrite arm spaces in the mushy region of a solidifying alloy. A representative geometry for a microsegregation analysis is the half-arm spacing in a “platelike” morphology (Figure 1). Models of microsegregation are based on a solute balance within this domain. A recent review by Kraft and Chen[1] covers the range of available models. Common assumptions used in modeling include a binary eutectic alloy; a fixed average composition, C0; equilibrium at the solid-liquid interface; a constant partition coefficient k ,1; and a straight liquidus line in the phase diagram. Two key features of the solute balance that need to be included in a comprehensive model are the following. (1) The mass diffusion of the solute. Typically, the solute diffusion in the liquid is rapid, and, at each instant in time, a uniform distribution of solute, Cl(t), can be assumed. In the solid, however, diffusion is much slower and the solute balance needs to account for the so-called “back-diffusion” of solute into the solid. (2) Changes in morphology. As solidification proceeds, the arm spacing will coarsen. If the overall solute balance is maintained in the half-arm domain, this feature will dilute the solute in the liquid. One class of microsegregation models involves expressions that contain integrals. When coarsening is not accounted for and the solid growth is parabolic, Wang and Beckermann[2] obtain an integral expression that approximates the segregation ratio (C1/C0). At the opposite extreme, accounting for coarsening but neglecting back-diffusion, analytical expressions can also be obtained. In the case of a constant cooling rate, Mortensen[3] presents an analytical integral expression for the solid fraction, f, and Voller and Beckermann[4] present an analytical integral expression for the segregation ratio when solid growth is parabolic. In recent work, Voller and Beckermann[4] show, analytically, that coarsening can be included in a microsegregation model by using the enhanced diffusion parameter

V.R. VOLLER, Professor, is with the Saint Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, MN 554550116. C. BECKERMANN, Professor, is with the Department of Mechanical Engineering, University of Iowa, Iowa City, IA 52243. Manuscript submitted April 5, 1999. 3016—VOLUME 30A, NOVEMBER 1999

a+ 5

X 2F 1 dX0 f 2 2 a 1 X0 X0 dt m 1 1

[1]

DtF X 2F

[2]

In Eq. [1],

a5

is the regular back-diffusion Fourier number, D is the diffusivity (m/s2) in the solid, XF is the length of the microsegregation domain at the conclusion of solidification—usually taken to be equal to half the final secondary arm spacing, and tF is the local solidification time. The other terms in Eq. [1] are X0(t), the time-dependent length of the half arm space; f, the solid fraction in the arm space; t 5 t/tF , the normalized time; and m, the order of the polynomial used to approximate the solid solute profile (m 5 2 to 2.5[2,4]). The first term on the right-hand side of Eq. [1] accounts for the back-diffusion and the second term accounts for the coarsening-induced dilution of the liquid solute concentration. An important observation from Eq. [1] is that, in the absence of back-diffusion, the effect of coarsening on microsegregation is characterized by the diffusion parameter

ac 5

1 dX0 f 2 X0 dt m 1 1

[3]

Voller and Beckermann[4] show that, across a wide range of cooling conditions and for a coarsening law of the form X0 5 t1/3, this term takes a constant value of ac 5 0.1. The objective of the current work is to use the result in Eqs. [2] and [3] to extend the current integral-based microsegregation models to arrive at general integral approximations that can take full account of both back-diffusion and coarsening. The starting points for the general model development are the available analytical expressions for microsegregation in the presence of coarsening but absence of back-diffusion. Under this condition, when the solid growth is parabolic, Voller and Beckermann[4] obtain the exact microsegregation expression C1 2n (1 2 f )(112n)k21 5 C0 f 2n

ef f

2n21

0

(1 2 f)2(112n)k df

[4]

where n is the exponent in a coarsening model of the form[5] X0 5 t n

[5]

When the solidification is controlled by a constant cooling rate, Mortensen (Eq. [12] in Reference 3) obtains the exact expression f5

1 1 n C[1/(k21)] 1 1 2 k (C1 2 C0)n

e

C1

C0

f[k/(12k) (f 2 C0)n df [6]

The microsegregation models in Eqs. [4] and [6] are analytical but only applicable in the limit of coarsening alone (i.e., there is no back-diffusion). A consequence of Eq. [3], however, is that coarsening can be considered to be a backdiffusion-like microsegregation process characterized by the enhanced diffusion term ac. This suggests that, with an appropriate definition of the coarsening exponent n, Eqs. [4] and [6] could be applicable to back-diffusion– controlled microsegregation. If the solidification is controlled by a parabolic growth of solid fraction METALLURGICAL AND MATERIALS TRANSACTIONS A

Cl

ef

[k/(12k)]

(f 2 C0)(m11)a df

C0

Equations [10] and [11] are approximate models for microsegregation in the absence of coarsening. Equation [10], which has been presented in the literature previously,[2] is for the case when the solidification in the arm space is controlled by a parabolic growth. Equation [11] is for the case when the solidification is controlled by a constant cooling rate; this expression has not been previously presented. Taking guidance from the main result of Voller and Beckermann,[4] (Eq. [2]), these approximate models can be extended to the general case that includes both back-diffusion and coarsening by replacing the Fourier number, a, by the diffusion parameter

a+ 5

X 2f n 2 a 1 X0 m11

[12]

In this way, the general version of the parabolic growth model, obtained from Eq. [10], is (1 2 f )(112Aa12n)k21 Cl 5 (2Aa 1 2n) C0 f 2Aa12n

Fig. 1—Microsegregation domain is half-secondary dendrite arm space in a platelike morphology.

[13]

f

ef

2Aa12n21

(1 2 f)2(112Aa12n)k df

0

f 5 t1/2

[7]

then, with reference to Eq. [3],

ac 5

n 1 dX0 f 2 5 X 0 dt m 1 1 m 1 1

[8]

This expression indicates that a coarsening-controlled microsegregation process, with a coarsening exponent, n 5 (m 1 1)a

[9]

is equivalent to a back-diffusion–controlled microsegregation process characterized by the Fourier number a. Using Eq. [9] to replace n in Eq. [4] results in the following approximate relationship:

where A 5 (m 1 1)[XF /X0]2. Because the time-averaged behavior of the term [XF /X0]2 is not known analytically, the parameter A is determined subsequently through a comparison with a full numerical solution of the microsegregation problem. In the limit of no coarsening (n 5 0), Eq. [13] reduces to the model proposed by Wang and Beckermann,[2] and in the limit of coarsening alone (a 5 0), it reduces to the analytical model presented by Voller and Beckermann.[4] Integration by parts leads to the alternative form of Eq. [13]: Cl (1 2 f )(112Aa12n)k21 5 C0 f 2Aa12n [ f (2Aa12n)(1 2 f )2(112Aa12n)k

[14]

((112(m11)a)k21

Cl 2(m 1 1)a(1 2 f ) 5 C0 f 2(m11)a

[10] 2

f

ef

e k(1 1 2Aa 1 2n)f

2Aa12n

(1 2 f)2(112Aa12n)k21 df]

0

2(m11)a21

(1 2 f)2(112(m11)a)kdf

0

This expression is identical to the parabolic growth microsegregation model developed by Wang and Beckermann (Eq. [23] in Reference 2). Although in a solidification controlled by a constant cooling rate the growth of the solid fraction is not parabolic, a parabolic growth may still be a reasonable “first cut” approximation. In this way, following from the arguments presented previously, the use of Eq. [9] to replace the coarsening exponent, n, in Eq. [6] will result in a back-diffusion only microsegregation model for a constant cooling rate. The result of this action is the approximate expression f5

f

C [1/(k21)] 1 1 (m 1 1)a l 12k (Cl 2 C0)(m11)a

This form is more suitable when the Fourier number, a, is small. For example, in the limit of a → 0 and n 5 0, the Scheil equation[2] Cl 5 (1 2 f )k21 C0

[15]

follows immediately from Eq. [14]. The general version of the constant cooling model, obtained by substituting Eq. [12] into Eq. [11] is f5

1 1 Ba 1 n C[1/(k21)] l 12k (Cl 2 C0)Ba1n Cl

ef

[k/(12k)]

[16]

(f 2 C0)Ba1n df

C0

[11] METALLURGICAL AND MATERIALS TRANSACTIONS A

VOLUME 30A, NOVEMBER 1999—3017

where B accounts for the time-averaged behavior of the product (m 1 1)[XF /X0]2. Note, in the limit of a 5 0, this equation matches the analytical model presented by Mortensen.[3] Equation [13] or [14] and Eq. [16] are the key results in this article. For a given solidification path (parabolic growth or constant cooling), these models can be used to determine the progress of the complete microsegregation process including both back-diffusion and coarsening. This step, however, requires an evaluation of the integrals in Eqs. [13], [14], and [16] and the specification of the model parameters A and B. For the parabolic growth models, the integrals in Eqs. [13] and [14] can be evaluated using a high-order numerical integration scheme. In this work, a 24-point Gaussian quadrature is used. If the Fourier number is small (a , 0.2), then Eq. [14] should be evaluated for microsegregation predictions. If the Fourier number is large (a . 1), then Eq. [13] should be evaluated. Practice shows that, when the Fourier number is small or large, a single application of the 24-point Gauss in the integration range [0, f ] is not of sufficient accuracy. In these cases, it is recommended that the integration domain be segmented (segments usually works well) with a 24-point Gauss applied in each segment. In terms of finding the parameter A, a crude fitting exercise (discussed subsequently) indicates that setting A 5 4.5 works well across a wide range of conditions. Fortran programs for the evaluation of Eq. [13], parbig.for, and Eq. [14], parsmall.for, can be found on the web site http://www.ce. umn.edu/voller/voller research/ The integral in the constant cooling model, Eq. [16], can also be evaluated with a single application of a 24-point Gaussian quatrature in the interval [C0, Cl]. Further, setting the parameter B 5 3.8 works well across a wide range of conditions. A Fortran program for the evaluation of Eq. [16], conapp.for, can be found on the web site http://www.ce. umn.edu/voller/voller research/ The proposed models, Eq. [13] or [14] and Eq. [16], are tested by comparing their predictive performance with complete numerical models of microsegregation. These numerical models, which include both parabolic growth (parb.for) and constant cooling rate (const.for) versions, are fully reported elsewhere.[6] Appropriate Fortran 77 codes are available on the web site http://www.ce.umn.edu/ voller/voller research/ The predictive measure used for comparison will be the fraction of eutectic formed. The nominal concentration of the alloy is C0 5 1 and the eutectic liquid concentration is Ceut 5 5. Interest will focus on the variations of eutectic fraction with Fourier number, a, and partition coefficient, k. In all cases, a standard coarsening exponent of n 5 1/3 will be used. [5] Note, when using the parabolic growth models, iterations need to be used to find the eutectic fraction. Figure 2 compares eutectic predictions from the parabolic growth, Eq. [13] or [14], with predictions obtained from the full numerical model. For practical values of the partition coefficient, k, agreement between the approximate and numerical solutions, over a wide range of Fourier numbers, is very close. As a reference, eutectic predictions obtained when coarsening is absent (n 5 0) and k 5 0.2 are added to the figure. These results indicate the effect of coarsening 3018—VOLUME 30A, NOVEMBER 1999

Fig. 2—Predicted eutectic fractions obtained with parabolic growth models. The continuous lines are the approximate model predictions; the points are numerical predictions.

Fig. 3—Predicted eutectic fractions obtained with constant cooling models. The continuous lines are the approximate model predictions; the points are numerical predictions.

and provide a visual reference for the relative accuracy of the approximate expressions. A similar comparison to those shown in Figure 2, but for the constant cooling model (Eq. [16]), is shown in Figure 3. Once again the comparison between the approximate and full numerical models is excellent. A potential weak feature of the proposed models could be the choice of the fitting parameters A, in Eq. [13] or Eq. METALLURGICAL AND MATERIALS TRANSACTIONS A

(a)

(b)

Fig. 4—The effect of the fitting parameters A and B: (a) A in the parabolic growth model and (b) B in the constant cooling model.

[14], and B, in Eq. [16]. The reason that the optimum choice of these values is not the same (A 5 4.5 and B 5 3.8) indicates the fact that the assumption of a parabolic solid growth for the constant cooling case is reasonable but not exact. Eutectic predictions, however, are reasonably insensitive to the choices of A and B. Figure 4 compares predictions obtained with the proposed models in which the parameters A and B have been increased and decreased by ,10 pct. The results in this figure indicate very little change in the predictive ability of the approximate models when nonoptimum values of A and B are used and also suggest that a universal value of A 5 B 5 4 would be appropriate for both models. Exact integral expressions for microsegregation in a coarsening microstructure in the absence of back-diffusion have been reported in the literature.[3,4] Recent work by Voller and Beckermann[4] indicates that coarsening can be modeled in a standard microsegregation model as a back-diffusion process characterized by an enhanced diffusion parameter ac (Eq. [3]). This result has been used to extend the analytical coarsening microsegregation models to approximate expressions that account for both coarsening and back-diffusion. The resulting integral expressions, one for a solidification controlled by a parabolic growth of solid (Eq. [13] or Eq. [14]) and one for a solidification controlled by a constant cooling rate (Eq. [16]), default to the appropriate limiting cases. In addition, across a wide range of practical conditions, predictions obtained with the approximate models compare closely with results from numerical models.

One of the authors (CB) gratefully acknowledges partial support provided by the National Science Foundation under Grant No. CTS-9501389. REFERENCES 1. T. Kraft and Y.A. Chang: J. Met., 1997, vol. 49, pp. 20-28. 2. C.Y. Wang and C. Beckermann: Mater. Sci. Eng., 1993, vol. 171, pp. 199-211. 3. A. Mortensen: Metall. Trans. A, 1989, vol. 20A, pp. 247-53. METALLURGICAL AND MATERIALS TRANSACTIONS A

4. V.R. Voller and C. Beckermann: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 2183-89. 5. D.H. Kirkwood: Mater. Sci. Eng., 1985, vol. 73, pp. L1-L4. 6. V.R. Voller: Int. J. Heat Mass Transfer, in press, 1999.

Tensile Properties of Duplex MetalCoated SiC Fiber and Titanium Alloy Matrix Composites S.Q. GUO, Y. KAGAWA, A. FUKUSHIMA, and C. FUJIWARA SiC(SCS-6) fiber-reinforced titanium alloy matrix composites have a great potential for high-temperature aerospace structural applications.[1,2,3] It is known that the interface reaction between the outermost SCS coating and Ti alloy matrix takes place during the fabrication process, and the formed reaction layer consists of a nonstoichiometric carbide (TiC12x) and silicides (TixSiy).[4,5,6] The reaction layer is brittle; however, this has only a slight effect on the quasistatic tensile strength.[7,8] On the other hand, the effect of the reaction layer cracking on the fatigue damage evolution is quite severe.[9,10,11] Such cracking under a cyclic fatigue loading condition leads to debonding of the SCS coating layer from the SiC fiber surface, which leads to a significant reduction in the fiber strength, because the debonding increases stress concentration at the SiC fiber surface, which originates from surface flaws of the fiber.[9,12] It was reported that the tensile strength of the SiC(SCS-6) fiber becomes about half of the original fiber strength after the debonding

S.Q. GUO, Postdoctoral Research Fellow, Japan Society for the Promotion of Science (JSPS), and Y. KAGAWA, Professor, are with the Institute of Industrial Science, The University of Tokyo, Tokyo 106-8558, Japan. A. FUKUSHIMA, Research Engineer, and C. FUJIWARA, Project Engineer, are with the Materials Research Section, Engineering Research Department, Nagoya Aerospace Systems, Mitsubishi Heavy Industries, Ltd., Nagoya 455-0024, Japan. Manuscript submitted February 23, 1999. VOLUME 30A, NOVEMBER 1999—3019

of the SCS coating layer from SiC fiber surface and the strength is nearly the same as that of SCS-uncoated SiC(SCS-0) fiber.[12] This mechanism is the cause of the fiber fracture behavior at an early stage of fatigue under cyclic loading.[12] The authors’ previous experimental research on the same kind of composites suggests that fiber fracture at the early stage of fatigue can be avoided if ductile metal layers exist between the SCS coating and Ti alloy matrix.[13] A preliminary study clearly demonstrated that fatigue life was improved by applying a Cu/Mo duplex metal coating on the SCS coating surface.[13] The effect of the duplex metal coatings on mechanical properties of both the individual SiC fiber and titanium alloy matrix composites under quasi-static tensile test have not yet been examined. The purpose of this article is to show the effect of the candidate duplex metal coatings on the tensile properties of both the SiC fiber and titanium alloy matrix composites. Continuous SiC fiber (SCS-6, Textron Specialty Materials, Lowell, MA) was used throughout the study. It has a b-SiC filament of '140-mm diameter with a '3.6-mm-thick outermost SiC particle dispersed carbon-rich coating (SCS coating).[12,14] Pure Cu (.99.90 wt pct in purity) was deposited on the surface of the SCS coating by a physical vapor deposition (PVD) process, and thereafter, Ta, Mo, or W (.99.90 wt pct in purity) was deposited on the surface of the Cu coated fiber by the same process. All the coatings were done at an atmospheric pressure of '1023 Pa at a temperature of 470 to 570 K. The Cu coating was selected because the reaction between the SCS coating and Cu was quite low.[15] Thus, if a Cu coating exists between the SCS coating and Ti alloy matrix, the interface reaction between them can be avoided. However, Cu reacts chemically with Ti to form intermetallic compounds,[15] and to prevent this, an additional metal coating between the Cu coating and Ti matrix is required. In this study, Ta, Mo, and W were used as the second coating materials. Their selection was based on the following properties of these alloying elements: (1) high melting point, (2) low diffusion coefficients inside b-Ti phase, and (3) no reaction to form an intermetallic compound with Ti at the processing temperature. (Although it is reported that W could react with Ti and form an intermetallic according to the Ti-W equilibrium diagram,[15] the intermetallic is unknown and thus this reaction between W and Ti is not considered here.). The properties of Ta, Mo, and W alloying elements suggest that they are stable at the processing temperature, so that they were selected as the second coating materials. A ductile b-Ti phase reportedly is formed near the interface when Ta diffuses into Ti for Ag/Ta coated SiC(SCS-6) fiber-reinforced Ti3Al matrix composite, and this b-Ti phase region serves as a compliant layer to relieve the large thermal residual stresses by plastic deformation, in this way improving the interfacial compatibility of the composite.[16,17] The effect of the coatings on the SiC(SCS-6) fiber strength after heat exposure was explored by heat exposing the pristine and duplex metal coated SiC(SCS-6) fibers at 1153 K for 1.5 hours in a vacuum atmosphere of 1024 to 1025 Pa using an electric furnace. This heat exposure condition was the same as a heat schedule of the hot isostatic pressing (HIP) condition of an SiC fiber-reinforced Ti-15-3 alloy matrix composite. To distinguish the reaction and diffusion 3020—VOLUME 30A, NOVEMBER 1999

behaviors between the duplex metal coating and the SCS coating, Ti coating was not applied. After heat exposure, the morphology of the coated fibers was observed by a scanning electron microscope (SEM) and stability of the duplex metal coatings was investigated by energy dispersive X-ray (EDX). The tensile strength of the heat-exposed pristine and duplex metal coated SiC(SCS-6) fibers was measured. The fiber was cemented at each end in a paper holder card with an epoxy base adhesive. The gage length, L, was fixed at 20 mm. The paper holder was gripped and both sides were cut just before the test. The test was performed using a screw-driven testing machine (UTM-II, Toyo Sokki, Co., Ltd., Tokyo) at room temperature (298 K) in air with a crosshead displacement rate of 0.04 mm/min. While 40 pristine fibers were tested, only 30 duplex metal coated fibers were because of their limited availability. The mean tensile strength was determined from an average value of the tested fibers using Weibull’s statistical method with the meanrank method.[12] The fiber strength was calculated from the applied force at fracture divided by the cross-sectional area of the SiC fiber (diameter: 140 mm). The effect of the duplex metal coatings on the tensile strength of the composites in an actual fabrication process was examined using composite specimens. Three kinds of unidirectional aligned duplex metal (Cu/Ta, Cu/Mo, and Cu/ W) coated SiC(SCS-6) fiber-reinforced Ti-15-3 alloy matrix composites were fabricated by a solid-state foil-fiber-foil consolidation technique using a HIP process. The HIP processing was done at a temperature of 1153 K for 1.5 hours under a hydrostatic pressure of 100 MPa. The thickness of Ti-15-3 foils, which were supplied by Kobe Steel Co., Ltd. (Kobe, Japan), was 130 mm. The chemical composition of the matrix alloy was 15.22 wt pct V, 3.26 wt pct Cr, 3.12 wt pct Al, 2.94 wt pct Sn, and the remainder Ti. To compare the effect of the duplex metal coatings on tensile properties of the composites, a duplex metal uncoated SiC(SCS-6) fiber-reinforced Ti-15-3 composite was also fabricated by the same HIP process. The nominal fiber volume fraction, Vf , in the composites was '0.18. After the fabrication, the composites were treated with a solution at 1053 K for 0.5 hours and then aged in air at 723 K for 16 hours to obtain stable microstructure of the matrix. Hereafter, these composites are denoted as SiC/Ti-15-3 (pristine fiber composite), SiC/Cu/Ta/Ti-15-3 (Cu/Ta coated fiber composite), SiC/Cu/ Mo/Ti-15-3 (Cu/Mo coated fiber composite), and SiC/Cu/ W/Ti-15-3 (Cu/W coated fiber composite), respectively. The composite panels were cut into a plate-type tensile test specimen with the long axis parallel to the fiber axis direction. The specimen was prepared with a diamond cutting saw, and its surfaces were repeatedly polished with a diamond paste up to a 1-mm finish. A dog-bone-shaped specimen 70 mm in length, 1.4 mm in thickness, and 4.2 mm in width was used. The gage length of the specimen was 20 mm. Tensile strength of the composites was measured using a screw-driven universal testing machine (Instron Model 8562, Instron Co., Ltd., Canton, MA). Strain of the specimen was measured with a resistance-type strain gage, which had a base area of 6.0 by 1.7 mm. The test was done at room temperature (298 K) in air with a constant crosshead speed of 0.1 mm/min. Figure 1 shows SEM photographs and EDX maps of the METALLURGICAL AND MATERIALS TRANSACTIONS A

(a)

(b)

(c)

Fig. 1—SEM microphotographs and EDX maps of the heat-exposed (a) Cu/Ta, (b) Cu/Mo, and (c) Cu/W coated SiC(SCS-6) fibers.

heat-exposed Cu/Ta, Cu/Mo, and Cu/W coated SiC(SCS-6) fibers. The photographs demonstrate that all three coatings are still present on the SCS coating of the fiber after heat exposure; and individual coatings (Cu, Ta, Mo, and W) are distinguishable. The thickness of the Cu coating is '1.2 mm and that of the Ta, Mo, and W coatings is '1.6 mm. This indicates that the applied duplex metal coatings are stable at 1153 K for 1.5 hours i.e., for the duration of the fabrication heat schedule of the composites. A weak signal from the Cu is detected on the outermost surface of the Cu/Ta and Cu/W coated SiC(SCS-6) fibers. The detected signal of the Cu/Ta coated SiC (SCS-6) fiber is much stronger than that of the Cu/W coated SiC(SCS-6) fiber, indicating that the Cu diffuses toward the surface through the Ta or W coatings during heat exposure. However, it is difficult to carry out quantitative treatment of the diffusion behavior because of a lack of diffusion data. On the contrary, the diffusion trace of Cu is not observed in the Cu/ Mo coated SiC(SCS-6) fiber. These results suggest that the Cu/Mo coating may have a greater possibility of being an effective diffusion barrier than either the Cu/Ta or Cu/W coating. Figure 2 shows Weibull plots of the tensile strength of the heat-exposed pristine and duplex metal coated SiC(SCS6) fibers. In these plots, ln ln [1/(1-PF)] is displayed as a function of ln s, where PF is the cumulative probability of failure at a given tensile stress, s. The straight lines in the figure are determined by least-squares regression. The fiber METALLURGICAL AND MATERIALS TRANSACTIONS A

strength distributions of the duplex metal coated SiC(SCS6) fibers are statistically different from that of the pristine SiC(SCS-6) fiber. Tensile strengths of the pristine fiber could be described by a single linear regression, the slope of which yields the Weibull modulus, m1 ' 17; however, the tensile strengths of the duplex metal coated fibers exhibit a bimodal distribution. For the Cu/Ta coated SiC(SCS-6) fiber, the Weibull modulus in the high strength region is m1 ' 2.8, whereas in the low strength region, the modulus is m2 ' 11. Approximately 60 pct of the tested Cu/Ta coated fibers failed in the low strength region (Figure 2(b)). The strength distributions of both the Cu/Mo and Cu/W coated SiC(SCS6) fibers are similar to that of the Cu/Ta coated fiber. Their Weibull moduli in the high strength region are determined to be m1 ' 15 and 17, respectively, whereas in the low strength region, they are m2 ' 3.5 and 5.2, respectively. Approximately 20 pct of the tested Cu/Mo and 10 pct of the Cu/W coated SiC(SCS-6) fibers failed in the latter region (Figures 2(c) and (d)). The bimodal behavior of the Weibull distributions suggests that the duplex metal coated SiC(SCS6) fibers introduce a new population of flaws during the duplex metal coating process and/or heat exposure, especially for Cu/Ta coated SiC(SCS-6) fiber. Table I summarizes the tensile properties of the heatexposed pristine and the duplex metal coated SiC(SCS-6) fibers. After heat exposure, the mean strengths of the duplex metal coated SiC(SCS-6) fibers are lower than that of the pristine SiC(SCS-6) fiber. A large reduction in mean tensile VOLUME 30A, NOVEMBER 1999—3021

(a)

(b)

(d )

(c)

Fig. 2—Weibull plots for the heat-exposed (a) pristine, (b) Cu/Ta, (c) Cu/Mo, and (d ) Cu/W coated SiC(SCS-6) fibers.

Table I. Tensile Mechanical Properties of the HeatExposed Pristine and Duplex Metal Coated SiC(SCS-6) Fibers

Fibers

Mean Fiber Strength sf (MPa)

Standard Deviation (MPa)

Pristine SiC(SCS-6) Cu/Ta coated SiC(SCS-6) Cu/Mo coated SiC(SCS-6) Cu/W coated SiC(SCS-6)

4374 3612 4220 3934

741 616 517 315

strength (,17 pct) is observed for the Cu/Ta coated SiC(SCS-6) fiber, while a significant reduction is observed for the Cu/W coated SiC(SCS-6) fiber (,10 pct). The mean tensile strength of the Cu/Mo coated SiC(SCS-6) fiber is slightly reduced (,4 pct) compared to that of the pristine SiC(SCS-6) fiber, however. Although these duplex metal coatings are stable on individual coated fibers, the interface between the coated fibers and the matrix changes due to an interdiffusion of the coatings and the matrix during the fabrication process of the

3022—VOLUME 30A, NOVEMBER 1999

composites. The diffusion behavior is another factor affecting the tensile mechanical properties of the composites. Figure 3 shows SEM photographs of the polished transverse cross section of the composites with the duplex metal coated SiC(SCS-6) fibers. A distinct region, which is termed an interface reaction region, is observed between the fibers and matrix in all the composites. The region in the SiC/Cu/W/Ti15-3 is complex, and a white phase, which was determined to be W-rich, exists within it. The thickness of the region is '2 mm, but the regions in both the SiC/Cu/Ta/Ti-15-3 and SiC/Cu/Mo/Ti-15-3 are simpler and their thickness values are '0.9 and '0.8 mm, respectively. These values are much lower than that of the initial duplex metal coatings. These photographs show that an interdiffusion of the duplex metal coatings and the matrix takes place during the HIP process. The EDX elemental mappings also indicate this interdiffusion behavior of Cu, Ta, Mo, W, and Ti (Figure 4). The Cu, Ta, and Mo alloying elements diffuse into a wide area of the matrix, while Ti diffuses toward the duplex metal coatings in the opposite direction. No significant diffusion behavior of W is observed and an enriched layer of W exists near the fiber (Figures 3(c) and 4(c)). These results suggest that the

METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 4—EDX elemental distribution maps of the duplex metal coatings in the (a) SiC/Cu/Ta/Ti-15-3, (b) SiC/Cu/Mo/Ti-15-3, and (c) SiC/Cu/W/Ti15-3 composites (F: fiber and M: matrix).

duplex metal coated SiC(SCS-6) fiber-reinforced Ti-15-3 composites are shown in Figure 5. The curves show nearly the same behavior independent of the duplex metal coating

Fig. 3—SEM photographs of the polished transverse cross section of the (a) SiC/Cu/Ta/Ti-15-3, (b) SiC/Cu/Mo/Ti-15-3, and (c) SiC/Cu/W/Ti-15-3 composites (F: fiber, SCS: SCS coating, RL: reaction layer, and M: matrix).

interfacial reaction occurs between the fiber and matrix during the fabrication process of the composites. However, a more detailed study is needed to understand the diffusion behaviors. The typical tensile stress-strain curves of the pristine and

METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 5—Typical tensile stress-strain curves for the pristine and duplex metal coated SiC(SCS-6) fiber-reinforced Ti-15-3 matrix composites.

VOLUME 30A, NOVEMBER 1999—3023

Table II. Tensile Mechanical Properties of the Pristine and Duplex Metal Coated SiC(SCS-6) Fiber-Reinforced Ti-15-3 Matrix Composites

Composites SiC/Ti-15-3 SiC/Cu/Ta/Ti-15-3 SiC/Cu/Mo/Ti-15-3 SiC/Cu/W/Ti-15-3

Young’s Modulus Ec (GPa)

Tensile Strength sc (MPa)

Strain to Failure «c (Pct)

135 122 126 124 129 133 123 124

1392 1259 1301 1256 1534 1541 1244 1399

1.14 1.23 1.21 1.16 1.44 1.38 1.14 1.32

materials, exhibiting an initial linear elastic region followed by a slight nonlinear stress-strain behavior. The transition of the tensile stress-strain curve from linear to nonlinear behavior occurs at a stress level around 780 MPa and this stress seems independent of the duplex metal coating materials, suggesting there is no effect of the diffusion near the interface on the macroscopic yield behavior of the matrix alloy. Table II summarizes the tensile mechanical properties of the composites. The mean tensile strength of SiC/Cu/Mo/ Ti-15-3 is about 16 pct larger than that of SiC/Ti-15-3. In contrast, the tensile strength of SiC/Cu/W/Ti-15-3 is nearly the same as that of SiC/Ti-15-3, while that of SiC/Cu/Ta/ Ti-15-3 is slightly ('4 pct) lower than SiC/Ti-15-3. The rule-of-mixtures (ROM) estimation is used to compare the mean tensile strength for each composite. The tensile strength of the composites is given by

sc 5 Vf sf 1 (1 2 Vf)s 8m

[1]

where Vf is the fiber volume fraction, sf is the mean tensile strength of the fiber (Table I), and s 8m is the tensile stress of the matrix at the failure strain of composite (Figure 5). The strength of both SiC/Cu/Ta/Ti-15-3 and SiC/Cu/W/Ti15-3 is about 93 pct of the estimated strength. This percentage of the ROM is slightly larger than that of the SiC/Ti15-3 composite (88 pct), while the tensile strength of the SiC/Cu/Mo/Ti-15-3 is coincident with that of the ROM. This means that fiber strength potential is fully achieved in the SiC/Cu/Mo/Ti-15-3 composite and that the low strength in the SiC/Cu/Ta/Ti-15-3 composite results from a decrease in the fiber strength of Cu/Ta coated SiC(SCS-6) fibers during the fabrication process. Summarizing the results, the tensile strength of the Cu/Ta and Cu/W coated SiC (SCS-6) fibers significantly decreases, while the strength of the Cu/Mo coated SiC(SCS-6) fiber is

3024—VOLUME 30A, NOVEMBER 1999

reduced only slightly compared to that of the pristine fiber. The tensile strength of the SiC/Cu/Mo/Ti-15-3, on the other hand, is greater than that of the SiC/Ti-15-3 and coincides with the estimated value by the ROM. Conversely, the tensile strength of SiC/Cu/W/Ti-15-3 is nearly the same as that of SiC/Ti-15-3, whereas the tensile strength of SiC/Cu/Ta/Ti15-3 is slightly lower than that of SiC/Ti-15-3; this is attributed to the decrease in fiber strength of the Cu/Ta coated SiC(SCS-6) fibers. Our previous research suggested that the fatigue life of the composite had a tendency to increase with application of a Cu/Mo coating.[13] Although these studies showed some advantages of the Cu/Mo coating, a more detailed study is needed to use the Cu/Mo duplex metal coating for SiC(SCS-6) fiber-reinforced Ti-15-3 alloy matrix composites.

One of the authors (SQG) to thanks the Japan Society for The Promotion of Science (JSPS) for its financial support of his research in Japan. REFERENCES 1. E.V. Zaretsky: Mach. Des., 1994, vol. 66, pp. 124-32. 2. J.M. Larsen, S.M. Russ, and J.W. Jones: Metall. Mater. Trans. A, 1995, vol. 26A, pp. 3211-24. 3. T. Nicholas and S.M. Russ: Mater. Sci. Eng., 1992, vol. A153, pp. 514-19. 4. P. Martineau, P. Pailler, M. Lahaye, and R. Naslain: J. Mater. Sci., 1984, vol. 19, pp. 2749-70. 5. C.G. Rhodes and R.A. Spurling: in Developments in Ceramic and Metal-Matrix Composites, K. Upadhya, ed., TMS, Warrendale, PA, 1991, pp. 99-103. 6. S.Q. Guo, Y. Kagawa, H. Saito, and C. Masuda: Mater. Sci. Eng., 1998, vol. A246, pp. 25-35. 7. B.S. Majumdar, G.M. Newaz, and J.R. Ellis: Metall. Trans. A, 1993, vol. 24A, pp. 1597-1610. 8. B.S. Majumdar and G.M. Newaz: Phil. Mag. A, 1992, vol. 66, pp. 187-212. 9. S.Q. Guo, Y. Kagawa, and K. Honda: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 2843-51. 10. S.Q. Guo, Y. Kagawa, J.-L. Bobet, and C. Masuda: Mater. Sci. Eng., 1996, vol. A220, pp. 57-68. 11. B.S. Majumdar and G.M. Newaz: Mater. Sci. Eng., 1995, vol. A200, pp. 114-29. 12. S.Q. Guo, Y. Kagawa, Y. Tanaka, and C. Masuda: Acta Mater., 1998, vol. 46, pp. 4941-54. 13. S.Q. Guo: Ph. D. Thesis, The University of Tokyo, Tokyo, 1997. 14. X.J. Ning and P. Pirouz: J. Mater. Res., 1991 vol. 6, pp. 2234-48. 15. Smithells Metals Reference Book, E.A. Brandes, ed., printed in England by Robert Hartnoll Ltd., Bodmin, Cornwall, 1983. 16. H.P. Chiu, S.M. Jeng, and J.-M. Yang: J. Mater. Res., 1993, vol. 8, p. 2040. 17. R.A. Naik, W.S. Johnson, and D.L. Dicus: in Titanium Aluminide Composites, P.R. Smith, S.J. Balsone, and T. Nicholas, eds., WrightPatterson AFB, OH, 1991, pp. 563-75.

METALLURGICAL AND MATERIALS TRANSACTIONS A