communications - university of...

CommunicationsPartial Fe-Ti Alloy Phase Diagrams atHigh Pressure

TOSHIMI YAMANE, KOJI HISAYUKI,RIYUICHIRO NAKAO, YORITOSHI MINAMINO,HIDEKI ARAKI, and KEIICHI HIRAO

Recently, high pressure treatments such as hot isostaticpressing have become more familiar in industrial processes.The high pressure induces changes of both the phase equilib-rium and the kinetics of the phase transformation in alloys. Fig. 1—Iron concentration profiles as a function of Boltzmann parameterThe iron-rich phase diagrams under high pressure have been 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.previously reported in the Fe-Mo,[1] Fe-W,[2] Fe-Cr,[3] Fe-V,[4] and Fe-Si[5] systems, which have the g loop in the iron-rich side at the ordinary pressure.[6] These systems exhibitthe astonishing changes in phase equilibrium under highpressure: the g loop expands under high pressure, and espe-cially the g loop type phase diagrams of Fe-Mo and Fe-Wsystems transform to the g shrink type phase diagram athigher pressures. So, it is very interesting to investigate theeffect of high pressure on phase equilibrium in the g loopphase diagram of the Fe-Ti system, which is practicallyimportant for hydrogen storage alloys, titanium clad steels,and so on. Therefore, the authors have established the iron-rich Fe-Ti phase diagrams at the high pressure up to 2.7 GPa.

The ingots of pure iron, pure titanium, and Fe-Ti alloyswere prepared from 99.9 mass pct purity electrolysis ironand 99.85 mass pct purity titanium by arc melting in argon Fig. 2—Titanium concentration profiles in Fe/Ti react diffusion couplesgas. These ingots were annealed at 1373 to 1573 K for annealed at 1373 K for 14.4 ks at 0, 2.3, and 2.7 GPa.28.8 ks for homogenization in argon gas. The chemicalcompositions of the ingots were 99.9 mass pct Fe, Fe-2.13at. pct Ti (quenched a Fe phase), Fe-4.31 at. pct Ti (quenched were converted to the concentrations of titanium and irona Fe phase), Fe-7.86 at. pct Ti (quenched a Fe phase), a with the aid of prepared alloy standards.Fe-30 at. pct Ti (Fe2Ti phase), Fe-81.4 at. pct Ti (quenched Figure 1 shows the diffusion profiles of iron concentra-b Ti phase), Fe-90.2 at. pct Ti (quenched b Ti phase), 99.85 tions in the diffusion couples annealed at 1173 K and 2.3mass pct Ti, and so on. The ingots of pure iron and titanium GPa for the various diffusion times of 14.4, 28.8, and 57.6were cut into discs, 2.5 mm in thickness and 4 mm in ks against the Boltzmann parameter, X/t1/2, where X is thediameter. The surfaces of the discs were metallographically distance from Matano interface and t the diffusion time. Aspolished by 0.05-mm alumina, and then the diffusion couples a result of react diffusion, the b Ti, Fe2Ti, FeTi, g Fe, andwere immediately assembled with discs of pure iron and a Fe phases appear in the react diffusion zones. All ofpure titanium. These diffusion couples were annealed at the the diffusion profiles are on the same curve against thepressures of 0, 2.3, and 2.7 GPa at 973 to 1643 K and for Boltzmann parameter. This means that the diffusion phenom-3.6 to 432 ks. The method for annealing of the diffusion ena are kept in partial equilibrium and the phase interfacecouples has been reported elsewhere.[1,2]

concentrations in the diffusion zones should be equal toThe annealed diffusion couples were cold mounted in the equilibrium concentrations in the Fe-Ti phase diagram.

resin and were cut to expose a section parallel to the diffusion Therefore, the react diffusion couple method enables us todirection. The section was metallogrphically polished. The clarify equilibrium for constructing the phase diagrams.concentrations of titanium and iron on the polished sections Namely, the phase diagrams can be established from thein these diffusion couples were measured by an electron interface concentrations between the adjacent phases in theprobe microanalyzer. The Ti Ka and Fe Ka X-ray intensities diffusion zone.

Figures 2 and 3 show, as an example, the diffusion profilesof titanium concentrations in the iron-rich part of the diffu-TOSHIMI YAMANE, Professor, and KOJI HISAYUKI, Graduate Stu-sion couples annealed at 1373 K for 14.4 ks under 0, 2.3,dent, are with the Department of Mechanical Engineering, Hiroshima Insti-

tute of Technology, Hiroshima 731-5193, Japan. RIYUICHIRO NAKAO, and 2.7 GPa, and those annealed at 1323, 1273, and 1223Graduate Student, HIDEKI ARAKI, Associate Professor, and KEIICHI K for 28.8 ks under 2.7 GPa, respectively. From the interfaceHIRAO, Technical Officer, Department of Materials Science and Engi- concentrations, the iron-rich Fe-Ti phase diagrams areneering, and YORITOSHI MINAMINO, Professor, Department of Adaptive

assessed as shown in Figures 4 through 6. As shown inMachine Systems, are with Osaka University, Osaka 565-0871, Japan.Manuscript submitted May 13, 1999. Figures 2 and 3, the diffusion distance in the a Fe phase is

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 30A, NOVEMBER 1999—3009

Fig. 3—Titanium concentration profiles in Fe/Ti react diffusion couplesannealed 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 thediffusion distance in the g Fe region is quite short andits concentration gradients are considerably steep, becausetitanium diffuses fairly faster in the a Fe phase than the gphase. Therefore, the concentrations at the a/(a 1 g) anda/(a 1 Fe2Ti) are not distinct, because the diffusion dis-tances in the g Fe region are about 4 mm, which is nearthe resolution area (about 1 or 2 mm in diameter) for theconcentration measurement by electron probe microanalysis.Therefore, The Cg/(a 1 g)’s are drawn by the bars in thephase diagrams. Both interface concentrations increase withincreasing pressures. As shown in Figure 3, the a and g Fephases are observed in the diffusion zones and interface

Fig. 6—Iron-rich Fe-Ti phase diagram at 2.7 GPa.concentrations are almost equal at both 1324 and 1273 Kunder the same pressure of 2.7 GPa. However, it is noticedthat the a Fe disappears in the diffusion zone at 1223 K and2.7 GPa, and thereby, the g Fe region phase is adjacent to the The a Fe phase is in equilibrium with the g Fe phase,

which forms the g loop, the experimental Ca/(a 1 g)’s, andFe2Ti phase. From these diffusion files, the concentrations atthe g/(g 1 Fe2Ti) interface, Cg/(g 1 Fe2Ti) are determined. also the Fe2Ti phase at 0 GPa, as shown in Figure 4. The

3010—VOLUME 30A, NOVEMBER 1999 METALLURGICAL AND MATERIALS TRANSACTIONS A

experimental Ca/(a 1 g)’s and Cg/(a 1 g)’s are in good agreement an example, we would like to comment on their main resultswith the Fe-Ti phase diagram of Massalski.[6] The and will show that deep undercooling can be achieved andCa/(a1Fe2Ti)’s are shown in Figure 4 with the previous data that the preceding transition does, indeed, exist.by Massalski, Tuji,[7] and Ko and Nishizawa.[8] These experi- There have been numerous studies on the large undercool-mental values are in good agreement with each other above ing of semiconductors under conditions of slow cooling[4–17]

about 1300 K, while they are scattered at lower temperatures. and rapid quenching.[18,19] With regard to the former, a fairlyGenerally speaking, the scattering of experimental data in complete list of experimental studies on undercooling Ge isphase equilibrium at low temperatures is due to the insuffi- summarized in Table I with respect to the maximum DT.cient annealing, fine structures of alloys for concentration First, it is seen from the listing that there has been a largemeasurements, and so on. At the high pressures of 2.3 and range of reported maximum undercooling for this material2.7 GPa, the g loop expands to higher titanium concentration due to different processing techniques and the difficulty ofwith increasing pressures, while the Ca/(a 1 Fe2Ti)’s slightly doing an experiment where all heterogeneities have beenshift to lower titanium concentration. As a result, a eutectoid removed or deactivated. In the well-known classic articlereaction a → g 1 Fe2Ti and a peritectoid reaction g 1 by Turnbull and Cech,[6] Ge was undercooled by 235 KFe2Ti → a appear. At high pressures over 2.3 GPa, the g using a microscope stage method. More impressively, thephase can be equilibrium with the Fe2Ti phase near 1150 degree of undercooling was reported to be up to 214 K[4,5] forK. These changes in the iron-rich binary phase diagrams at 150-g Ge samples processed in an open vertical cylindricalhigh pressure are observed in the Fe-Mo and Fe-W furnace without using vacuum or protective gas. In thesystems.[1,2]

1980s, Ge droplets were successfully undercooled by up to415 K[13,14] in a B2O3 flux in a clean environment. It maybe argued that deep undercooling occurred only in very smallREFERENCESdroplets of less than 1 mm in diameter. However, studies[20]

1. Y. Minamino, T. Yamane, H. Araki, H. Hiraki, and Y. Miyamoto: J.in other systems have verified that both melt fluxing andIron Steel Inst. Jpn., 1988, vol. 74, pp. 733-40.containerless processing can also lead bulk millimeter size2. T. Yamane, Y.S. Kang, Y. Minamino, H. Araki, A. Hiraki, and Y.

Miyamoto: Z. Metallkd., 1995, vol. 86, pp. 453-56. specimens to a substantial degree of undercooling compara-3. Y. Minamono, A. Araki, T. Yamane, H. Deguchi, A. Hiraki, S. Saji, ble with that in small droplets. The results in the last row

and Y. Miyamoto: J. High Temp. Soc. Jpn., 1992, vol. 18, pp. 356-64.of Table I might be partially caused by a melting point4. R.E. Hanneman, R.E. Ogilvle, and H.G. Gatos: Trans. AIME, 1965,

vol. 233, pp. 685-91. depression for the Ge nanoparticles due to the Gibbs–5. L. Tanner and S.A. Kulin: Acta Metall., 1961, vol. 9, pp. 685-91. Thomson effect. However, the sample diameter ranging from6. Binary Alloy Phase Diagrams, 2nd ed., T.B. Massalski, ed., ASM hundreds of microns to a few millimeters should not be aINTERNATIONAL, Materials Park, OH, 1990, vol. 2, pp. 1783-86.

crucial factor in determining the maximum undercooling7. 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. obtained using state-of-the-art denucleation techniques. The9. E.Y. Tonkov: Phase Diagrams of Elements, Nauka, Moscow, 1979, maximum DT attained in the EML of Reference 1 is 180 K

pp. 115-17. (derived from their Figure 4(b)), which is the smallest valuegiven in Table I. The discrepancy between Reference 1 andthe others cannot be simply imputed to the temperatureerrors, as concluded by Aoyama et al.,[1] who did not refer

Discussion of “Dendrite Growth to the closely relevant articles. Second, it is seen from TableI that thermocouples were used in most of the experimentsProcesses of Silicon andthat have nothing to do with the emissivity change. As forGermanium from Highly the levitation processing, our EML approach[15,16] differs

Undercooled Melts”* from that of Aoyama et al.[1] in preheating and temperaturemeasurements. In our experiment, Ge samples were pre-heated by a graphite holder (preheater), which was removedD. LI and D.M. HERLACHfrom the coil after the sample was levitated as soon as the

Aoyama et al.[1] used electromagnetic levitation (EML) electrical conductivity became sufficiently high at elevatedwith a laser preheating[2] and photodiode method[3] to investi- temperatures, while the laser heating was used by the authorsgate the solidification behavior of undercooled Ge and Si. of Reference 1. Our pyrometer looked through a quartzThe authors of Reference 1, referred to hereafter as the viewport at the top of the chamber. The advantage for topauthors, have taken account of the emissivity change during view is that the EML coil does not block the optical pathmelting and solidification for temperature calibrations and at all and the pyrometer focuses on the top surface of themeasured the growth velocity as a function of undercooling sample that is in the liquid state, as the triggered recalescenceDT. The authors have not observed the faceted to nonfaceted

started from the bottom. Furthermore, a clean environmenttransition in microstructure evolution with increasing under-was established in our work by evacuating the experimentalcooling, which has been revealed previously. Using Ge aschamber to a pressure of 1024 Pa and then back-fillingwith high-purity He-20 pct H2 gas through a liquid-nitrogen-cooled trap (Table I), which is conducive to deep*T. AOYAMA, Y. TAKAMURA, and K. KURIBAYASHI: Metall. Mater.

Trans. A, 1999, vol. 30A, pp. 1333-39. undercooling.D. LI, NASA/NRC Resident Research Associate, is with the Drop Facili- There is convincing evidence by several independent

ties/SD47, NASA/MSFC, Huntsville, AL 35812. D.M. HERLACH, Profes-experiments applying both melt fluxing[7,8,11–13] and contain-sor, is with Institute of Space Simulation, DLR, D-51170 Cologne, Germany.

Discussion submitted May 21, 1999. erless processing[16,21] that sufficiently large undercooling


Table I. Partial Summary of Experimental Studies on Undercooling and Solidified Microstructure of Ge

Maximum Sample Size Prior Vacuum Protective StructuralDT (K) Method D (mm) Pressure (Pa) Gas Transition References

180 EML, OP 5 1023 Ar no 1214 SLG, TC 40 no vacuum not used yes 4, 5235 HSM, TC 0.015 0.7 He unreported 6

250 to 300 SLG, TC 3 to 5 5 3 1023 N2 yes 7, 8280 BOF, TC 0.4 to 0.8 0.7 He-20 pct H2 unreported 9316 PCF, TC 0.1 to 0.5 unreported unreported unreported 10342 BOF, TC 7 to 11 ,0.1 not used yes 11, 12415 BOF, TC 0.3 to 0.5 0.7 He-20 pct H2 yes 13, 14426 EML, OP 6 to 8 1024 He-20 pct H2 yes 15, 16

439 to 472 TEM, TC 1025 to 1024 ,1023 not used unreported 10, 17

SLG, soda-lime glass; HSM, hot stage microscope; BOF, boron oxide flux; PCF, potassium chloride flux; TEM, transmission electronmicroscope; 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 non-faceted morphology of the as-solidified microstructures insome materials such as Ge. But this transition has not beenreproduced by Aoyama et al.[1] Before further discussionhere, it should be noted that (a) free growth of an undercooledliquid is dendritic in nature and (b) the so-called faceted tononfaceted transition has been determined from microstruc-ture examination and not from the relationship between DTand growth velocity. In contrast to the statement of Aoyamaet al., the undercooling-growth velocity relation is mono-tonic and no jump is detected at all in the measuring rangeof our experiments 60 K , DT # 426 K. Devaud andTurnbull[13] first observed the structural transition from^211&[22] or ^110&[12] twin dendrites to ^100& twin-free den-drites for Ge, at a critical undercooling DT* of about 300K. Later, this transition was confirmed,[7,11] but at a differentcritical DT*, which was found to decrease with the additionof a small amount of impurities. These observations clearlyreveal that even small amounts of impurities to pure Ge canchange the microstructural development in an essential way.We employed EML to undercool bulk Ge samples and repro-ducibly observed the transitions from twin dendrites to twin-free dendrites and to refined equiaxed grains.[15] Moreover,the critical undercoolings for microstructural transitions areconsistent with the previous report.[13,23] In addition, weperformed containerless processing of Ge using an 8.5-mdrop tube[16] in order to eliminate a possible stirring effectduring EML. Figure 1 illustrates the surface relief morphol-ogy of two Ge particles solidified in free fall in the droptube. Please note that this picture is at the microscopic scale,which is almost identical to that of the upper schematicdiagram[24] serving to depict the clear distinction betweenfaceted and nonfaceted structure. On the basis of the pro-nounced edge faces in Figure 1(a), the sample can beassumed to grow by lateral mechanism at small DT. In con-trast, Figure 1(b) presents a microscopically flat, or nonfac-eted, surface, which should be induced by a continuousgrowth in the deeply undercooled droplet of pure Ge. Judgingby the common results of fluxing,[7,8,11–14] EML,[15] pulsed-laser quenching,[23] and drop tube experiments, it can beconcluded that the transition from lateral to continuousgrowth in Ge is a general effect of undercooling. Fig. 1—Scanning electron micrographs of (unetched) surface relief of two

While looking at the impurity-rich dendrites at the center Ge particles solidified in free fall in an 8.5-m drop tube: (a) jagged andfaceted surface and (b) microscopically flat and nonfaceted structure.of each grain in Figure 6(c) of Reference 1, it became evident


11. C.F. Lau and H.W. Kui: Acta Metall., 1991, vol. 39, pp. 323-27.that some impurities have been drawn into the sample during12. C.F. Lau and H.W. Kui: Acta Metall. Mater., 1994, vol. 42, pp. 3811-16.processing. In the case of the presence of impurities, the13. G. Devaud and D. Turnbull: Acta Metall., 1987, vol. 35, pp. 765-69.

dendrite growth velocity markedly deviates from that of pure 14. D. Turnbull: Mat. Res. Soc. Symp. Proc., 1986, vol. 51, pp. 71-81.materials, especially for semiconductors.[25] On the other 15. D. Li, K. Eckler, and D.M. Herlach: Acta Mater., 1996, vol. 44, pp.

2437-43.hand, it has been suggested that the fraction of interfacial16. D. Li and D.M. Herlach: J. Mater. Sci., 1997, vol. 32, pp. 1437-42.sites at which attachment can occur is about 0.01[23,26] for17. V.N. Skokov, A.A. Dik, V.P. Koverda, and V.P. Skripov: Sov. Phys.the covalently bonded Ge and Si because their electronic Crystallogr., 1985, vol. 30, pp. 236-37.

state changes from metallic to semiconducting upon solidifi- 18. H.A. Davies and J.B. Hull: Scripta Metall., 1973, vol. 7, pp. 637-42.19. S.R. Stiffler, M.O. Thompson, and P.S. Peercy: Appl. Phys. Lett., 1990,cation. Evans et al.[23] numerically simulated the relative

vol. 56, pp. 1025-27.morphological instability in undercooled Ge and predicted20. See, for example, D.J. Thoma and J.H. Perepezko: Metall. Trans. A,that the growth of faceted materials requires relatively large

1992, vol. 23A, pp. 1347-62.kinetic undercooling in contrast to what Aoyama et al. have 21. R.F. Cochrane, P.V. Evans, and A.L. Greer: Mater. Sci. Eng., 1988,reported. In light of these arguments, the agreement between vol. 98, pp. 99-103.

22. D.R. Hamilton and R.G. Seidensticker: J. Appl. Phys., 1960, vol. 31,the measured growth velocities and the calculations of so-pp. 1165-68.called no fitting parameters in Reference 1 might be fortu-

23. P.V. Evans, S. Vitta, R.G. Hamerton, A.L. Greer, and D. Turnbull:itous, for instance, due to a conspiring effect of impurity Acta Metall. Mater., 1990, vol. 38, pp. 233-42.and negligence of the kinetic attachment factor. Certainly, 24. W. Kurz and D.J. Fisher: Fundamentals of Solidification, 3rd ed., Trans

Tech Publications Ltd., Aedermannsdorf, Switzerland, 1989 (reprintedmore work is needed in the area of measuring and modeling1992), pp. 37-37.the dendrite growth in undercooled melts of semiconducting

25. D. Li and D.M. Herlach: Phys. Rev. Lett., 1996, vol. 77, pp. 1801-04.materials. Further measurements[27] of the solidification26. X. Xu, C.P. Grigoropoulos, and R.E. Russo: Appl. Phys. Lett., 1994,

velocity in highly undercooled semiconductors are underway vol. 65, pp. 1745-47.using a high speed digital camera in an electrostatic levitator, 27. M.B. Robinson: NASA/Marshall Space Flight Center, private commu-

nication, Huntsville, AL, Mar. 1999.where the preheating and cooling gas are unnecessary andthe heating is decoupled with the levitation.

In conclusion, the undercooling observed by Aoyama etal.[1] from their EML is considerably less than that of variousstudies since the early 1950s. This discrepancy may not Authors’ Reply: “Emissivity Changebe simply ascribed to the temperature calibration of the and Adiabatically Solidified Structurepyrometer, despite the fact that we completely agree withthe authors that pyrometric measurements on levitated drops during Rapid Solidification inneed great care with regard to calibration and the change in Semiconductor”the emissivity of semiconductors during melting or freezing.Nevertheless, a number of previous studies have clearlydemonstrated the transition from lateral to continuous T. AOYAMA, Y. TAKAMURA, and K. KURIBAYASHIgrowth for the achieved undercooling exceeding a threshold.

The growth behavior of a semiconductor from anThere is, in principle, one possible reason for missing thisundercooled melt was investigated by us (ATK, hereafter),[1]result: the maximum undercooling obtained in Reference 1where we found that the growth velocity (V ) measurementis too small to reach the transition regime.predicted the growth behavior to be thermally controlled inthe measured range of undercooling, 36 to 181 K. Li andHerlach (LH) claimed that our results negate the transition

The experiments were performed while one of the authors from a lateral growth to a continuous growth with increasing(DL) held the Alexander von Humboldt Fellowship. The undercooling, DT. The critical undercooling for the transitionauthors also thank Dr. M.B. Robinson, Mr. T.J. Rathz, and (DT*), however, is estimated by ATK[1] to be about 30 KProfessor K. Kuribayashi for stimulating discussions and for Ge by microstructural observation, while the estimationMr. T. Aoyama for sending us the proof ahead of publication. of LH is DT* 5 300 K on the basis of the measured V-DT

relationship.[2] Therefore, this discussion should focus onwhat gives rise to the large difference in DT*. From theREFERENCESfollowing points of view, the consistency of Reference 1 is

1. T. Aoyama, Y. Takamura, and K. Kuribayashi: Metall. Mater. Trans. verified: (1) temperature calibration of pyrometric outputA, 1999, vol. 30A, pp. 1333-39. caused by difference in emissivity between solid and liquid,

2. J.K.R. Weber, S. Krishnan, R.A. Schiffman, and P.C. Nordine: Adv. (2) determination of a suitable spot for microstructural obser-Space Res., 1991, vol. 11, pp. 43-52.vation to estimate DT*, and (3) comparison with the previ-3. D.M. Herlach and B. Feuerbacher: Adv. Space Res., 1991, vol. 11,

pp. 255-62. ous report.[8–10,14,18,19]

4. G.L.F. Powell: Trans. TMS-AIME, 1967, vol. 239, pp. 1662-63. The morphological changes were shown in Figures 65. G.L.F. Powell: Mater. Sci. Eng., 1997, vol. A237, pp. 119-20. through 8 of ATK.[1] Figures 7(a) and 8(a), respectively,6. D. Turnbull and R.E. Cech: J. Appl. Phys., 1950, vol. 21, pp. 804-10.

show a twin dendrite for Si and a faceted structure for Ge,7. S.E. Battersby, R.F. Cochrane, and A.M. Mullis: Mater. Sci. Eng.,both of which demonstrate the stepwise lateral growth at1997, vols. A226–A228, pp. 443-47.

8. S.E. Battersby, R.F. Cochrane, and A.M. Mullis: J. Mater. Sci., 1999, low undercooling. At higher undercooling, dendrites con-vol. 34, pp. 2049-56. taining no twin planes for Ge and typical ^100& dendrites

9. G. Devaud and D. Turnbull: Appl. Phys. Lett., 1985, vol. 46, pp. 844-45. with the fourfold symmetry for Si are, respectively, observed10. V.P. Skripov: in Current Topics in Materials Science, Crystal Growthin Figures 8(b) and 6(c), both of which appear to growand Materials, E. Kaldis and H.J. Scheel, eds., North-Holland Publish-

ing Co., New York, NY, 1977, vol. 2, pp. 327-78. continuously. It should be noted that the morphological


changes in Figures 7 and 8 were observed by optical micros-copy 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 fromedgewise to normal growth is estimated to be about 30 Kfor Ge by microstructural observation.[1]

Based on the aforementioned reason, it is necessary tomodify Table I in LH’s discussion with regard to the struc-tural transition. Therefore, experimental studies on theundercooled Ge are summarized again in Table I, particularlyfor the studies in which specimens with similar diameterare used, because the sample size has a crucial influenceon cooling rate and convection, and the morphologies of

Fig. 1—Temperature-time profile of an undercooled Ge. Output of thespecimens of very different sizes cannot be indiscriminately monocolor pyrometer is corrected by a single emissivity, although thiscompared. The maximum undercooling observed by ATK calibration technique is not applicable for semiconductors. (a) Recalescence

curve measured from the top of the chamber. (b) Fluctuations measuredis 235 K, which has been reported previously[3] and is notfrom the side. The upper and lower limits of the fluctuation correspond toreferred to in LH’s discussion. All undercoolings in Figurethe radiation of the solid and the liquid phases at the coexistence state,4(b) of Reference 1 are measured when the solidification is respectively.

initialized by a trigger at given temperatures and do notinclude the maximum undercooling measured at spontane-ous solidification. Although the purity of Ge used by ATK their discussion. The electromagnetic levitation coil, how-is higher than 99.999 pct as a guaranteed value, the measured ever, does not block the optical path when measurementsresistivity is larger than 45 V?cm, which is equivalent to are made from the side, as apparently shown in Figures 1,99.999999 pct purity or higher.[4] Table I shows that DT* 9, and 10 of Reference 1. Furthermore, it is difficult to keepestimated by LH is much larger than those estimated by the focusing the pyrometer on the liquid surface from the topother three studies. or the side even when the triggered recalescence started

One primary factor behind this conflict is the difference from the bottom. This is because rapid solidification fromin the temperature calibration techniques between LH and the undercooled melt makes the thermal boundary layer thin,ATK, as mentioned in Reference 1. The temperature-time the thickness of which can be estimated approximately basedprofiles of Ge are shown in Figures 1(a) and (b), which are on the ratio of the thermal diffusivity to the interface velocityobtained by calibrating ATK’s raw data in the same way[5,6] and is of the order of 1 mm at V 5 1 m/s. In fact, Figureas LH; that is, the output of a monocolor pyrometer is 1(a) was obtained by measuring the specimen temperaturecorrected by a single emissivity from beginning to end, so from the top using ATK’s facility. Comparing Figure 1(a)that the temperature recorded after recalescence is consid- to 1(b), the temperature after recalescence from a sufficientlyered to be the melting point. Figure 1(b) shows the fluctua- undercooled state is apparently measured on the solid sur-tions measured from the side of the chamber. The upper and face. ATK measured the radiations of liquid Si and Ge atlower limits of the fluctuation correspond to the radiation the coexistence state by separating from the solid,[1,3] whileof the solid and liquid phases at the coexistence state, respec- LH did not.[5,7] This measurement, which derives the spectraltively.[1] The temperature difference between the upper and emissivity of each phase, is essential to infer the true temper-the lower limits is 142 K. In reality, these temperatures must ature of semiconductors using the pyrometer. The undercool-be the same and equal to the melting point. This difference ing is overestimated by 142 K without this measurement.results in the overestimation of the undercooling, and the Devaud and Turnbull[8] observed the cross sections ofbulk undercooling shown in Figure 1(a) is evaluated as if Ge droplets and suggested structural transition at criticalit were 330 K. LH measured the temperature of the sample undercooling, the value of which is almost the same as LH’sthrough a quartz view window at the top of the chamber result.[2] Much attention, however, should be paid to the

microstructural observation of the samples solidified from anand suggested the advantage of top-view measurement in

Table I. Partial Summary of Experimental Studies on Solidification from Undercooled Ge

DTmax D Purity DT* Method for(K) (mm) (Pct) (K) Spot of MO Estimating DT* References

235 5 .99.999 30 triggered point MO 1, 3426* 6 to 8 99.999 300* cross section VM 2, 16342 ,7 99.999 93 surface MO 9, 18, 19300 3 to 5 99.9999 170 cross section VM 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.


undercooled melt, particularly of semiconducting materials.Their large heat of fusion may influence the microstructureafter nucleation, even if some experimental modification isadded to remove the released latent heat effectively. As ATKdiscussed in Reference 1, the volume fraction of the solidsolidified adiabatically during recalescence, fs , is very smallin the case of semiconductors. For Ge, fs 5 0.04 at DT 550 K and fs 5 0.25 at DT 5 300 K. Following adiabaticsolidification, the remaining liquid with the volume fraction(1 2 fs) begins to solidify at the melting point, growing ina lateral manner. Even if continuous growth occurs at lowundercoolings, it may be extremely difficult to find anytraces of twin-free dendrites by observing the cross sectionof the sample. To make matters worse, the scarce tracesmay have disappeared by remelting, which is driven by thecapillarity effect. Actually, Lau and Kui reported DT* 5 93K by observing the surface structure.[9] Although it may be

Fig. 2—Relationship between bulk undercooling and growth velocity foreasier to find the traces on the surface than in the cross pure Ge measured by Aoyama et al.,[1] Li et al.,[2, 13] and Battersby et al.[14]

section, the most suitable section for observing the adiabati-cally solidified structure at any given undercooling may bearound the first nucleation site. Therefore, ATK observed

As pointed out by LH in their discussion, the kineticthe surface relief at the point where solidification was initi-undercooling predicted by ATK[1] is lower than that by Evansated by the trigger.[1]

et al.[10] The prediction of Evans et al. however, was simu-Evans et al. estimated the critical interface undercoolinglated for a concentrated alloy and a dilute one (Figure 7 infor the transition, DT*i , to be 153 K by employing a numeri-Reference 10), while that of ATK was for a pure material.cal model for spherical growth, presuming that dendritesIn pure Ge, the contribution of kinetic undercooling to thefirst appear in pure Ge for bulk undercoolings greater thantotal undercooling is expected to decrease with increasing300 K.[10] The interfacial undercooling, DTi , is defined as theundercooling, particularly around the critical undercooling.undercooling below the equilibium temperature, Te (5Tm 2

In conclusion, the structural transition from lateral to con-DTr), where Tm is the melting temperature and DTr is thetinuous growth has already been observed by ATK at DT* 5curvature undercooling. LH expressed the undercooling30 K.[1] One of the major points of Reference 1 is that theequation using the value of DT*i estimated by Evans et al.undercoolings in LH’s article[2,5,7,13,15–17] might be overesti-as follows (Eq. [1] in Reference 6):mated by about 140 K due to experimental error. Measuring

DT 2 DT*i 5 DTt 1 DTr 1 DTk 1 DTs [1] the spectral emissivities of the solid and liquid phases isessential to avoiding this overestimation. The most suitablewhere DTt , DTk , and DTs are the thermal, kinetic, and consti-section for observing the adiabatically solidified structuretutional undercooling, respectively. The total undercooling,is concluded to be around the first nucleation site in the casehowever, is defined as follows by the commonly used den-of semiconductors. The results of Reference 1 are demon-drite growth theory:[11,12]

strated to be consistent by comparing with the previousDT 5 DTt 1 DTr 1 DTk 1 DTs [2] reports.

Equation [2] shows that Eq. [1] is not valid. The theoreticalvalue predicted using Eq. [1] inflates the undercooling REFERENCESunsubstantially by 153 K. Although the growth velocities

1. T. Aoyama, Y. Takamura, and K. Kuribayashi: Metall. Mater. Trans.measured by LH seem to correspond well with the theoreticalA, 1999, vol. 30A, pp. 1333-39.prediction by the dendrite growth theory[11,12] modified

2. D. Li, K. Eckler, and D.M. Herlach: Acta Mater., 1996, vol. 44, pp.slightly using Eq. [1],[2] this agreement may be caused by2437-43.

a coincidence between the inflation of the prediction (153 3. T. Aoyama, Y. Takamura, and K. Kuribayashi: Jpn. J. Appl. Phys.,K) and the overestimation of the measurement (142 K). 1998, vol. 37, pp. L687-L690.

4. Physics of Semiconductor Devices, S.M. Sze, ed., Wiley Interscience,The relationships between the bulk undercooling and theNew York, NY, 1969.growth velocity for pure Ge measured by ATK,[1] LH,[2,13]

5. D. Li and D.M. Herlach: J. Mater. Sci., 1997, vol. 32, pp. 1437-42.and Battersby et al.[14] are made into a graph, as shown in 6. M. Przyborowski, T. Hibiya, M. Eguchi, and I. Egry: J. Cryst. Growth,Figure 2. The three studies have a comparatively similar 1995, vol. 151, pp. 60-65.

7. D. Li and D.M. Herlach: Europhys. Lett., 1996, vol. 34, pp. 423-28.tendency if the set of data measured by LH can be shifted8. G. Devaud and D. Turnbull: Acta Metall., 1987, vol. 35, pp. 765-69.down to the lower undercooling for a given amount of over-9. C.F. Lau and H.W. Kui: Acta Metall. Mater., 1993, vol. 41, pp.estimation. This is also supported by the contradiction that

1999-2005.the growth velocity of LH (about 0.8 m/s at DT 5 400 K) 10. P.V. Evans, Satish Vitta, R.G. Hamerton, A.L. Greer, and D. Turnbull:is much smaller than that predicted by Evans et al. (17.3 Acta Metall. Mater., 1990, vol. 38, pp. 233-42.

11. W.J. Boettinger, S.R. Coriell, and R. Trivedi: in Rapid Solidificationm/s at DT 5 400 K),[10] though LH mentioned in theirProcessing—Principles and Technologies IV, R. Mehrabian and P.A.discussion that the critical undercooling is consistent withParrish, eds., Claitor’s, Baton Rouge, LA, 1988, pp. 13-25.the prediction of Evans et al. A high growth velocity is 12. J. Lipton, W. Kurz, and R. Trivedi: Acta Metall., 1987, vol. 35, pp.

necessary to initiate the continuous growth from an atomi- 957-64.13. D. Li and D.M. Herlach: Phys. Rev. Lett., 1996, vol. 77, pp.1801-04.cally roughened interface.


14. S.E. Battersby, R.F. Cochrane, and A.M. Mullis: J. Mater. Sci., 1999,vol. 34, pp. 2049-56. a+ 5

X 2F

X 20

a 11X0

dX0

dtf 2

m 1 1[1]

15. D. Li, K. Eckler, and D.M. Herlach: Europhys. Lett., 1995, vol. 32,pp. 223-27.

In Eq. [1],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, a 5DtF

X 2F

[2]1995, vol. 152, pp. 101-04.

18. C.F. Lau and H.W. Kui: Acta Metall. Mater., 1991, vol. 39, pp. 323-27.is the regular back-diffusion Fourier number, D is the diffu-19. C.F. Lau and H.W. Kui: Acta Metall. Mater., 1994, vol. 42, pp. 3811-16.sivity (m/s2) in the solid, XF is the length of the microsegrega-tion domain at the conclusion of solidification—usuallytaken to be equal to half the final secondary arm spacing,and tF is the local solidification time. The other terms inApproximate Models ofEq. [1] are X0(t), the time-dependent length of the half arm

Microsegregation with Coarsening space; f, the solid fraction in the arm space; t 5 t/tF , thenormalized time; and m, the order of the polynomial usedto approximate the solid solute profile (m 5 2 to 2.5[2,4]).V. R. VOLLER and C. BECKERMANNThe first term on the right-hand side of Eq. [1] accounts for

Microsegregation refers to the processes of solute rejec- the back-diffusion and the second term accounts for thetion and redistribution at the scale of the dendrite arm spaces coarsening-induced dilution of the liquid solute concentra-in the mushy region of a solidifying alloy. A representative tion. An important observation from Eq. [1] is that, in thegeometry for a microsegregation analysis is the half-arm absence of back-diffusion, the effect of coarsening on micro-spacing in a “platelike” morphology (Figure 1). Models of segregation is characterized by the diffusion parametermicrosegregation are based on a solute balance within thisdomain. A recent review by Kraft and Chen[1] covers the ac 5

1X0

dX0

dtf 2

m 1 1[3]

range of available models. Common assumptions used inmodeling include a binary eutectic alloy; a fixed average Voller and Beckermann[4] show that, across a wide range ofcomposition, C0; equilibrium at the solid-liquid interface; a cooling conditions and for a coarsening law of the formconstant partition coefficient k ,1; and a straight liquidus X0 5 t1/3, this term takes a constant value of ac 5 0.1.line in the phase diagram. Two key features of the solute The objective of the current work is to use the result inbalance that need to be included in a comprehensive model Eqs. [2] and [3] to extend the current integral-based micro-are the following. segregation models to arrive at general integral approxima-

tions that can take full account of both back-diffusion and(1) The mass diffusion of the solute. Typically, the solutecoarsening.diffusion in the liquid is rapid, and, at each instant in

The starting points for the general model developmenttime, a uniform distribution of solute, Cl(t), can beare the available analytical expressions for microsegregationassumed. In the solid, however, diffusion is much slowerin the presence of coarsening but absence of back-diffusion.and the solute balance needs to account for the so-calledUnder this condition, when the solid growth is parabolic,“back-diffusion” of solute into the solid.Voller and Beckermann[4] obtain the exact microsegrega-(2) Changes in morphology. As solidification proceeds, thetion expressionarm spacing will coarsen. If the overall solute balance

is maintained in the half-arm domain, this feature will C1

C05

2n (1 2 f )(112n)k21

f 2n ef

0f2n21 (1 2 f)2(112n)k df [4]dilute the solute in the liquid.

One class of microsegregation models involves expres- where n is the exponent in a coarsening model of the form[5]

sions that contain integrals. When coarsening is notX0 5 t n [5]accounted for and the solid growth is parabolic, Wang and

Beckermann[2] obtain an integral expression that approxi- When the solidification is controlled by a constant coolingmates the segregation ratio (C1/C0). At the opposite extreme, rate, Mortensen (Eq. [12] in Reference 3) obtains theaccounting for coarsening but neglecting back-diffusion, exact expressionanalytical expressions can also be obtained. In the case ofa constant cooling rate, Mortensen[3] presents an analytical

f 51 1 n1 2 k

C[1/(k21)]1

(C1 2 C0)n eC1

C0f[k/(12k) (f 2 C0)n df [6]integral expression for the solid fraction, f, and Voller and

Beckermann[4] present an analytical integral expression forThe microsegregation models in Eqs. [4] and [6] are analyti-the segregation ratio when solid growth is parabolic.cal but only applicable in the limit of coarsening aloneIn recent work, Voller and Beckermann[4] show, analyti-(i.e., there is no back-diffusion). A consequence of Eq. [3],cally, that coarsening can be included in a microsegregationhowever, is that coarsening can be considered to be a back-model by using the enhanced diffusion parameterdiffusion-like microsegregation process characterized by theenhanced diffusion term ac. This suggests that, with anappropriate definition of the coarsening exponent n, Eqs.

V.R. VOLLER, Professor, is with the Saint Anthony Falls Laboratory, [4] and [6] could be applicable to back-diffusion–Department of Civil Engineering, University of Minnesota, MN 55455- controlled microsegregation.0116. C. BECKERMANN, Professor, is with the Department of Mechanical

If the solidification is controlled by a parabolic growthEngineering, University of Iowa, Iowa City, IA 52243.Manuscript submitted April 5, 1999. of solid fraction


eCl

C0

f[k/(12k)](f 2 C0)(m11)a df

Equations [10] and [11] are approximate models for microse-gregation in the absence of coarsening. Equation [10], whichhas been presented in the literature previously,[2] is for thecase when the solidification in the arm space is controlledby a parabolic growth. Equation [11] is for the case whenthe solidification is controlled by a constant cooling rate;this expression has not been previously presented. Takingguidance from the main result of Voller and Beckermann,[4]

(Eq. [2]), these approximate models can be extended to thegeneral case that includes both back-diffusion and coarsen-ing by replacing the Fourier number, a, by the diffusionparameter

a+ 5X 2

f

X 20

a 1n

m 1 1[12]

In this way, the general version of the parabolic growthmodel, obtained from Eq. [10], is

Cl

C05 (2Aa 1 2n)

(1 2 f )(112Aa12n)k21

f 2Aa12n

[13]Fig. 1—Microsegregation domain is half-secondary dendrite arm space ina platelike morphology.

ef

0

f2Aa12n21 (1 2 f)2(112Aa12n)k df

f 5 t1/2 [7] where A 5 (m 1 1)[XF /X0]2. Because the time-averagedbehavior of the term [XF /X0]2 is not known analytically, thethen, with reference to Eq. [3],parameter A is determined subsequently through a compari-son with a full numerical solution of the microsegregationac 5

1X0

dX0

dtf 2

m 1 15

nm 1 1

[8]problem. In the limit of no coarsening (n 5 0), Eq. [13]reduces to the model proposed by Wang and Beckermann,[2]

This expression indicates that a coarsening-controlled micro-and in the limit of coarsening alone (a 5 0), it reduces tosegregation process, with a coarsening exponent,the analytical model presented by Voller and Beckermann.[4]

Integration by parts leads to the alternative form of Eq. [13]:n 5 (m 1 1)a [9]

is equivalent to a back-diffusion–controlled microsegrega- Cl

C05

(1 2 f )(112Aa12n)k21

f 2Aa12ntion process characterized by the Fourier number a. UsingEq. [9] to replace n in Eq. [4] results in the followingapproximate relationship: [ f (2Aa12n)(1 2 f )2(112Aa12n)k [14]

Cl

C05

2(m 1 1)a(1 2 f )((112(m11)a)k21

f 2(m11)a [10]

2ef

0

k(1 1 2Aa 1 2n)f2Aa12n(1 2 f)2(112Aa12n)k21 df]

ef

0

f2(m11)a21(1 2 f)2(112(m11)a)kdfThis form is more suitable when the Fourier number, a, issmall. For example, in the limit of a → 0 and n 5 0, theScheil equation[2]This expression is identical to the parabolic growth microse-

gregation model developed by Wang and Beckermann (Eq.[23] in Reference 2).

Cl

C05 (1 2 f )k21 [15]

Although in a solidification controlled by a constant cool-ing rate the growth of the solid fraction is not parabolic, follows immediately from Eq. [14].a parabolic growth may still be a reasonable “first cut” The general version of the constant cooling model,approximation. In this way, following from the arguments obtained by substituting Eq. [12] into Eq. [11] ispresented previously, the use of Eq. [9] to replace the coars-ening exponent, n, in Eq. [6] will result in a back-diffusion f 5

1 1 Ba 1 n1 2 k

C[1/(k21)]l

(Cl 2 C0)Ba1n

[16]only microsegregation model for a constant cooling rate.The result of this action is the approximate expression

eCl

C0

f[k/(12k)] (f 2 C0)Ba1n dff 51 1 (m 1 1)a

1 2 k

C [1/(k21)]l

(Cl 2 C0)(m11)a

[11]METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 30A, NOVEMBER 1999—3017

where B accounts for the time-averaged behavior of theproduct (m 1 1)[XF /X0]2. Note, in the limit of a 5 0, thisequation matches the analytical model presented byMortensen.[3]

Equation [13] or [14] and Eq. [16] are the key results inthis article. For a given solidification path (parabolic growthor constant cooling), these models can be used to determinethe progress of the complete microsegregation processincluding 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 parametersA and B.

For the parabolic growth models, the integrals in Eqs.[13] and [14] can be evaluated using a high-order numericalintegration scheme. In this work, a 24-point Gaussian quad-rature is used. If the Fourier number is small (a , 0.2),then Eq. [14] should be evaluated for microsegregation pre-dictions. If the Fourier number is large (a . 1), then Eq.[13] should be evaluated. Practice shows that, when theFourier number is small or large, a single application of the24-point Gauss in the integration range [0, f ] is not ofsufficient accuracy. In these cases, it is recommended thatthe integration domain be segmented (segments usually Fig. 2—Predicted eutectic fractions obtained with parabolic growth models.

The continuous lines are the approximate model predictions; the points areworks well) with a 24-point Gauss applied in each segment.numerical predictions.In terms of finding the parameter A, a crude fitting exercise

(discussed subsequently) indicates that setting A 5 4.5 workswell across a wide range of conditions. Fortran programsfor 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], canalso be evaluated with a single application of a 24-pointGaussian quatrature in the interval [C0, Cl]. Further, settingthe parameter B 5 3.8 works well across a wide range ofconditions. 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 withcomplete numerical models of microsegregation. Thesenumerical models, which include both parabolic growth(parb.for) and constant cooling rate (const.for) versions, arefully reported elsewhere.[6] Appropriate Fortran 77 codesare available on the web site http://www.ce.umn.edu/voller/voller research/

The predictive measure used for comparison will be thefraction of eutectic formed. The nominal concentration ofthe alloy is C0 5 1 and the eutectic liquid concentration isCeut 5 5. Interest will focus on the variations of eutecticfraction with Fourier number, a, and partition coefficient, Fig. 3—Predicted eutectic fractions obtained with constant cooling models.

The continuous lines are the approximate model predictions; the points arek. In all cases, a standard coarsening exponent of n 5 1/3numerical predictions.will be used. [5] Note, when using the parabolic growth

models, iterations need to be used to find the eutecticfraction.

Figure 2 compares eutectic predictions from the parabolic and provide a visual reference for the relative accuracy ofgrowth, Eq. [13] or [14], with predictions obtained from the the approximate expressions.full numerical model. For practical values of the partition A similar comparison to those shown in Figure 2, but forcoefficient, k, agreement between the approximate and the constant cooling model (Eq. [16]), is shown in Figurenumerical solutions, over a wide range of Fourier numbers, 3. Once again the comparison between the approximate andis very close. As a reference, eutectic predictions obtained full numerical models is excellent.when coarsening is absent (n 5 0) and k 5 0.2 are added A potential weak feature of the proposed models could

be the choice of the fitting parameters A, in Eq. [13] or Eq.to the figure. These results indicate the effect of coarsening


(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.

4. V.R. Voller and C. Beckermann: Metall. Mater. Trans. A, 1999, vol.[14], and B, in Eq. [16]. The reason that the optimum choice30A, pp. 2183-89.of these values is not the same (A 5 4.5 and B 5 3.8)

5. D.H. Kirkwood: Mater. Sci. Eng., 1985, vol. 73, pp. L1-L4.indicates the fact that the assumption of a parabolic solid 6. V.R. Voller: Int. J. Heat Mass Transfer, in press, 1999.growth for the constant cooling case is reasonable but notexact. Eutectic predictions, however, are reasonably insensi-tive to the choices of A and B. Figure 4 compares predictionsobtained with the proposed models in which the parameters Tensile Properties of Duplex Metal-A and B have been increased and decreased by ,10 pct.The results in this figure indicate very little change in the Coated SiC Fiber and Titaniumpredictive ability of the approximate models when nonopti- Alloy Matrix Compositesmum values of A and B are used and also suggest that auniversal value of A 5 B 5 4 would be appropriate for

S.Q. GUO, Y. KAGAWA, A. FUKUSHIMA, andboth models.C. FUJIWARAExact integral expressions for microsegregation in a coars-

ening microstructure in the absence of back-diffusion have SiC(SCS-6) fiber-reinforced titanium alloy matrix com-been reported in the literature.[3,4] Recent work by Voller posites have a great potential for high-temperature aerospaceand Beckermann[4] indicates that coarsening can be modeled structural applications.[1,2,3] It is known that the interfacein a standard microsegregation model as a back-diffusion reaction between the outermost SCS coating and Ti alloyprocess characterized by an enhanced diffusion parameter matrix takes place during the fabrication process, and theac (Eq. [3]). This result has been used to extend the analytical formed reaction layer consists of a nonstoichiometric carbidecoarsening microsegregation models to approximate expres- (TiC12x) and silicides (TixSiy).[4,5,6] The reaction layer issions that account for both coarsening and back-diffusion. brittle; however, this has only a slight effect on the quasi-The resulting integral expressions, one for a solidification static tensile strength.[7,8] On the other hand, the effect ofcontrolled by a parabolic growth of solid (Eq. [13] or Eq. the reaction layer cracking on the fatigue damage evolution[14]) and one for a solidification controlled by a constant is quite severe.[9,10,11] Such cracking under a cyclic fatiguecooling rate (Eq. [16]), default to the appropriate limiting loading condition leads to debonding of the SCS coatingcases. In addition, across a wide range of practical condi- layer from the SiC fiber surface, which leads to a significanttions, predictions obtained with the approximate models reduction in the fiber strength, because the debondingcompare closely with results from numerical models. increases stress concentration at the SiC fiber surface, which

originates from surface flaws of the fiber.[9,12] It was reportedthat the tensile strength of the SiC(SCS-6) fiber becomesabout half of the original fiber strength after the debondingOne of the authors (CB) gratefully acknowledges partial

support provided by the National Science Foundation underGrant No. CTS-9501389.

S.Q. GUO, Postdoctoral Research Fellow, Japan Society for the Promo-tion of Science (JSPS), and Y. KAGAWA, Professor, are with the Instituteof Industrial Science, The University of Tokyo, Tokyo 106-8558, Japan.REFERENCESA. FUKUSHIMA, Research Engineer, and C. FUJIWARA, Project Engi-neer, are with the Materials Research Section, Engineering Research Depart-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. ment, Nagoya Aerospace Systems, Mitsubishi Heavy Industries, Ltd.,Nagoya 455-0024, Japan.199-211.

3. A. Mortensen: Metall. Trans. A, 1989, vol. 20A, pp. 247-53. Manuscript submitted February 23, 1999.


of the SCS coating layer from SiC fiber surface and the behaviors between the duplex metal coating and the SCScoating, Ti coating was not applied. After heat exposure,strength is nearly the same as that of SCS-uncoated

SiC(SCS-0) fiber.[12] This mechanism is the cause of the the morphology of the coated fibers was observed by ascanning electron microscope (SEM) and stability of thefiber fracture behavior at an early stage of fatigue under

cyclic loading.[12] duplex metal coatings was investigated by energy dispersiveX-ray (EDX).The authors’ previous experimental research on the same

kind of composites suggests that fiber fracture at the early The tensile strength of the heat-exposed pristine andduplex metal coated SiC(SCS-6) fibers was measured. Thestage of fatigue can be avoided if ductile metal layers exist

between the SCS coating and Ti alloy matrix.[13] A prelimi- fiber was cemented at each end in a paper holder card withan epoxy base adhesive. The gage length, L, was fixed atnary study clearly demonstrated that fatigue life was

improved by applying a Cu/Mo duplex metal coating on 20 mm. The paper holder was gripped and both sides werecut just before the test. The test was performed using athe SCS coating surface.[13] The effect of the duplex metal

coatings on mechanical properties of both the individual SiC screw-driven testing machine (UTM-II, Toyo Sokki, Co.,Ltd., Tokyo) at room temperature (298 K) in air with afiber and titanium alloy matrix composites under quasi-static

tensile test have not yet been examined. The purpose of this crosshead displacement rate of 0.04 mm/min. While 40 pris-tine fibers were tested, only 30 duplex metal coated fibersarticle is to show the effect of the candidate duplex metal

coatings on the tensile properties of both the SiC fiber and were because of their limited availability. The mean tensilestrength was determined from an average value of the testedtitanium alloy matrix composites.

Continuous SiC fiber (SCS-6, Textron Specialty Materi- fibers using Weibull’s statistical method with the mean-rank method.[12] The fiber strength was calculated from theals, Lowell, MA) was used throughout the study. It has a

b-SiC filament of '140-mm diameter with a '3.6-mm-thick applied force at fracture divided by the cross-sectional areaof the SiC fiber (diameter: 140 mm).outermost SiC particle dispersed carbon-rich coating (SCS

coating).[12,14] Pure Cu (.99.90 wt pct in purity) was depos- The effect of the duplex metal coatings on the tensilestrength of the composites in an actual fabrication processited on the surface of the SCS coating by a physical vapor

deposition (PVD) process, and thereafter, Ta, Mo, or W was examined using composite specimens. Three kinds ofunidirectional aligned duplex metal (Cu/Ta, Cu/Mo, and Cu/(.99.90 wt pct in purity) was deposited on the surface of

the Cu coated fiber by the same process. All the coatings W) coated SiC(SCS-6) fiber-reinforced Ti-15-3 alloy matrixcomposites were fabricated by a solid-state foil-fiber-foilwere done at an atmospheric pressure of '1023 Pa at a

temperature of 470 to 570 K. The Cu coating was selected consolidation technique using a HIP process. The HIP pro-cessing was done at a temperature of 1153 K for 1.5 hoursbecause the reaction between the SCS coating and Cu was

quite low.[15] Thus, if a Cu coating exists between the SCS under a hydrostatic pressure of 100 MPa. The thickness ofTi-15-3 foils, which were supplied by Kobe Steel Co., Ltd.coating and Ti alloy matrix, the interface reaction between

them can be avoided. However, Cu reacts chemically with (Kobe, Japan), was 130 mm. The chemical composition ofthe matrix alloy was 15.22 wt pct V, 3.26 wt pct Cr, 3.12Ti to form intermetallic compounds,[15] and to prevent this,

an additional metal coating between the Cu coating and Ti wt pct Al, 2.94 wt pct Sn, and the remainder Ti. To comparethe effect of the duplex metal coatings on tensile propertiesmatrix is required. In this study, Ta, Mo, and W were used

as the second coating materials. Their selection was based of the composites, a duplex metal uncoated SiC(SCS-6)fiber-reinforced Ti-15-3 composite was also fabricated byon the following properties of these alloying elements: (1)

high melting point, (2) low diffusion coefficients inside b-Ti the same HIP process. The nominal fiber volume fraction,Vf , in the composites was '0.18. After the fabrication, thephase, and (3) no reaction to form an intermetallic compound

with Ti at the processing temperature. (Although it is composites were treated with a solution at 1053 K for 0.5hours and then aged in air at 723 K for 16 hours to obtainreported that W could react with Ti and form an intermetallic

according to the Ti-W equilibrium diagram,[15] the interme- stable microstructure of the matrix. Hereafter, these compos-ites are denoted as SiC/Ti-15-3 (pristine fiber composite),tallic is unknown and thus this reaction between W and Ti

is not considered here.). The properties of Ta, Mo, and W 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/alloying elements suggest that they are stable at the pro-

cessing temperature, so that they were selected as the second W/Ti-15-3 (Cu/W coated fiber composite), respectively.The composite panels were cut into a plate-type tensilecoating materials. A ductile b-Ti phase reportedly is formed

near the interface when Ta diffuses into Ti for Ag/Ta coated test specimen with the long axis parallel to the fiber axisdirection. The specimen was prepared with a diamond cut-SiC(SCS-6) fiber-reinforced Ti3Al matrix composite, and

this b-Ti phase region serves as a compliant layer to relieve ting saw, and its surfaces were repeatedly polished with adiamond paste up to a 1-mm finish. A dog-bone-shapedthe large thermal residual stresses by plastic deformation,

in this way improving the interfacial compatibility of the specimen 70 mm in length, 1.4 mm in thickness, and 4.2mm in width was used. The gage length of the specimencomposite.[16,17]

The effect of the coatings on the SiC(SCS-6) fiber strength was 20 mm. Tensile strength of the composites was measuredusing a screw-driven universal testing machine (Instronafter heat exposure was explored by heat exposing the pris-

tine and duplex metal coated SiC(SCS-6) fibers at 1153 K Model 8562, Instron Co., Ltd., Canton, MA). Strain of thespecimen was measured with a resistance-type strain gage,for 1.5 hours in a vacuum atmosphere of 1024 to 1025 Pa

using an electric furnace. This heat exposure condition was which had a base area of 6.0 by 1.7 mm. The test was doneat room temperature (298 K) in air with a constant crossheadthe same as a heat schedule of the hot isostatic pressing

(HIP) condition of an SiC fiber-reinforced Ti-15-3 alloy speed of 0.1 mm/min.Figure 1 shows SEM photographs and EDX maps of thematrix composite. To distinguish the reaction and diffusion


(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) strength distributions of the duplex metal coated SiC(SCS-6) fibers are statistically different from that of the pristinefibers. The photographs demonstrate that all three coatings

are still present on the SCS coating of the fiber after heat SiC(SCS-6) fiber. Tensile strengths of the pristine fiber couldbe described by a single linear regression, the slope of whichexposure; and individual coatings (Cu, Ta, Mo, and W) are

distinguishable. The thickness of the Cu coating is '1.2 mm yields the Weibull modulus, m1 ' 17; however, the tensilestrengths of the duplex metal coated fibers exhibit a bimodaland that of the Ta, Mo, and W coatings is '1.6 mm. This

indicates that the applied duplex metal coatings are stable distribution. For the Cu/Ta coated SiC(SCS-6) fiber, theWeibull modulus in the high strength region is m1 ' 2.8,at 1153 K for 1.5 hours i.e., for the duration of the fabrication

heat schedule of the composites. whereas in the low strength region, the modulus is m2 '11. Approximately 60 pct of the tested Cu/Ta coated fibersA weak signal from the Cu is detected on the outermost

surface of the Cu/Ta and Cu/W coated SiC(SCS-6) fibers. failed in the low strength region (Figure 2(b)). The strengthdistributions of both the Cu/Mo and Cu/W coated SiC(SCS-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) 6) fibers are similar to that of the Cu/Ta coated fiber. TheirWeibull moduli in the high strength region are determinedfiber, indicating that the Cu diffuses toward the surface

through the Ta or W coatings during heat exposure. However, to be m1 ' 15 and 17, respectively, whereas in the lowstrength region, they are m2 ' 3.5 and 5.2, respectively.it is difficult to carry out quantitative treatment of the diffu-

sion behavior because of a lack of diffusion data. On the Approximately 20 pct of the tested Cu/Mo and 10 pct ofthe Cu/W coated SiC(SCS-6) fibers failed in the latter regioncontrary, the diffusion trace of Cu is not observed in the Cu/

Mo coated SiC(SCS-6) fiber. These results suggest that the (Figures 2(c) and (d)). The bimodal behavior of the Weibulldistributions suggests that the duplex metal coated SiC(SCS-Cu/Mo coating may have a greater possibility of being an

effective diffusion barrier than either the Cu/Ta or Cu/W 6) fibers introduce a new population of flaws during theduplex metal coating process and/or heat exposure, espe-coating.

Figure 2 shows Weibull plots of the tensile strength of cially for Cu/Ta coated SiC(SCS-6) fiber.Table I summarizes the tensile properties of the heat-the heat-exposed pristine and duplex metal coated SiC(SCS-

6) fibers. In these plots, ln ln [1/(1-PF)] is displayed as a exposed pristine and the duplex metal coated SiC(SCS-6)fibers. After heat exposure, the mean strengths of the duplexfunction of ln s, where PF is the cumulative probability of

failure at a given tensile stress, s. The straight lines in the metal coated SiC(SCS-6) fibers are lower than that of thepristine SiC(SCS-6) fiber. A large reduction in mean tensilefigure are determined by least-squares regression. The fiber


(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 Heat- composites. The diffusion behavior is another factor affect-Exposed Pristine and Duplex Metal Coated ing the tensile mechanical properties of the composites. Fig-

SiC(SCS-6) Fibers ure 3 shows SEM photographs of the polished transversecross section of the composites with the duplex metal coatedMean Fiber StandardSiC(SCS-6) fibers. A distinct region, which is termed anStrength Deviation

Fibers sf (MPa) (MPa) interface reaction region, is observed between the fibers andmatrix in all the composites. The region in the SiC/Cu/W/Ti-Pristine SiC(SCS-6) 4374 74115-3 is complex, and a white phase, which was determined toCu/Ta coated SiC(SCS-6) 3612 616

Cu/Mo coated SiC(SCS-6) 4220 517 be W-rich, exists within it. The thickness of the region isCu/W coated SiC(SCS-6) 3934 315 '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 valuesare '0.9 and '0.8 mm, respectively. These values are muchlower than that of the initial duplex metal coatings. Thesestrength (,17 pct) is observed for the Cu/Ta coatedphotographs show that an interdiffusion of the duplex metalSiC(SCS-6) fiber, while a significant reduction is observedcoatings and the matrix takes place during the HIP process.for the Cu/W coated SiC(SCS-6) fiber (,10 pct). The meanThe EDX elemental mappings also indicate this interdiffu-tensile strength of the Cu/Mo coated SiC(SCS-6) fiber ission behavior of Cu, Ta, Mo, W, and Ti (Figure 4). The Cu,slightly reduced (,4 pct) compared to that of the pristineTa, and Mo alloying elements diffuse into a wide area of theSiC(SCS-6) fiber, however.matrix, while Ti diffuses toward the duplex metal coatings inAlthough these duplex metal coatings are stable on indi-the opposite direction. No significant diffusion behavior ofvidual coated fibers, the interface between the coated fibersW is observed and an enriched layer of W exists near theand the matrix changes due to an interdiffusion of the coat-

ings and the matrix during the fabrication process of the fiber (Figures 3(c) and 4(c)). These results suggest that the


Fig. 4—EDX elemental distribution maps of the duplex metal coatings inthe (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 and M: matrix).

duplex metal coated SiC(SCS-6) fiber-reinforced Ti-15-3composites are shown in Figure 5. The curves show nearlythe 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-15-3composites (F: fiber, SCS: SCS coating, RL: reaction layer, and M: matrix).

interfacial reaction occurs between the fiber and matrix dur-ing the fabrication process of the composites. However, amore detailed study is needed to understand the diffusion

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

The typical tensile stress-strain curves of the pristine and


Table II. Tensile Mechanical Properties of the Pristine and reduced only slightly compared to that of the pristine fiber.Duplex Metal Coated SiC(SCS-6) Fiber-Reinforced Ti-15-3 The tensile strength of the SiC/Cu/Mo/Ti-15-3, on the other

Matrix Composites hand, is greater than that of the SiC/Ti-15-3 and coincideswith the estimated value by the ROM. Conversely, the tensileYoung’s Tensile Strain tostrength of SiC/Cu/W/Ti-15-3 is nearly the same as that ofModulus Strength FailureSiC/Ti-15-3, whereas the tensile strength of SiC/Cu/Ta/Ti-Composites Ec (GPa) sc (MPa) «c (Pct)15-3 is slightly lower than that of SiC/Ti-15-3; this is attrib-SiC/Ti-15-3 135 1392 1.14uted to the decrease in fiber strength of the Cu/Ta coated122 1259 1.23SiC(SCS-6) fibers. Our previous research suggested that theSiC/Cu/Ta/Ti-15-3 126 1301 1.21fatigue life of the composite had a tendency to increase with124 1256 1.16application of a Cu/Mo coating.[13] Although these studiesSiC/Cu/Mo/Ti-15-3 129 1534 1.44

133 1541 1.38 showed some advantages of the Cu/Mo coating, a moreSiC/Cu/W/Ti-15-3 123 1244 1.14 detailed study is needed to use the Cu/Mo duplex metal

124 1399 1.32 coating for SiC(SCS-6) fiber-reinforced Ti-15-3 alloymatrix composites.

materials, exhibiting an initial linear elastic region followedOne of the authors (SQG) to thanks the Japan Society forby a slight nonlinear stress-strain behavior. The transition

The Promotion of Science (JSPS) for its financial supportof the tensile stress-strain curve from linear to nonlinearof his research in Japan.behavior occurs at a stress level around 780 MPa and this

stress seems independent of the duplex metal coating materi-REFERENCESals, suggesting there is no effect of the diffusion near the

interface on the macroscopic yield behavior of the matrix 1. E.V. Zaretsky: Mach. Des., 1994, vol. 66, pp. 124-32.alloy. Table II summarizes the tensile mechanical properties 2. J.M. Larsen, S.M. Russ, and J.W. Jones: Metall. Mater. Trans. A, 1995,

vol. 26A, pp. 3211-24.of the composites. The mean tensile strength of SiC/Cu/Mo/3. T. Nicholas and S.M. Russ: Mater. Sci. Eng., 1992, vol. A153, pp.Ti-15-3 is about 16 pct larger than that of SiC/Ti-15-3. In

514-19.contrast, the tensile strength of SiC/Cu/W/Ti-15-3 is nearly 4. P. Martineau, P. Pailler, M. Lahaye, and R. Naslain: J. Mater. Sci.,the same as that of SiC/Ti-15-3, while that of SiC/Cu/Ta/ 1984, vol. 19, pp. 2749-70.

5. C.G. Rhodes and R.A. Spurling: in Developments in Ceramic andTi-15-3 is slightly ('4 pct) lower than SiC/Ti-15-3. TheMetal-Matrix Composites, K. Upadhya, ed., TMS, Warrendale, PA,rule-of-mixtures (ROM) estimation is used to compare the1991, pp. 99-103.mean tensile strength for each composite. The tensile

6. S.Q. Guo, Y. Kagawa, H. Saito, and C. Masuda: Mater. Sci. Eng.,strength of the composites is given by 1998, vol. A246, pp. 25-35.

7. B.S. Majumdar, G.M. Newaz, and J.R. Ellis: Metall. Trans. A, 1993,sc 5 Vfsf 1 (1 2 Vf)s 8m [1] vol. 24A, pp. 1597-1610.

8. B.S. Majumdar and G.M. Newaz: Phil. Mag. A, 1992, vol. 66, pp.where Vf is the fiber volume fraction, sf is the mean tensile 187-212.strength of the fiber (Table I), and s 8m is the tensile stress 9. S.Q. Guo, Y. Kagawa, and K. Honda: Metall. Mater. Trans. A, 1996,

vol. 27A, pp. 2843-51.of the matrix at the failure strain of composite (Figure 5).10. S.Q. Guo, Y. Kagawa, J.-L. Bobet, and C. Masuda: Mater. Sci. Eng.,The strength of both SiC/Cu/Ta/Ti-15-3 and SiC/Cu/W/Ti-

1996, vol. A220, pp. 57-68.15-3 is about 93 pct of the estimated strength. This percent- 11. B.S. Majumdar and G.M. Newaz: Mater. Sci. Eng., 1995, vol. A200,age of the ROM is slightly larger than that of the SiC/Ti- pp. 114-29.

12. S.Q. Guo, Y. Kagawa, Y. Tanaka, and C. Masuda: Acta Mater., 1998,15-3 composite (88 pct), while the tensile strength of thevol. 46, pp. 4941-54.SiC/Cu/Mo/Ti-15-3 is coincident with that of the ROM. This

13. S.Q. Guo: Ph. D. Thesis, The University of Tokyo, Tokyo, 1997.means that fiber strength potential is fully achieved in the14. X.J. Ning and P. Pirouz: J. Mater. Res., 1991 vol. 6, pp.

SiC/Cu/Mo/Ti-15-3 composite and that the low strength in 2234-48.the SiC/Cu/Ta/Ti-15-3 composite results from a decrease in 15. Smithells Metals Reference Book, E.A. Brandes, ed., printed in England

by Robert Hartnoll Ltd., Bodmin, Cornwall, 1983.the fiber strength of Cu/Ta coated SiC(SCS-6) fibers during16. H.P. Chiu, S.M. Jeng, and J.-M. Yang: J. Mater. Res., 1993, vol. 8,the fabrication process.

p. 2040.Summarizing the results, the tensile strength of the Cu/Ta 17. R.A. Naik, W.S. Johnson, and D.L. Dicus: in Titanium Aluminideand Cu/W coated SiC (SCS-6) fibers significantly decreases, Composites, P.R. Smith, S.J. Balsone, and T. Nicholas, eds., Wright-

Patterson AFB, OH, 1991, pp. 563-75.while the strength of the Cu/Mo coated SiC(SCS-6) fiber is


communications - university of...

Documents