Liquidus temperatures and solidification behavior in the copper–niobium system

Liquidus temperatures and solidification behavior in the copper–niobium system

PII: Acta mater. Vol. 46, No. 11, pp. 3849±3855, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in...

454KB Sizes 0 Downloads 39 Views

PII:

Acta mater. Vol. 46, No. 11, pp. 3849±3855, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain S1359-6454(98)00063-9 1359-6454/98 $19.00 + 0.00

LIQUIDUS TEMPERATURES AND SOLIDIFICATION BEHAVIOR IN THE COPPER±NIOBIUM SYSTEM D. LI{1{, M. B. ROBINSON1, T. J. RATHZ2 and G. WILLIAMS2 Space Sciences Laboratory, NASA/Marshall Space Flight Center, Huntsville, AL 35812, U.S.A. and 2 University of Alabama, Huntsville, AL 35899, U.S.A.

1

(Received 26 September 1997; accepted 13 February 1998) AbstractÐThe copper±niobium phase diagram has been under active debate; thus, a corroboratory experimental study is needed. In this investigation, the melts of Cu±Nb alloys at compositions ranging from 5 to 86 wt% Nb were processed in di€erent environments and solidi®ed at relatively low cooling rates of 50± 758C/s to determine liquidus temperatures and to study solidi®cation behavior. For all samples processed under very clean conditions, only Nb dendrites in a Cu matrix were observed; while in the presence of oxygen impurities, the alloys containing 5±35 wt% Nb exhibited microstructure of Nb-rich spheroids and Nb dendrites in the Cu matrix. The results obtained from clean conditions are in fair agreement with the Cu± Nb phase diagram having an S-shaped, near-horizontal appearance of the liquidus. The formation of Nbrich droplets at slow cooling rates is discussed in terms of a stable liquid miscibility gap induced by oxygen. # 1998 Acta Metallurgica Inc.

1. INTRODUCTION

There has been a considerable interest in copper alloyed with refractory metals, especially in the Cu± Nb system for its combination of good electrical and thermal conductivity and high mechanical strength. Since these excellent properties are achieved by large deformation of solidi®ed Cu±Nb billets, it has been shown [1±3] that they are not only dependent on the alloy composition and subsequent deformation strain, but also strongly in¯uenced by the solidi®ed morphology. Accordingly, the binary Cu±Nb phase diagram would be extremely useful in understanding and predicting the solidi®ed microstructures. However, due to the high melting point of Nb and its strong anity to oxygen and carbon, melt homogenization and accurate temperature measurements are very dicult. It is not surprising that at present there are two types of proposed Cu±Nb phase diagrams exhibiting an important discrepancy: a liquid immiscible characteristic [4, 5] and a ¯attened liquidus but no immiscibility [6±8], as depicted in Fig. 1. An early constructed phase diagram [4] of Cu± Nb alloys includes two temperature-invariant transformations, i.e. a monotectic at 15458C and a peritectic reaction at 10908C. About two decades later, Terekhov et al. [5] used di€erential thermal analysis (DTA) to re-examine this system and came to similar conclusions that both of the above reactions take place but the transformation temperatures are {NASA NRC Resident Research Associate. {To whom all correspondence should be addressed (Fax: 205-544-2178; E-mail: [email protected]).

slightly higher. In spite of some metallographic analysis on two compositions (5 and 35 wt% Nb) in that paper, no convincing evidence was found for the monotectic reaction since most of the specimens chosen for demonstrating microstructures were merely heated to below the liquidus. On the contrary, the familiar structure of Nb dendrites in a Cu matrix solidi®ed from above the liquidus implies that the liquid miscibility gap may be absent. Very recently, it was noted that a mistake appeared in the literature [9, 10] compiling Terekhov et al.'s phase diagram [5], involving a conversion error between wt% and at.%. Other researchers like Allibert et al. [6], Chakrabarti and Laughlin [7], Smith et al. [8], and Hamalainen et al. [11] evaluated the Cu±Nb phase diagram and thermodynamic properties, and have vindicated the assertion that a near plateau liquidus rather than a miscibility dome persists across a wide composition. There are some arguments among them, though, about the nature of the temperature-invariant reaction around 10908C, namely eutectic or peritectic at a very dilute Nb content, and uncertainties in the liquidus temperature values. A number of published studies of solidi®ed microstructures [12±17] have complemented the thermodynamic assessments of the Cu±Nb alloys. First, regarding the in¯uences of cooling rate and composition, it was observed that the niobium morphology changed from dendritic ``¯owers'' to welldispersed spheres when the cooling rate was increased or the Nb concentration was decreased [13, 14]. In addition, some insight into the e€ects of crucibles and cooling rates on the solidi®-

3849

3850

LI et al.:

THE COPPER±NIOBIUM SYSTEM

Fig. 1. The equilibrium phase diagrams of Cu±Nb. Dashed lines are from Ref. [5], solid lines from Refs [6, 7], and the small squares denote the present measurements under clean conditions.

cation behavior has been provided by Verhoeven and co-workers [1, 15]. They noticed that the appearance of Nb-rich spheroids in Cu±15 and 20 wt% Nb alloys was brought about by both rapid cooling, and the addition of 00.2 at.% O2 impurity. Relying in part on that study [15], Zeik et al. [17] utilized a high-pressure gas atomization to produce rapidly solidi®ed Cu±21Nb±2Mo (wt%) powders, and correlated the microstructures with the particle diameter. It has been shown that ®ne particles (<15 mm) were characterized by a predominance of multiphase spheroids and a small population of Nb dendrites in a Cu matrix, while large powders (45± 75 mm) contained only Nb dendrites in the Cu matrix. The former observation was attributed to the existence of a submerged miscibility gap at high solidi®cation rates. This type of metastable liquid separation has been demonstrated in similar systems such as Cu±Co [18], Co±Fe [19], and Al±Be [20] possessing a nearly ¯at liquidus and positive deviation from the Raoult's law [21], as the undercooling or cooling rates exceeded a critical value. All of the earlier work on the phase diagram and solidi®ed microstructure of the Cu±Nb system can be summarized brie¯y as follows: 1. Two con¯icting phase diagrams are encountered and it is generally assumed that the diagram of S-shaped liquidus is nearly correct, but armative temperature measurements on this system are still missing, especially under clean conditions.

2. Oxygen contamination or/and severe cooling rates are apt to cause a spheroid microstructure in the Cu-rich Nb alloys. Regarding these two aspects, further convincing studies are still awaited, including a thermal analysis on di€erent compositions and a separate study of the impurity and cooling rate e€ects on the solidi®cation mechanism. The object of this paper is to determine accurate liquidus temperatures and to examine the microstructures of the Cu±Nb alloys which could be solidi®ed both in a very clean environment and at a low cooling rate with the purpose of de®ning the correct phase diagram. 2. EXPERIMENT

Two types of experimental conditions were designed. First, all samples were prepared from 99.999% pure Cu (Angstrom Sciences) and 99.99% pure Nb (ROC/RIC) by an in situ alloying procedure. Each sample had a mass of 1.4 g and was washed with 10% HCl aq. solution before being inserted into an alumina crucible (8.0 mm internal diameter) which was placed in an induction coil connected to a Lepel RF generator. A vacuum was ®rst established to less than 2.0  10ÿ7 torr (2.7  10ÿ5 Pa). Under this high vacuum, the sample was heated to about 11008C (after Cu melted) for 5 min to evaporate water vapor and the other surface impurities. When the vacuum returned to the initial level after the in vacuo treatment, argon gas of 5N purity was introduced to a pressure of 550±

LI et al.:

THE COPPER±NIOBIUM SYSTEM

580 torr (076 kPa). Then, the sample was superheated and held between 1800 and 19508C (dependent upon the composition) for 2 min. During this period, the alloy was homogenized by electromagnetic stirring. Finally, the melt was allowed to cool spontaneously after the RF power was switched o€. The above process is termed ``clean condition'', while the following is termed ``impure condition''. The di€erence between the two conditions is that for the impure condition, experiments were performed under low vacuum, i.e. the system was roughly evacuated to 5  10ÿ2 torr (6.7 Pa) prior to back-®lling with argon gas. Under each condition, at least three samples were processed for a given composition. The temperature of the open surface of the sample was measured using a single color pyrometer (Mikron, Model M190 with resolution of 0.18) looking through a quartz viewport at the top of the chamber. The range of the pyrometer was set from 800 to 20008C and it was interfaced with an IBM/ AT computer using Labview 4.0 software. Temperatures were calibrated with an accepted invariant transformation in this system. After processing, the bulk compositions were measured by a Cameca SX50 electron microprobe through WDS (wavelength dispersive spectroscopy) quantitative analysis (30±40 point average) on the largest longitudinal section of the specimens. Nitrogen and oxygen analyses of specimens were made by Leco Corporation, St. Joseph, Missouri. The solidi®ed microstructure was examined using optical microscopy and scanning electron microscopy (SEM), either previous to or after etching in a solution consisting of HNO3:CH3COOH:H3PO4:ethyl alcohol in a 1:2:3:4 ratio. 3. RESULTS

3.1. Under clean conditions Since volatilization of the lower melting copper was evident when superheating the Cu±Nb alloys, analysis of the average composition of the solidi®ed specimens was necessary. Figure 2 describes the relationship between the nominal composition and the actual value of processed specimens determined by WDS for one set of experiments. A polynomial ®tted curve is included for showing the tendency for change. This WDS analysis composition corresponds to the specimens which underwent a single heating/cooling cycle. Based on this relationship, the composition variation could be estimated as the same processing variables were applied during the experiment. The real compositions of solidi®ed samples were adopted in the reporting of the results. Figure 3 contains (a) a measured uncorrected temperature±time pro®le and (b) a calibrated pro®le for a Cu±15 wt% Nb sample. For clarity the curves

3851

Fig. 2. The correlation between nominal composition before processing and actual composition after solidi®cation.

were shifted along the time axis. During heating, two thermal arrests appeared on the temperature± time pro®le. After melting was complete, the sample was overheated to about 19008C. It can be seen from the cooling pro®le that two solidi®cation events happened across a relatively large temperature gap. The ®rst arrest on the cooling curves, which is roughly at 17008C in Fig. 3, re¯ects the beginning of primary phase solidi®cation. The plateau at the lower temperature indicates a temperature-invariant reaction. For noncontact measurement techniques, the apparent temperatures are usually not identical to the true values since the spectral emissivity data for high-temperature liquid are not available in most cases. But the true temperature of a real surface, T in K, can be calculated from the measured apparent temperature, Ta in K, using the following equation [22]: 1=T ˆ 1=Ta ‡ C

…1†

where C can be assumed a constant. Previous studies on the Cu±Nb system have found that there is

Fig. 3. Temperature±time pro®les for a Cu±15 wt% Nb specimen processed under clean conditions. (a) Apparent temperatures, (b) calibrated temperatures.

3852

LI et al.:

THE COPPER±NIOBIUM SYSTEM

Fig. 4. A set of cooling curves for specimens undergoing a clean environment. The numbers among the curves stand for the Nb content in wt%.

a temperature-invariant transformation around 1080±10958C, regardless of whether it is a peritectic or eutectic. Striking an average over Refs [8, 11], this temperature is set at 10918C in this paper. From this calibration point, the temperature curves can be corrected, as shown in Fig. 3(b). A series of corrected cooling curves of the Cu±Nb melts at di€erent compositions are illustrated in Fig. 4. Owing to the similar processing condition, the cooling rate only varied between 50 and 758C/s. With increasing Nb content, a small amount of undercooling was achieved, thus leading to a recalescence. For Cu±86 wt% Nb, the undercooling is 60 K in the presence of the crucible. The ®rst thermal arrest temperatures (or the recalescence peak temperatures on slightly undercooled samples) were used to determine liquidus temperatures. Alloy compositions and the corresponding liquidus temperatures are listed in Table 1. Each liquidus temperature represents the assessed results of several measurements, and are also supported by melting data derived from the heating curves. The measured liquidus temperatures (small squares in Fig. 1) are plotted on the Cu±Nb phase diagram. The present liquidus temperatures agree well with the values of the S-shaped diagram which was ®rst established by Allibert et al. [6]. The experimental values cannot be ®tted to the dashed line diagram containing the monotectic reaction. In the SEM or optical microscopy studies of all Cu±Nb specimens processed under very clean conditions, there was no evidence for any solidi®ed microstructure other than Nb dendrites in a nearly Table 1. Composition and liquidus temperature TL for the Cu±Nb alloys Nb (wt%) 5.0 8.1 12.0 15.0 21.6 26.0

TL (8C)

Nb (wt%)

TL (8C)

1380 1520 1596 1658 1668 1670

35.0 40.2 50.0 55.5 68.6 86.0

1675 1688 1718 1728 1765 1848

Fig. 5. Optical micrographs of (a) Cu±15 wt% Nb and (b) Cu±55.5 wt% Nb alloys processed under clean conditions.

pure Cu matrix. The dissimilarities among the specimens of various compositions lie only in the dendrite size and the volume fraction of dendrites which both clearly tend to increase with the increasing concentration of Nb. Two representative micrographs are provided in Fig. 5. On both the cross section and the longitudinal section of the specimens, the Nb dendritic morphology has been observed. Because of the low cooling rates in this study, it can be considered that the Nb dendrites were primarily formed under near equilibrium conditions. Therefore, the present results from samples processed under clean conditions con®rm the phase diagram of an S-shaped liquidus in Fig. 1. 3.2. Under impure conditions As has been previously pointed out [9], the solidi®cation pathway of this system is very sensitive to processing variables such as oxygen content and cooling rate. Since chill casting or gas atomization

LI et al.:

THE COPPER±NIOBIUM SYSTEM

3853

spherical Nb-rich particles from 8 to 80 mm in diameter emerged in the Cu matrix for the 5±35 wt% Nb alloys, as presented in Fig. 6(a) and (b) for 12 and 15 wt% Nb specimens, respectively. These Nbrich spheres consist of some Cu; for instance, there are 75 wt% Nb and 25 wt% Cu within a spheroid arbitrarily selected from a bulk sample of Cu± 15 wt% Nb, as determined by WDS. The spheres are usually composed of an outer shell of Nb and an interior which is a two-phase mixture of Cu (bright phase) and Nb (dark), as illustrated at a high magni®cation in Fig. 6(c). It can be seen that the dendrites of nearly pure Nb have nucleated and grown from the Nb shell, the crucible walls, or other nucleation sites within the melts, indicating that the Nb shells have solidi®ed before the Nb dendrites. For alloy compositions over 35 wt% Nb, no droplet-shaped microstructure has been found, even though more oxygen impurity was added. 4. DISCUSSION

Fig. 6. Microstructures of (a) Cu±12 wt% Nb (etched), (b) Cu±15 wt% Nb alloys solidi®ed under impure conditions. (c) SEM micrograph of one of the spheroids in specimen (b). The bottom of picture (a) shows an interface between alloy and crucible.

techniques characteristic of fast cooling were utilized in previous studies [15, 17], the resulting microstructures may be ascribed to the two conspiring e€ects of cooling rate and impurity. Hence, another set of experiments was performed to isolate the impurity e€ects from the cooling rate e€ects and to examine the microstructure transition. In this case, some oxygen was intentionally left in the chamber (the so-called impure condition). A striking e€ect of oxygen impurity can be noticed by examination of solidi®ed microstructures: aside from Nb dendrites,

Liquidus temperatures of the Cu±Nb system have been measured using a noncontact method in which the absolute temperature was calibrated by a known invariant reaction at 10918C. The reproducibility of liquidus apparent temperature measurements were found to be 25 for the invariant reaction and 2158C for the liquidus for a given composition, respectively, which leads to an absolute error of <2158C in true liquidus temperature. For alloy compositions below 15 and above 70 wt% Nb, the liquidus temperatures reported herein are slightly lower than the values of Allibert et al.'s phase diagram, while they are in nice accord with each other for compositions between 15 and 70 wt% Nb (Fig. 1). This is interpreted as follows: owing to a great disparity between the melting points, the mass loss of Cu was signi®cant (up to 30% for a nominal composition of Cu±80 wt% Nb) after processing. However, this composition variation has not been taken into account in previous studies during construction of the Cu±Nb phase diagram. Fortuitously, in the range of 15±70 wt% Nb, the liquidus of Allibert et al.'s phase diagram exhibits a relatively weak dependence of temperature on composition, which means that some change in Nb content will not lead to a remarkable impact on the liquidus temperature. Although alumina crucibles were used and wetted by the Cu±Nb melts, it appeared that there was not a signi®cant chemical reaction between them. After processing under clean conditions, the specimens could be readily separated from the crucibles and yielded a clean, smooth surface. Moreover, chemical analysis revealed that oxygen content of the samples processed in this clean atmosphere is only somewhat higher than that of the ``starting materials''. For example, the solidi®ed Cu±15 wt% Nb specimens contained an oxygen content of 680 p.p.m.,

3854

LI et al.:

THE COPPER±NIOBIUM SYSTEM

Table 2. Oxygen and nitrogen contents (p.p.m. weight) of the starting metals (Cu and Nb) and Cu±15 wt% Nb specimens solidi®ed under di€erent conditions (clean and impure) Cu Oxygen Nitrogen

618 1

Nb

Clean

430

680 2

Impure 2800 2

while the starting copper contained 618 p.p.m., as seen in Table 2. This oxygen content in the resulting alloys is also equivalent to the reported value [15] in an ingot of Cu±20 wt% Nb where the Y2O3 stabilized ZrO2 crucibles were used and thus no large spheroids were formed. On the other hand, the microstructural observations of this work's samples processed under clean conditions have clearly demonstrated that solidi®cation proceeded with the growth of primary Nb dendrites. Equilibrium solidi®cation of the binary Cu±Nb system was closely approached in this work by using a slow cooling rate and a clean environment, consequently supporting Allibert et al.'s proposed phase diagram [6]. From the above discussions, a monotectic reaction on the binary Cu±Nb phase diagram is not expected. However, a ¯attening of the liquidus across a wide composition in this system will give rise to a strong tendency for immiscibility, resulting from a positive excess Gibbs free energy of the liquid. According to its analytical form for the binary alloys, the free energy of mixing of the liquid at undercooled temperatures could be calculated. Below a certain undercooling, the curves of free energy will exhibit two negative humps from which the metastable binodal points are obtained graphically by the common tangent method. For alloys of Cu±10±35 wt% Nb, the calculated metastable liquid immiscibility boundary is approximately 1008C below the equilibrium liquidus. By means of containerless processing in the 105 m NASA drop tube [23] or rapid cooling techniques such as gas atomization [17] (cooling rate of the latter up to 105 8C/s), undercoolings of this order have been readily accessed. This undercooling results in the separation of the melt into two liquids and then in the formation of spherical droplets of Nb-rich liquid embedded in a matrix of the other. However, the appearance of Nb-rich spheroids under both impure conditions and at slow cooling rates probably originates from another mechanism besides undercooling, such as the formation of a stable liquid miscibility gap within the Cu±Nb±O ternary system [15, 17]. By contrast with the results from a clean environment, the oxygen concentration of Cu±15 wt% Nb specimens undergoing the impure condition process is up three-fold, as seen in Table 2. This concentration is well beyond the oxygen level for the microstructural transition from Nb dendrites to Nb-rich spheroids. The Leco combustion analysis also shows that there is a very low

content of nitrogen among the di€erently processed samples. Therefore, it can be concluded that the Nb-rich spheroids observed in this paper are induced by oxygen. Data which indicate a correlation of the observed droplet-shaped microstructure with the recorded cooling curves have not yet been compiled. For the alloys (Cu±5±35 wt% Nb) processed under impure conditions, microstructural Nb-rich spheres were found; nevertheless, the cooling curves did not di€er as much from the specimens solidi®ed in the clean environments. The reason is probably that the temperature change caused by the enthalpy of demixing is too small to be detected by the pyrometer. Another type of cooling curve was recorded under impure conditions, as illustrated in Fig. 7. When the content of Nb was higher than 35 wt%, the solidi®cation path was presumed to enter the hypomonotectic composition. There are three solidi®cation events corresponding to the slope change of the cooling curves, and the most likely paths for solidi®cation are as follows. First, the homogeneous melt was slightly undercooled from which the b.c.c. Nb phase was primarily grown and responsible for a small recalescence. Secondly, a short plateau at around 17008C indicates the possibility of a temperature-invariant reaction. Coupled with previous work, this is assumed to be monotectic and due to the oxygen involvement. These cooling curves were generated under conditions similar to those used for previous DTA measurements [5] which could account for the Cu±Nb phase diagram containing a monotectic reaction. Finally, a relatively long plateau at 10918C arises from the second invariant solidi®cation of a dilute Cu±Nb liquid (<0.5 wt% Nb). Concerning the solidi®cation microstructure of alloys containing more than 35 wt% Nb, no spheres with distinct boundaries were observed regardless of the processing circumstances. For these alloys, relatively large amounts of Nb-rich liquid will be pro-

Fig. 7. Typical cooling curves of Cu±40.2 and 55.5 wt% Nb alloys processed under impure conditions. The short plateau at around 17008C suggests a monotectic reaction.

LI et al.:

THE COPPER±NIOBIUM SYSTEM

duced when the phase separation occurs, thus leading to a less sharply de®ned boundary between the spheres and the Cu matrix. Of course, as the content of Nb is increased to the range of hypomonotectic, no droplet structure will be formed.

5. CONCLUSIONS

Liquidus temperature measurements and solidi®ed microstructure analyses on the Cu±Nb system have been carried out. The results point to the fact that the solidi®cation pathway of this system is contingent upon processing conditions. For the alloys of Cu±5±86 wt% Nb processed in a very clean environment (oxygen content is only 680 p.p.m., for example, in Cu±15 wt% Nb), niobium dendrites in a copper matrix are formed without exception. Combining the presence of microstructures with the temperature data, the equilibrium phase diagram of an S-shaped liquidus has been con®rmed to be correct, rather than that with a miscibility gap in the liquid state. However, there is an alternative mechanism for solidi®cation of this system. When the specimens were processed under impure conditions (O level amounts to 2800 p.p.m. in the resulting samples), observations have been made of spherical structures solidi®ed in alloys from 5 to 35 wt% Nb and of a short thermal plateau appearing on the cooling curves for alloys above 35 wt% Nb. This has been explained by a suggestion that an equilibrium liquid miscibility gap exists within the Cu± Nb±O ternary system.

AcknowledgementsÐThis work was performed while one of the authors (D.L.) held a National Research Council± (NASA MSFC) Research Associateship. The authors also thank H. Alexander and G. Jerman for composition analyses, and R. Grugel for stimulating discussions.

3855

REFERENCES 1. Verhoeven, J. D., Spitzig, W. A., Schmidt, F. A. and Trybus, C. L., Materials & Manufacturing Processes, 1989, 4, 197. 2. Ellis, T. W., Anderson, I. E., Downing, H. L. and Verhoeven, J. D., Metall. Trans., 1993, 24A, 21. 3. Spitzig, W. A., Pelton, A. R. and Laabs, F. C., Acta metall., 1987, 35, 2427. 4. Prokoshkin, D. A. and Vasil'eva, E. V., Alloys of Niobium. Daniel Davey, New York, 1965, p. 129. 5. Terekhov, G. I. and Aleksandrova, L. N., Russ. Metall., 1984, 4, 218. 6. Allibert, C., Driole, J. and Bonnier, E., C. R. Acad. Sci. Paris Serie C, 1969, 268, 1579. 7. Chakrabarti, D. J. and Laughlin, D. E., Bull. Alloy Phase Diagrams, 1982, 2, 455. 8. Smith, J. F., Lee, K. J. and Bailey, D. M., Bull. Alloy Phase Diagrams, 1984, 5, 133. 9. Chakrabarti, D. J. and Laughlin, D. E., in ASM's Binary Alloy Phase Diagrams on CD-ROM, 2nd edn. ASM International, 1996. 10. Okamoto, H., J. Phase Equilibria, 1991, 12, 614. 11. Hamalainen, M., Jaaskelainen, K., Luoma, R., Nuotio, M., Taskinen, P. and Teppo, O., Calphad, 1990, 14, 125. 12. Tsuei, C. C., J. appl. Phys., 1974, 45, 1385. 13. Fihey, J. L., Nguyen-Duy, P. and Roberge, R., J. Mater. Sci., 1976, 11, 2307. 14. Roberge, R. and Fihey, J. L., J. appl. Phys., 1977, 48, 1327. 15. Verhoeven, J. D. and Gibson, E. D., J. Mater. Sci., 1978, 13, 1576. 16. Verhoeven, J. D., Spitzig, W. A., Schmidt, F. A., Krotz, P. D. and Gibson, E. D., J. Mater. Sci., 1989, 24, 1015. 17. Zeik, K. L., Koss, D. A., Anderson, I. E. and Howell, P. R., Metall. Trans., 1992, 23A, 2159. 18. Munitz, A. and Abbaschian, R., Metall. Mater. Trans., 1996, 27A, 4049. 19. Drbohlav, O., Botta Filho, W. J. and Yavari, A. R., Mater. Sci. Forum, 1996, 225±227, 359. 20. Elmer, J. W., Aziz, M. J., Tanner, L. E., Smith, P. M. and Wall, M. A., Acta metall. mater., 1994, 42, 1065. 21. Pelton, A. D., in Physical Metallurgy, ed. R. W. Cahn and P. Haasen. Elsevier Science/North-Holland, Amsterdam, 1996, p. 472. 22. Anderson, C. D., Hofmeister, W. H. and Bayuzick, R. J., Metall. Trans., 1993, 24A, 61. 23. Li, D. and Robinson, M. B., The NRC Progress Report, 1997 (unpublished).