EPM method of synthesizing intermetallics based on Ti

EPM method of synthesizing intermetallics based on Ti

Materials Science and Engineering A329– 331 (2002) 50 – 56 www.elsevier.com/locate/msea EPM method of synthesizing intermetallics based on Ti H.S. Pa...

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Materials Science and Engineering A329– 331 (2002) 50 – 56 www.elsevier.com/locate/msea

EPM method of synthesizing intermetallics based on Ti H.S. Park a, K.L. Park b, S.K. Hwang a,c,* a

Di6ision of Materials Science and Engineering, Inha Uni6ersity, Incheon, 402 -751, South Korea b Shinhan Diamond Industrial Co. Ltd., Incheon, 405 -100, South Korea c Center for Ad6anced Aerospace Materials, POSTECH, Pohang, South Korea

Abstract Elemental powder metallurgy (EPM) is a powerful means of synthesizing intermetallics of high melting points. In this study, two intermetallic compounds based on Ti were investigated using different consolidation techniques: TiAl– Mn– Mo– C by hot extrusion and Ti5Si3 –Nb–C by electro-pressure sintering (EPS). Full density compounds were obtainable in both cases. Aided by interstitial carbon atoms, each intermetallic compound showed attractive mechanical properties such as high tensile yield strength and creep resistance in TiAl–Mn–Mo–C and high fracture toughness and transverse rupture strength in Ti5Si3 –Nb–C. The roles of carbon atoms, being less than 1 at.% in each material system, were, refinement of the lamellar microstructure and precipitation hardening in the former, and a possible modification of the crystal structure towards easier slip and less thermal anisotropy in the latter. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Intermetallics; Elemental powders; Extrusion; Sintering; Microstructure; Tensile properties; Carbon effect

1. Introduction Elemental powder metallurgy (EPM) is an efficient processing technique to produce intermetallic compounds difficult to cast due to the high melting point and high reactivity. The method has been successfully applied to Ni3Al-base compounds and TiAl-base compounds [1,2]. In both cases, high temperature direct extrusion was adopted as the consolidation technique. In the TiAl case, an experimental alloy composition of Ti – 51.3Al –1.5Mn – 2.2Mo alloy was developed by the present authors through the EPM technique. From the alloy design standpoint, a microstructural refinement — particularly that of the lamellar structure — is necessary to render desirable mechanical properties such as fracture toughness in the alloys consisting of g and a2 [1,2]. To optimize desired mechanical properties, therefore, it is essential to control the size of lamellar colonies and individual lamellae. A considerable amount of alloy design effort has been devoted to fine-tuning the specific traits of the lamellar structure, the interlamellar spacing being a crucial parameter [3,4]. In this respect, the role of interstitial alloying elements draws much * Corresponding author. E-mail address: [email protected] (S.K. Hwang).

attention since they can reduce the interlamellar spacing quite effectively. Despite the interesting effect reported in recent literature, however, the cause of microstructural refinement by interstitial elements in gamma TiAl alloys is not well understood. In Ti –Si system, monolithic Ti5Si3 has a mixture of covalent bonding, metallic bonding and ionic bonding, which results in a high melting temperature (2130 °C) and a low density (4.32 g cm − 3). The high temperature strength, creep resistance, oxidation resistance and wear resistance of Ti5Si3 are cited as the merits for elevated temperature applications [5]. For the case of Ti5Si3 the technique of consolidation must be different from that for TiAl because of difficulty in extrusion, mainly due to the high melting point. Frommeyer et al. [6] successfully synthesized a bulk-form Ti5Si3 by hot-isostatically pressing pre-alloyed powder. In the EPM approach, however, despite many attempts based on reactive sintering [7], consolidation was hampered by serious porosity. Recently it was found that electro-pressure sintering (EPS) can be a potentially viable route for consolidation of this material. The main purpose of the present work was to develop a viable EPM alloy development route, specifically the proper consolidation method, for producing the two structurally important Ti-base intermetallic

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compounds. For the case of TiAl, hot extrusion was adopted for the consolidation step in utilizing interstitial carbon atoms to refine the lamellar microstructure of Ti – 51.3Al–1.5Mn – 2.2Mo. For the case of Ti5Si3, the objective the research was to synthesize Ti5Si3-base intermetallic compounds with a near full density and high fracture toughness by employing alloying elements like Nb and C.

2. Experimental procedure Two groups of Ti-based intermetallic alloys were studied, TiAl and Ti5Si3. The nominal compositions of the TiAl group were Ti– 46.6Al – 1.4Mn – 2Mo and Ti– 46.6Al–1.4Mn–2Mo – 0.3C. The nominal compositions of the Ti5Si3 group were designed on the basis of (Ti1 − x Nbx )5Si3Cy with x and y varying at 0, 0.05, 0.1, 0.15 and at 0, 0.1, 0.3 and 0.5, respectively. A total of 16 compositions were prepared. The procedure to make TiAl-base compounds from elemental powders is described elsewhere [8]. For consolidation, either direct hot extrusion or indirect hot extrusion was conducted. For Ti5Si3-base compounds, elemental powders of Ti and Si were of 99.8% in purity and 12.5 and 6.5 mm, respectively, in the average particle size. The average particle sizes of Nb and C were 80 and 6.3 mm, respectively. Elemental powder mixtures were milled in an attritor filled with ethanol for 6 h. Stainless steel balls of 4.75 mm in diameter and 35 times the weight of powder were used for milling the powder mixtures. Milled powders were sieved and dried for 24 h in oven. Dried powder aggregates were further milled in a tubular shaker mixer for 30 min in argon atmosphere, which yielded powders of 37 mm in the average particle size. Using a double-piston compacting machine, the mixed powders were cold-compacted into round buttons and square rods. Under a compaction pressure of 700 MPa, specimens weighing about 10 g and with a relative density of 60% of the theoretical were obtained. The optimum condition of EPS was found to be 1200 °C/82 MPa/150 s. To ensure consolidation without undesirable reaction such as fire and explosion it was crucial to increase the temperature and the external pressure gradually. For this purpose, a stepwise enhancement of the two processing variables was used in the present study. Density of specimens was measured using the Archimedes’ method. Micro-Vickers hardness of consolidated specimens was measured with an applied load of 200 g. Tensile testing was conducted at room temperature as well as elevated temperatures in air using rod-shape specimens of 16 mm in gage length and 4 mm in gage diameter. A strain rate of 1× 10 − 3 s − 1 was employed during tensile testing. The fracture toughness (KIC) was measured by an indentation

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method under a load of 2 kg applied for 15 s, according to the procedure of JIS R1607/IF. For the evaluation of micro-hardness and KIC, five measurements were conducted for each specimen from which an average value was obtained. Transverse rupture strength (TRS) was measured by a three-point bend test using a universal testing machine (Zwick Z100 UTM) according to the procedure of ASTM B406 under a cross head speed of 0.5 mm min − 1. For the bend test, parallelepiped-shape specimens of 5.0× 8.3 mm in cross section and 27.8 mm in length were used. Transmission electron microscopy (TEM) was conducted with the maximum accelerating voltage of 200 kV using samples made by dimple grinding and ion milling. Scanning electron microscopy (SEM) was conducted at an operating voltage of 25 kV. X-ray diffraction analysis was conducted using a CuKa target under an acceleration condition of 40 kV and 25 mA with a scanning rate of 0.04° s − 1. Energy dispersive spectroscopy (EDS) analysis was conducted in SEM under accelerated voltage of 20 kV with 180 mm by 120 mm in the analysis spot size1.

3. Results and discussion

3.1. Microstructure-refining effect of carbon in TiAl –Mn –Mo alloy In order to determine the correct heat treatment procedure, the transformation characteristics of TiAl– Mn –Mo alloy as affected by C addition were studied. During a differential thermal analysis, C addition was found to decrease the a“ a+ g transformation temperature, Ta, slightly, from 1367 to 1361 °C at 0.3% carbon addition. This result was confirmed by optical microscopy of specimens heat treated at various temperatures in the a field and the a+g phase field. A heat treatment at 1364 °C for 1h followed by air cooling resulted in a near lamellar (NL) microstructure in Cfree Ti–51.3Al–1.5Mn–2.2Mo alloy but a fully lamellar (FL) microstructure in Ti–51.2Al–1.5Mn– 2.2Mo– 0.3C alloy, which demonstrated the a-stabilizing effect of C in gamma TiAl alloy. The effect of carbon addition on the transformation characteristics was also studied in terms of the transformation kinetics. An isothermal heat treatment was designed to study the transformation kinetics as follows, 1400 °C/1 h + (1100, 1200, 1300 °C)/(0, 20, 40, 80, 120, 160 s)/WQ. Direct cooling from 1400 °C (0 s at 1200 °C) resulted in equiaxed a2 that retained the characteristics of

1 All concentrations in this paper refer to atomic percent unless stated otherwise.

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the high temperature a phase except for the difference in the ordered crystal structure. Upon holding for 40 s at 1200 °C, however, a massive microstructure appeared with irregularly undulated grain boundaries. Fibrous transformation products found in local areas are thought to be the g phase transformed from the high temperature a during holding at 1200 °C. Plateshape g phases as well as equiaxed g phase at prior a grain boundaries started to appear during 80 s of holding, the former morphology seemingly emanating from the latter. The whole microstructure closely resembled a Widmanstatten microstructure. A lamellar microstructure was first observed in the specimen heat treated for 120 s at 1200 °C, and an FL microstructure upon 160 s of holding. Details of the FL microstructure were studied in the two experimental alloy compositions, the base and the carbon-added, by varying the cooling rate subsequent to a high temperature a-phase heat treatment at 1400 °C. Three different cooling rates were employed: air cooling (AC), 200 °C min − 1 and furnace cooling (FC). The grain size, more specifically the size of FL colony, was uninfluenced by C-addition under all heat treatment conditions. However, the grain size increased with slow cooling regardless of C presence in alloy composition, 70, 100 and 150 mm corresponding to AC, 200 °C min − 1 and FC, respectively. C-addition on the other hand, resulted in a significant reduction of lamellar thickness. The thickness of a2 and g in the lamellar structure were measured by TEM in the specimens cooled from 1400 °C at a rate of 200 °C min − 1. Carbon-addition clearly reduced the thickness of the lamel-

Fig. 1. Carbide precipitation at the lamellar boundaries of TiAl – Mn–Mo alloy.

lae, from the average of 141 to 68 nm for g, and from the average of 53 to 25 nm for a2. Carbides were found in the specimens containing 0.3% carbon. Two different types of carbide morphology were identified: globular type and lenticular type. While the globular type carbides were found along prior a grain boundaries the lenticular carbides were observed at a2/g lamellar interface. Typical TEM images of the two different carbides are shown in Fig. 1. The microstructure in Fig. 1 was obtained by an aging heat treatment of 800 °C/12 h/AC subsequent to 1400 °C/1 h/AC solution heat treatment. In both cases, the carbides, approximately 100× 20 nm in size, were identified as Ti3AlC of Perovskite structure (P-phase). It is noted in Fig. 1 that carbides formed at prior a grain boundary from which the lamellar phase also nucleated. The apparent nucleation site of g-lamellae was found by EDAX to have higher C concentration than other areas. In fact the C concentration along prior a grain boundaries showed regular peaks. The cause of the lamellar structure refinement by carbon addition was contemplated. First, carbon addition increased nucleation rate of the lamellar plates by two independent mechanisms, lowering the stacking fault energy [9] and providing heterogeneous nucleation sites. Grain boundary carbides and interlamellar carbides formed as shown above constitute a good evidence for the promoted heterogeneous nucleation sites. Reduction of the stacking fault energy promotes homogeneous nucleation rate of the lamellar plates because the plates are believed to originate from the lattice plane faults. Secondly, the carbon addition is expected to reduce the growth rate of the lamellar plates by segregating at the lamellar interface. At present there is only weak experimental evidence to support this hypothesis. As stated above, the EDS analysis of a grain boundary region showed a periodic distribution of carbon, indicating some form of carbon segregation. The amplitude of the periodic distribution close to the interlamellar spacing. High temperature tensile properties of the experimental TiAl-base alloys were improved by C addition as shown in Fig. 2. The most significant effect of C was enhancement of the yield strength at all temperature range of testing. All the experimental alloys maintained good yield strength up to 800 °C. Moreover all the experimental alloys showed a yield strength anomaly at about 800 °C. In terms of the anomalous strength increment, the difference between the peak strength and the minimum strength, the carbon-containing alloys showed greater anomalous strengthening than the base composition. Among the carbon-containing alloys, the anomalous strengthening peaked at 0.3% C, reaching to an average of 700 MPa at 800 °C. Also shown in Fig. 2 are the yield strengths of other TiAl-base alloys reported in the literature. The level of the yield strength

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Fig. 2. Tensile properties of TiAl –Mn–Mo– C alloy directly extruded and stabilization heat treated, yield strength.

of the present carbon-containing alloys is comparable with that of more complicated composition, for example, Ti–46Al–2Cr – 1.8Nb – 0.2W – 0.15B [10]. Interestingly, the strengthening effect of carbon peaked at 0.3% C thereby resulted in an enhancement of the room temperature yield strength over that (527 MPa) of carbon-free alloy by 83 MPa. Tensile elongation of experimental alloys, on the other hand, was unaffected by carbon addition. An abrupt brittle-to-ductile transition occurred at approximately 800 °C. The transition temperature also was not influenced by carbon addition. Fracture characteristics of the two alloys were essentially same at all test temperatures. A fibrous teartype fracture with limited ductility was predominant during room temperature testing. Apparently, the ductility of the room temperature test specimens originated from fine-scale secondary cracking along interlamellar boundaries. In addition to these interlamellar secondary cracks, brittle-type transgranular secondary cracks were also found. The brittle secondary cracking showed no tertiary branching. Specimens tested at temperatures above the brittle-to-ductile transition showed severely deformed fracture surface with significantly increased ductility. The fracture surfaces retained the same interlamellar microcracking features of the room temperature fracture surface. However, the microcracks showed some degree of plastic deformation and brittle secondary cracks were not observed. The creep resistance of the experimental TiAl-base

alloys was also improved by C addition as shown in Fig. 3. Carbon addition suppressed the primary creep strain and the secondary creep rate as well, thus increasing the creep rupture life of the alloy. The beneficial effect of carbon was proportional to the amount of carbon added; in terms of suppressing the early-stage strain within the primary creep regime, however, 0.3% C addition was most effective.

Fig. 3. Effect of carbon on the creep resistance of TiAl – Mn–Mo alloy, directly forged and stabilization heat treated, entire creep range.

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Fig. 4. Relative density of Ti5Si3 –Nb–C alloy as a function of C and Nb content.

Fig. 5. Fracture toughness of Ti5Si3 –Nb–C alloy as a function of C and Nb content.

3.2. Effects of C and Nb on the consolidation characteristics of Ti5Si3 alloy For poreless densification of the Ti5Si3-base alloy from the elemental powder compact, it was crucial to optimize the EPS process variables. Many trial and errors were made prior to successful densification of experimental specimens. The major obstacle for densification was the porosity induced by an explosive reaction among elemental powder particles. Rapid heating occurred through a synergistic effect of the exothermic reaction heat among elemental powders in addition to the external heat applied to the EPS apparatus. The exothermic reactions during heating were reported to be most active at two temperatures, 630 and 760 °C [11,12]. Attempts to control the reaction rate by varying the average particle size of powders, the mixing time in

the attritor or the temperature and pressure of EPS were all unsuccessful. The most effective means of controlling the reaction rate was to decrease the heating rate, particularly near 800 °C, to 80% of the maximum rate, which was done by manually controlling the power input unit. In this way, a heating rate as low as 2.5 °C s − 1 was obtained which resulted in satisfactory densification. The optimum heating rate was somewhat lower than what was obtained in the stress-free reactive sintering by the present author [8]. In the samples containing Nb, Ti5Si3 phase as well as extra phases formed. Through XRD analysis, it was confirmed that these extra phases were either carbides or unknown Nb-rich phases. All the consolidated alloys had high relative densities as shown in Fig. 4. For several cases, a positive deviation from 100% occurred, which was presumably caused by adopting the unit cell volume of Ti5Si3 as the standard for calculation. In most specimens, relative densities higher than 95% of the theoretical were obtained. Also, by microscopy, it was confirmed that porosity in specimens was insignificant. Therefore, it was concluded that the present EPS method, starting from elemental powders, yielded Ti5Si3-base compound of a near full-density. Carbon addition decreased the density of the compounds regardless of their Nb content. Assuming no change in crystal structure, the density would not have decreased if carbon atoms were present as interstitial solid solutes. Therefore, the density decrease was attributed to carbon atoms participating in forming a third phase such as carbide, which was confirmed by SEM analysis. All the Nb-containing compounds showed lower densities than that of Nb-free Ti5Si3 –C, which indicates that Nb promoted carbide precipitation. Besides, isolated regions enriched with Nb were found in the (Ti(1 − x)Nbx )5Si3Cy alloy. The hardness of experimental alloys showed an interesting dependence on the carbon content. Monolithic Ti5Si3 showed a micro-Vickers hardness of 1367 whereas that of the compound with additional alloying elements varied from 1242 to 1430. In the absence of carbon, the hardness of (Ti0.9Nb0.1)5Si3 and (Ti0.85Nb0.15)5Si3 were higher than that of Ti5Si3. In these two compositions, however, the hardness decreased appreciably with carbon addition. For the compositions of Ti5Si3 and (Ti0.95Nb0.05)5Si3, the hardness was unaffected by carbon addition. In contrast to the case of hardness, the fracture toughness of most alloys consistently increased with carbon addition. The fracture toughness of the sixteen Ti5Si3 –Nb –C compositions is shown in Fig. 5. The fracture toughness of the present experimental materials was in the range of 5–12 MPa m, which is higher than what have been reported in the literatures [13–15] or than the value earlier obtained by the present authors using direct hot processing of elemental powder

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mixtures [16]. The major reasons for the toughness improvement were, poreless densification by the EPS process and the beneficial effects of the alloying elements. Carbon addition also resulted in an enhancement of the TRS. Monolithic Ti5Si3 specimens showed little ductility in the testing. The highest TRS of 329MPa was obtained in Ti5Si3 – 3.62at.% C composition. Nbaddition into this composition decreased TRS but the decrement was not proportional to the Nb content. Adding 6.02at.% Nb was least harmful but the less or the more Nb addition resulted in a significant reduction of TRS. The beneficial effect of carbon on the fracture toughness as well as the TRS of Ti5Si3 was attributed to the crystal symmetry. Being D88 structure, monolithic Ti5Si3 suffers from the brittleness caused by the lack of crystal symmetry. The inherent cleavage energy of each crystal plane in the monolithic Ti5Si3 was calculated recently by Zhang and Wu [17]. From this calculation the authors concluded that the cleavage energy could be increased by stoichiometric alloying with Nb or Cr due to increased bonding energy. Enhancement of the KIC value from 5 to 7–9.5 MPa m was obtained by an addition of Nb at 0% C, which agrees with the rationale. The beneficial effect of carbon addition in KIC value was attributed to the anisotropy in the thermal expansion coefficient as follows. Brittle cracks may also originate from thermal strain due to difference in thermal expansion coefficients —along the a-axis and the c-axis —of the hexagonal unit cell. According to Thom et al. [18] monolithic Ti5Si3 shows a severe anisotropy in the thermal expansion coefficient: 8.7× 10 − 6 K − 1 along the a-direction versus 20.4×10 − 6 K − 1 along the cdirection. As an interstitial solute element, carbon is expected to reduce the thermal anisotropy [18]. In case of Ti5Si3C0.85, the difference in the thermal expansion coefficients along the two directions was reduced to 8.5× 10 − 6 K − 1 as compared with 11.7 ×10 − 6 K − 1 in the monolithic Ti5Si3. It is also possible that carbon addition promoted dislocation glide in this type of material [19]. From the microstructure point of view, the effects of the alloying elements, Nb and C, on the mechanical properties of Ti5Si3 could in part be attributed to macroscopic presence of soft phases. As mentioned above, extra phase other than Ti5Si3 was not clearly identifiable by XRD due to overlapping peaks. By microscopy, however, the extra phases were clearly visible. Intermediate phases formed a shell-like feature, the content of Nb increasing from the outer rim toward the core. Based on EDS analysis of the chemical composition, it was surmised that Nb-rich core phase was Nb5Si3. The hardness of the Nb-rich phase

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was lower than that of the matrix Ti5Si3 phase by about 24%.

4. Conclusions From the present study of EPM processed intermetallic compounds based on TiAl and Ti5Si3 the following conclusions were made, carbon addition in Ti –51.3Al–1.5Mn–2.2Mo alloy considerably reduced the lamellar thickness as well as the interlamellar spacing of the FL microstructure. The mechanism of the microstructural refinement originates from enhanced heterogeneous nucleation rate and suppressed lamellae growth rate. At 0.3 at.%, carbon addition in this alloy increased the tensile yield strength and creep resistance of the alloy significantly without sacrificing the tensile ductility. The primary causes of strengthening were the microstructural refinement and precipitation hardening by Ti3AlC precipitates. Near-full-density compounds of Ti5Si3 –Nb –C as large as 25 mm in diameter and 5 mm in height were obtained by EPS processing of elemental powder mixtures. Carbon addition in this alloy improved the fracture toughness, TRS and the oxidation resistance of monolithic Ti5Si3. At 3.6at.% C, the best mechanical properties obtained were KIC of 11.6 MPa m, Hv of 1315 and TRS of 329 MPa. In addition to carbon, Nb-addition also improved the fracture toughness and TRS of Ti5Si3 although the effect as a single addition was less than that of carbon. EPM method should be considered as a potentially viable route for producing structural intermetallics.

Acknowledgements This work was performed under the auspices of the Korean Science and Engineering Foundation through the 1999 Engineering Research Center program of POSTECH-CAAM.

References [1] E.H. Yoon, J.K. Hong, S.K. Hwang, J. Mater. Eng. Perf. 6 (1997) 106. [2] H.S. Park, S.K. Hwang, S.W. Nam, N.J. Kim, Scr. Mater. 41 (1999) 1197. [3] Y.W. Kim, Intermetallics 6 (1998) 623. [4] K.S. Chan, Y.W. Kim, Acta Metall. Mater. 43-2 (1995) 439. [5] J.J. Petrovic, MRS Bull. 7 (1993) 35. [6] G. Frommyer, R. Rosenkranz, C. Ludeke, Z. Metallkd. 81 (1990) 307. [7] K.J Park, S.K. Hwang, Korean J. Mater. Res. 6-3 (1996) 318. [8] T.K. Lee, J.H. Kim, S.K. Hwang, Metall. Meter. Trans. A 28 (1997) 2723. [9] K. Kawahara, S. Tsurekawa, H. Nakashima, J. Japan

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Inst. Metals 62 (1998) 246. [10] C.T. Liu, J.H. Schneibel, P.J. Maziasz, J.L. Wright, D.S. Easton, Intermetallics 4 (1997) 429. [11] S.C. Glade, N.N. Thadhani, Metall. Meter. Trans. A 28 (1995) 2565. [12] P.J. Counihan, A. Counihan, A. Crawford, N.N. Thadhani, Mater. Sci. Eng. A 276 (1999) 26. [13] R. Rosenkranz, G. Frommyer, W. Smarsly, Mater. Sci. Eng.A 152 (1992) 288.

[14] [15] [16] [17] [18]

S. Ruess, H. Vehoff, Scr. Metall. Mater. 24 (1990) 1021. R. Mitra, Metall. Mater. Trans.A 29 (1998) 1629. H.C. Park, M.S. Kim, S.K. Hwang, Scr. Mater. 39 (1998) 1585. L. Zang, J. Wu, Mat. Res. Soc. Symp. Proc. 487 (1999) 1. A.J. Thom, M. Akinc, O.B. Cavin, C.R. Hubbard, J. Mater. Sci. Lett. 13 (1994) 1657. [19] A.J. Thom, M.K. Meyer, Y.M. Kim, M. Akinc, in: V.A. Ravi, T.S. Sarivastan, J.J. Moore (Eds.), Processing and Fabrication of Materials III, TMS, Warrendale, PA, 1994, p. 413.