Magnesium Isotopic Composition of Interplanetary Dust Particles
The magnesium isotopic composition of some extraterrestrial dust particles has been measured. The particles are believed to be samples of interplanetary dust, a significant fraction of which originated from the disaggregation of comets and may contain preserved isotopic anomalies. Improvements in mass spectrometric and sample preparation techniques have made it possible to measure the magnesium isotopic composition of the dust particles, which are typically 10 micrometers in size and contain on the order of 10-10 gram of magnesium. Of the 13 samples analyzed, nine have the terrestrial magnesium isotopic composition within 2 parts per thousand, and one shows isotopic mass fractionation of 1.1 percent per mass unit. A subset of the particles, described as chondritic aggregates, are very close to normal isotopic composition, but their normalized isotopic ratios appear to show nonlinear effects of 3 to 4 parts per thousand, which is near the present limit of detection for samples of this size. The isotopic composition of calcium was also determined in one particle and found to be normal within 2 percent. It is clear that the isotopic composition of interplanetary dust particles can be determined with good precision. Collection of dust particles during the earth's passage through a comet tail or an intense meteor stream may permit laboratory analysis of material from a known comet.
Importance in catalysis of a magnesium ion with very low affinity for a hammerhead ribozyme
Atsushi Inoue, Yasuomi Takagi and Kazunari Taira
Available evidence suggests that Mg2+ ions are involved in reactions catalyzed by hammerhead ribozymes. However, the activity in the presence of exclusively monovalent ions led us to question whether divalent metal ions really function as catalysts when they are present. We investigated ribozyme activity in the presence of high levels of Mg2+ ions and the effects of Li+ ions in promoting ribozyme activity. We found that catalytic activity increased linearly with increasing concentrations of Mg2+ ions and did not reach a plateau value even at 1 M Mg2+ ions. Furthermore, this dependence on Mg2+ ions was observed in the presence of a high concentration of Li+ ions. These results indicate that the Mg2+ ion is a very effective cofactor but that the affinity of the ribozyme for a specific Mg2+ ion is very low. Moreover, cleavage by the ribozyme in the presence of both Li+ and Mg2+ ions was more effective than expected, suggesting the existence of a new reaction pathway-a cooperative pathway-in the presence of these multiple ions, and the possibility that a Mg2+ ion with weak affinity for the ribozyme is likely to function in structural support and/or act as a catalyst.
Naturally existing hammerhead ribozymes were originally identified in some RNA viruses, and it was demonstrated that they act in cis during viral replication by the rolling circle mechanism. In the laboratory, ribozymes have been engineered such that they act in trans against other RNA molecules and catalyze the cleavage of phosphodiester bonds at specific sites to generate specific products, each of which has a 2',3'-cyclic phosphate and a 5'-hydroxyl group. The transesterification mechanism includes deprotonation of the 2'-hydroxyl moiety of a ribose group, nucleophilic attack of the 2'-oxygen on the adjacent phosphorus atom, and protonation of the 5'-oxyanion leaving group. A large body of evidence also indicates that the P9/G10.1 site binds a metal ion with high affinity, with other metal ion-binding sites being located around the G5 nucleobase and A13 phosphate near the site of cleavage. Thus, the idea that ribozymes are metalloenzymes has been generally accepted. However, it was reported recently that hammerhead ribozymes are active in the presence of very high concentrations of monovalent cations, such as Li+ or NH4+ ions, in the absence of divalent metal ions. This finding raises the possibility that hammerhead ribozymes should not be classified as metalloenzymes. Therefore, we decided to investigate ribozyme activity in the presence of Mg2+ ions and the effects of Mg2+ ions in the presence of Li+ ions on ribozyme activity, using a well-studied model hammerhead ribozyme (R32) and its substrate (S11)
Preparation of the hammerhead ribozyme and its substrate
The ribozyme (R32) and its substrate (S11) were synthesized chemically on a DNA/RNA synthesizer (model 394; PE Applied Biosystems, Foster City, CA) using phosphoramidic chemistry with 2'-tert butyldimethylsilyl (TBDMS) protection as described previously. Chemically synthesized oligonucleotides were deprotected in a mixture of 28% ammonia and ethanol (3:1) at 55°C for 8 h. The mixture was evaporated to dryness and the residue was allowed to dissolve in 1 ml of 1 M tetrabutylammonium fluoride (TBAF; Sigma-Aldrich, Japan K.K., Tokyo, Japan) at room temperature for 12 h. After the addition of 1 ml of water, the mixture was desalted on a gel-filtration column (Bio-Gel P-4; Bio-Rad Laboratories, Hercules, CA). Fully deprotected oligonucleotides were purified by gel electrophoresis on a 20% polyacrylamide gel that contained 7 M urea, the respective bands were excised from the gel, and oligonucleotides were extracted in water. The oligonucleotides were recovered by ethanol precipitation and then solutions were desalted on a gel-filtration column (TSK-GEL G3000PW; TOSOH, Tokyo, Japan) by high-performance liquid chromatography (HPLC) with ultrapure water. All of the RNA oligomers were quantitated in terms of absorbance at 260 nm.
The dependence of the activity of the hammerhead ribozyme on the concentration of Mg2+ ions
We attempted first to determine how many Mg2+ ions might be involved in our model ribozyme reaction and the saturating concentration of Mg2+ ions in the reaction, beyond which the cleavage rate constant no longer increases. We examined the dependence on the concentration of Mg2+ ions of the activity of the R32 hammerhead ribozyme up to 1 M Mg2+ ions. We performed reactions with R32-S11 under single-turnover conditions with a saturating amount of ribozyme with respect to the amount of S11 for the same reasons as noted above. The reaction in the presence of Mg2+ ions is accelerated with increases in pH, with a slope of unity. We adjusted the pH of reactions to 6.0 to slow down the reaction so that we could determine the rate constants of rapid reactions precisely. As shown by closed circles in, the dependence on Mg2+ ions was approximately first-order. However, no plateau was reached under our conditions, even above 800 mM Mg2+ ions. The continuous increase in rate constant upon the addition of more and more Mg2+ ions indicates the involvement of one Mg2+ ion that has low affinity for the hammerhead ribozyme-substrate complex. At 800 mM Mg2+ ions, the rate constant approached 1.1 min-1 at pH 6.0, and this is the limit of detection of a rapid cleavage reaction under standard laboratory conditions.
Analyses of the structure of hammerhead ribozymes and of the conformational changes caused by interactions with Mg2+ ions have indicated that two major conformational changes occur: the formation of domain II, which is followed by the formation of domain I, as shown in. The formation of domain II results in coaxial stacking of helices II and III, induced by the binding of a higher-affinity Mg2+ ion(s) to P9 phosphate and N7 of G10.1(P9/G10.1) of the ribozyme-substrate complex. The second transition is the formation of the catalytic domain with movement of stem I toward stem II, which is induced by the binding of a lower-affinity Mg2+ ion(s). The Kd values of the two domains have been determined by various methods to be several hundred micromolar and several millimolar, respectively. Thus, at several hundred millimolar Mg2+ ions, the formation of domains II and I should be complete.
Taking this structural information into consideration, we can reasonably conclude that the very-low-affinity Mg2+ ion that we detected in the present study might be involved in some step other than the formation of domains I and II. This step might be a conformational change or the binding of a catalytic species to the ribozyme-substrate complex. Walter and coworkers recently reported that a third and previously undetected metal ion at rather high concentrations might play a role in the induction of a minor conformational adjustment that leads to the formation of the active state after the formation of domains I and II. The Mg2+ ion that we detected had very low affinity, and the relative level of truly active ribozyme species at a concentration of several millimolar Mg2+ ions corresponded to < 1% of all the ribozyme-substrate complexes in the reaction mixture [compare 1 min-1 in 10 mM MgCl2 at pH 8 and 25°C with 100 min-1 in 800 mM MgCl2 at the same pH and the same temperature.
What is the catalyst in the hammerhead reaction?
To the best of our knowledge, this report is the first to describe the dependence of ribozyme activity on a high concentration of Mg2+ ions under single-turnover conditions. The reaction did not reach a plateau even at 800 mM Mg2+ ions. Under these conditions at pH 6, the observed rate constant was 1.1 min-1. The activity of the ribozyme is known to depend on pH, with a slope of unity. Thus, we can estimate an observed rate constant for the ribozyme reaction of 110 min-1 at pH 8. It is very unlikely that this rate constant of cleavage can occur without an effective catalyst(s). So, what is the catalyst(s) of the reaction?
In studies of solvent isotope effects on the ribozyme reaction in the presence of deuterium and Li+, Mg2+ NH4+ or ions, we failed previously to observe any proton transfers in the transition state during the ribozyme reaction in the presence of either Li+ or Mg2+ ions but we did observe proton transfer in the presence of NH4+ ions. We interpreted such results by suggesting that metal ions, such as Mg2+ and Li+, function as a Lewis acid catalyst while NH4+ ions function as a general acid catalyst during the ribozyme reaction. Thus, the catalyst can change according to the conditions around the ribozyme. On the basis of this hypothesis and the involvement of two other kinds of Mg2+ ions in the formation of domains I and II, it is possible that the newly identified Mg2+ ion with very low affinity that we observed in this study might be the true catalyst. Our novel cooperative pathway might involve an Mg2+ ion in a catalytic role after monovalent cations and other Mg2+ ions have acted to generate the pre-active conformation just before chemical cleavage by the hammerhead ribozyme. In the presence of monovalent ions exclusively, monovalent ions can also function as the catalyst but they are not as effective. Mg2+ ions have a higher charge density than Li+ ions and would function better as catalyst in the reaction. Thus, when both Mg2+ and Li+ ions are present in the reaction mixture, the high activity of the ribozyme reaction is likely due to an Mg2+ ion catalyst. The Li+ ions act to support the formation of the domains I and II in cooperation with Mg2+ ions, as discussed above.
PAPER: TRANSITION OF DOMINANT DIFFUSION PROCESS DURING SUPERPLASTIC DEFORMATION IN AZ61 MAGNESIUM ALLOYS
The superplastic behavior of the AZ61 magnesium alloy sheet, processed by one-step hot extrusion and possessing medium grain sizes of ~12 m, has been investigated over the temperature range of 523 to 673 K. The highest superplastic elongation of 920 pct was obtained at 623 K and a deformation rate of 1 10-4 s-1. In the lower and higher strain rate regimes, with apparent m values of ~0.45 and ~0.25, respectively, grain-boundary sliding (GBS) and dislocation creep appeared to dominate the deformation, consistent with the scanning electron microscopy (SEM) examination. The SEM examination also revealed that individual GBS started to operate from the very initial deformation stage in the strain rate range with m ~0.45, which was attributed to the relatively high fraction (88 pct) of high-angle boundaries. The analyses of the superplastic data over 523 to 673 K and 5 10-5 to 1 10-3 s-1 revealed a true stress exponent of ~2, and the activation energy was close to that for grain-boundary and lattice diffusion of magnesium at 523 to 573 K and 573 to 673 K, respectively. The transition temperature of activation energy is ~573 K, which is attributed to the change in the dominant diffusion process from grain-boundary diffusion to lattice diffusion. It is demonstrated that the effective diffusion coefficient is a valid parameter to characterize the superplastic behavior and the dominant diffusion process.
Magnesium alloys have high potential as lightweight structure materials owing to their low density. However, they usually exhibit low formability attributed to their hexagonal close-packed crystal structure with a limited number of operative slip systems near room temperature, and thus cold forming of magnesium alloys is restricted to mild deformation. As a result, most magnesium products have been fabricated by casting, in particular, by die casting. Magnesium alloys are found to be much more workable at elevated temperatures as additional slip systems become available. Thus, hot rolling, extrusion, and forging have been used commercially to produce magnesium plates, rods, and tubes. Recently, applications of the superplastic pressing (or forming or forging) technique to magnesium alloys have attracted much attention,[1-15] and this may effectively produce complex
engineering components directly from the wrought products. It is expected that superplastic pressing for commercial low-priced magnesium alloys could be developed into one important future fabrication means for the automobile, architecture, and electronic appliance industries.
It is well known that superplasticity is associated with a small grain size. Smaller grain size is desirable in enhancing ductility and promoting high strain rate superplasticity (HSRSP) and low-temperature superplasticity (LTSP). Recently, equal channel angular press has been used to produce microstructure with fine grain sizes in the submicrometer range in commercial magnesium AZ3I,1'6' AZ61,'I7] and AZ91 alloys,"8'19,201 and proven to be effective in enhancing mechanical properties at room temperature, as well as in achieving superior LTSP or HSRSP. However, from the industrial point of view, the warm-extrusion process seems to be one of the most economical and practical methods to attain fine-grained magnesium sheets, bars, or tubes that are feasible for press forming (or press forging) and hydroforming into final products of complicated shapes. In order to obtain fine-grained magnesium alloys, a warmextrusion process with high extrusion ratio around 100:1 was usually used to develop superplastic microstructure in AZ31 and AZ91 alloys.[11,5,8-101] In these fine-grained (1 to 5 m) magnesium alloys, the dominant accommodative diffusion process during LTSP or HSRSP was reported to be grain-boundary diffusion. In order to understand the global picture of the dominant diffusion process, it is interesting to examine the superplastic behavior in Mg alloys with relatively coarser (10 to 20 m) and fully recrystallized grains. These may be the economic materials actually applied in forming industry.
For Mg or Al alloys, even under the LTSP and HSRSP conditions, grain-boundary sliding (GBS) accommodated by dislocation slip plus climb still appears to be the dominant deformation process,[6,13,141] with a true strain rate sensitivity (OT) of ~0.5 and a dominant diffusion process for dislocation climb. In this article, the characteristics of deformation mechanisms and the effective diffusion under various working temperature and strain rate ranges are examined in the AZ61 Mg warm-extruded sheets with an average grain size of 12 m, an intermediate grain size range as compared with the coarse (50 to 100 m) or fine grain size (0.5 to 5 m) for most commercial Mg alloys. Emphasis was placed on the superplastic deformation occurring at the intermediate temperature (-573 K) and strain rate (-1 10-3 s-1) region, which appears to be the practical forming window for current applications.
II. Experimental procedures
The material used is a commercial AZ61 alloy (Mg-6 wt% Al-I wt% Zn), purchased from the CDN Company (Deltabc, Canada). One-step extrusion using a medium extrusion ratio of 40:1 was undertaken at a temperature of 350 C, resulting in a sheet with a width of 100 mm and a thickness of 2 mm. The average grain size, d (d = 1.74 L; L is the liner intercept size), of the as-extruded sheet is 12 m.
The typical microstructure is shown in Figure l(a), revealing the nearly equiaxed and dynamically recrystallized grains. The texture and grain misorientation are shown in Figures l(b) and (c),'2'1 from which it can be seen that there is a strong basal texture, especially with a-type axes aligning parallel to the extruded direction, but the grain mutual misorientation possesses a high portion of high-angle grain boundaries (HABs, >15 deg) favorably for GBS.
The tensile specimens, machined directly from the extruded sheets, have a gage length of 10 mm, width of 3 mm, and thickness of 2 mm, with the loading axis parallel to the extrusion direction. Constant crosshead speed tensile tests were conducted using an Instron (Canton, MA) 5582 universal testing machine equipped with a three-zone furnace at temperature ranging from 523 to 673 K and initial strain rates ranging from 1 × 10-5 s-1 to I 10 s-1. The specimens required 3.6 ks to equilibrate at the testing temperature prior to tensile straining.
In order to characterize the grain size dependence of the superplastic flow, the as-extruded specimens were further annealed to develop coarser grain sizes. Two specimens with grain sizes measuring 18 and 26 m were prepared for the tests. Strain rate change tests were performed to investigate the effects of grain size on the mechanical properties. In some cases, jump strain rate tests were also carried out to evaluate the variation in apparent strain rate sensitivity (ma) value as a function of strain. In these tests, the strain rate difference between the base and jump (or step) was about 25%.
To examine the evolution of microstructure and operation of dislocation process and GBS, the tensile tests to different strain levels, e.g., ε = 10, 30, 50, 90 and 200%, were performed. The surface and fracture morphologies were examined by scanning electron microscopy (SEM). The specimens were etched by the reagent of 10% acetic acid + 10 mL water + 1OO mL ethanol + 5 g picric acid for grain structure examination.
III. Results and discussion
A. Superplastic elongation
The results of elongation to failure for the current AZ61 alloy are shown in Figure 2.'2'1 The highest tensile elongation over the test regime was 920%, occurring at 623 K and 1 10-4 s-1. Temperatures higher than 623 K would lead to significant grain growth and hence result in decreased elongations. The static grain growth tendency from room temperature to 700 K is shown in Figure 3. It can be seen that limited grain growth occurred at the optimum superplastic temperature of 623 K, which corresponds to the transition temperature between limited and pronounced grain coarsening.
B. Apparent strain rate sensitivity ma
The variations of flow stress as a function of strain rate over the temperature ranges tested are plotted in Figure 4. The flow stress for each strain rate was determined at a small strain of 0.1. For such a small strain, the change in microstructure occurring during superplastic flow was negligible. The apparent strain rate sensitivity exponent, ma, was estimated from the slope of the curve. In the relatively lower temperature range of 523 to 573 K, the average ma was estimated to be 0.42 and 0.22 in the lower and higher strain rate ranges of 1 10-4 s-1 (stage 1) and 1 10-2 s-1 (stage II), respectively, as listed in Table I. At higher temperatures of 573 to 673 K, the average ma was 0.46 and 0.25 in stages I and II (Table I). It seems that the dominant \deformation mechanisms might be different during stages I and II with different strain rates. As shown in later analyses, after invoking the threshold stress consideration,[22,23,24] the true strain rate sensitivity m would reach 0.5 and 0.33 over these stages, suggesting that GBS and dislocation glide-controlled (or solute drag) creep were the controlling mechanism, respectively.
C. SEM observations
In order to explore the deformation mechanisms at different strain rates for the present medium-grain-sized AZ61 alloy, the surface morphology of tensile specimens strained to 10% at the lower temperature of 523 K were subjected to SEM examinations, as shown in Figure 5. At the lowest strain rate of 1 10-5 s-1, the characteristics of GBS were dominant, and no apparent slip bands within the grains owing to extensive dislocation processes was observed, as shown in Figure 5(a). Under this condition, GBS was the controlling deformation mechanism with ma ~0.45. As the strain rate increased to 1 10-4 s-1 with ma ~0.42, GBS was still dominant. However, few slip bands within the grains were occasionally seen, as illustrated in Figure 5(b). At the strain rate of 1 10-3 s-1, appreciable amounts of slip bands within the grains became evident, as shown in Figure 5(c), suggesting that dislocation creep started to play an important role with ma ~0.25. As the strain rate increased to 1 10-2 s-1, the slip bands were also pronounced, and the surface marking offsets owing to grain-boundary sliding became rarely observed, as shown in Figure 5(d). This observation is consistent with the dislocation creep processes with ma ~0.22. These SEM observations suggest the competing operations of GBS and dislocation creep at 523 K and various strain rates.
At a relatively higher temperature range of 573 to 673 K and a lower strain rate of 1 10-3 s-1 or less, GBS was also dominant with ma ~0.46. The evolutions of GBS in the AZ61 specimens strained to tensile elongations of 10, 55, 200, and failure (-500%) at 623 K and 1 10-3 s-1 are illustrated in Figure 6.'2'1 In the initial stage of superplastic deformation, as the strain reached -10%, GBS could be readily seen from some clear offsets of the prescratched marked lines and, especially, from the large number of grainboundary "steps," as shown in Figure 6(a). Formation of striated bands (SBs) and fibers was not significant in this region. It should be noted that almost all surface grains in the AZ61 alloy have been involved in GBS operation; namely, individual grain-boundary sliding rather than cooperate grain-boundary sliding was undertaken from the very beginning stage of superplastic straining. With increasing straining to 55% (Figure 6(b)), 200% (Figure 6(c)), and failure of 500% (Figure 6(d)), GBS offsets at individual grains were progressively further developed. Formation of SBs was more pronounced and the SB height also increased in these deformation stages. At 573 to 673 K and the higher strain rate of 1 10-2 s-1, the ma value was 0.25, suggesting a dominant dislocation creep process. Figure 7 provides the direct evidence for the extensive dislocation movement.
Previous analyses on this alloy revealed that the strains contributed by GBS over this temperature (573 to 673 K) and strain rate (10-5 to 10-3 s-1) range were around 55 and 60% at strains of 0.10 and 0.44, respectively, as illustrated in Table II. Since the procedure used to measure GBS will lead to a maximum possible value of ~50 to 70% for the GBS contribution because of the inherent difficulties in the measuring procedure, the current measurements of RGRS = 55 and 60% already represent nearly 90 to 100% of the total strain contributed by GBS in the present AZ61 alloy. The high contribution from GBS was found to be related to the high fraction of high-angle boundaries (>15 deg) in the as-extruded AZ61 sheets, as shown in Figure 1(c). The HAB occupied 88 pct of the total grain-boundary population, significantly higher than the 45 to 65% determined in the Albase alloys.[26,27,28] The high HAB fractions, as well as the high contributions of GBS to the total strain, provide a model system in analyzing the deformation mechanisms and controlling diffusion processes.
IV. Data analyses
A. Analysis of superplastic deformation
The relationship between the normalized strain rate, ε (T/ G)(d/b)², and the reciprocal temperature is plotted in Figure 10, where e (T/G)(d/b)² was determined at a fixed normalized stress of (σ - σ0)/G = 6.5 10-4 for the typical superplastic region. The slope of the curve is the true activation energy for ssuperplastic flow operated by GBS (n = 2). It can be seen that the curve is divided into two regions. The true activation energy value over 523 to 573 K is 90 kJ/mol, which is close to that for grain-boundary diffusion of magnesium (92 kJ/ mol). In contrast, the true activation energy at 573 to 673 K is 137 kJ/mol, which is close to that for lattice diffusion of magnesium (135 kJ/mol). The transition temperature evaluated from the intersection of the curve is ~573 K. Based on the preceding analysis, it is suggested that the dominant superplastic deformation mechanism in the current medium-grain-size alloy is GBS accommodated by dislocation slip and climb, which are in turn controlled by grain-boundary diffusion over 523 to 573 K and by lattice diffusion over 573 to 673 K, respectively.
B. Diffusion paths
The variation in diffusion and grain-size-compensated strain rate, (ε Deff)(kT/Gb)(d/b)², as a function of modulus and threshold-stress compensated flow stress, (σ - σ0)/G, is shown in Figure 12, where Deff is taken to be [D1 + 10-2(πδ/d)Dgb]. The superplastic behavior in the present AZ61 Mg alloy, with well recrystallized grain structures and medium grain sizes, is well represented by a single straight line with a slope of n = 2 in the normalized plot compensated by the effective diffusion coefficient, which involves the different contributions of lattice and grain-boundary diffusion at various temperatures. This indicated that the notion of effective diffusion could satisfactorily interpret the dominant diffusion process during superplastic flow.
As mentioned in Section I, the dominant accommodative diffusion process during LTSP or HSRSP at 473 to 623 K was reported to be grain-boundary diffusion in fine-grained (1 to 5 m) Mg alloys.[1,5,8-10] The fine grain size and thus the high grain-boundary area would favor grain-boundary diffusion over this working temperature range to play the dominant role in dislocation slip plus climb; the latter in turn acts as the accommodation mechanism for GBS. In contrast, for Mg alloys with a coarser grain size of 20 m, the dominant diffusion process at the optimum working temperature of 573 K would then be lattice diffusion, since Ttrans for such a case is 548 K. If the working speed applied during press forming (forging) or hydro forming is too high, the lattice diffusion might not be able to provide sufficient accommodation. The undesired cavitation problem might thus be inevitable.
1. An AZ61 magnesium alloy sheet with a medium grain size of ~12 m was produced by means of one-step hot-extrusion processing, and exhibited the highest superplastic elong\ation of 920 pct at 623 K and 1 10-4 s-1.
2. Over the temperature range of 523 to 673 K, the average apparent strain rate sensitivity ma was around 0.42 to 0.46 in the lower strain-rate range ~1 10-4 s-1, and around 0.22 to 0.25 in the high strain rate range ~1 10-2 s-1, suggesting the GBS and dislocation creep dominating processes, respectively, consistent with the SEM examination.
3. After invoking the threshold stress consideration, the superplastic data on 523 to 673 K and 5 10-5 to 1 10-3 s-1 revealed a true stress exponent of ~2. The extracted activation energy was close to that for grain-boundary diffusion of magnesium over 523 to 573 K, and close to that for lattice diffusion of magnesium over 573 to 673 K.
4. The transition temperature of activation energy is ~573 K, which is in correspondence with the cooperation of grain boundary and lattice diffusions, and is attributed to the change in the dominant diffusion process from grain-boundary diffusion to lattice diffusion. The decrease in grain size will increase the transition temperature toward to a higher temperature. This means that, as the grain size decreases, the grain-boundary diffusion will sustain to be the dominant diffusion path up to a higher temperature.
5. It is demonstrated that the effective diffusion coefficient is a valid parameter to characterize the superplastic behavior and the dominant diffusion process.
The authors gratefully acknowledge the sponsorship from the National Science Council of the Republic of China under project NSC 89-2216-E-110-043 and NSC 90-2216-E-110-024. One of the authors (YNW) is grateful for the postdoctoral sponsorship from NSC under Contract Nos. NSC 90-2816-E-110-0001-6 and NSC 91-2816-E-l 10-0001-6.
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