Non-steady state solidification of the Nd-123 superconducting oxides

Non-steady state solidification of the Nd-123 superconducting oxides

Physica C 330 Ž2000. 191–202 www.elsevier.nlrlocaterphysc Non-steady state solidification of the Nd-123 superconducting oxides M. Kambara a a,),1 ,...

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Physica C 330 Ž2000. 191–202 www.elsevier.nlrlocaterphysc

Non-steady state solidification of the Nd-123 superconducting oxides M. Kambara a

a,),1

, K. Miyake

b,2

, K. Murata b, T. Izumi c , Y. Shiohara c , T. Umeda

a

Department of Metallurgy, Graduate School of Engineering, The UniÕersity of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan b Graduate School of Engineering, Shibaura Institute of Technology, 3-9-14, Shibaura, Minato-ku, Tokyo, 108-8548, Japan c SuperconductiÕity Research Laboratory, ISTEC, 1-10-13, Shinonome, Koto-ku, Tokyo, 135-0062, Japan Received 8 October 1999; accepted 19 November 1999

Abstract Crystal growth of the melt-textured bulk Nd 1qx Ba 2yx Cu 3 O6qd ŽNd123. superconducting oxides was investigated by employing isothermal undercooling solidification with hot-seeding in air. From the relationship between growth length and holding time, the Nd123 crystal was found to have almost stopped growing after a certain growth period, while the growth length increased proportionally to the holding time at an early stage of the crystal growth. As a result of quantitative analysis for the Nd123 crystal of which solidification was terminated, the distribution of the NdrBa substitution was observed to decrease in the Nd123 single crystal matrix from the seed crystal to the edge of the Nd123 crystals. Also, the substitution content at the edge of the Nd123 crystal, which corresponds to that at the final stage of the crystal growth, was found to be in good agreement with the minimum substitution of the Nd123 solid solution phase in the equilibrium phase diagram at this process temperature. These compositional changes could be explained using the equilibrium phase diagram as associated with the solid solution formation, which is responsible for the non-steady state solidification of the Nd123 crystals even for the isothermal undercooling processing. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Nd 1q x Ba 2yx Cu 3 O6qd ; Solid solution; Non-steady state solidification

1. Introduction Neodymium superconducting oxides, Nd 1qx Ba 2y x Cu 3 O6qd ŽNd123., are known to show relatively low critical superconducting temperature ŽTc .,

) Corresponding author. Department of Engineering, University of Cambridge, Madingley Road, West Cambridge Site CB3 0HE, UK. Tel.: q44-1223-337443; fax: q44-1223-337074. 1 Research fellow of the Japan Society for the Promotion of Science. 2 Present address: Mitsubishi Motors, 3-1, Mizushima, Kurashiki, 712-8011, Japan.

since the Nd123 crystal forms a solid solution due to NdrBa substitution and includes a consequent problem that the Tc decreases with increasing substitution content w1x. This substitution, therefore, should be optimally controlled to attain superior superconducting properties. Recent investigations w2x revealed that synthesis in a low oxygen partial pressure atmosphere, OCMG, is an effective method to yield the Nd123 crystals which exhibit higher Tc and higher critical current density Ž Jc . values especially under the high applied magnetic fields compared with those of Y1 Ba 2 Cu 3 O6qd ŽY123. crystals. On the other hand, the melt processing has been widely recog-

0921-4534r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 6 0 7 - 3

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nized as an effective technique to enhance Jc properties of the bulk RE123 superconductors ŽRE: rare earth element. especially in the lower magnetic fields w3x. This is mainly because it enables not only reduction of the weak-link problems due to highly aligned structure, but also introduction of the high temperature stable phase particles as strong flux pinning sites into the RE123 matrix during the peritectic solidification of RE123 crystals. Regarding the Tc property, it was found from our phase diagram studies that the solid solution range of the Nd123 phase becomes narrower with decreasing oxygen partial pressure of the atmosphere w4x, which made it possible to produce the Nd123 crystals with smaller substitution contents. Our phase diagram studies in air w5x have also revealed that the substitution content in the Nd123 phase decreases with increasing BaOrCuO ratio of the tie-line liquid composition, which in turn suggests the prospective process that can control substitution by selecting the BaO-enriched initial composition. On the basis of this idea, Nd123 single crystals with a small amount of substitution were successfully produced even in air atmosphere by the top-seeded solution growth ŽTSSG. technique, which resulted in higher Tc values w6x. Another unique phenomenon involved in this technique for the bulk crystal processing is that the high temperature stable phase particles wSm 2 BaCuO5 ŽSm211., Nd 4y x Ba 2qx Cu 2yxO 10y2 x ŽNd422.x become smaller with increasing BaOrCuO ratio of the initial composition, which is effective for further enhancement of the Jc properties w8,9x. Although high Jc values of RE123 in high magnetic fields are mainly due to peak effect w10x, the mechanism of the anomalous peak effect has not yet been clarified completely. However, it has also reported that the peak effect can be controlled by optimization of oxygen annealing after melt growth w11x. Therefore, by combining these techniques mentioned above, it is promising to produce RE123 crystals with smaller substitution contents which can exhibit higher Jc values from lower to higher magnetic fields due to both the anomalous peak effect and the dispersion of the fine high temperature stable phase particles. Recent studies on bulk materials processing have also focused on the improvement of the magnetic trapped field aiming at the practical applications such as magnetic bearings. In general, the magnetic

trapped field increases with increasing the Jc values of RE123 crystals and with increasing the current loop size that corresponds to the single domain crystal size of the ab-plane. The enlargement of the RE123 single domain crystals is, therefore, as much as necessary an enhancement of the Jc of the RE123 crystals. Many attempts have been carried out to produce the larger single domain bulk crystals by employing the top-seeded melt-growth process with slow cooling especially for the Y123 system w12,13x. So far, the satellite crystals that nucleated from the undercooled melts have been recognized to prevent the advancement of the Y123 crystal epitaxially grown from the seed crystal. At present, however, it seems that scaling-up the single domain crystal still contains the limitation in size, nevertheless the satellite crystals are significantly suppressed within the sample. One of the growth-limiting factors considered is the accumulation phenomenon of the high temperature stable phase particles during the peritectic solidification of the RE123 crystal w14x. On the other hand, in the case of the Nd123 system, it might be considered that other essential factors would also dominate the evolution of the Nd123 crystals, since the Nd123 system includes the solid solution formation different from the case of the stoichiometric compound of Y123. In this paper, melt-textured Nd123 superconducting oxides were produced in air from different BaOrCuO ratio of the initial compositions by isothermal undercooling solidification with hot-seeding. Crystal growth of Nd123 phase was investigated from the viewpoint of solid solution formation using the quasi-ternary equilibrium phase diagram in comparison with the Y123 system.

2. Experimental Different overall average compositions were selected from the generally used tie-line composition of Nd123q 10 mol% Nd422 to the Ba-enriched side. The volume fraction of the RE211 phase particle in the initial composition has been reported to affect the distribution of the RE211 particles in the RE123 crystal and the resultant Jc properties. Therefore, in order to maintain the volume fraction of Nd422 particles which arrive at the Nd123 growing inter-

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face to be almost constant, the initial composition was selected almost parallel to the metastable liquidus of the Nd422q liquid ŽL. region at the Nd123 phase growth temperature ŽTg . as shown in Fig. 1. Raw materials of Nd 2 O 3 , BaCO 3 and CuO powders were ground thoroughly and calcined twice at 8908C for 24 h. Resultant precursor powders were uniaxially pressed into the pellets 20 mm in diameter and 10 mm in height. The precursor pellets were set on MgO single crystal substrate and placed in the furnace at room temperature as depicted in the experimental set up of Fig. 2Ža.. Melt-processing was performed in the air atmosphere. The sample pellets were processed using the heating pattern as shown in Fig. 2Žb.. The sample was first heated up to 11508C and held for 1 h in order to obtain the semi-solid state of Nd422 and liquid. It was then immediately cooled down to a Tg of interest below the peritectic temperature ŽTp . which is estimated to be approximately 10868C w15x. During the rapid cooling to Tg , a tiny cleaved Nd123 single crystal Ž; 1 = 1 = 0.2 mm3 . prepared by the TSSG method was seeded on the center of the pellet to

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grow the Nd123 crystal epitaxially from the seed crystal. The precursor pellets kept at Tg for several holding periods were quenched to room temperature for interrupting solidification of Nd123 to observe the growth length. The growth length was defined as the distance from the edge of the seed crystal to the Nd123rL interface. These melt-textured samples were mounted in resin and polished for microstructural observation and quantitative analysis. For the analysis of the distribution of NdrBa substitutions, the concentrations of Nd, Ba, and Cu in a spot area were measured along the growth direction by the electron probe microscopic analyzer ŽEPMA.. Since the crystal size in the ab-plane is responsible for the superconducting current loop, the microstructures were mainly investigated for the growth in the a-direction ²100:.

3. Results and discussion 3.1. Holding time dependence of the growth length

Fig. 1. Schematic quasi-ternary phase diagram of the NdO–BaO– CuO system in air showing the initial compositions used in the experiment.

Fig. 3 shows a typical top view of the melt-textured sample quenched during solidification. It is found that Nd123 crystal was grown epitaxially from the Nd123 seed single crystal with a squared shape of ab-plane, and no other satellite crystals that nucleated from the undercooled melt could be observed at least at the surface of the sample pellet. For the Nd123 crystals grown from the usual composition with BaOrCuO ratio of 3:5 at 10708C, the growth lengths in both a- and c-directions were measured and plotted as a function of the growth time as shown in Fig. 4. It is clearly recognized for both growth directions that growth length increases nearly proportional to holding time at an early stage of solidification, while the crystal does not grow in the same manner after holding for about 5 h Ž18 ks. or longer. Fig. 5 illustrates the relationship between growth length and growth time for the samples grown from different BaOrCuO ratios in the initial composition at 10658C and 10558C. At the beginning of solidification, the growth rate of the Nd123 crystal, which is represented as the incline of the graph, is found to become lower with increasing BaOrCuO

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Fig. 2. Schematic illustration of the experimental procedure: Ža. experimental set-up, Žb. typical heating pattern.

ratio in the initial composition, as had been reported elsewhere w16x. More noticeably, a similar tendency that the growth rate suddenly decreases at a certain growth time during solidification can be found for all the Nd123 crystals grown under different growth conditions. Regarding the final crystal size after a remarkable decrease in the growth rate, it is basically found that the growth length is smaller as BaOrCuO ratio becomes higher, except for the sample with BaOrCuO ratios of 3:4 and 3:4.5 at 10558C. Since the growth lengths of Nd123 crystals grown under

Fig. 3. Typical top view of the Nd123 crystal grown in air.

any condition are smaller than 5 mm, it can be supposed that the pellet size of 20 mm in diameter is not responsible for the limitation in size. Nor would

Fig. 4. Holding time dependence of growth length of Nd123 crystal that was grown isothermally at 10708C from initial composition with the BaOrCuO ratio of 3:5.

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Fig. 5. Relationship between growth length and growth time for the Nd123 crystals grown in the Ža. a- and Žb. c-directions from different BaOrCuO ratios of the initial composition at 10658C and in the Žc. a- and Žd. c-directions at 10558C. Time dependence of the volume fraction of 211 particles both in solid and liquid.

the satellite crystals that nucleated from the undercooled melt prevent advancement of the Nd123 crystal epitaxially grown from the seed crystal as shown in Fig. 3. Therefore, it can be considered that the crystal growth of Nd123 is non-steady state solidification, and that the proportional dependence of the growth length on the holding time at the early stage of solidification is due to apparent constant-growth rate solidification. 3.2. Microsegregation of substitution content in the Nd123 solid solution In general, in the case of the non-steady state solidification, such as the condition of complete

mixing in liquid represented by the Scheil type solidification w17x, both solid and liquid compositions are changed with time due to a decrease in temperature at the solidrliquid interface under the local equilibrium assumption. Also, microsegregation should be observed in the solidified crystal as a trace of nonsteady solidification if back-diffusion into the solid is not so rapid. However, it is hardly considered that the non-steady state solidification of the Nd123 crystals is due to the decrease in the interface temperature, since the Nd123 crystals were grown under the isothermal undercooling conditions. Accordingly, distribution of the NdrBa substitution was investigated in the Nd123 single crystal that has almost stopped growing after a long growth period.

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Fig. 6Ža. shows the schematic illustration of the quantitative analysis procedure. The solid composition was measured at an interval of 40 mm from the seed crystal to the solidrliquid interface along the a-growth direction by the beam spot analysis. The measuring position in the Nd123 matrix was selected arbitrarily avoiding the Nd422 particles that were entrapped into the Nd123 crystal during solidification. The relationship between the substitution and the distance from the seed crystal was shown in Fig. 6Žb. for the Nd123 crystal grown from the usual composition with BaOrCuO ratio of 3:5 held for 35 h Ž126 ks. at 10708C. It was found that Nd123

crystal with substitution content of 0.1 was first grown from the seed crystal with substitution of about 0.06. It should be noticed that as the growth length becomes longer, i.e., the crystal growth proceeds, the substitution content decreases gradually and reaches to the substitution of 0.04 at the edge of the crystal. Combining with the relationship between the growth length and the holding time as depicted in Fig. 4, the distribution of substitution can be related with the holding time as shown in Fig. 7. It can be found that the substitution content has begun to decrease already at the early stage of solidification, and more interestingly, it decreases remarkably and

Fig. 6. Schematic drawing of the Ža. quantitative analysis and Žb. distribution of the NdrBa substitution content, x in the Nd123 crystal along the a-direction. Maximum and minimum substitution contents of the Nd123 solid solution phase at the process temperature of 10708C are also indicated.

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Fig. 7. Growth time dependencies of the substitution and growth length for the Nd123 crystal grown from BaOrCuO of 3:5 at 10708C.

reaches to a minimum amount of 0.04 at the same time with the decrease in the growth rates after a long holding time. Under the assumption of the local equilibrium between solidrliquid interface, the Nd123 solid composition should be determined by the Nd123 growing interface liquid composition according to the equilibrium tie-line in the two-phase field of Nd123q L. The liquid composition plays an important role in affecting the microstructure of the solid solidified by the solidification processing. Accordingly, the compositional change in the liquid corresponding to the distribution of the substitution was evaluated using the approximate equations of tie-line and the partitioning coefficient w5x as shown in Fig. 8. It is clearly found that as solidification proceeds, each solute element in the Nd123 interface liquid composition is changed in the respective directions that the concentrations of Nd Ž C LNd . and Ba Ž C LBa . become higher and that of Cu solute Ž C LCu . becomes lower. This compositional change is then described onto the quasi-ternary phase diagram at this process temperature of 10708C as demonstrated in Fig. 9. The interface liquid composition was travelling along the liquidus surface into the Ba-enriched side, and it reached nearly to the liquid in the three-phase region of Nd123q Nd422q L. At the same time, the Nd123 solid composition moved towards the field of the smaller substitution contents and, finally, the Nd123

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Fig. 8. Liquid and solid composition changes with the solidification of Nd123 crystal. The liquid compositions were converted using the equilibrium partitioning equation w5x.

with the minimum substitution content of 0.04 was solidified at the end of the solidification. It is noticeable that the substitution at the final stage of the solidification is surely in a good agreement with the minimum substitution of the Nd123 solid solution phase estimated from the phase diagram at this process temperature w5x.

Fig. 9. Traveling of the liquid composition at the Nd123 crystal growth interface during isothermal undercooling solidification on the equilibrium phase diagram at 10738C w5x.

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On the other hand, in the case of the Nd123 crystals that were grown from different BaOrCuO ratios in the initial composition at the same Tg of 10658C, the relationship between the substitution content and the distance from the seed crystal is presented in Fig. 10. It is found that the substitution near the seed crystal, i.e., at the early stage of solidification, becomes smaller with increasing BaOrCuO ratio of the initial compositions, as has been reported in a previous paper w16x. Noticeably similar to the solidification at 10708C, the substitution is found to decrease gradually followed by a sudden decrease at the edge of the crystal. It was further noticed that despite the different initial compositions, the substitution content at the edge of each crystal exhibits almost the same value Ž x s 0.02., which is the minimum substitution at 10658C. Consequently, it can be concluded that as solidification proceeds, the solid and liquid compositions at the crystal interface travel towards the Ba-enriched region, correlating with each other through the tie-line. At further isothermal holding, the crystal growth would be terminated when its interface liquid composition reaches the three-phase field at the process temperature. Several diffusion control growth models for the crystal growth of RE123 have been proposed w18–20x, in which the necessary solute needed for the RE123 crystal growth is supplied through the liquid phase from RE211 particles dispersed in the liquid. In the

Fig. 10. Distributions of substitution content in the Nd123 crystals grown from different initial compositions at the same growth temperature of 10658C.

case of the usual initial composition with the BaOrCuO ratio of 3:5, which is on the quasi-binary section of the Y211–Y123–Ba 3 Cu 5 O 8 Ž‘‘035’’., the Y211 particle interface liquid composition Ž C L211 . can be on the intersection of the quasi-binary line with the metastable liquidus of Y211 q L field. Under the assumption that diffusivities are the same for all the solute elements, the interface liquid composition at the Y123 growing interface Ž C L123 . would be determined according to the equilibrium tie-line in the Y123q L region that passes through C L211 as illustrated in the schematic ternary phase diagram of Fig. 11Ža.. Since the Y123 phase is a stoichiometric compound, the equilibrium tie-line can be in accordance with the quasi-binary line of Y211–Y123– ‘‘035’’. Here, the average solid ŽC S . and liquid ŽC L . compositions are considered in an arbitrary minute area that includes the trapped andror pushed Y211 particles at the growing interface. In this circumstance, C S and C L could change in the direction indicated by arrows during solidification as depicted in Fig. 11Ža.. That is, although the directions are just opposite due to the particle pushingrtrapping behavior, both the average compositions should be on the quasi-binary line across the initial composition. Therefore, the crystal growth of Y123 can be basically discussed within the quasi-binary line since the mass conservation is maintained in this section. In the case of Nd123, on the other hand, the growth mechanism should differ from that of Y123 because of the solid solution formation as shown in Fig. 11Žb.. Similar to the Y123 system, Nd422 interface liquid composition Ž C L422 . corresponds to the intersection of the Nd422–‘‘035’’ line with the liquidus curve under the assumption of a stoichiometric Nd422 phase. Then, the Nd123 growth interface liquid composition Ž C L123 . should locate at the tieline in the Nd123q L region that passes through C L422 assuming the same diffusivities for all elements. Compared with the Y123 system, however, neither the liquid nor the solid composition at the Nd123 growing interface is located on the quasi-binary line, because the Nd123 crystal is not a stoichiometric compound but a solid solution with some substitutions of Nd ions for Ba ion sites. Under this situation, when a small amount of ‘‘Nd123 q Nd422’’ solid is solidified from the ‘‘Nd422q L’’ liquid, C S in this area should be at the tie-line

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grown from this Ba-rich C L422 through the Ba-rich C L123 . Therefore, as long as the solid solution of the Nd123 crystal grows, C L422 and C L123 would travel into the Ba-enriched side Žarrows 4 and 5. and the substitution in the Nd123 crystal subsequently becomes smaller Žarrow 3., which is responsible for the non-steady state solidification of the Nd123 crystal. This solidification path can be simply explained by the following mass balance calculation. Fig. 12 shows the schematic illustration of the concentration distribution ahead of the crystal growth interface. Focused on the Ba element that was rejected during solidification by the crystal-growing interface into the liquid, when we assume the complete mixing in the liquid due to the relatively long diffusion length, the following mass balance equation can be established under the local equilibrium, Ba Ž C LBa422 y CS123 . D f S s Ž 1 y f S . DC LBa422

Ž 1.

where f S is the fraction of solid. Under the assumptions that liquid diffusivities and stoichiometric compound of the Nd422 phase are the same for all Ba Nd elements, the relationship between C L422 and CS123 could be calculated as a function of f S using the liquidus surface and the partitioning equations w5x. Ba Ba Fig. 13 shows the calculated result of C L422 , CS123 Nd and CS123 as a function of the growth length in the

Fig. 11. Schematic phase diagram showing the composition changes during the isothermal undercooling solidification Ža. of Y123 system and Žb. of Nd123 system. As solidification proceeds, the Nd123 crystals with different substitution contents are growing along the equilibrium tie-lines as in arrow 3, corresponding to the interface liquid compositions of the Nd123 and Nd422 phases that travel in the directions in order to maintain the mass conservation as indicated in arrows 4 and 5, respectively. Considering the Nd422 particles that are entrapped andror pushed at the interface, average solid and liquid compositions would change with solidification as indicated in arrows 1 and 2, respectively.

connecting the CS422 with CS123 . C L then should be in the Ba-enriched region across the initial composition in order to maintain the mass conservation. This in turn indicates that C L422 becomes higher in C LBa than that at the beginning of solidification, and the Nd123 with smaller substitution contents would be

Fig.12. Schematic illustration of the spatial concentration distributions ahead of the crystal growth interface.

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particles could be pushed by the Nd123 crystal advancing at slower growth rates according to the pushingrtrapping theory w21,22x. Considering the particle behaviors, C S would change so that the volume fraction of the Nd422 particles becomes smaller in the Nd123 crystal as indicated by arrow 1 in Fig. 11Žb.. On the other hand, C L changes in the direction that the volume fraction becomes higher in the liquid as indicated by arrow 2. 3.3. Effect of the excess Nd422 particles on the Nd123 crystal growth Fig.13. Calculated result of the relationship between the interface concentrations as a function of the distance from the seed crystal.

case of solidification at 10708C. It is clearly found Ba that as solidification proceeds, C L422 increases, acBa companying the increase in C L123 and the decrease in substitution content of the Nd123 crystal even if the crystal grows isothermally. However, the crystal, of which the substitution content is 0.04 of the three-phase field, was estimated to be 3.5 mm, which does not agree well with the experimental results as shown in Fig. 4. The Nd422 particle pushingrtrapping behavior and the diffusion of all elements, i.e., flux balance at the interface, should be involved in this model to describe the crystal growth more precisely. According to the diffusion growth model w18–20x, the concentration difference in the interface liquid between RE211 and RE123 could be a driving force for the crystal growth of RE123 crystal. One can understand from the schematic phase diagram, as shown in Fig. 11, that the equilibrium liquidus of Nd123q L and the metastable liquidus of Nd422q L approach each other and intersect at the three-phase field of Nd422q Nd123q L region. This phase relationship implies that as the interface liquid compositions of Nd422 and Nd123 move towards the Ba-enriched side with solidification, the concentration difference between them becomes smaller. That is, the driving force for solidification also decreases as solidification proceeds. Therefore, the growth rate of Nd123 decreases gradually during solidification and crystal growth is stopped because of zero supersaturation when the liquid compositions arrive at the three-phase field. The decrease in the growth rate with solidification also indicates that more Nd422

It has been recognized that Jc property can be enhanced further when larger amounts of finer RE211 particles could be introduced into the RE123 crystal. It is therefore important to investigate the effect of the excess Nd422 content in the initial composition on the growth features of Nd123 crystals. In the case of Nd123q 20 mol% Nd422, the relationship between the growth length and the holding time was investigated as shown in Fig. 14 for the Nd123 crystals grown from the initial composition with the BaOrCuO ratio of 3:4. Similar to the case of the Nd123q 10 mol% Nd422, the growth length increased proportionally with the holding time at the early stage of solidification, and the growth rate of Nd123 decreased suddenly after a certain growth time. However, it should be noticed that the final crystal size for the Nd123q 20 mol% Nd422 is much smaller than that of the Nd123q 10 mol% Nd422 for both a- and c-growth directions, although no remarkable difference in the growth rate at the beginning of solidification could be found. According to the growth mechanism investigation, the increase in the excess RE211 content in the initial composition can increase the solute diffusion flux supplied from the RE211 to the RE123 crystal interface and, subsequently, it may lead to the increase in the growth rate of RE123 crystals. However, the increase in the excess RE211 content is not considered to affect the interface liquid compositions of RE123 and RE211, at least at the beginning of the solidification. Therefore, the liquid composition in the case of Nd123q 20 mol% Nd422 should travel towards the Ba-rich side along the liquidus as described in Fig. 11Žb., as is the case of Nd123q 10 mol% Nd422. Accordingly, it can be considered that higher excess Nd422 contents in the initial composi-

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Fig.14. Effect of the excess Nd422 particles in the initial composition on the holding time dependence of the growth length in the Ža. a- and Žb. c-directions for the isothermal undercooling solidification. Nd123 crystal was grown at 10558C from the initial composition with BaOrCuO ratio of 3:4.

tion affect so as only to promote the change in liquid composition during solidification. That is, when the many Nd422 particles exist in front of the Nd123 crystal growing interface, the Ba andror Cu solute that should be rejected from the Nd123 interface could not be adequately diffused into the liquid ahead of the interface, because of decreases in effective diffusion area and diffusion distance in front of the growing interface. Under this circumstance, the Nd422 interface liquid composition would be easily changed, which in turn enhances the change in Nd123 interface liquid composition through liquid diffusion. Therefore, the higher the excess Nd422 content in the initial composition is, the more remarkably the liquid compositions move towards that of the three

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phase region of Nd123q Nd422q L, which can explain the difference in the growth length as depicted in Fig. 14. During solidification, some of the Nd422 particles are pushed by the growing Nd123 crystal and accumulated gradually ahead of the Nd123 interface. This means that the spatial distribution of Nd422 particles in the liquid at the final stage of solidification would be similar to the situation of the higher excess Nd422 content in the initial composition. Therefore, after solidification proceeds for a long growth time, the Nd422 particles are accumulated and could cause the liquid composition to change remarkably. This phenomenon would cause a sudden decrease in substitution content at the edge of the Nd123 crystal as shown in Fig. 10. The effect of the accumulation phenomena of the primary phase particle is discussed in a separate paper in the case of Y123 which is a stoichiometric compound w14x. In principle, the solidification pass, the liquid composition change and the resultant microsegregation of substitution in the RE123 crystal must be observed for all the cases of the solidification processing of the Nd123 solid solution. However, no significant microsegregation of substitution could be found in the Nd123 single crystals that were produced by the single crystal pulling technique, which resulted in higher Tc w6x. It is considered that this difference is mainly attributed to the compositional change in the liquid due to the formation of the solid solution phase during solidification. In the case of the single crystal pulling, the large Nd123 crystal, which is at most several 20 mm2 in size, was grown from the relatively larger bulk solution which is several hundred times larger than the crystal size. That is, the compositional change in liquid due to the solid solution formation could be compensated by the huge liquid bath and regarded to be negligibly small, which produces the Nd123 single crystal with almost constant substitution from the solution with an almost constant composition during solidification w7x. On the other hand, for bulk material processing in which the Nd422 particles are distributed ahead of the Nd123 crystal growing interface, it is considered that the liquid is not large enough to neglect the change in the liquid composition, which enhances the compositional change and finally leads to the cessation of solidification.

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4. Conclusions The crystal growth mechanism of the Nd123 solid solution was investigated using the isothermal undercooling solidification technique. Every Nd123 crystal grown under different growth conditions was found to grow proportionally with the growth time at the early stage of solidification, but stop growing after a certain growth time. Also, quantitative analysis revealed the decrease in substitution of NdrBa from the seed crystal to the edge of the Nd123 crystal so produced. That is, crystal growth of the Nd123 was clarified to be a non-steady state solidification. It can be explained qualitatively from the equilibrium quasi-ternary phase diagram that this non-steady state solidification was caused by the compositional change toward the Ba-enriched side due to the formation of solid solution. It is also considered that the larger amount of Nd422 particles ahead of the Nd123 crystal growing interface could promote the change in liquid composition indirectly. Therefore, in order to obtain relatively uniformed distribution of substitution in the large Nd123 single domain crystal, it should be reminded, at first, that solidification processing enables the liquid composition change to relax. A low oxygen partial pressure process atmosphere is considered to be one of the effective techniques because the solid solution range of the Nd123 phase is relatively narrow enough to neglect the compositional change. Even under such conditions, it is also necessary to consider the melt processes that can be free from the particle accumulation phenomenon during solidification.

Acknowledgements This work was supported by the New Energy and Industrial Technology Development Organization for the R & D Industrial Science and Technology Frontier Program.

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