Nestler, Britta

Schmitz, G.J.

Seeßelberg, M.

Steinbach, I.

Schmitz, G. J.

KITopen

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 7, NO. 2, JUNE 1997 Macroscopic and Microscopic Modeling of the Growth of YBaCuO Bulk Material 1739 M. SeeBelberg, G. J. Schmitz, B. Nestler and I. Steinbach ACCESS e. V., Intzestrasse 5 ,  D-52072 Aachen, Germany Abstruct- Melt processing of YBaCuO is widely accepted to yield the best superconducting properties in bulk spec- imens of this material. Modeling of melt processing is a promising tool to optimize the production of bulk YBaCuO material. In a macroscopic simulation, temperature fields in YBaCuO specimen of arbitrary geometry in e. g .  Bridg- man or VGF furnaces are calculated during solidification. This allows the visualization of the shape of the solidifica- tion isotherm and its dependence on cooling rate and the geometries of furnaces and samples. Microscopic modeling of microstructural evolution dur- ing YBaCuO growth is of great interest to deepen the un- derstanding of growth kinetics. For this purpose, YBaCuO growth can be simulated numerically using the multiphase field model. I. INTRODUCTION Melt processing of small samples of YBaCuO material in principle is accepted to  yield superconducting proper- ties exceeding the requirements for several technical appli- cations such as magnetic bearings and fault current lim- iters. However, industrial applications of this high T, su- perconducting material require improved manufacturing processes. Scaling up the sample size of single domain bulk material is as necessary as a reduction ofthe process- ing time. Macroscopic and microscopic simulations yield a deeper insight in the melt texturing process and help to overconie problems related with it. In this paper results of macroscopic and microscopic simulations are presented. Macroscopic thermal field calculations allow the predici- tion of the temperature distribution even in large specimen of complex geometry and accordingly enable process opti- mization. Thermal field calculations are carried out using the finite element code CASTS (=Computer Aided Solidi- fication Technologies) [l]. The prediction of the microstructure resulting from a specific process also is mor ' important with respect to the control of good superconc tive resp. magnetic properties of the resulting specimen. imulations of the grain growth and the resulting microst ctures are performed with the multiphase field method [ . Manuscript received August 27, 1996. This work is financially supported by the Bundesministerium fur Bildung, Wissenschaft, Forschung und Technologie (BMBF) under Grant No. 13 N6661 4. 11. MACROSCOPIC SIMUL.4TIONS OF MELT GROWTH OF YBACUO In process optimization of the melt growth process, both minimization of the processing time as well as ,an improved texture of the bulk material is sought. This demands an optimal choice for the temperature program of the heaters of the furnace being used for the melt growth process. For this purpose information about the procesls is required which can hardly be measured experimentalky, e. g. the point of time and the spot where the isotherm of solidifi- cation enters the YBaCuO specimen. The quality of the melt growth process also depends on the curvature of this isotherm. Therefore, the numerical simulation of the tem- perature field during the process is a valuable tool to re- cover this data. The software CASTS [l] is designed to  perform such calculations. Besides solving the heat con- duction equation this software also takes into account the transport of energy from the heaters to the specimen (and vice versa) via infrared radiation as well as the release of latent heat. With this kind of process simulation the time required for t,he melt growth process can he reduced significantly. This can be done by choosing an appropriate temperature program for the heaters of the furnace ensuring t h t  the isotherm of solidification enters the specimen exactly after a specified time. Furthermore, the cooling rate can be in- creased after the retirement of the solidification front from the specimen, Fig. 1. Also the distortion of the tempera- ture field in the YBaCuO specimen by the holding devices becomes visible. The temperature fields in a Bridgman furnace are visu- alized in Fig. 2. The temperatures of the heating zone and the water-cooled cooling zone were assumed to be 1150" C and 20" C respectively; the height of the bafflje (i. e. the thermal insulation zone) was 3.4 cm. The temperature field was calculated for cylindrical YBaCuO specimen with two different diamekrs (10 mm and 32 mm). The withdrawal velocity was set to 1 rnm/h. As shown in Fig. 2, the devia- tions of the isotherm of solidification from a planar surface are negligible. The temperature gradient parallel to  the furnace axis at the isotherm of solidification is 80 K/cm. The magnitude of this gradient can be increa,sed by de- creasing the height of the ba,ffle. Also the visualization of the shape of the isot:herm of so- lidification is helpful to  imp:rove the melt growth process. As an example the isotherms were calculated jn cylindri- 1051-8223/97$10.00 0 1997 IEEE Authorized licensed use limited to: Hochschule Karlsruhe. Downloaded on June 9, 2009 at 06:00 from IEEE Xplore.  Restrictions apply.First published in: EVA-STAR (Elektronisches Volltextarchiv – Scientific Articles Repository) http://digbib.ubka.uni-karlsruhe.de/volltexte/1000019285 1740 1 ---->1025.00 t = 816 min t = 916 min t = 1216 min Fig. 1: Simulations of the temperature field in a conventional furnace with vertical temperature gradient. Sections through the specimen (diameter 30 mm, height 15 mm) are shown. The cooling rate is T = -2 K/h. The isotherm of solidification is marked with black color. Experimental set-up is from IPHT Jena, Germany. >I250 >I195 >I140 >I  085 > I  030 > 975 > 920 > 865 > 810 > 755 > 700 "C Fig. 2 Simulations of the temperature field in a Bridgman furnace Sections through the furnace are shown The specimens have a diameter of 10 mm (left diagram) and 32 mm (right diagram). Withdrawal velocity is 1 mm/h A mirror surface attached to  the baffle ensures that the baffle does not become too hot The black drawn isotherm of solidification is planar t = O h  t = l  h t = 2 h  t = 3 h  >I  200 >1150 >1100 > 1050 >I 000 > 950 > 900 > 850 > 800 > 750 > 700 @ = I O "  t = O h  t = 1 . 5 h  t = 3 h  ["Cl 0 = 3 2 m m  Fig. 3 .  Simulations of the temperature field in a VGF furnace Sections through the specimen with height 5.4 cm and diameter 10 mm (above diagrams) and 32 mm (below diagrams) arw shown Cooling rate IS T =-lOK/h The isotherms of solidification are marked with black color. The curvature of the isotherms increases sllghtly with the diameter of the speclmen Authorized licensed use limited to: Hochschule Karlsruhe. Downloaded on June 9, 2009 at 06:00 from IEEE Xplore.  Restrictions apply.Fig. 4: Left side: Micrograph of a quenched YBaCuO specimen. Dark (medium, light) grey corresponds to  the liquid (211, 123) phases respectively. Engulfed 211 partivcles are clearly seen. Also bridge formation Is observed. Middle and right side: Microscopic simulation also reveals engulfment and bridge formation. Black (grey, white) color indicates the 123 matrix (211 particles, liquid), respectively. H lorm Fig. 5: Left side: Experimental observation of grain selection 123 grains grow from the NdBaaCusO7-, powder on the left side. A short distance (75 pm) is sufficient for grain coarsening. Closer examinations reveal that the selected grains have c-axis orientsation. Right side: The effect of grain selection was also studied by numerical simulations using the phase field method. Different 123 grains are visualized by different grey levels. cal specimen of different radii in a Vertical Gradient Freeze (VGF) furnace with 8 ring-shaped heaters with a diameter of 8.9 cm [3], Fig. 3. In this example the cooling rate was T =-lo K/h. In the specimen with 10 mm diameter thc curvature of the isotherm is almost planar. A small cur- vature of the isotherm of solidification is observed in the specimen with a diameter of 3 2  mm. For values of the cool- ing rate below -10 K/h the curvature of the isotherms does not depend on the cooling rate. The temperature gradi- ent parallel to  the furnace axis is 40 K/cm (45 K/cni) in the specimen with diameter 10 mm ( 3 2  mm). In further in- vestigations, the temperature program of the heaters in the VGF furnace could be optimized to  minimize the curvature of the isotherms. 111. MICROSCOPIC SIMULfl'l'IONS OF YBACUO GRAIN GROWTH Modeling of microstructulre formation is a relative new topic in materials' sciences. Three differcnt approaches can be distinguished: Monte-Carlo-simulations [4] icellular au- tomata models [5] and the phase field method [6], [7] .  R.e- cently, t,he phase field concept has been extendled to mul- tiphase systems [ 2 ] .  This model allows simulations of the Authorized licensed use limited to: Hochschule Karlsruhe. Downloaded on June 9, 2009 at 06:00 from IEEE Xplore.  Restrictions apply.1742 peritectic solidification process of YBaCuO fronl thci I i i d t .  In the multi phase field concept each phnse field variable represents either the liquid or a single grain of the phases Y1Ba2Cu30T-zor YaBalCul 05-rrespcictiyely. Their eye- lution in time is described by a. set of nonlinear pariibolic. differential equations being coupled with a diffusion equ;~- tion determining the local concentration of 1-ttriuin at, any position and time. These equat,ions are discret.izeti i i  finite difference technique using explicit algorithms on a workstation. The first example deals with bridge formation and en- gulfment of Y2Bal Cul 05-,particles into the solidification front of the Y1Ba2Cus07-Lphase [8]. Below the perit temperature, 211 particles are dissolving in the prcscnce of growing 123 grains. As a. result. a gradient, of the  Y- concentration occurs and growth of 123 grains toiyiirds thc  dissolving 211 grains is favoured (bridge formation). If the 211 particles are too big there is not enough time to (lis- solve before the arrival of the 123 solidification front. As ;I result, they are trapped in the 123 matrix and may ~ ( Y V P  as pinning centers (engulfment). These processes are os- perimentally observed and are also amenable to nurneric:;il simulations. Fig. 4. Another example is a recently proposed geometrically organized grain growth process [9], [lo]. This process is supposed to have the potential for an economic isorhcir- mal production of e. g. superconducting tapcts. Essenri;illi. for this process is grain selection of 123 grains causid Iiy anisotropic growth conditions. Of particular interest is t l i c  grain selection distance required for the 11-ell orientcd graiIis to overgrow the misaligned ones. The phase field iiic:rliocl is used to study this process, Fig. 5. For example. the c+f'err of variations of the diameter of the heterogeneous weds m t l  their mean distance can be investigated. I\r. CONCLUSIONS :\XD OUTLOOK Modeling of YBaCuO melt, processing is a valiiablo tool to optimize the production of I,ulli YB;LCUO inatcri;il. Macroscopic simulations of t,he thermal fields in the speci- men during the melt texturing growth process provide in- formation about position, curvature and velocity of the isotherms of solidification. This alloms for a substantial shortening of the processing time as well as a minimization of the curvature of the isotherms during so1idific;ition of large samples. A quasi isothermal seeded melt growth pro- cess with a cold finger at the site of the seed is most promis- ing for an economic large scale production of YBaCuO bull: material. In contrast to  the directional solidification pro- cesses discussed above, the temperature gradients occuring in these processes are very small. Thus) the temperature field in the specimen is dominated by the release of la- tent heat. Simulation of the temperature fields makes an important contribution to exploit the potential of process optimization. Microscopic simulations assist to deepen the understand- ing of the evolution of the microstructure in YBaCuO bulk Authorized licensed use limited to: Hochschule Karlsruhe. Downloaded on June 9, 2009 at 06:00 from IEEE Xplore.  Restrictions apply.

Macroscopic and Microscopic Modeling of the Growth of YBaCuO Bulk Material

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Macroscopic and Microscopic Modeling of the Growth of YBaCuO Bulk Material

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