Ivan A. Parinov

Mechanics and Applied Mathematics Research Institute, Rostov State University, Rostov-on-Don 344090, Russia

Abstract—The possible structural mechanisms leading to a nonmonotonous behavior of critical current in dependence on the annealing time in BPSCCO/Ag monofilamentary tapes are discussed. It is assumed, the main cause finding a diminution of critical current in long times of reaction after attainment of maximum value is the pore transformations rather than a decrease of the pinning efficiency in the grains due to lead expelling during calcination. The phenomenological models of pore drag, shrinkage, coarsening and coalescence at the grain boundaries and possible pore breakaway into framework of diffusion processes study are developed. These models allow to qualitatively estimate effects of initial porosity, grain boundary and pore mobilities, boundary and surface diffusivities, and other parameters on the critical current in monocore Bi-2223/Ag tape for different annealing regimes. It is shown, that pores separated from grain boundaries on some degrees surpass a coherence length, can not serve effective pinning centres and due to percolation properties must considerably decrease the critical current in long annealing.



As it has been shown in [1] the critical current in the monofilamentary Bi-2223/Ag tape, at first, increases with annealing time, attains maximum value and then decreases with reaction time. This behavior has been connected by authors with action of competing mechanisms which initially cause an improvement of the grain boundary quality and then to lower pinning strength. The critical current decrease has been explained by the lead expelling during sintering and corresponding pinning strength degradation. However, during BSCCO/Ag tape processing considerable pore formation and transformations due to CO2 release have been observed [2], in particular leading to bubbles arising and the critical current decrease. For example, 200 ppm of carbon has caused up to 36% porosity in the core of Bi-2212/Ag tapes [2].

The aim of the present paper is to discuss another than in [1] possible mechanisms of the critical current diminution during long annealing due to inevitable transformations of pores which attach to grain boundaries. Some regimes of pore transformations, namely pore drag, shrinkage, coarsening, coalescence and breakaway are considered.



In phenomenological analysis the grain growth and corresponding motion of pores located initially at triple grain junctions are assumed. The complete separatrion of pore from grain boundary occurs after pore movement on two-grain interface. Then preliminary transition of pore occurs from triple junction on two-grain interface in accompaniment of the grain disappearance process involved in grain growth. Latter is accompanied by coalescence of the triple grain junction pores. The motion of pore together with grain boundary takes place because of inducing a flux of atoms from the leading to the trailing surface of the pore. In this, the pore distortion stated by the pore velocity is a necessary consequence of pore motion caused by surface diffusion. At first in analysis, a steady-state motion is considered. Then all replacements of pore change regimes are connected with unstable state behavior. This approach allows to describe different pore motions accompanying grain growth, namely pore drag, shrinkage, coarsening, coalescence and breakaway. Moreover, corresponding critical velocities and sizes are estimated in dependence on the annealing temperature, initial grain and pore sizes, dihedral angle (the angle between grain boundary and pore surfaces), grain boundary and pore mobilites, boundary and surface diffusivities. Then the pore and grain size trajectories defining various regimes are deduced.


Though a grain size observed in monocore Bi-2223/Ag tapes has remained constant during various durations of annealing [1] (there annealing times have changed in the interval from 40 to 240 hours), nevertheless, the grain size distribution could be altered during reaction. This is supported by considerable lead expelling monotonously increasing with annealing time [1]. But then these additions heterogeneously distributed into material can inhibit only a local grain growth in Bi-2223 core. Moreover, the phenomenological analysis has shown, that for shrinkage of grain boundary pores and averting of pore separation there are two main conditions: (i) a small grain boundary mobility, and (ii) a large boundary diffusivity. However, simultaneously both these conditions can only be satisfied in the presence of appreciable addition drag, throughout the grain disappearance process. Finally, as it has been shown in modeling of fracture processes in YBCO the size distributions play more important role to compare with mean sizes [3]. Hence, a preservation of grain size value in different annealing times does not allow to assert an absence of grain growth and microstructural alterations.

In discussion of pore breakaway processes, at first it should be noted, that pores attached to grain boundaries decrease due to boundary grain diffusion, but when pore separates from grain boundary and locates into grain, one can shrinkage only thanks to much more slow diffusion process of crystalline lattice. Further, the steady growth of pore is possible at the dihedral angles of Y <p , and pore stability rises with decrease of Y . In Bi-2223 core there is a spectrum of dihedral angles, connected with various grain boundary structures which form during processing. This spectrum corresponds to critical size interval of pores, as rule located at the low angle boundaries (those especially are character for Bi-2223/Ag tapes, where effective misalignment angle between grains is equal to approximately 7.5o [1]). Then, the distributions of different diffusivities and grain boundary mobilities exist thanks to heterogeneous distributions of additions. The material changes which suppress pore separations can be estimated by comparison of critical pore size with trajectories of pore and grain sizes at the final stage of annealing. Developed approach allows to determine intervals of pore size change for avoidance from pore separation. It is most desirable behavior in annealing when grain boundary mobility, initial pore size (a0) and boundary diffusivity are very small. In this case a peak size of pore for the process of pore and grain coarsening coincides with initial pore size in precursor sample. Then the pore coarsening excludes during annealing. In other case it is necessary to consider processes of optimum pore coarsening and averting of pore separation.

At the ac >>a0>>a* (where ac is the critical size of pore breakaway, a* is the critical size for exclusion of pore coarsening) the pore separation may be avoided by increasing the ratio of the boundary to surface diffusivity, consistent with a0< ac , until the condition of pore coarsening exclusion is satisfied. When a0» a* the large values of surface diffusivity are necessary to carry out a condition of ac >a (where a is the pore size) during following pore coarseniung. But this requirement distinctly distinguishes with conditions of initial stage of densification. Hence, different temperature regimes are desirable at the initial and final stages of calcination.

The phenomenological analysis states that a lower bound for pore separation at all reasonable values of a0 /R (where R is the grain radius) is
ac2» 2DSd Sg SW 1/3(3-Y )/31/2MbkTg b
where DSd S is the surface diffusion parameter, W is the atomic value, g S and g b are the surface and grain boundary energies, respectively, Y is the dihedral angle,  Mb is the grain boundary mobility, k is Boltzmann constant, T is the annealing temperature. Selecting above parameters as following [1,4]: W =2.2* 10-30m3, DSd S=2.5* 10-21m3/s, g S=2g b, Y max=p /2, T=1110K, 2R=25m m (here some parameters have been taken for Al2O3, because of thier absence for Bi-2223), we obtain a very high value of  Mb » 7000m/(Ns) even for ac=100nm. For less pores separated from grain boundary the more grain mobility is demanded. Obviously, the size of pores which can separate from grain boundaries during annealing on some orders of value more than coherence length (» 1nm) in Bi-2223. Then these separated pores can not serve effective pinning centres and because of percolation features must considerably diminish the critical current. Apparently, in long annealing this effect is more important, than deteriorating pinning strength due to lead expelling [1]. It is possible, that namely numerous pore separations and their movement into grain inside have found the critical current decrease in more long calcination after observed Ic maximum at about 180 hours annealing [1]. This assumption needs a careful experimental checking. So, the lead expelling causes a decrease of critical current in long reaction, but rather due to pore transformations occured during calcination, than thanks to decrease of the pinning efficiency in the grains. Therefore, the observance of annealing regimes inhibiting coarsening of grain boundary pores and following pore breakaway demands special attention with aim to improve the critical current in Bi-2223/Ag monocore tapes.

This work was supported by Russian Department of Common and Professional Education in Program of Aviation and Rocket-Cosmic Techniques.


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