ISSN 1063-7834, Physics of the Solid State, 2006, Vol. 48, No. 2, pp. 207–212. © Pleiades Publishing, Inc., 2006. Original Russian Text © D.A. Balaev, I.L. Belozerova, D.M. Gokhfeld, L.V. Kashkina, Yu.I. Kuzmin, C.R. Michel, M.I. Petrov, S.I. Popkov, K.A. Shaikhutdinov, 2006, published in Fizika Tverdogo Tela, 2006, Vol. 48, No. 2, pp. 193–198. 207 1. INTRODUCTION The recently discovered superconducting foams [1, 2] are superconducting materials of a new kind which have interesting physical properties [3–5]. A foamed superconductor is a percolation system in which there are an infinite superconducting cluster conducting a transport current and pores of different shape, both closed and open. Pores also form clusters. In a certain range of material densities, the infinite superconducting cluster can coexist with the infinite cluster of open pores. Such a system gives an interesting example of polychromatic percolation [6], where the percolation of an electric current along a superconducting cluster and the percolation of a magnetic flux penetrating into a pore cluster proceed concurrently. An essential prob- lem regarding the magnetic and transport properties of superconducting foams is how the topology of an infi- nite cluster, which is a multiply connected supercon- ducting region, affects the pinning and transport of vor- tices. From the practical point of view, it is important that superconducting foams have a high specific surface area to provide effective heat removal by a cooling agent (liquid nitrogen or helium), which penetrates into open pores. This feature, as well as the still not fully understood peculiarity of the vortex pinning and trans- port [4, 5], allows foamed high-temperature supercon- ductors (HTS) to have high magnetic critical currents that make these materials promising for practical appli- cations. 2. FRACTAL STRUCTURE OF SUPERCONDUCTING FOAMS Low-density samples of Bi 1.8 Pb 0.3 Sr 2 Ca 2 Cu 3 O x (BPSCCO) were produced through solid-phase synthe- sis. The synthesis was about 400 h long. We used tech- nology similar to that described in [7] but with the final annealing conditions modified in such a way that they favored the growth of superconductor microcrystallites along the ab plane. As a result of random crystallite ori- entation, such a growth process leads to material bulk- ing. Another specific feature of the synthesis technique used is that the calcium-deficient precursor was sup- plied with calcium carbonate, which ultimately decom- posed during the final annealing. The excess pressure of Current–Voltage Characteristics of a Foamed Bi 1.8 Pb 0.3 Sr 2 Ca 2 Cu 3 O x High-Temperature Superconductor with Fractal Cluster Structure D. A. Balaev 1 , I. L. Belozerova 2 , D. M. Gokhfeld 1 , L. V. Kashkina 3 , Yu. I. Kuzmin 4 , C. R. Michel 5 , M. I. Petrov 1 , S. I. Popkov 1, 2 , and K. A. Shaikhutdinov 1 1 Kirensky Institute of Physics, Siberian Division, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036 Russia e-mail: smp@iph.krasn.ru 2 Reshetnev Siberian State Aerospace University, Krasnoyarsk, 660014 Russia 3 Krasnoyarsk State University, Krasnoyarsk, 660041 Russia 4 Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politechnicheskaya ul. 26, St. Petersburg, 194021 Russia e-mail: yurk@mail.ioffe.ru 5 CUCEI Universidad de Guadalajara, Guadalajara, Jalisco, 44430 Mexico Received April 28, 2005 Abstract—The influence of the structure of foamed polycrystalline bismuth-based superconductors on their critical currents and current–voltage characteristics is studied. It is found that superconducting foams have a fractal structure, and the fractal dimension of the boundary between the normal and superconducting phases is estimated. The magnetic and transport properties of superconducting foams are investigated, and the current– voltage characteristics are obtained in a wide range of currents. The effect of percolation phenomena on vortex pinning in a foamed superconductor is considered. The current–voltage characteristics of the superconducting foams at the beginning of the resistive transition are found to be in good agreement with a model in which a magnetic flux is assumed to be trapped in the fractal clusters of a normal phase. PACS numbers: 74.72.Hs, 74.81.Bd, 74.25.Fy, 61.43.Hv DOI: 10.1134/S1063783406020016 METALS AND SUPERCONDUCTORS