HTSC's are the Heterogeneous Materials Indeed

The few levels of scaling hierarchy are treated using the volume averaging theory (VAT) to obtain the non-local governing equations of typical HTSC tape. Starting from the atomic scale level of imperfect microcrystallines, the thermal transport is being described in terms of VAT. The next hierarchical level includes the layered-like polycrystalline ceramic structure of a single filament. One of important questions addressed is the density and characteristics of structural (crystalline morphology) defects and impurities presence causing an influense on the thermal conductivity in HTS ceramics. Also, using the VAT based governing equations analysis was made for features and models of the grain boundaries (GB) medium. Whether the GB is taken as imperfect interface surface or specific volumetric object does the influence on the models of electrical and thermal conductivities. There is also considered the models for electrodynamics in inhomogeneous medium.

At the third scale the description is undertaken for a single multifilament tape produced. The model transport on the atomic subcrystalline level analysis includes consideration of different approaches. Analysis in terms of VAT of the theory by Bardeen, Rickayzen, and Tewordt of thermal conductivity in application to HTS as well as other models based on the Boltzmann equation have been conceived.

The first public presentation of the scaled models for the HTSC's was made at the conference of American Ceramic Society in 1998 - Travkin, V.S. and I.Catton, "A Non-Local Hierarchical Model of Thermal Transport in HT Superconductors", in Proc. Amer. Ceramic Soc. PCR BSD Conf., p. 49, (1998). At that talk I had shown the pictures from the paper by Norton, M.G. and Carter, C.B., (1995), "Moire Patterns and their Application to the Study of the Growth of YBa2Cu3O7-d Thin Films", J. Mat. Sci., Vol. 30, pp. 381-389. Those pictures are of the high resolution electron microscopy (HREM) photographs permit direct observation of the grain boundaries and defect structures in thin films of HTSC.

The following picture was taken from the paper by Kim, C.-J., Kim, K.-B., Kuk, I.-H., Hong, G.-W., Park, S.-D., Yang, S.-W., Shin, H.-S., (1997), "Fabrication and Properties of YBa2Cu3O_{7-d} - Ag Composite Superconducting Wires by Plastic Extrusion Technique", J. Mat. Sci., Vol. 32, pp. 5233-5242.

These pictures are the typical images of HTSC's. It is obvious that the both groups of images taken from HTSC's with the difference in spatial scales as large as 3 orders of magnitude, are clearly demonstrating the heterogeneity of the materials at the very distant scales.

Also, many works have been done on the subject of parameters of multilayers with superconductive components, as the example see - Boikov, Yu.A., Ivanov, Z.G., Olsson,E., and Claeson, T., "Epitaxial Ferroelectric/Superconductor Heterostructures," Physica C, Vol. 282-287, pp. 111-114, 1997.

The role of grain boundaries (interface surfaces) has been stressed in many studies. Thus, in the paper by Müller, G., Klein, N., Brust, A., Chaloupka, H., Hein, M., Orbach, S., Piel, H., and Reschke, D., (1990), "Survey of Microwave Surface Impedance Data of High - T_{c} Superconductors - Evidence for Nonpairing Charge Carriers", J. Superconductivity, Vol. 3, No. 3, pp. 235-242, the significant role of the "surface impedance" data and its influence on HTSC's outlined, expressing how important it is for surface resistance R{s} and the interface - grain boundaries surfaces magnetic field. On page 235 - "typical results for the surface resistance R{s} as a function of temperature and surface magnetic field are presented for polycrystalline as well as for single crystalline samples of oxide superconductors." The data measured for the specific model (accounting for Josephson coupling between grains) are shown regarding the surface resistance on pages 236 and 237 - Figs. 1,2. It is important to say here that the difference between the bulk effective resistance R{eff} and the intrinsic surface resistance is recognized - "In Fig. 2, the corresponding difference between R{eff} and R{s} is demonstrated for a YBa2Cu3O7 film...".

Will be published more on Heterogeneous HTSC current events.

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