40 Ë 2 Superconducting materials
is approximately constant. The thermal conductivity in the superconducting state is
smaller than that in the normal state and almost vanishes at very low temperatures.
Even in the superconducting state, the existence of normal electrons cannot be
completely avoided, due to the so-called quasiparticles in the superconducting state.
The amounts of these quasiparticles in YBCO will affect the thermal conductivity, and
their effect has been observed to decrease rapidly with temperature. It is now widely
accepted that the rapid increase ofkbelowTcand the peak ofkare mostly due to the
contribution of quaispartides located in the CuO 2 planes. However, further study is
needed to clarify the effects of phonons and quasiparticles to the specific contribution.
Marchal et al. [130] reported the dependence of thermal conductivity, ther-
moelectric power, and electrical resistivity on temperature for a bulk, large-grain
melt-processed YBCO HTS containing two grains separated by a well-defined grain
boundary (see Fig. 2.9). Transport measurements at temperatures between 10 and
300 K were carried out both within a single grain (intra-granular properties) and
across the grain boundary (inter-granular properties). The influence of an applied ex-
ternal magnetic field of up to 8 T on the measured sample properties was also investi-
gated. The presence of the grain boundary is found to strongly affect the electrical
resistivity of the melt-processed bulk samples; however, it has almost no effect on
its thermoelectric power and thermal conductivity, within experimental error. The
results of this study provide direct evidence that the heat flow in multi-granular melt-
processed YBCO bulk samples should be virtually unaffected by the presence of grain
boundaries in the material.
The coefficient of thermal conductivity of HTS bulk is about 2-10 W/mK at 77 K and
very small below 10 K. Generally, there is a peak at around 50 K (see Fig. 2.9a–c). The
planar structure of HTSCs makes the thermal conductivity anisotropic. The thermal
conductivity of bulk YBCO is anisotropic: 3.5 W/mK along thec-axis and 14 W/mK
along thea-bplane [110]. Other anisotropic results are 4 and 20 W/mK along thec-axis
and thea-bplane, respectively [131].
2.5.3Thermal expansion
The thermal expansion coefficients,훼, are defined as the change of length or volume
per degree of temperature under constant pressure. The linear thermal expansion
coefficient is defined by훼l=dl/(ldT), dl/lis the change rate of length, dTis tem-
perature change. The unit of linear thermal expansion coefficient is K.−^1 Thermal
expansion of superconducting materials, the change of the superconductor dimension
between room and low operating temperature, is important for both trapped flux
and engineering applications. The stresses resulting from the differential thermal
expansion should be as small as possible. This is especially important for highly brittle
HTS bulk materials, where these stresses may actually damage the superconducting
bulks. The stresses also directly affect the maximum trapped flux in YBCO bulks. The