2.5 Thermal properties of HTS bulk Ë 39Fig. 2.8:Variation of specific heatC(T) of GdBa 2 (Cu 1 −xMnx) 3 O 7 −훿forx⩽0.02 in the temperature
range of 90–100 K [128].
local heating when HTS bulks are activated by pulsed fields and the phenomenon of
flux jumps at low temperature.
2.5.2Thermal conductivity
According to Fourier’s law, the temperature gradient훥Timposed across an isotropic
sample of a cross-sectional areaAresults in a heat flowQgiven by
Q= −kA훥T, (2.2)With the minus sign indicating that heat always flows from a warmer to a colder
region of a substance. The units of thermal conductivity are W/(m⋅K). The thermal
conductivitykconsists of both the thermal conductivity of the electronskeland the
lattice or phononkph.
In pure metals, the electronic component accounts for nearly all the heat con-
ducted, while the lattice component is almost negligible. In superconductors at tem-
peratures well belowTc, electrons condense into Cooper pairs that cannot transport
entropy. Thus, they do not contribute to the thermal conductivity. The phenomenon
can also be understood in terms of the superconducting state being a perfectly ordered
state, i.e. one of zero entropy, thus vanishing thermal conductivity due to the elec-
trons. At sufficiently low temperatures, the thermal conductivity is attributable entire-
ly to lattice waves and is similar to the form of the thermal conductivity of an insulating
material. The thermal conductivity in the normal state(kn)approaches that in the
superconducting state(ks)as the temperature approaches the transition temperature
for all materials, either pure or impure. In normal metals like copper, large electrical
conductivity is accompanied by large thermal conductivity. The ratio between the two