2.5 Thermal properties of HTS bulk Ë 37When a small amount of heat is put into a superconductor, some of the heat is used
to increase the lattice vibrations, and the rest is used to increase the energy of the
conduction electrons. The specific heat of the electrons in a superconductor varies
with the temperature in the normal and the superconducting state. The electronic
specific heat in the superconducting stateCelsis smaller than in the normal state
Celnat enough low temperatures, and the precise measurements indicate that at
temperatures considerably below the transition temperature, the logarithm of the
electronic specific heat is inversely proportional to the temperature. However,Cels
becomes much larger thanCelnas the transition temperatureTcis approached. The
transition to the superconducting state is accompanied by quite drastic thermodyna-
mic changes in the superconductor. The specific heat at the transition from the normal
to the superconducting state in zero magnetic field appears as a jump at the critical
temperatureTc.
Specific heat experiments on bulk superconductors are insensitive to the phase of
the order parameter. However, they can provide valuable information on the density
of states near the Fermi level because the electronic specific heatCeis proportional to
the density of states.
Due to the low specific heat of LTS materials in superconducting state, practical
LTS wires are produced as multifilamentary composites in order to prevent quenching.
In contrast to LHS materials, there are some peculiar features in the specific heat
of YBCO compared with those of conventional BCS superconductors, namely bulk
HTS are thermally stable even in large sample sizes due to their relatively large
specific heat in the superconducting state [126]. However, when a HTS bulk magnet
is activated, another new thermal instability is brought in by the flux motion. For
thermal stability, the cooling power of the system must be larger than the local heat
generation.
Myers et al. [126] reported the specific heats of four superconducting materials
at temperatures from 0 to 300 K and in magnetic fields from 0 to 14 T (Fig. 2.6). The
specific heat of the Bi2212 samples was relatively independent of applied field, the
zero-field specific heat of a two-dimensional random oriented single stack sample
increased from 0.155 J/(kg⋅K) at 4 K to 254 J/(kg⋅K) at 250 K. At 2 K, the specific heat
of a Nb 3 Sn rod-in-tube strand increased from 0.0257 J/(kg⋅K) at 0 T to 0.0716 J/(kg⋅K) at
14 T. In the zero field, the specific heat of a MgB 2 sample increased from 0.623 J/(kg⋅K)
at 4 K to 382 J/(kg⋅K) at 250 K.
Naitoa et al. [127] have measured the temperature dependence of specific heatC(T)
for a Ag (10-20μm thick) deposited YBCO coated conductor (YCC) film (about 1.5μm
thick), YCC reinforced by a thin Cu tape (300μm thick), and a Hastelloy substrate with
a buffer layer. Figure 2.7 shows the temperature dependence of the specific heat of YCC-
Ag20 (20μm), YCC-Ag10 (10μm)+Cu300(300μm), and Hastelloy+buffer. TheC(T) of all
the samples decreases monotonically with decreasing temperature. Absolute values
ofC(T) at 300 K are about 370, 390, and 400 J/(kg⋅K) for YCC-Ag20, YCC-Ag10Cu300,
and Hastelloy+buffer, respectively.