8.5 Applications of Superparamagnetic Materials 171
entropy of a crystal, being the state with the highest degree of order.) As in
these considerations, only the differences of the thermodynamic quantities
caused by the magnetic field are under consideration, one may set S H=0 = 0 and
consequently S H>0 < 0. The change of enthalpy U magn due to an external magnetic field H, is U magn = TS H>0 . The magnetic energy of a specimen with the
susceptibility x is given by
U
H
magn =
1
2
2
χ .
(8.15)
Assuming an adiabatic process, one has the thermodynamic equilibrium
C T U C T
T U U
C T
H
v
v
v
+
=
+
(
) + −
=
−
0
0
2
0
1
2
∆
∆
magn
χ .
(8.16)
Inserting the value for x given in Eq. (8.11) and the proportionality between
the magnetization and the number of unpaired spins N ∝ nm, one obtains
∆T
H
C
nm
kT
H
C
Nm
H
T
v
v
=
=
∝
1
2
1
2 3
2
2
2
2
χ
.
(8.17)
This result proposes to use particles with large magnetic moment to maximize
the magnetocaloric effect. Additionally, one sees that this effect works best at
low temperatures.
It is possible to maximize the magnetocaloric effect by using a material with a
large number of unpaired spins per particle or molecule. Additionally, as this effect
is indirectly proportional to the temperature, it works best at low temperatures.
These are the reasons why this phenomenon was applied until now at temperatures close to zero Kelvin using rareearth salts as paramagnetic materials. The
situation has changed since the superparamagnetic particles have been available,
as instead of a few unpaired spins per molecule, now a few thousand unpaired
spins per particle are available. This allows application at room temperature in
refrigerators. As the lowest temperature in such household appliances is rarely
below 250 K the lowtemperature limit, restricted by the blocking temperature, is
not essential.
Looking at the technical realization, one has to realize that the possible temperature difference is proportional to the magnetic field squared; therefore, the
application of highperformance permanent magnets is necessary and expensive.
One could improve the cooling effect by selecting a material where the Curie
temperature is in the temperature window passed during the cooling cycle; in
this case, the enthalpy of phase change is added to the change of the magnetic
energy.
In technical realization (Figure 8.24), magnetocaloric cooling is applied in a
circular process in four steps:
entropy of a crystal, being the state with the highest degree of order.) As in
these considerations, only the differences of the thermodynamic quantities
caused by the magnetic field are under consideration, one may set S H=0 = 0 and
consequently S H>0 < 0. The change of enthalpy U magn due to an external magnetic field H, is U magn = TS H>0 . The magnetic energy of a specimen with the
susceptibility x is given by
U
H
magn =
1
2
2
χ .
(8.15)
Assuming an adiabatic process, one has the thermodynamic equilibrium
C T U C T
T U U
C T
H
v
v
v
+
=
+
(
) + −
=
−
0
0
2
0
1
2
∆
∆
magn
χ .
(8.16)
Inserting the value for x given in Eq. (8.11) and the proportionality between
the magnetization and the number of unpaired spins N ∝ nm, one obtains
∆T
H
C
nm
kT
H
C
Nm
H
T
v
v
=
=
∝
1
2
1
2 3
2
2
2
2
χ
.
(8.17)
This result proposes to use particles with large magnetic moment to maximize
the magnetocaloric effect. Additionally, one sees that this effect works best at
low temperatures.
It is possible to maximize the magnetocaloric effect by using a material with a
large number of unpaired spins per particle or molecule. Additionally, as this effect
is indirectly proportional to the temperature, it works best at low temperatures.
These are the reasons why this phenomenon was applied until now at temperatures close to zero Kelvin using rareearth salts as paramagnetic materials. The
situation has changed since the superparamagnetic particles have been available,
as instead of a few unpaired spins per molecule, now a few thousand unpaired
spins per particle are available. This allows application at room temperature in
refrigerators. As the lowest temperature in such household appliances is rarely
below 250 K the lowtemperature limit, restricted by the blocking temperature, is
not essential.
Looking at the technical realization, one has to realize that the possible temperature difference is proportional to the magnetic field squared; therefore, the
application of highperformance permanent magnets is necessary and expensive.
One could improve the cooling effect by selecting a material where the Curie
temperature is in the temperature window passed during the cooling cycle; in
this case, the enthalpy of phase change is added to the change of the magnetic
energy.
In technical realization (Figure 8.24), magnetocaloric cooling is applied in a
circular process in four steps: