
Crystallographic defects may locally depress c(r). If
a core sits on one of these defects, the energy of
the vortex decreases. This position-dependent energy
distorts the lattice and produces vortex pinning, i.e.,
flux line motion is prevented until J surpasses J
c
.
Controlling the structure of defects in the material
is thus the key for the optimization of vortex pinning.
The relationship between the elementary pinning
force, f
p
, of one defect and J
c
is rather complex, but
several basic rules exist (Ullmaier 1975). First, the
best pinners are those defects that are just large
enough to accommodate a vortex core, of transverse
size Bx. Second, to increase the total pinning force
the density of defects should be large. Finally, defects
elongated along the H direction (columnar defects)
are particularly appropriate, as they are able to con-
fine large portions of a core.
3. Irradiation Effects in Superconductors
The methods of optimizing pinning in conventional
superconductors have improved (Brown 1981). The
inclusion of nonsuperconducting particles (as in Nb–
Ti wires) or the introduction of dislocations by met-
allurgical techniques are well-known procedures.
Amorphous superconductors are less sensitive to ra-
diation damage, owing to the absence of pre-irradi-
ation crystalline order. Irradiation of clean materials
with very low initial J
c
has been used as a tool to
investigate vortex pinning in samples with a well-
characterized structure of defects.
The very small x of HTSs (B1–2 nm) suggests that
irradiation may be a very appropriate tool for pin-
ning enhancement. The small x and the lack of duc-
tility prevent the use of many metallurgical
techniques to create defects. The controlled genera-
tion of defects by irradiation is a powerful tool in
exploring the novel properties of the vortex matter.
Irradiation of HTSs with light particles, which
produce a random distribution of localized defects
(Civale 1993), reduces T
c
and increases the normal
state resistivity. The initial dT
c
/dF for different ions
and energies is proportional to the nuclear energy loss
rate, confirming that damage is only due to atomic
collisions. For higher F the defective regions start to
merge, and T
c
decreases faster.
Vortex pinning effects of irradiation in HTSs are
best explored in high-quality single crystals, where
weak links are absent and J
c
before irradiation is low.
The introduction of random defects in HTS crystals
enhances J
c
, and cascade defects generated by fast
neutrons are very effective. In YBCO, for instance, J
c
may increase by an order of magnitude (up to
B10
7
Acm
2
) at 5 K and H of a few tesla, and by
two orders of magnitude (up to B10
5
Acm
2
)at77K
and low H. Protons of 2–3 MeV produce similar re-
sults. J
c
increases with F at low doses, reaches a
broad maximum, and eventually drops abruptly at
the F range where T
c
also starts to collapse. As ex-
pected, optimum J
c
occurs when the distance between
defects is a few times the value of x. The damage
produced by electrons in the 1–3 Me V energy range,
which consists mostly of point defects (Frenkel pairs),
also produces a small, but still considerable increase
in J
c
in YBCO and Bi-2212.
Aligned columnar defects (CD) produced by
heavy-ion irradiation are the strongest pinning cen-
ters in HTSs, because of simple geometrical reasons
(Civale 1993). First, they can confine the whole length
of the core, gaining a large pinning energy without
the energy cost of an elastic distortion. Second, their
diameter (5–10 nm) is appropriate to exert a very
large pinning force (Wheeler et al. 1993). The advan-
tage with respect to random defects is dramatic at
high T and H. For instance, for YBCO at 77 K and
5T, J
c
410
5
Acm
2
can be obtained. The density of
CD can be expressed in terms of the equivalent
matching field, the field at which the CD and vortex
densities are the same.
CD generate uniaxial pinning, i.e., the J
c
increase is
anisotropic, being largest when H is parallel to the
tracks. Uniaxial pinning gives rise to the lock-in effect
(Blatter et al. 1994): in the solid phase, H can be tilted
away from the direction of the tracks by a finite angle
and the vortices will still remain trapped in the CD.
Irradiation of Bi-2212 and Bi-2223 with B1GeV
protons has been used to produce fission of the bis-
muth nuclei (Civale 1993). The damage created by the
fission fragments consists of amorphous tracks sim-
ilar to the aligned CD, but randomly oriented. These
isotropic distributions of CD also produce large in-
creases in J
c
, with the technological advantage that
the penetration range of the protons is large
(B50 cm), in contrast to the few micrometers of
heavy ions. Similar fission damage has been intro-
duced in uranium-doped YBCO by irradiation with
thermal neutrons.
See also: High-temperature Superconductors: Thin
Film and Multilayers; Superconducting Materials:
Types of; Superconducting Permanent Magnets:
Principles and Results
Bibliography
Blatter G, Feigel’man M V, Geshkenbein V B, Larkin A I,
Vinokur V M 1994 Vortices in high temperature supercon-
ductors. Rev. Mod. Phys. 66, 1125–388
Brown B S 1981 Radiation effects in superconducting fusion-
magnet materials. J. Nucl. Mater. 97, 1–14
Civale L 1993 In: Jin S (ed.) Processing and Properties of High
T
c
Superconductors. World Scientific, Singapore, pp. 299–369
Szenes G 1996 Formation of columnar defects in high-T
c
su-
perconductors by swift heavy ions. Phys. Rev. B 54, 12458–63
Ullmaier H 1975 Irreversible Properties of Type II Supercon-
ductors. Springer, Berlin
1155
Superconducting Materials: Irradiation Effects