Review Article
Open Access

Critical Current Degradation in Superconducting Materials
with Nano-Defects Induced by Heavy Ions Irradiation

Sosnowski J

Electrotechnical Institute, Pożaryskiego 28, 04-703 Warsaw, Poland

***Corresponding author:**Sosnowski J, Electrotechnical Institute, Pożaryskiego 28, 04-703 Warsaw, Poland, email:

Received: March 06, 2014; Accepted: July 11, 2014; Published: July 16, 2014

**Citation:**Sosnowski J (2014) Critical Current Degradation in Superconducting Materials with Nano-Defects Induced by Heavy Ions Irradiation. Nanosci Technol 1(3): 1-4.

AbstractTop

This paper has been considered an influence of the nano-defects
created in the process of the heavy ions or fast neutrons irradiation
on the current-voltage characteristics and critical current of multilayered
high temperature superconducting materials. Theoretical
model based on an energy balance analysis for the system of the vortex
captured on pinning centre has been presented and used for the
critical current description. The regular arrangement of the columnar
type defects caused by irradiation has been considered. In the model
has been taken into account, a Lorentz force acting on pancake type
vortices induced by current flow and elasticity energy of deformed
vortex lattice. The calculations of the I-V characteristics and critical
current have been performed in the function of nano-sized defects
dimensions and their concentration. The results of calculations
indicate in which way the degradation of critical current occurs under
the irradiation process for HTc sample with optimal concentration of
internal defects. For such optimally prepared tapes the irradiation
leads to the decrease of the critical current and appropriate change
of the current-voltage characteristics. Elaborated model has been
applied to the second generation tapes. While it is possible extend it
also on tapes of the first generation and low temperature wires.

**Keywords:**Nano-Sized defects; HTc Superconductivity; Neutrons irradiation; Critical currentIntroductionTop

Physical properties of the superconducting materials,
both high temperature HTc as well as low temperature LTc
superconductors are very sensitive to their stoichiometry
including existence of structural defects. While chemical
composition is responsible mainly for critical temperature
of superconductor, second crucial from applied point of view
parameter of superconductors, which is critical current is very
strongly dependent on the nano-sized defects appearance. The
nano-defects in superconducting tapes can arise in the nuclear
physics devices, such as accelerators, with the superconducting
windings focusing the ionic beam and in current leads. In these
devices superconducting materials are frequently exposed to
the direct irradiation by the heavy ions or fast neutrons, creating
defects of the nanometric size, it is nano-defects. But it is not
unique way of creation the nano-sized defects in superconductors.
They arise too in the usual technological process of fabrication
these wires and their handling, as is shown in Figure 1. Black points indicate mainly nano-pores and CuO2 grains. During the
winding process of the superconducting coils the defects in the
superconductors will arise in the form of the micro crushes. These
nano-defects appearing in the superconducting tapes used in the
windings of the superconducting magnets of the accelerators
influence their proper work through the pinning interaction,
enhancing the critical current but too large ions bombardment
damages the structure of superconductor. It is important
task therefore to investigate function and mechanism of the
degradation of the critical current under the irradiation existence.
It concerns especially HTc superconducting tapes characterised
by 2D superconductivity mechanism, as well as Nb3Sn, which are
also sensitive to irradiation creating disorder in linear chains of
Nb atoms, responsible for superconductivity. For NbTi materials
indicating 3D mechanism of superconductivity irradiation
effects should be not so important from the superconducting
critical temperature point of view. Onto relevance of this pinning
interaction for properties of superconductors indicate many
papers devoted to this field, from which are referred here [1-7].

Model of the Current-Voltage Characteristics

Theoretically influence of heavy ions irradiation on the

**Figure 1:**Scanning Electron Microscopy (SEM) image of the cross-section, superconducting Bi-based tape, indicating an existence of nanostructural defects. The length of the cross-section is about 50 μm.

critical current of multi-layered HTc superconductors, in
which structure pancake type vortices are generated, has been
considered basing on an analysis of the energy balance of the
system of captured vortex in the nano-defect, caused by the heavy
ions irradiation. Described geometry is presented in Figure 2.
Cylindrical defects shown here schematically are generated by
irradiation of superconducting material in the form of tape or
film by heavy ions, while rectangular defects can arise during
the winding procedure of the superconducting coils, leading to
the micro-crashes generation, as it was stated previously. Shift
of the vortex from the captured, equilibrium position, as shown
in Figure 2 causes an increase of the normal energy of the system
[8-11]. From the other side pinning of an individual vortex leads
to its displacement in the regular vortex lattice and causes an
enhancement in the elasticity energy of the system because the
regular vortex lattice is disturbed then. Also current flow leads
to rise of the Lorentz force tearing the pancake vortices, which
start to diffuse inside the superconductor [12]. Energy barrier
appears then, in which each pancake shape vortex should pass in
the flux creep process. An enhancement of the energy of system
connected with the normal state development during the shift of
the pancake type vortex, leads to potential well appearance and
is given for defects of cylindrical geometry by an expression:

$${U}_{}=\frac{{\mu}_{0}{H}_{c}^{2}l}{2}[{\xi}_{}^{2}(\alpha -\pi -\frac{\mathrm{sin}2\alpha}{2})-{R}_{0}^{2}(\beta -\frac{\mathrm{sin}2\beta}{2})]$$
In Equation 1 has been used notation shown in Figure 2.
In the case of large diameters of defects and especially microcrushes
flat geometry of the pinning centres shown in left part
of Figure 2 can be considered. For that geometry potential well
shape is given by:

$${U}_{}=\frac{{\mu}_{0}{H}_{c}^{2}l{\xi}_{}^{2}}{2}(\alpha -\pi -\frac{\mathrm{sin}2\alpha}{2})$$
In Equations 1-2 has been applied energy scaling in such a
way that normal state energy is on zero level. Then the depth of
the pinning potential well is equal to the condensation energy
because it is just the gain of the system energy with totally
pinned vortex. Hc denotes thermodynamic magnetic field,
angles α and β shown in Figure 2, describe the deflection of
the vortex core against its equilibrium position in the pinning
centre. R0 is the radius of the pinning centre - columnar defect;

**Figure 2:**Scheme of the geometry of the interaction of the pancake vortex of the core radius equal to the coherence length ξ captured on the rectangular (left) and cylindrical (right) defect.

coherence length ξ describes the radius of the core of the vortex,
while l is the thickness of the vortex, for HTc superconductors
of the thin pancake form, approximated by the thickness of the
superconducting layer. The pinning potential determined above
is supplemented by the Lorentz force potential, connected with
the interaction of the local current density surrounding vortex
and magnetic induction B, tearing it off from an initial, equilibrium
capture position. It has been considered here an initial vortex
position onto the depth of the coherence length ξ inside the
pinning centre, which is favorable from the point of view of the
shielding currents configuration. Potential well is also influenced
by vortex lattice elasticity energy, as it was stated previously.
The tilting of the potential energy wells, given by Equation 2
caused by the current flow and Lorentz force potential leads to
the expression for an energy barrier, which should cross vortex
in the flux creep process, in the function already of the reduced
current density i = j/jc. j is here transport current density, while
jc critical current density expressing the transitions between flux
creep and flux flow states:

$${j}_{c}=\frac{{\mu}_{0}{H}_{c}^{2}}{\pi {\xi}_{}B}\cdot \frac{S(1-S/{d}^{2})}{{d}^{2}}$$
*B*is applied magnetic induction,

*μ0*magnetic permeability. Parameter S is the cross-section of nano-defect, while d the lattice constant of the regularly arranged nano-defects into the square lattice. Potential barrier height is given then as follows for flat defects:

Potential barrier ΔU given by Equation 4 is strongly
dependent on the kind of defects, their size and concentration
and determines the shape of the current-voltage characteristics
of the superconductors:

$$E=-B\omega d\left[\mathrm{exp}\left[-\frac{\Delta U(0)}{{k}_{B}T}\left(1+\frac{j}{{j}_{C}}\right)\right]-\mathrm{exp}\left(-\frac{\Delta U}{{k}_{B}\text{\hspace{0.17em}}T}\right)\right]$$
E is electric field, while ω the flux creep frequency, k

_{B}Boltzmann’s constant,*T*temperature.Equation 5 describes both forward as well as backward flux
creep processes and has been used according to presented model
for investigations of the current-voltage characteristics and
then critical current, filling electric field criterion, dependence
on the heavy ions irradiation. This task has great importance
for an improvement of our knowledge on the work of the
superconducting windings in accelerators used in nuclear physics
investigations. As the result of irradiation the columnar defects
are created in superconducting tapes. In model it was assumed
that these defects, acting as pinning centres form square array.
Their lattice constant is inversely proportional then to the square
root from the surface concentration of the defects. The results of
the numerical calculations of the current-voltage characteristics
of the HTc superconducting tape under influence of irradiation are shown in Figures 3-4. Figure 3 presents the influence of the
irradiation dose on the current-voltage characteristics of HTc
superconductor with optimal initial concentration of inherent
defects. Current-voltage characteristics are strongly shifted then,
which indicates that the tape is passing onto the over-doped with
nanodefects region, while its structure is damaged.

In Figure 4 from other side is shown the influence of the diameter of the nano-sized defects on the current-voltage characteristics of HTc superconductor. Also in this case strong influence of this parameter is observed here.

At an aim of comparison the theoretical results predicted by proposed model with experimental data the calculations have been peformed of the influence of the static magnetic field amplitude on the current-voltage characteristics. Measured I-V characteristics on YBaCuO sample in static magnetic field, of value given at each curve are shown in Figure 5. Temperature of measurements was 77 K, while critical temperature of superconducting ceramic above 90 K. These measurements are in qualitative accordance with theoretical predictions of model presented in the Figure 6.

In Figure 4 from other side is shown the influence of the diameter of the nano-sized defects on the current-voltage characteristics of HTc superconductor. Also in this case strong influence of this parameter is observed here.

At an aim of comparison the theoretical results predicted by proposed model with experimental data the calculations have been peformed of the influence of the static magnetic field amplitude on the current-voltage characteristics. Measured I-V characteristics on YBaCuO sample in static magnetic field, of value given at each curve are shown in Figure 5. Temperature of measurements was 77 K, while critical temperature of superconducting ceramic above 90 K. These measurements are in qualitative accordance with theoretical predictions of model presented in the Figure 6.

Influence of Created by Heavy Ions Irradiation
Defects on the Critical Current

Above described theoretical model has been used then
for determining the influence of the irradiation by heavy ions
and fast neutrons on the critical current of HTc tapes. The
irradiation changes the lattice constant of the defects array
influencing the critical current density given by Equation 3 as
well as critical current filling electric field criterion, described
by Equation 5 and diminishes therefore the superconductor
volume. Calculations of the critical current as well as currentvoltage
characteristics have been performed for optimally
initially defected sample, in the technological process, as shown
in Figure 1. Then additional concentration of nano-defects
arising through the ions bombarding process destroys mainly
superconductivity. Simplified model leading to the expression
3 for critical current, based on individual interaction of vortex
with pinning centre has been extended on the case of the regular
ordering of defects into lattice, taking into account the decrease

**Figure 3:**Influence of the nano-sized defects on the current-voltage characteristic of HTc superconductor optimally initially doped with nano-defects, for surface concentration of defects equal to: (1) 105·10

^{10}cm

^{-2}, (2) 99·10

^{10}cm

^{-2}, (3) 92,5·10

^{10}cm

^{-2}, (4) 80·1010 cm

^{-2}, (5) 74·1010 cm

^{-2}, (6) 68·1010 cm

^{-2}.

**Figure 4:**The influence of the dimension of the nano-sized defects on the current-voltage characteristics of HTc superconductor

**Figure 5:**Measured in liquid nitrogen temperature magnetic field dependence of the current-voltage characteristics of YBaCuO superconducting ceramic. The static magnetic field values are given in milliteslas at each curve.

**Figure 6:**Calculated current-voltage characteristics of the HTc superconductor in static magnetic field of the amplitude: (1) B=21,5 mT, (2) 16,3 mT, (3) 8,5 mT.

of the cross-section of the deformed by nano-defects regions and
increase of the pinning interaction. Then HTc superconducting
tape of the second generation has been treated as long thin film
composed from the regions of smaller cross-section, in which
appear defects and regions non-deformed. The same current
I flow through both of these connected in raw domains, but
different is already the current density j. Because these domains
are electrically connected, so total electric field registered on the voltage taps is superposition of electric fields generated on each
of them. For simplifying the calculations, especially concerning
the separation of these two parts it has been assumed the square
cross-section shape of the defects. The strong influence on the
critical current of the division of tape onto un-defected and
defected regions is presented in Figure 7. It is shown here the
comparison of the dependence of the critical current received
in the simple homogeneous approximation given by Equation
3 with modified inhomogeneous approach taking into account
just existence of these two electrically connected in raw regions.
For both cases it is observed strong decrease of the critical
current with irradiation for optimally initially defected tape.
This approximation concerns especially HTc superconducting
tapes of the second generation (2G), in which superconducting
current flows mainly in thin superconducting layer, strongly
sensitive therefore to the nano-defects. On the other hand in the
case of the first generation wires, thin filaments are immersed
into the silver matrix. Then beside this partition effect should
be additionally treated parallel connection of both un-deformed
and deformed regions with the silver matrix, as is in the sharing
current process. This should additionally modify the critical
current dependence on irradiation. In Figure 8 is shown the
critical current dependence not only on irradiation of heavy ions
concentration but also on the nano-defects dimension, which is
other important parameter.

**Figure 7:**Theoretically predicted influence of the heavy ions irradiation on the critical current of the HTc superconducting tape for the model: (1) connected in raw un-defected and defected domains, (2) homogeneous approach.

**Figure 8:**Calculated influence of the irradiation dose, creating nanosized defects of the dimensions given at each curve, on the critical current of HTc superconducting tape.

Conclusions

Summing up we state that results of present investigations
indicate on the relevant meaning of heavy ions irradiation for
the proper work of superconducting windings used in cryogenic
accelerators. The case of HTc superconducting tapes of second
generation was investigated, while this model can be applied
too for the first generation tapes, as well as low temperature
superconductors, especially Nb3Sn wires with linear chains of
transitions atoms responsible for superconductivity.

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