# Enhancement of functional properties of V0.6Ti0.4 alloy superconductor by
the addition of yttrium

SK. Ramjan  Free Electron Laser Utilization Laboratory, Raja Ramanna Centre
for Advanced Technology, Indore - 452 013, India.  Homi Bhabha National
Institute, Training School Complex, Anushakti Nagar, Mumbai 400 094, India.
L. S. Sharath Chandra<EMAIL_ADDRESS>Free Electron Laser Utilization
Laboratory, Raja Ramanna Centre for Advanced Technology, Indore - 452 013,
India.  Rashmi Singh  Nano-Functional Materials Laboratory, Laser and
Functional Materials Division, Raja Ramanna Centre for Advanced Technology,
Indore 452 013, India  P. Ganesh  Materials Engineering Laboratory, Raja
Ramanna Centre for Advanced Technology, Indore - 452 013, India.  Archna
Sagdeo  Hard X-ray Applications Laboratory, Synchrotrons Utilization Section,
Raja Ramanna Centre for Advanced Technology, Indore-452 013, India  Homi
Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai
400 094, India.  M. K. Chattopadhyay  Free Electron Laser Utilization
Laboratory, Raja Ramanna Centre for Advanced Technology, Indore - 452 013,
India.  Homi Bhabha National Institute, Training School Complex, Anushakti
Nagar, Mumbai 400 094, India.

###### Abstract

We show here that the yttrium is immiscible and precipitates with various
sizes in the body centred cubic V0.6Ti0.4 alloy superconductor. The number and
size of the precipitates are found to depend on the amount of yttrium added.
Precipitates with various sizes up to 30 $\mu$m are found in the V0.6Ti0.4
alloy containing 5 at.% yttrium. The large amount of line disorders generated
by the addition of yttrium in this alloy are found to be effective in pinning
the magnetic flux lines. While the superconducting transition temperature
increases with the increasing amount of yttrium in the V0.6Ti0.4 alloy, the
critical current density is maximum for the alloy containing 2 at. % yttrium,
where it is more than 7.5 times the parent alloy in fields higher than 1 T. We
found that the effectiveness of each type of defect in pinning the flux lines
is dependent on the temperature and the applied magnetic filed.

††preprint: J. Appl. Phys.

##  I Introduction

The V1-xTix alloys are promising materials as an alternate to the Nb based
superconductors for high field applications tai2007superconducting ;
matin2015critical ; matin2013magnetic ; paul2021grain ; paul21  especially in
the neutron radiation environment. ivanov1992structural ; sekula1978effect ;
higashiguchi1985microstructure ; weber1982neutron ; audi2003nubase  Moreover,
the V1-xTix alloys are highly machinable and ductile. tai2007superconducting ;
takeuchi2008multifilamentary ; bellin1970critical  However, the critical
current density (JC) of the V1-xTix alloys is about $10^{7}A/m^{2}$ at 4 K,
which is two orders of magnitude less than the commercially available Nb-based
superconductors. matin2015critical  Previous attempts to increase the $J_{C}$
of these alloys by the introduction of defects through the addition of
transition and non-transition elements were ineffective.
efimov1970superconducting  Recently, we have shown that the poly-crystalline
V1-xTix alloys form with large grains having sizes ranging from few $\mu$m to
few millimetres. matin2015critical ; matin2013magnetic  We have established
that the low grain boundary density and the presence of flux flow channels in
the V1-xTix alloys are the main reasons for the low JC of these alloys.
matin2015critical ; matin2013magnetic

The rare-earth elements are found to be immiscible in vanadium and titanium.
Immiscible ; komjathy ; yre ; smi88 ; bus77 ; cha10 ; collin59 ;
peng2017formation  Buschow showed by estimating the energy of formation that
no binary compound containing rare earth and titanium or vanadium will form.
bus77  The solubility of rare earths in the liquid vanadium or titanium is
limited to very low concentrations (< 1 %). yre ; smi88 ; cha10 ; collin59  We
have used this property to introduce a large number of pinning centres by
adding gadolinium in the V0.6Ti0.4 alloy, which resulted in the enhancement of
the JC by about 20 times. paul2021grain  However, the gadolinium precipitates
order ferromagnetically paul21 , which seem to hinder the attempts to improve
the $J_{C}$ further.

In this direction, here we present a detailed study on the yttrium (non-
magnetic) containing V0.6Ti0.4 alloys and establish a correlation between the
microstructure and the physical properties in the normal and superconducting
states. We show that there is an enhancement of JC of V0.6Ti0.4 by about 7.5
times in fields higher than 1 T when 2 at.% yttrium is added. Our analysis
shows how different defects contribute to the enhancement of JC of the
(V0.6Ti0.4)-Y alloys at different temperatures and field regimes.

Table 1: Sample name and the at.% of elements in the samples Name of the Sample | at.% of elements
---|---
|  V |  Ti |  Y
Y0 |  60 |  40 |  -
Y1 |  59 |  40 |  1
Y2 |  58 |  40 |  2
Y3 |  57 |  40 |  3
Y5 |  55 |  40 |  5

##  II Experimental

A series of samples were synthesized by arc melting paul2021grain ;
matin2013magnetic ; matin2014influence  the constituent elements (purity
better than 99.9%) in 99.999% pure Ar atmosphere. The elemental compositions
(in at.%) of the samples are presented in table 1. The samples were cut using
diamond saw. The details of metallography experiments can be found elsewhere.
matin2015critical ; matin2015high  Images of the etched samples were taken
using a high power optical microscope (Leica DMI 5000M). The elemental
analysis was done using the energy dispersive analysis of x-rays (EDAX) setup
attached to the scanning electron microscope (SEM, Carl Zeiss, Germany). X-Ray
diffraction (XRD) measurements were performed using $\lambda$ = 0.817 Å
radiation from the BL12 beamline of the Indus-2 synchrotron facility sin00 .
The resistivity and heat capacity of the samples were measured using the 9 T
Physical Property Measurement System (PPMS, Quantum Design, USA). For
resistivity measurements, the sample sizes were about 8 mm $\times$ 1 mm
$\times$ 0.5 mm. The magnetization was measured using Superconducting Quantum
Interference Device based Vibrating Sample Magnetometer (MPMS-3 SQUID-VSM,
Quantum Design, USA). The samples used for heat capacity and magnetization
measurements have sizes about 3 mm $\times$ 1 mm $\times$ 1 mm.

Figure 1: (a-d) SEM images of the polished surfaces of yttrium containing
alloys before etching. The size of precipitates (white patches) in the
V0.6Ti0.4 alloy increases with the increasing yttrium content.  Figure 2:
Elemental analysis of the Y3 sample showing immiscibility of yttrium in the
V0.6Ti0.4 alloy.

##  III Results and Discussion

###  III.1 Microstructural characterization

Figure 1 shows the SEM images of the (V0.6Ti0.4)-Y alloys up to 5 at.% of
yttrium. These images were taken before etching the samples. Precipitation of
secondary phase (white patches) were observed in all the yttrium containing
samples. Studies by Love yre  as well as by Komjathy and coworkers komjathy
on the vanadium-rare earth and titanium-rare earth binaries reveal that the
rare earth elements precipitate in the vanadium or titanium matrix. The
elemental analysis of a portion of Y3 is shown in Fig. 2. The white
precipitates in Fig.1 are rich in yttrium. The titanium and vanadium are
uniformly distributed as a matrix. From Fig.1, we see that the precipitation
follows certain pattern in the Y1 and Y2 samples. This pattern is partially
lost in the Y3 sample, whereas the precipitates are more uniformly distributed
in the Y5 sample. The size of the precipitates are presented in table 2.
While, the precipitate size in the Y1 and Y2 samples are more or less uniform,
there is a distribution of precipitate sizes in the Y3 and Y5 samples. Few
precipitates in Y5 are found to be bigger than 30 $\mu$m in size.

Figure 3: (a-e) Optical metallography images of the polished (V0.6Ti0.4)-Y
alloys after etching. Dendritic growth in alloys containing yttrium indicates
the presence of large amount of disorders. The average dendritic cell size
reduces initially with increasing yttrium content, but increases for 3 at.%
yttrium or higher. Figure 4: schematics of the phase diagram of the pseudo
binary dilute (V0.6Ti0.4)-Y alloys. At low yttrium content, the homogenous
liquid formed at high temperatures phase-separates into a yttrium-rich liquid
and solid V0.6Ti0.4 when cooled below 1935 K. This results in the formation of
fine yttrium-rich precipitates below 1430 K.

The optical metallography images in Fig. 3 of the (V0.6Ti0.4)-Y alloys reveal
the microstructure. These images were taken after etching the polished sample
surfaces by a solution containing water, HF and HNO3 in the 98:1:1 volume
ratio. Dendritic growth is observed in all the alloys containing yttrium
indicating a spacial compositional variation. The grain size of the V0.6Ti0.4
alloy is about 200-300 $\mu$m. The dendritic cell size in Y1, Y2, Y3 and Y5
are 31$\pm$9, 24$\pm$7, 32$\pm$10 and 43$\pm$13 microns respectively. Further
studies are required to establish whether these cells are different grains.
Nevertheless, thin layers of an alloy which has the lowest melting point,
solidifies in between these cells. The cell size reduces initially with
increasing yttrium content. This indicates that these yttrium-rich precipitate
hinders the cell growth due to the presence of strain field. Thus, there is an
enhancement of cell boundary density in the (V0.6Ti0.4)-Y alloys up to 2 at.%
yttrium addition and yttrium is precipitated only along the cell boundaries.
The cell size is found to increase with further addition of yttrium. The
precipitates in these alloys are of larger size and this reduces the number
density of precipitates and the strain field in these alloy compositions.

Table 2: Average sizes of the precipitates  Sample |  Precipitate size
---|---
|  ($\mu$m)
Y1 |  1.3$\pm$0.6
Y2 |  2.3$\pm$1
Y3 |  2.8$\pm$1.8
Y5 |  4.7$\pm$3.3

The vanadium alloys containing small amount of yttrium ($<$ 0.5 at.%) undergo
monotectic transition at about $T_{mt}$ = 2173 K (1900 0C) from homogeneous
liquid above $T_{mt}$ to solid $\beta$-vanadium phase and a yttrium-rich
liquid below $T_{mt}$. cha10  The enrichment of yttrium in this liquid leads
to phase separation of yttrium-rich and vanadium-rich liquids. If the
enrichment of yttrium in the yttrium-rich liquid reaches 96 at.%, an eutectic
transition at about 1730 K ($\approx$ 1460 0C) occurs within this phase. cha10
On the other hand, the titanium alloys containing small amount of yttrium ($<$
20 at.%) undergoes eutectic transition at about $T_{et}$ = 1673 K (1400 0C).
sav62  The melting point ($T_{m}$) of yttrium is about 1793 K (1520 0C). cha10

The V0.6Ti0.4 alloy has a $T_{m}$ of about 1933 K (1660 0C) and the
$\beta$-phase (body centred cubic) is stabilized below $T_{m}$. melting point
Our metallography results match closely with those of the V-Y alloys
indicating that the phase diagram of the (V0.6Ti0.4)-Y alloys must be similar
to the V-Y phase diagram. On comparing the literature available on the
vanadium/titanium-rare earth binary phase diagrams yre ; komjathy  and our
experimental observations, we present a schematic phase diagram for the dilute
(V0.6Ti0.4)-Y alloys in Fig. 4.

The small size of the precipitates in the alloys containing 3 at.% or less
yttrium indicates that these alloys, while cooling from the melt undergo
monotectic transition from the homogeneous V-Ti-Y liquid to solid $\beta$-V-Ti
alloy and a yttrium-rich liquid. Figure 5 shows the typical compositions of
the precipitates and matrix of the Y2 alloy. The composition of the matrix is
about V0.626Ti0.374 with a minor local variation of the composition. The
oxygen content within a precipitate varies substantially among the
precipitates. We found that higher the oxygen content, higher is the amount of
titanium and vanadium present in the precipitate. In the cases where oxygen is
absent in the precipitates, the composition is close to 95 at. % of yttrium.
This indicates that eutectic microstructure may be present within the yttrium-
rich precipitates. cha10  In order to get a clear picture of the different
phases present in the samples, we show in Fig. 6, the x-ray diffraction (XRD)
pattern of the Y2 alloy. The symbols ’$\star$’, ’$\\#$’ and ’+’ represent
reflections from the $\beta$-V0.60Ti0.40, yttrium precipitates and Y2O3 phases
respectively. The lattice parameter of $\beta$-V0.60Ti0.40 is about 3.1412 Å
while that of Y2O3 is about 10.4 Å. The lattice parameters of the yttrium
precipitates are about $a$ = 3.647 Å and $c$ = 5.728 Å. The lattice parameters
of $\beta$-V0.60Ti0.40 and yttrium precipitates are in agreement with
literature. spe56 ; paul21  On the other hand, the lattice parameter of Y2O3
is slightly less than that of bulk which may be due to oxygen off-
stiochiometry. han84  Thus, the reduction of the cell size in these
compositions is related to the formation of fine yttrium-rich precipitates
during the phase separation of the homogeneous liquid into solid
$\beta$-V0.6Ti0.4 and L′-Y phases (Fig. 4). On the other hand, a two phase
microstructure seen in between the large V-Ti cells in the Y5 sample
(Fig.3.(e)) is caused by the liquid immiscibility.

Earlier, we have shown that the V1-xTix alloys have large grain sizes of the
the order of few microns to few millimetres. Our microstructural studies
reveal that the yttrium can introduce large amount of defects in the V1-xTix
alloys which is helpful in improving the critical current density in the mixed
state of these superconducting alloys. Therefore, we characterize the present
alloys in the superconducting as well as normal states.

###  III.2 Electrical and thermal properties of the (V0.6Ti0.4)-Y alloys and
the superconducting transition temperature ($T_{C}$)

Figure 7 shows the temperature dependence of electrical resistivity
($\rho$($T$)) of the (V0.6Ti0.4)-Y alloys in the range 2-300 K. The yttrium
containing alloys have higher $\rho$($T$) in comparison with that of the
parent V0.6Ti0.4 alloy. Residual resistivity ($\rho_{0}$) increases up to 3
at.% yttrium due to the increased static defects (precipitates, grain/cell
boundaries, dislocations and point defects). The reduced number density of
defects in the Y5 alloy due to the larger size of the precipitates results in
the lower $\rho_{0}$ as compared to the other yttrium containing alloys. The
inset to Fig. 7 shows the expanded view of resistivity around the TC. The TC
is obtained as that temperature at which the temperature derivative of
resistivity shows a peak. The TC increases from 7.68 K for the V0.6Ti0.4 alloy
to 7.85 K for the Y5 sample.

Figure 5: Compositional analysis of yttrium-rich precipitates and V0.60Ti0.40
matrix using EDAX. Presence of oxygen is found in many of the yttrium-rich
precipitates. No trace of yttrium is found in the matrix. Figure 6: X-ray
diffraction pattern of the Y2 alloy (a) The major peaks are indexed to
$\beta$\- V0.60Ti0.40 phase. (b) Weak reflections corresponding to $\alpha$-Y
and Y2O3 phases are also seen.

Normally, the $T_{C}$ is expected to decrease with increasing disorder.
aoki1967non ; aoki1969non  However, the increase in the $T_{C}$ in the present
alloys can be due to (i) suppression of spin fluctuations by the disorder,
matin2014influence ; stritzker1979superconductivity ; bose1990effect  (ii)
increase in the electron-phonon coupling due to phonon softening by the
defects, shy15  and/or (iii) removal of the trace oxygen by yttrium from the
V-Ti matrix. peng2017formation ; collin59

The TC of the V1-yTiy alloys is limited by the spin fluctuations
matin2014influence  and increases from 5.4 K for $y$ = 0 to about 7.68 K for
the $y$ = 0.4 alloy. We have argued that the suppression of spin fluctuation
by the disorder introduced when vanadium is alloyed with titanium increases
the $T_{C}$ of the V1-yTiy alloys. matin2014influence  Palladium is also found
to be superconducting when certain type of disorder is introduced to suppress
the spin fluctuations. stritzker1979superconductivity ; bose1990effect  Thus,
the increase in the TC of the yttrium containing alloys can be attributed to
the suppression of spin fluctuations with increase in disorder. However, this
should result in the reduction of the normal state $\rho$($T$), paul21  which
is contrary to the observed result that the yttrium containing alloys have
higher normal state $\rho$($T$) as compared to the parent V0.6Ti0.4 alloy. The
normal state $\rho$($T$) in the range 20-120 K is fitted using the
equationrice67 ; shy15 :

$\displaystyle\rho(T)=\rho_{0}$ $\displaystyle+$
$\displaystyle\rho_{sf}\left(\frac{T}{T_{sf}}\right)^{2}F_{2}\left(\frac{T_{sf}}{T}\right)$
(1) $\displaystyle-$
$\displaystyle\rho_{sf}\left(\frac{T}{T_{sf}}\right)^{5}F_{5}\left(\frac{T_{sf}}{T}\right)$
$\displaystyle+$
$\displaystyle\rho_{sd}\left(\frac{T}{\theta_{D}}\right)^{3}F_{3}\left(\frac{\theta_{D}}{T}\right)$

where $\rho_{0}$ is residual resistivity, $\rho_{sf}$ is the coefficient of
resistivity for spin-fluctuation, $\rho_{sd}$ is the coefficient of
resistivity corresponding to interband scattering, $T_{sf}$ is the spin
fluctuation temperature, $\theta_{D}$ is the Debye temperature and
$F_{k}$($M$) is the Fermi-integral given by

$F_{k}(M)=\int_{0}^{M}\frac{{\text{d}}zz^{k}\exp(z)}{(\exp(z)-1)^{2}}$ (2)

The fitting is shown in Fig. 7 and coefficients obtained by the fitting are
presented in the table 3. The errors in the estimation of parameters are
within 10%. We found that $\rho_{sf}$ increases with increasing yttrium
content. The large $\theta_{D}$ and small $\rho_{sd}$ for Y3 and Y5 alloys
indicate a negligible contribution from the interband scattering to
resistivity in these alloys. The $T_{sf}$ also increases with yttrium content
up to 3 at. %. Therefore, the enhancement of $T_{C}$ in the yttrium containing
alloys is not due to the suppression of spin fluctuations.

Figure 7: Temperature dependence of electrical resistivity of the (V0.6Ti0.4)-Y alloys. The residual resistivity and critical temperature increases with yttrium addition. Open symbols are the experimental data points and the solid lines are the fits using eq.(1). The parameters of fitting are presented in table 3. The inset shows expanded view of the resistivity around the superconducting transition. Table 3: Parameters obtained from the fitting of resistivity Sample | $\rho_{0}$ | $\rho_{sf}$ | $\rho_{sd}$ | $T_{sf}$ | $\theta_{D}$
---|---|---|---|---|---
| ($\mu\Omega$ cm) | ($\mu\Omega$ cm) | ($\mu\Omega$ cm) | (K) | (K)
Y0 | 54.6 | 9.1 | 25.8 | 196 | 300
Y1 | 56.9 | 18.0 | 14.0 | 198 | 366
Y2 | 56.9 | 19.6 | 12.3 | 204 | 382
Y3 | 57.7 | 30.4 | 3.4 | 308 | 561
Y5 | 55.7 | 26.1 | 7.9 | 217 | 433
Figure 8: (a) Temperature dependence of heat capacity of the V0.6Ti0.4, Y3 and
Y5 alloys measured in the zero and 8 T magnetic fields. The symbols are the
experimental data points and the solid lines are the linear fits. (b)
Sommerfeld coefficient $\gamma$ and Debye temperature $\theta_{D}$ as a
function of yttrium content in the present alloys. The solid lines are guide
to eye.

The higher $\rho$($T$) with a different curvature for the yttrium containing
alloys as compared to that of the parent V0.6Ti0.4 alloy hints at the
enhancement of electron-phonon coupling due to the softening of phonon modes
by disorder. To verify the correlation between the $T_{C}$ and phonon
softening, we have measured the heat capacity of the yttrium containing alloys
in zero and 8 T fields (Fig. 8(a)). The normal state $C/T$ v/s $T^{2}$ data in
8 T in the range 5-10 K is used to fit a straight line to obtain the
Sommerfeld coefficient of electronic heat capacity ($\gamma$) and the Debye
temperature ($\theta_{D}$) using the relation $C=\gamma T+\beta T^{3}$ where
$\theta_{D}^{3}=1943.66/\beta$. matin2014influence  The maximum change in the
$\theta_{D}$, $\gamma$ (Fig. 8(b)) and $T_{C}$ with the yttrium content are
about 6.5%, 4%, and 2.3% respectively. Since, change in $T_{C}$ is quite
smaller in comparison with the other two variables, it is unlikely that the
enhancement of the $T_{C}$ is due to changes in the electron-phonon coupling
by the addition of yttrium.

The $T_{C}$ of vanadium is about 5.4 K. tcv  The presence of oxygen suppresses
the $T_{C}$ of vanadium. wexler1952superconductivity  It is well known that
the addition of 0.5-2 at.% yttrium in titanium or vanadium improves the
ductility. collin59  This improvement is caused by the scavenger effect of
yttrium in removing oxygen from the grain boundaries of vanadium and titanium.
collin59  Therefore, we infer that the addition of yttrium to the V1-xTix
alloys improves the $T_{C}$ by removing oxygen from the matrix. Our studies on
the (V0.6Ti0.4)50Y50 alloy showed that the superconductivity is induced in
yttrium-rich phase by the proximity effect ram21hfpme . Therefore, we infer
that the region of yttrium-rich precipitates where the oxygen is absent become
superconducting below $T_{C}$ due to proximity effect and the boundaries
between the precipitates and the matrix can act as effective pinning centres.

###  III.3 Magnetic properties of the (V0.6Ti0.4)-Y alloys: Role of
microstructure on the enhancement of critical current density

Figure 9: Temperature dependence of magnetisation of (a) Y2 and (b) Y5 in the
temperature range 2-10 K measured in the presence of 10 mT field. The insets
show the expanded view of the FCC and FCW response in 10 mT field. Figure 10:
(a) Magnetic field dependence of magnetisation for the (V0.6Ti0.4)-Y alloys at
4 K. The hysteresis is observed to increase with yttrium addition and is
maximum for the Y2 alloy. (b) Magnetic field dependence of magnetisation for
the Y2 alloy at 2 K, 4 K and 6 K.

The temperature dependence of magnetization ($M$($T$)) of the Y2 and Y5 alloys
are shown in Fig. 9. The $M$($T$) is measured in the presence of 10 mT field
while warming up after cooling down the sample from $T>T_{C}$ to 2 K in zero
field (ZFC), while cooling down in the same field after warming above $T_{C}$
(FCC), and then again while warming up in the same field (FCW). The TC is
estimated as that temperature at which the $M$($T$) starts to decrease towards
negative values when the temperature is decreased from 10 K. The TC estimated
from $M$($T$) is in agreement with that estimated from the resistivity
measurements. The insets to the Fig. 9 show the expanded view of $M$($T$)
measured during FCC and FCW cycles. The Meissner fraction ($M_{f}$) is
estimated as the ratio $M_{FCC}$/$M_{ZFC}$ at 2 K. The $M_{f}$ is about 0.095%
for the V0.6Ti0.4 alloy which decreases with increasing amount of yttrium in
this alloy. The $M_{FCC}$/$M_{ZFC}$ is about 0.032% for the Y3 alloy
indicating that the magnetic flux line pinning improves when yttrium is added
to the V0.6Ti0.4 alloy. This indicates that the yttrium containing alloys have
higher $J_{C}$ than the parent V0.6Ti0.4 alloy.

In order to quantify the the enhancement of $J_{C}$ in the yttrium containing
alloys, we have measured the field dependence of magnetisation ($M$($H$)) for
all the alloys at different temperatures. The Fig. 10(a) shows the $M$($H$) at
4 K for all the alloys. The size of the hysteresis increases with increasing
yttrium content in the V0.6Ti0.4 alloy up to 2 at.%, and then it starts
shrinking. Figure 10(b) shows the $M$($H$) of the Y2 alloy at different
temperatures. The hysteresis in the $M$($H$) is symmetric along the $H$ axis
indicating that the Bean-Livingston surface barrier effect bean1964surface  is
negligible in Y2 alloy. The upper critical field ($H_{C2}$) and magnetic
irreversibility field ($H_{irr}$) at various temperatures below $T_{C}$ are
estimated from the isothermal magnetisation curves. The magnetic field at
which $M$($H$) deviates from its behaviour in the normal state is taken as the
$H_{C2}$. The magnetic field at which the $M$($H$) for increasing $H$
bifurcates from that during the $H$ decreasing cycle is taken as the
$H_{irr}$.

The $H_{C2}$ and $H_{irr}$ as a function of temperature for all the alloys are
plotted in Fig. 11. The $H_{C2}$($T$) is almost the same for all the yttrium
containing alloys and $H_{irr}<H_{C2}$. Addition of yttrium to V0.6Ti0.4 alloy
increases the $H_{irr}$. The solid line in Fig. 11 represents the fit to the
$H_{C2}$($T$) using the Werthamer-Helfand-Hohenberg (WHH) formalism for dirty
limit superconductors. werthamer1966temperature  From the fitting, the
parameters $\alpha$ (corresponding to the Pauli paramagnetic effect) and
$\lambda_{SO}$ (which is the measure of strength of spin-orbit interaction)
are found to 1.49 and 2.5 respectively. The HC2 in the limit of absolute zero
(H${}_{C2}(0)$) is found to be about 13.2 T which is comparable to the Nb-Ti
alloys. poo00

Figure 11: The temperature dependence of upper critical fields (closed
symbols) and irreversibility fields (open symbols) for the (V0.6Ti0.4)-Y
alloys. The solid line is the fit to the $H_{C2}$ using WHH formalism.

The critical current density (JC) of the (V0.6Ti0.4)-Y alloys estimated from
the $M$($H$) is shown in Fig.12. The JC is estimated using the Bean’s critical
state model as zheng1995reversible ; martinez2007flux ; sundar2015magnetic ;
bean1964magnetization

$J_{C}=2\Delta M\left[a\left(1-\frac{a}{3b}\right)\right]^{-1}.$ (3)

Here, the $\Delta M$ at every $H$, is the difference between the $M$ measured
during increasing and decreasing $H$ cycles. The parameters a and b ($b>a$)
are the dimensions of the rectangular cross section of the sample in the
direction normal to the applied magnetic field.

The zero field JC value at 2 K for the V0.6Ti0.4 alloy is estimated to be
$2\times 10^{8}$ A/m2, which is in close agreement with the literature.
matin2015critical  The JC increases significantly with the addition of yttrium
up to 2 at.%, and then it decreases with further addition. The Y2 alloy has a
JC of $7\times 10^{6}~{}A/m^{2}$ at 4 K and 1 T field, which is an order of
magnitude higher than that of the V0.6Ti0.4 alloy. The drop in JC with the
application of low magnetic fields is found to be less steep for all the
yttrium containing alloys in comparison with the parent V0.6Ti0.4 alloy. The
$J_{C}$ of the parent V0.6Ti0.4 alloy exists only up to 5 T at 4 K. On the
other hand, the yttrium containing alloys have significant $J_{C}$ above 5 T
at 4 K. The value of $J_{C}$ as well as the range over which a significant
$J_{C}$ is present increase with the increasing yttrium content up to 2 at.%.
The $J_{C}$ at 2 K (Fig.12) exceeds 2$\times$107 Am-2 at 7 T for the Y2 alloy.
The increase in the defects when yttrium is added to the V0.6Ti0.4 alloy
(section 3.1) results in the enhancement of flux line pinning, which in turn
increases the $J_{C}$. Though the enhancement of $J_{C}$ by adding yttrium in
V0.6Ti0.4 alloy is significant, the $J_{C}$ is still considerably lower than
that of commercial Nb-Ti alloys sha19 ; end73 ; che91 ; bou06 ; miy06 ; lin15
; mou17 .

Figure 12: Field dependence of critical current density of the (V0.6Ti0.4)-Y
alloys at (a) 4 K and (b) 2 K. The $J_{C}$ increases by approximately 8 times
at 2 K when 2 at.% yttrium is added to V0.6Ti0.4. Figure 13:  (a) Field
dependence of pinning force density for the (V0.6Ti0.4)-Y alloys at 4 K.
Addition of yttrium results in the enhancement of the maximum pinning force
density by about 8 times. (b) The reduced pinning force density as a function
of reduced field from the plots in (a).  Figure 14: (a) Field dependence of
$F_{p}$ of Y2 at different temperatures. The shape of the $F_{p}$ curves
changes with temperature. (b) The reduced pinning force density as a function
of reduced field from the plots in (a). Large improvement in the pinning force
density at high magnetic fields is achieved below 5 K.

In order to establish a correlation between the nature of the defects and the
enhancement of $J_{C}$, we have estimated the pinning force density ($F_{P}$)
at 4 K as $F_{P}=J_{C}\times H$ and the same is plotted in Fig. 13(a). In the
V1-yTiy alloys, the grain boundaries are the major pinning centres in the low-
field regime, whereas the point defects and dislocations are the effective
pinning centres in the high-field regime. matin2015critical ;
matin2013magnetic  The maximum $F_{P}$ of the V0.6Ti0.4 alloy at 4 K is in the
range of 107 Nm-3. Addition of yttrium increases this value up to 2 at.%. The
maximum $F_{P}$ of the Y2 alloy at 4 K is about 7.6$\times$107 Nm-3 which is
about 7.6 times that of the parent V0.6Ti0.4 alloy. Significant pinning
strength above 5 T is found in the yttrium containing alloys. In all the
samples at 4 K, the $F_{p}$ increases sharply in very low fields and falls of
gradually in high magnetic fields.

The Fig. 13(b) presents the plot of reduced pinning force density
($f=F_{p}/F_{p-max}$) of all the alloys as a function of reduced field
$h=H/H_{irr}$. According to Dew-Hughes dewhughes , the $f$ depends on the
spacing, size and nature of the pinning centres and is proportional to
$h^{p}(1-h)^{q}$. Each type of pinning centre yields an unique set of p and q
values ekin2010unified  and a maximum of $f$ at $h_{m}=p/(p+q)$. The values of
$p$, $q$ and $h_{m}$ provides information on the nature of the pinning centres
responsible for the $J_{C}$. All the curves in Fig. 13(b) tend to scale on the
falling edge, while significant variation of $f$ among the alloys is observed
for $h<$ 0.1. This indicates that the pinning mechanism at high magnetic
fields is same for all the alloys. The experimental value of $h$ at which
$F_{p}$ becomes maximum ($h_{m}$) for the V0.6Ti0.4 alloy is about 0.06. The
$h_{m}$ increases with the addition of yttrium and is about 0.14 for the Y2,
Y3 and Y5 alloys at 4 K. The comparison of the curvature of the different
pinning mechanisms for $h$ close to unity dewhughes  with the curvature of $f$
of the present alloys indicates that the pinning at high fields is due to the
regions with large change in the superconducting properties (large change in
the Ginsburg-Landau parameter $\kappa$ or large $\Delta\kappa$). dewhughes ;
ekin2010unified  The known mechanisms of flux pinning have $h_{m}\geq$ 0.2.
The $h_{m}<$ 0.2 for all the alloys indicates that the pinning that exists at
low magnetic fields may not be effective at high fields.

In such cases where multiple types of pinning centres become available for
pinning at different magnetic fields, $F_{p}$ can be expressed as,muz11 ; li06

$F_{p}=F_{p1}+F_{p2}+F_{p3}+.......$ (4)

where, $F_{pi}$ is the pinning force density of individual pinning centres.
The solid blue line in Fig. 13(b) shows the fit to the $f$ by considering
three types of pinning centres viz.,
(i) normal surface pinning ($h^{0.5}(1-h)^{2}$) by grain/cell boundaries
(violet dot-dashed line)
(ii) $\Delta\kappa$ surface pinning ($h^{1.5}(1-h)$) by dislocations (purple
dashed line) and
(iii) normal surface pinning with $H^{\prime}_{irr}=0.22\times H_{irr}$
(orange dotted line).

One can see that pinning centres of type (i) and (ii) combined (red dash-dot-
dotted line in Fig. 13(b)) can account for pinning in the high field range
$h>$ 0.35. The variation of $F_{p-max}$ with the composition follows the cell
boundary and dislocation density in these alloys. The $F_{p}$ is maximum for
the Y2 alloy which has the smallest cell size. The number of precipitates is
largest for Y2 alloy which hints that the dislocation density may be maximum
for this alloy. Thus, the grain/cell boundaries and dislocations are the
effective pinning centres in all the present alloys. Therefore, the $f$ versus
$h$ plots for all the alloys at 4 K scale at high fields. To explain the
pinning in the low field region, one needs to consider pinning mechanism of
type (iii) with a very low irreversibility field $H^{\prime}_{irr}$ which is
about 0.22$\times H_{irr}$. We have observed a positive magnetization signal
just below $T_{C}$($H$) of all the (V0.6Ti0.4)-Y alloys in low magnetic
fields. ram21hfpme  This is an effect what is known as ’High Field
Paramagnetic Effect (HFPME)’ where the positive magnetization arises from the
flux compression as well as creeping of flux lines from weak pinning-centres
to strong pinning-centres leading to anisotropic distribution in flux line
pinning. matinHFPME ; shyamHFPME ; Dias  The flux compression is found to be
due to the yttrium-rich precipitates become superconducting by the proximity
effect. ram21hfpme  We believe that the pinning mechanism of type (iii) is
related to the pinning centres that contributes to HFPME.

The shape of the $F_{p}$ curve and its peak position change with temperature
(Fig. 14(a)). The position of the maximum $F_{p}$ changes from $h_{m}$ = 0.08
at 6 K to about 0.23 at 2 K (Fig. 14(b)). The $F_{p}$ curves are extrapolated
linearly to get $h_{m}$ ($H_{irr}$) at temperature 3 K and 2 K. The sharpness
of the peak reduces and the curvature of the falling edge changes with
decreasing temperature. This behaviour is an indication of different pinning
centres becoming effective at different temperatures. The Fig. 14(b) shows
that the pinning mechanism present in high fields and low temperatures is
absent at temperatures close to $T_{C}$. The thermal conductivity studies on
(V0.6Ti0.4)-Gd alloys indicated that the dislocations become effective in
scattering the phonons at low temperatures and high magnetic fields which in
turn renormalizes the electron-phonon coupling. paul21  We infer that the
dislocation become effective in pinning flux lines in high magnetic fields at
low temperatures which is inline with the analysis related to Fig. 13(b).

##  IV Conclusion

We have shown that the yttrium is immiscible and precipitates with various
sizes in the V0.60Ti0.40 alloy. Dendritic microstructure is observed in all
the yttrium containing alloys. For $\leq$ 2 at.% yttrium in the V0.60Ti0.40
alloy, fine yttrium-rich precipitates are generated because of phase
separation of the homogeneous V-Ti-Y liquid into a solid $\beta$-V0.60Ti0.40
alloy and a yttrium-rich liquid. The size of the yttrium-rich precipitates
increases for higher yttrium content due to liquid immiscibility. The
dendritic cell size reduces with increasing yttrium content up to 2 at.% in
the V0.60Ti0.40 alloy which results in the generation of a large number of
line defects. Yttrium removes oxygen from the V0.60Ti0.40 alloy matrix due to
which the $T_{C}$ of the yttrium containing alloys is enhanced. The defects
generated by the addition of yttrium are found to be effective in pinning the
flux lines and also increase the $H_{irr}$. The critical current density is
increased by more than 7.5 times in fields higher than 1 T for the
V0.58Ti0.40Y0.02 alloy at 4 K.

##  V Data availability statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

##  VI References

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