Enhancement of 𝐓𝐜, the Unit Cell Volume and AC Magnetic [603171]

Enhancement of 𝐓𝐜, the Unit Cell Volume and AC Magnetic
Shielding in High 𝑻𝒄 Superconductors

Abdeljabar Aboulkassima, Abdelhakim Nafidi, Keltoum Khall ouq, Essediq
Youssef El Yakoubi

Laboratory of Condensed Matter Physics and Nanomaterials for Renewable Energy, Faculty of Sciences; University
Ibn Zohr, Agadir, Morocco

a)E-mail address:[anonimizat] (Abdeljabar Aboulkassim)

Abstract. X-ray diffraction with Rietveld refinement, AC magnetic susceptibility measurement (χac= χ’+ iχ”) and
resistivity are experimentally studied in the transition region of (Y1−xNd x)BaSr Cu3O6+z polycrystal samples, under heat
treatment s effect s. Two types of heat treatment are examined, oxygen annealing [O] and argon annealing followed by
oxygen annealing [AO]. [AO] heat treatment, increase Tc for x>0.2 and by 9.8K for x=1, increase the orthorhombicity
 for 0<x<1 and decrease the distance dCu (1)−(Sr/Ba) for x>0.2. This heat treatment reduced the linear resistivity
ρ(T) parameters in the normal state indicating a diminution of the interactions of carrer charges with phonons. At all T<
Tc and at any applied magnetic field, in the case of [AO] heat treatme nt, there was a remarkable improvement in the
shielding effect S (amplitude of the χ’(T)). For each value of x, S(x) decreases when 𝐻𝑑𝑐 and the temperature increases.
Correlations were observed between Tc(x) and the number of holes psh(x) by Cu(2) superconduc ting planes on the one
hand, and the unit cell volume V(x) on the other hand. All these factors such as a decrease in d[Cu(1)−(Sr/Ba)], increase
in cationic and chain oxygen ordering (psh) and in -phase purity of the [AO] samples may account the results obtai ned.
INTRODUCTION
The magnetic, electric and crystalline properties of the high -Tc superconductors have been widely studied by
several research laboratories around the world since their discovery. In relation to the magnetic properties, the
Shielding effect is one important signature of the superconductivity. In the transition region of these materials, a
diamagnetic moment is observed due to the exclusion of the magnetic flux by the interior of the superconducting
sample when the temperature is below the critical temperature ( Tc).
Large grain high critical temperature superconductors (H TS) of the form ReBCO (Re: Rare -earth) can trap more
intense magnetic fields at low temperatures and can be used for permanent magnet applications [1]. Various potential
engineering applications for such magnets have emerged [2,3], and some have already be en commercialized [4].
The superconducting characteristics can rather easily be varied by substituting elements in the compounds [5,6] or
varying the content of oxygen in these compounds. The effect of substitution on the structural and superconducting
properties of YBa2Cu3O6+z has been extensively investigated [7]. Single -phase LnBa2Cu3O6.95 in bulk form can be
prepared with the superconducting transition temperature Tc near to 92K. All these compounds show an
orthorhombically distorted oxygen -deficient tr ipled -perovskite structure, Tc and both the orthorhombic distortion
depends sensitively on the oxygen content (6+z) [8,9].

It is interesting to check if an isovalent substitution of Ba2+ by Sr2+ with a smaller ionic radius would modify
some of the results di scussed above when Y3+ is replaced by the rare earth Nd3+ with bigger ionic radius. In order to
study the role played by the Y and Ba atomic planes in the YBCO systems and to discover the factors which act on
the superconducting property in these materials , we studied the effect of heat treatment on the structural, electrical
and magnetic properties of (Y1−xNd x)BaSr Cu3O6+z (x=0,0.2,0.4,0.5,0.6,0.8,1). Then, we found that the
influence of argon heat treatment on these properties depended on x(Nd) content.
EXPERIMENTAL TECHNIQ UES

The polycrystalline samples have been prepared by solid -state sintering of the respective oxides and carbonates.
The chemicals were of 99.999% purity except in the case of BaCO 3 which was 99.99% pure. Nd 2O3, SrCO 3, BaCO 3
and CuO were thoroughly mixed in required proportions and calcined at 950°C in air for a period of 12−18 hours.
The resulting product was ground, mixed, pelletized and heated in air at 980°C for a period of 16−24 hours. This
was repeated twice. The pellets were annealed in oxygen at 450°C for a period of 60−72 hours and furnace cooled.
This was denoted as sample [O] for each x.
XRD data of the samples were collected with Philips diffractometer fitted with a secon dary beam graphite
monochromator and using CuK α (40 kV/20 mA) radiation. The angle 2θ was varied from 20° to 120° in steps of
0.025° and the counting time per step was 10 sec. The XRD specters were refined with Rietveld refinement.
Superconducting transitio ns were checked by measuring both the real ( χ′ ) and the imaginary ( χ′′ ) parts of the
AC magnetic susceptibility as a function of temperature in a field of 0.11 Oe and at a frequency of 1500 Hz. In
addition, χ′ and χ′′ were measured in a static field (0 < H=Hdc < 150 Oe) superimposed on the AC field of
Hac = 0.11 Oe.
The resistivity ρ(T) was measured by the Van der Pauw method. Using a cryostat with closed helium circuit
supplied of a cryogenic pump, a regulator of temperature (1 μA−10 mA) and 1 μV resolution d igital voltmeter that
was fully computer controlled. Tc was checked by measuring χ′(T) and confirmed by the measure of the ρ(T).
For each value of x, the same sample [O] was then heated in argon at 850 °C for about 12 h, cooled to 20 °C, the
oxygen was allowed to flow instead of argon and the sample was annealed at 450 °C for about 72 h. This sample is
denoted as [AO]. Resistivity and AC susceptibility measurements were done on a part of this sample.
RESULTS

-10 Hdc= 0 (Oe)
27,75
56,7
90,8
126,5
' [a.u] '' [a.u](a) [O]
' [a.u]
-10
[AO] (b) Hdc= 0 (Oe)
27,5
56,7
90,8
126,5

30 40 50 60 7001 '' [a.u](c)

T [K]40 50 60 70 8001 (d)

T [K]

FIGURE 1. (a,b) ′ and (c,d) ′′ of NdSrBa Cu3O6+z as a function of the temperature and heat treatment at five fields Hdc
(0 <Hdc< 126 .5 Oe).

The Shielding effect S is one of the properties of a superconducting material. For a magnetic material, the magnetic
flux density B, the applied magnetic field strength Ha and the magnetization M are related by:
B = µ0(Ha+ M) (1)
Since B = 0 inside a superconductor, the previous equation gives us:
M =−Ha (2)
and the magnetic susceptibility by:
χ =dM/(dHa ) = −1 (3)

The su perconducting transition width ∆Tc for each sample (Y1−xNd x)BaSr Cu3O6+z is taken as the midpoint
temperature between 10% and 90% of the transition region. All the samples have a superconducting transition width
∆Tc, measured between 10% and 90% of the height of the real parte χ′ signal, increased from 0.58 K (for x=0 [O])
to ≈3 K (for x=1 [O]) and from 0.94 K (x=0 [AO] to ≈8 k (for x=1 [AO]) “Fig. 2 ”. The imaginary part signal
of susceptibility (χ″) has been subject to noticeable changes . The full width at half -maximum ∆Tp of the χ″ transitions,
gradually increased from 0.4 K (for x=0 [O]) to ≈2 K (for x=1 [O]) and from ≈1 K (for x=0 [AO]) to ≈7 K
(for x=1 [AO]) “ Fig. 2 ”. However, for the [AO] samples, ∆Tp decreased remarkably from 1.3 K to 0.5 K when x
decreas es to 0. After the [AO] treatment, we showed the maximum ∆Tp of 7 K (and ∆Tc of 8 K) indicating the [AO]
treatment rather de creased intergranular coupling (and shielding) in this case.
We focus now on the real part ′(T) of AC magnetic susceptibility measurements, which give information about
several properties of high -Tc superconductors, such as S (shielding effect) and Tc (superconducting critical
temperature) in “Fig. 1( a-b)”. We use the same sample for the two heat treatments, and we compare the diamagnetic
response and note that screening current of the [AO] sample increased considerably compar ed to that of the [O] sample
for x=1 in “Fig.1(a -b)”.
The real and imaginary parts of the AC susceptibility of the samples are shown respectively in “Fig. 1(a -b)” and
“Fig. 1(c -d)”. The critical temperature Tc, of the sample [O] occurred at 68 K “Table 1”. The maximum Tp of ′′(T)
was found to occur at 67.3 K with a full width at half -maximum (FWHM) of around 1.54 K. Our value of Tc [O] is
smaller (but Tc [AO] is higher) compared to that of 74 K reported by Wang et al. [10]. The sample [AO] showed a
critical temperature Tc(χ’)=77.2 K and Tc(ρ)=77.2 K, which was higher by around 9 K for χ’(T) and ρ(T)
compared to that of the sample [O]. There was a net displacement of Tp also to 76.5 K indicating that the coupling of
the superconducting grains took place at a higher temperature when the sample was heated in argon followed by
oxygen annealing.

We note that our XRD patterns of all the Y1−xNd xBaSr Cu3O6+z samples allowed the clear identification of the
orthorhombic splitting, which mean an increase of the orthorhombicity, as well as the observation of some weak
unidentified impurity peaks, are eliminated in the samples [AO] [11]. This indicates an improvem ent of
crystallographic quality of the samples [AO].
The effect of [AO] heat treatment on Tc was remarkable. The temperature at which the diamagnetism sets in is
taken as Tc and it was found to be dependent on both x and the heat treatment employed in “ Table. 2”.

0,0 0,2 0,4 0,6 0,8 1,0-202468

Tp (K) Tc [O]
Tc [AO]
x (Nd)Tc (K)
02468
Tp [O]
Tp [AO]

FIGURE 2. Variation of the ∆Tc and ∆T p as a function of x and heat treatments of (Y 1-xNdx)SrBaCu 3O6+z.

Table 1 . Results of resistivity and susceptibility measurements of NdBaSr Cu3O6+z for samples [O] and [AO].
𝐒𝐚𝐦𝐩𝐥𝐞 𝐓𝐜(𝛒)(𝐊) 𝐓𝐜(𝛘’)(𝐊) 𝐓𝐩(𝛘”)(𝐊) 𝐓𝐜(𝐊) 𝐓𝐩(𝐊)  𝟎(𝐜𝐦) 𝟐𝟗𝟒 (𝐜𝐦)  (𝐜𝐦
/𝐊)
[𝐎] 67.32 68.02 67.3 2.97 1.537 1011 2053 2.93
[𝐀𝐎] 77.20 77.18 76.5 7.965 7.391 468 970 1.43

As seen in “Table 2”, when x increases from 0 to 1, the orthorhombicity ε decreases and took the value 0, with
the transition from orthorhombic to the tetragonal structure. The orthorhombicity ε[O] decreases with Tc [O].
However, Tc [AO] decreases with ε[AO] until x = 0.2, increases for x=0.4 and after it decreases by 9.8 K to 77.18 K
for x =1 [AO]. For each x, the [AO] heat treatment makes increase Tc for x>0.2 and decreases it for x ≤ 0.2 as
seen in the upper of “Fig. 7 ”. A maximum of increase in Tc of 10 K was observed for x = 1 [AO]. For each x, the
[AO] heat treatment increased ε for 0 ≤ x <1. The increa se was maximum, from 2.23 10−3 to 5.81 10−3 for x=
0.6.
Thus, we believe that the feature of the resistivity curves shows that the no superconducting phase exists within
the grain boundaries, plays a role of weak links and consequently reduces the intergran ular coupling.
The superconducting critical temperature for our samples was also cheeked from resistivity measurement. For
example, the data points of the resistivity ρ for the sample NdSrBa Cu3O6+z [AO] lie clearly below those for the sample
[O] in “Fig. 3(a)”. The values of Tc (ρ=0) are in good agreement with those of Tc(χ′). Note that for a given heat
treatment Tc(χ′). is superior to Tc (ρ=0) by 1 to 2 K with Tc (ρ=0)≈Tp(χ′′).
The normal state resistivity of the granular superconducting sample given by ρ(T), obeys th e relationship:
ρ=ρ0+α.T (4)
Contributed by the resistivity due to grains and grain boundaries. The former component is dependent on
temperature, while the later is temperature independent. Therefore, the inter -grain coupling parameter at absolute zer o
temperature given by the intercept ρ0 of “Eq. (4) ” on Y -axis (as shown in “Fig. 3 (a)”).
Where ρ0 is the residual resistivity extrapolated to T= 0 K and α is the slope dρ / dT.
For example, NdSrBa Cu3O6+z [O] has α[O] = 2.93(μΩcm/K), ρ0[O]=1011 (μΩcm) and ρ294[O]=
2053 (μΩcm). The treatment [AO] reduced considerably these parameters; in particular α[AO] = 1.43 (μΩcm/K),
ρ0[AO] = 468 (μΩcm) and ρ294[AO]=970 (μΩcm). This indicates a better inter -grain connectivity and a reduction
of the interaction of carrier cha rges with phonons.
It is known that the high critical temperature granular superconductors having a well -defined superconducting
transition temperature, display a two -step resistive transition ρ(T) and correspondingly the derivative of the ρ(T)
displays a peak and a tail in the lower temperature side [12]. The tail is related to the intergranular coupling and the
peak marks the superconducting transition within the grains.
Figure 4(a) shows the resistive transition behavior of the samples [O] and [AO]. All the samples show a
superconducting transition to zero resistance and metallic behavior in the normal state. It can also be seen from these
curves that; the normal state resistivity r egularly increases from sample [AO] to [O]. More information is gained by
plotting the derivative of the resistivity curves of the samples [O] and [AO], as shown in “Fig. 4 (b)”. The transition
temperature Tc taken as the maximum of the derivative of the ρ(T) curves, is almost the same for all samples [O]
50 100 150 200 250 3000123  [AO]
 [O]
 (m cm)
T(K) = +60 70 80 900,00,4

50 100 150 200 250 3000,00,10,20,30,4
[AO]
[O]
ddT
T(K)

FIGURE . 3. (a) Variation of the resistivity (𝑇) and (b) Temperature dependence of the derivative of the resistivity of
𝑁𝑑𝐵𝑎𝑆𝑟 𝐶𝑢3𝑂6+𝑧 as a function of the temperature and heat treatment.

Table (2): Results of Tc and orthorhombicity  of Y1−xNd xSrBa Cu3O6+z. for [O] and [AO] samples
𝐱(𝐍𝐝) 𝟎 0.2 0.4 0.5 0.6 0.8 1
(𝟏𝟎−𝟑) [𝐎] 9.19 6.91 5.09 4.04 2.23 0.89 0
[𝐀𝐎] 10.09 8.12 7.04 6.66 5.81 2.23 0
𝐓𝐜(𝐊) [𝐎] 83.06 79.87 78.95 78.86 78.11 72.64 68.02
[𝐀𝐎] 81.8 80.13 80.96 80.54 79.62 79.36 77.18

and [AO] (see “Table 1”). All samples show almost a single peak indicating a single superconducting transition in
these samples.
Below Tc, the decrease in the real part χ′(T) is a manifestation of diamagnetic shielding whereas the peak Tp in
the imaginary part χ′′(T) represents the AC losses.
Let us now look at the amplitude of the real part χ′(T) of the AC magnetic susceptibility in “Fig. 1( a-b)”; of
NdSrBa Cu3O6+z as a function of the static magnetic field Hdc ( 0 Oe< Hdc < 126 .5 Oe ) and heat treatment; for
example, wh ich is nothing but the shielding effect S [13]. In “Fig. 4”, S was set arbitrarily equal to 1 for Hdc=0 Oe.
This was measured at three temperatures 60 K, 63 K and 66 K for x=1 and 0.8; and 71 K, 73 K and 75 K for
x=0.5; in the presence of an externally applied magnetic field Hdc. S represents the exclusion of magnetic flux by
the sample in alternative dynamic mode. An improvement in the shielding effect has been noticed in the case of the
samples [AO] for any applied fi eld Hdc and at all T<Tc. For example, in NdSrBa Cu3O6+z (x=1) at T = 66 K, S
at a field of 126 .5 Oe was a factor of nearly six higher in the case of the sample [AO] compared to that of the sample
[O]. Further, the decrease in S as a function of the field was much slower in the case of the sample [AO]. For example,
at T=66K, the sample [AO] showed a decrease in S of about 35% as the field was increased from 0 to 126 .5 Oe,
whereas the sample [O] showed a decrease of nearly 95% . An improvement in the intergranula r coupling and grain
quality was clearly shown in the [AO] samples.
0 50 100 1500,00,20,40,60,81,0
S(a.u)
H(Oe) S(T=71)[O]
S(T=73)[O]
S(T=75)[O]
S(T=71)[AO]
S(T=73)[AO]
S(T=75)[AO]x=0.5
0 50 100 1500,00,20,40,60,81,0
S(a.u)
H(Oe) S(T=60)[O]
S(T=63)[O]
S(T=66)[O]
S(T=60)[AO]
S(T=63)[AO]
S(T=66)[AO]x=0.8

FIGURE 4. Shielding effect 𝑆 of (𝑌1−𝑥𝑁𝑑 𝑥)𝑆𝑟𝐵𝑎 𝐶𝑢3𝑂6+𝑧.as a function of the field H dc and heat treatment at three different
temperatures (x=1, 0.8 : T=60 K, 63 K, 66 K) and (x=0.5 : T=71K, 73K, 75K) .

DISCUSSION

In the normal state, the [AO] heat treatment reduced considerably the linear resistivity parameters indicating better
inter-grain connectivity and a diminution of the interaction of carrier charges with phonons. The critical temperature
Tc(ρ =0) and Tc(χ′) for all the Y1−xNd xSrBa Cu3O6+z samples were in good agreement.
χ’ reflects the shielding ability. Below Tc, the decrease in the χ′(T) is a manifestation of diamagnetic shielding S.
An improvement in the shielding effect S (amplitude of χ′(T)) was noticed in the case of the [AO] samp les at all T <
Tc and for any applied field Hdc. For each x and heat treatment, S(x) decreases when Hdc and the temperature increase.
This is the result of deterioration of the bonds between grains (Josephson junctions) by the magnetic field and the
temperature. Below the inflection point I of χ′(T), the grains are coupled, the induced current from the exte rnal
magnetic field result in shielding currents S along the sample’s outermost surface. For temperatures above T(I), for a
given field, the grains are decoupled. These results are justified by our XRD spectra with Rietveld refinement that
showed an improv ement in the crystallographic quality of the samples [AO] [11]. This explains the quality
improvement of the grains and inter grain contacts and coupling by Josephson junctions. This argument is justified by
the fact that the difference between inter – and intragrain currents vanishes and the two steps in χ′(T) (and peaks in
χ′′(T)) merge as in our case in “Fig. 1 ”.
As we argued for LnSrBa Cu3O6+z (Ln=Eu,Nd,Sm) [14], the heat treatment in argon at 850 °C permits to hunt
the oxygen from the structure and inc rease the atomic diffusion in the structure. So the departure from reduced (6+
z), after the argon heat treatment, decreases the disorder of Y/Nd on the Sr/Ba site and increases the Y/Nd−Sr/Ba−
Y/Nd order along c axis. This increases the anionic order in the basal plane and leads to an increase of the number of
oxygen atoms by chains Cu(1)−O (NOC ) which enhances the transfer of holes to the superconducting planes
Cu(2)−O2, via the apical oxygen O(1) between Cu(1) and Cu(2), and increase Tc “Fig.6”.
The crystalline parameter b is constant but a (and c) increase ([11]) indicating an increase of the number of oxygen
atoms by chain (NOC) along a axis leading to a decrease of ε (Tc [O]) from orthorhombic toward tetragonal structure
for x=1 [O].
In “Fig. 5”, we show the variation of the volume V of the unit cell as a function of x and heat treatment. Note that
the volume V increased with x, this increase is in agreement with the fact that the ionic radius of Nd3+(0.98 Å) is
superior to that of the substitut ed Y3+(0.90 Å).
Whereas for each x, the [AO] heat treatment increases the orthorhombicity ε = (b−a)/(b+a) for 0≤x<1,
the Tc for x>0.2 and decrease the distance d[Cu(1)−(Sr/Ba)] for x> 0.2 (for distance show ref [11]). This
enhances the transfer of the hole s from chains along b axis to the superconducting plans Cu(2)−O2 via the apical
oxygen O(1) along c axis and Tc.
Also, for each x, the [AO] heat treatment makes decreases a and increases b. This increases the number of oxygen
by chain (NOC) along the b axis (decrease the cationic disorder, of Y/Nd on the Ba/Sr site, along c axis and increase
the anionic order in the basal plane) leading to an increase of the number psh(x) of holes by Cu(2)−O2

0,0 0,2 0,4 0,6 0,8 1,0166168170172174 [O]
[AO]
x (Nd)V (Å3)

FIGURE 5. V olume V as a function of x and heat treatment and Unit cell volume of 𝑌1−𝑥𝑁𝑑 𝑥𝑆𝑟𝐵𝑎 𝐶𝑢3𝑂6+𝑧

0,0 0,2 0,4 0,6 0,8 1,00,100,110,120,13

Tc(K)
x(Nd)psh
psh[AO]
psh[O]
607080

Tc[O]
Tc[AO]
FIGURE 6. Correlation between 𝑝𝑆ℎ and 𝑇𝑐 as a function of 𝑥 and heat treatment of 𝑌1−𝑥𝑁𝑑 𝑥𝑆𝑟𝐵𝑎 𝐶𝑢3𝑂6+𝑧 samples
superconducting planes (deduced from the under saturation zone of the universal relation Tc/Tcmax (pSh) [15]) and Tc
for x > 0.2 in “Fig. 6”. The decrease of d[Cu(1)−(Sr/Ba)] distance for x>0.2 can be seen as an argument in the
increase of the formation of the Cooper pairs and the increase in pSh and Tc “Fig. 6”.
The two arguments (cationic and anionic disorders) are justified here by the two remarkable correlations observed
between Tc(x) and the number pSh(x) in “Fig. 6”, and on the other hand, between the unit cell volume V and x (the
ionic radius of Nd3+ (0.98 Å) larger than the ionic radius of Y3+ (0.90 Å)) in “Fig. 5”. The later show a rearrangement
of the unit cell volume witch control Tc. So the structural, electrical and superconducting properties are correlated
with the effect of argon heat treatment.

CONCLUSIONS
In the samples [AO], the remarkable increase of the Shielding effect (amplitude of χ’(T)) is explained by the
improvement of the quality of the intergranular coupling as a result of the improvement of the crystallographic quality
of these samples. In the normal state, the [AO] treatment reduced the linear resistivity parameters indicating a
diminution of the i nteraction of carrier charges with phonons.
When x increases from 0 to 1, the orthorhombicity ε decreases to 0 with transition from orthorhombic to tetragonal
structure. For each x, the [AO] heat treatment increases the orthorhombicity ε = (b−a)/(b+a) (for 0<x≤1), Tc
(for x>0.2 and by 9.8 K for x=1) and the distance d[Cu(1)−(Sr/Ba)] (decrease Tc) for x<0.25 and decrease it
(increase Tc) for x> 0.25. The argon heat treatment decreases the diso rder of Y/Nd on the Sr/Ba site and increases
the Y/Nd−Sr/Ba−Y/Nd order along c axis. This increases the anionic order in the basal plane, leads to an increase
of the number of oxygen atoms by chains Cu(1)−O (NOC) which enhances the transfer of holes to the
superconducting planes Cu(2)−O2, via the apical oxygen O(1) between Cu(1) and Cu(2) and increase Tc in
agreement with the transfer charges model.
The structural and superconducting properties are correlated with the effect of argon heat treatment. These r esults
are the outcome of interplay between cationic disorder along the c axis and oxygen disorder in basal plane. A
combination of several factors such as decrease in d[Cu(1)−(Sr/Ba)] for x> 0.2; increase in cationic and chain
oxygen ordering; the number psh(x) of holes by Cu(2)−O2 superconducting plans and in -phase purity for the [AO]
samples may account for the observed data.

ACKNOWLEDGMENTS

This work was supported by University Ibn Zohr in Agadir Morocco.

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