Since the late 1980s, with the discovery of high-temperature superconductors [1] , considerable attention has focused on substituting atoms within them. The superconductive prototype YBa₂Cu₃O_6+z, reaching a critical temperature Tc = 93 K [2] , has emerged from these substitutions. These substitutions influence the prototype’s atoms, affecting the number of holes (p) in the Cu(2)O₂ superconductive plane. Experimental evidence supports that these holes have a pivotal role in achieving a high critical temperature, thus optimizing the Cu(2)O₂ plane conditions in these cuprates [3] [4] [5] [6] .

The critical temperature of LnBaSrCu₃O_6+z samples involving rare earths, as reported by multiple authors [7] [8] [9] , is solely dependent on the ion size of the rare earth element. We studied the structural and superconductive properties of SmSrBaCu₃O_6+z [10] . Annealing this compound in oxygen at 450˚C revealed a tetragonal structure and Tc of 79 K. Subjecting the same sample to argon heating and subsequent oxygen annealing unveiled an orthorhombic structure with a Tc increase of 6 K. We also establish that the structure is orthorhombic for EuSrBaCu₃O_6+z and tetragonal for NdSrBaCu₃O_6+z, irrespective of thermal treatment. Heat treatment under argon heightens the critical temperature (Tc [AO] > Tc [O]), underscoring Tc’s dependence on thermal processing.

Our study assesses how the quantity of holes (p) in Cu(2)O₂ planes affects structural, electrical, and superconductive properties of our samples.

The respective oxides and carbonates were solid-state sintered to prepare the polycrystalline samples. The chemicals were of 99.999% purity, with the exception of BaCO₃, which had a purity of 99.99%. Were meticulously blended in necessary proportions and subjected to calcination at 950˚C in the air for a duration of 12 - 18 hours. The product obtained was ground, pelletized, and subjected to air heating at 980˚C for 16 - 24 hours. The pellets were annealed in oxygen at 450˚C for a period of 60 - 72 h and furnace cooled. This was denoted as sample [O] for each Ln. XRD data of the sample were collected with Philips diffractometer fitted with a secondary beam graphite monochromator and using CuKα (40 kV/20 mA) radiation. The angle 2θ, was varied from 20˚ to 120˚ in steps of 0.025˚ and the courting time per step was 10 sec. The XRD specters were refined with Rietveld refinement [11] . Superconducting transitions were checked by measuring both the real, χ' and the imaginary χ'' parts of the AC susceptibility as a function of temperature in a field of 0.11 Oe and at a frequency of 1500 Hz.

For each Ln, the same sample [O] was then heated in argon at 850˚C for about 12 h, cooled to 20˚C, and oxygen was allowed to flow instead of argon and the sample was annealed at 450˚C for about 72 h. This sample is represented as [AO]. XRD and AC susceptibility measurements were performed on a part of this sample. The resistivity ρ(T) was measured by the Van Der Pauw method [12] . Using a cryostat with closed helium circuit supplied of a cryogenic pump, a regulator of temperature (1 μA - 10 mA) and 1 μV resolution digital voltmeter that was fully computer controlled. The same sample [O] was then heated in argon at 850˚C for about 12 h, cooled to 20˚C, 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]. XRD, susceptibility, and resistivity measurements were conducted on a portion of this sample.

The magnetic susceptibility AC allows studying the dynamics of the system, which gives information about the relaxation processes in the superconductor. The real part χ' gives an expression for flux that penetrates the sample. In the case of complete field expulsion (Meissner effect), χ' = −1 and for total flow penetration, χ' = 0. In the superconducting state, the imaginary part χ'' = 0 and in the mixed state χ'' < 1 and reflects losses AC.

In Figure 1(a), we present the real part of the AC susceptibility (χ') for the samples [AO]. The data is plotted as a function of temperature, with the measurements taken under the influence of two externally applied DC fields. In the case of Ln = Eu [AO], we obtained the maximum critical temperature Tc = 87.1 K in LnSrBaCu₃O_6+z. It is above the maximum critical temperature 86 K obtained by [7] and below 89 K measured by B. Hellebrand et al. [13] in GdBaSrCu₃O_6+z. In the Nd case, the application of the [AO] treatment resulted in a significant enhancement of Tc by 10 K, elevating it from 68 K to 78 K. Remarkably, this increase in Tc did not alter the crystal symmetry, which remained tetragonal throughout the process, and there was no variation in the oxygen content either. Moreover, our computation indicated a rise in the hole density (p) following the [AO] treatment.

The peak moves to lower temperatures as the Hdc field increase from 0 to 126.5 Oe, for each Ln Figure 1(b). The data for the crystalline and superconducting properties of LnSrBaCu₃O_6+z, varying with the heat treatment, can be found in Table 1.

The highest temperature is achieved in the scenario where the EuSrBaCu₃O_6+z [AO] compound adopts an orthorhombic structure, whereas the lowest temperature is observed when the NdSrBaCu₃O_6+z [O] compound takes on a tetragonal structure.

The relationship between lattice parameters “a” and “b” and the critical temperature “Tc” exhibits a linear evolution during heat treatment [AO]. The slope of the b [AO] (Tc) curve is small (Equation (1)), which shows that b is almost constant.

The other parameters b [O], a [O] and a [AO] decrease when the critical temperature Tc increases Figure 2(a).

b [ AO ] = 2.012 × 10 − 4 Tc [ AO ] + 3.85122 : (Å) (1)

The fit of the points of curve a/b [AO] (Tc) gives the following equations:

a/b [ AO ] = − 0.00187 Tc [ AO ] + 12.53186 (2)

The structure of the LnSrBaCu₃O_6+z (Ln = Nd [O], Nd [AO] or Sm [O]) compounds is tetragonal (a/b » 1), In contrast to the orthorhombic crystal structure (a/b ≠ 1) observed in LnSrBaCu₃O_6+z compounds (where Ln represents Eu [O], Eu [AO], or Sm [AO]), Figure 2(b). Heat treatment [AO] changed the tetragonal structure of the sample SmSrBaCu₃O_6+z [O] to an orthorhombic structure of the sample SmSrBaCu₃O_6+z [AO]. Therefore, the structural properties also depend on heat treatment.

The superconductors’ oxides exhibit a remarkable feature—a high critical temperature Tc, which is profoundly influenced by the concentration of holes present on the two-dimensional layers Cu(2)O₂. The universal relation between standardized Tc (τc = Tc/Tc_max) and the concentration p of the holes in the Cu(2)O₂ plane of superconductors oxides (La214, Y123, Bi2212, Bi2223, Tl2201 and Tl1212) shows that Tc independent of the considered sample [3] .

The hole density (p) in the Cu(2)O₂ planes as a function of Tc, can be inferred using the following relationship [14] [15] :

p = 0.16 − ( ( 1 − Tc Tc max ) / 82.6 ) 1 / 2 (3)

The Tc_max parameter represents the maximum critical temperature equal to 93 K in the case of cuprates.

Note here that this relation is deducted from the universal relation Tc/Tc_max (p) given by [4] . We used this universal relationship to infer the number of holes in our Y1-xSmxBaSrCu₃O_6+z compounds [16] .

Figure 3 shows the critical temperature Tc as a function of p. The increase of p from 0.10295 for Nd [O] or Tc = 68 K to 0.13229 for Eu [AO] or Tc = 87.1 K indicates that the critical temperature Tc increases with the hole density (p) in the Cu(2)O₂ planes. The look of this figure is characterized by a sharp increase of Tc, with hole content in the range 0.06 < p < 0.16 [17] [18] [19] .

The impact of holes density (p) on the superconducting properties in our samples is clearly remarkably in this figure. The addition of oxygen or the substitution of isovalentcations generally leads to changes in the superconducting Cu(2)O₂ planes’ charge density, which, in turn, affects the evolution of Tc. The maximum Tc occurs at the optimum p value of ~0.15 - 0.16 for several compounds.

A correlation has been established between the number of holes (p) and the critical temperature (Tc) as function of the lattice parameter (c) and heat treatment in LnSrBaCu₃O_6+z (Ln = Eu, Nd, Sm) as depicted in Figure 4. An almost linear curve is obtained when plotting the p [AO] values as a function of the c [AO]-axis values. The fit of the points gives the following equations:

p [ AO ] = − 0.22448   c [ AO ] + 22.88536 (4)

These authors are shown in the phase diagram that temperature as a function of hole doping, (p) and as a function of oxygen content, (y) superconducting YBa₂Cu₃O_y prototype are correlated. The negative slope of the concentration (p) of holes in the Cu(2)O₂ planes as a function of the lattice parameter (c) during heat treatment under argon (Equation (4)) compared by the slope of oxygen content, (y) as a function of this parameter in the case of YBa₂Cu₃O_y obtained by several authors [20] [21] [22] . The augmented oxygen content in the Cu(1)O basal plane or heightened hole concentration in the Cu(2)O₂ planes resulted in a reduction of the lattice parameter, (c).

The superconducting critical temperature (Tc) and the lattice parameter (c) of the LnSrBaCu₃O_6+z [AO] compound demonstrate an evident and inverse correlation with R (Ln³⁺) as depicted in Figure 5(a) and Figure 5(b), respectively. Run Zhao et al. [23] observed the variation of the critical temperature (Tc) and the lattice parameter (c) as a function of R (Ln³⁺) in the (YBa₂Cu₃O)_1−x:(BaZrO₃)_x compound, while systematically changing x from 0 to 0.4.

The Tc decreases with increasing c. This agrees with the expectation that large c value is accompanied by oxygen deficiency [24] . The justification for this is based on the increase in c correlated with a reduction in the number of p holes in the Cu(2)O₂ planes Figure 4.

Since the doping of these planes by holes, (p) is the result of increased oxygen content in the base plane. This is indicated by several searches [17] [18] .

Heat treatment [AO] (Figure 6) increases the surface (s [AO] > s [O]), volume (v [AO] > v [O]) and critical temperature (Tc [AO] > Tc [O]) of the LnSrBaCu₃O_6+z compound for each Ln. The increase in volume can be attributed to the introduction of extra oxygen into the base plane, which leads to a rise in the number of oxygen atoms per chain. (displacement of the oxygen towards the axis b). The correlation depicted in this figure, relating the critical temperature (Tc) to the surface (s) and volume (v), indicates that the superconducting properties are present within the Cu(2)O₂ planes.

This correlation shows a relationship between the order of oxygen in the base plane and the doping, which corresponds to a transfer of the charges from the blocks of reserves toward the Cu(2)O₂ planes. Please note that the movement of the vacant site oxygen O(5) along axis (a) to the site O(4) along axis (b) occurs due to a greater lattice parameter b compared to lattice parameter a. This is due to the increase in oxygen number per chain, which also increases the critical temperature Tc [25] . Our maximum critical temperature (Tc [AO] = 71.1 K) is obtained in EuSrBaCu₃O_6+z [AO] which correspond or optimal lattice parameter (b = 3.8695Å) compared, with the maximum lattice parameter b = 3.8872Å of Tc_max = 91.8 K obtained in case YBa₂Cu₃O_6+z [26] for z = 0.96, and (b = 3.89Å, Tc = 89 K) in the GdSrBaCu₃O_6+z compound for z = 0.93 [13] . Note here that the ratios of the a/b lattice parameters are almost equal (a/b [AO] = 0.982 Å » a/b [26] = 0.983 Å » a/b [13] = 0.984 Å), which shows a similar orthorhombic structure.

The orthorhombicity (ε), defined by the ratio (a − b)/(a + b), exhibited a significant increase from 0.38 × 10⁻³ for the sample [O] to 5.72 × 10⁻³ for the sample [AO] in SmSrBaCu₃O_6+z. This suggests a transition in the structural phase

from tetragonal to orthorhombic Figure 7. The variations in holes density (p) and orthorhombicity (ε) as a function of the critical temperature (Tc) are illustrated in the plot for LnSrBaCu₃O_6+z [AO] (refer to Figure 7(b)). This makes it possible to say that the concentration of holes influenced by orthorhombicity. The rise in orthorhombicity indicates a notable increase in the number of oxygen atoms per chain (NOC). This increase can be attributed to the expansion of the b [AO] lattice parameter when compared to the a [AO] lattice parameter. Therefore, the critical temperature Tc has subsequently enhanced.

For each Ln element, the application of heat treatment [AO] leads to a notable increase in orthorhombicity (ε), hole density (p), and critical temperature (Tc) in LnSrBaCu₃O_6+z (Ln = Eu, Nd, Sm).

When subjected to a specific heat treatment, the critical temperature of our sample is influenced by the ionic radius of the rare earth Ln. A noteworthy observation from Figure 8 is that the critical temperature exhibits a decrease trend as the ionic radius increases. This correlation highlights the significance of ionic radius in determining the critical temperature during the heat treatment process. Heat treatment [AO] increases Tc for each Ln.

The resistivity (ρ) of the samples, concerning their heat treatment [AO], is depicted in Figure 9(a) as a function of temperature.The data points for the large sample ionic radius are unmistakably situated below those of the small ionic radius. In all instances, ρ reaches zero at 76, 82, and 85 K, respectively, for the samples NdSrBaCu₃O_6+z [AO], SmSrBaCu₃O_6+z [AO], and EuSrBaCu₃O_6+z [AO].

These values are in agreement with the results obtained from the AC susceptibility measurements. Please note that for a given set of samples, Tconset (χ') exhibits a superiority of 2 - 3 K over Tc (ρ = 0), while Tc (χ'') is approximately equal to Tc (ρ = 0). In its usual condition, the linear segment of ρ (T) follows the equation ρ = ρ₀ + αT, where ρ₀ represents the residual resistance extrapolated to T = 0 K, and α represents the slope dρ/dT. This relationship is obtained recently

by several authors in the case studies of the different types of superconducting oxides [27] [28] [29] . The slope α exhibits a noticeable decrease as we consider the ionic radius of the rare earth Ln, as illustrated in Figure 9(a). This indicates a decrease of the normal electron interactions-phonons.

The rise in hole concentration within the Cu(2)O₂ planes led to noticeable changes in several key parameters as shown in Table 2. Specifically, it resulted in

a decrease in α, ρ at 295 K, and ρ at 0 K, while simultaneously increasing Tc at p = 0. These observations highlight the significant impact of hole concentration on the material’s electrical properties. The effect of the holes on these electrical and superconducting parameters is quite remarkable in several samples concerning the studies of these properties [30] [31] .

The linear relationship between resistivity and temperature is a widely observed characteristic in cuprates [30] [31] [32] . These electric coefficients are specific to the Cu(2)O₂ planes and are influenced by hole doping, as shown in Figure 9(a). This behavior is prevalent across various cuprate materials.

At elevated temperatures, the slope exhibits a reduction in correlation with the ionic radius. This phenomenon becomes more evident when observing the resistivity derivative with respect to temperature, as graphically depicted in the upper panel of Figure 9.

The reduction in p-hole doping leads to a notable enhancement in the peaks of the resistivity derivative concerning temperature (dρ/dT). These changes are clearly depicted in Figure 9(b), where the critical temperature of these peaks (Tp) is prominently observed. We have made a noteworthy observation in our systems where a single peak temperature (Tp) is evident, closely approaching the transition temperature. Of particular interest is the comparison between two specific systems: Eu [AO] and Nd [AO]. At a hole concentration of p = 0.128, corresponding to Eu [AO], we have observed a higher TP value of 86.7 K. In contrast, the Nd [AO] system, with a hole concentration of p = 0.113, exhibits a slightly lower TP value of 80 K. This disparity between the two systems adds an intriguing dimension to our findings. The data presented reveals a clear trend where curves shift towards lower temperatures as the ionic radius increases.

This observation strongly suggests that the introduction of Ln (lanthanide) elements into the Y sites of the YSrBaCu₃O_6+z system has a significant impact on its superconducting properties. The aforementioned phenomenon was similarly noted in other doped systems where x > 0.01 in Y_1−xCe_xBa₂Cu₃O_7−δ [33] . This observation is attributed to the higher ionic radius of cerium (Ce) compared to yttrium (Y). This decrease in (Tp) is also observed recently when (PbS) is added in Bi_1.6Pb_0.4Sr₂CaCu₂O(PbS)_x [34] . Tp (x = 0) = 74 K decreases to Tp (x = 10) = 61 K, so adding the (PbS) increases the volume of this sample. Here, we compare the introduction of (PbS) with the increased ionic radius of the rare earth of our samples, which decreased Tp when it increased. Note here that the temperature of peak Tp follows that of Tc.

The introduction of rare earth elements (Ln) in place of yttrium (Y) within the YBaSrCu₃O_6+z systems has led to significant modifications in their structural, electrical, and superconducting properties. In heat treatment [O], different lanthanides (Ln) yield distinct structures: Nd results in a tetragonal structure, Sm leads to a pseudo-tetragonal structure, and Eu forms an orthorhombic structure. Additionally, these structures are accompanied by critical temperatures (Tc) of 68 K, 79 K, and 81.1 K, respectively. Heat treatment [AO] induces an enhancement in orthorhombicity while simultaneously leading to a reduction in the electrical parameters α, ρ_295K, and ρ₀. Further, it increased the Tc from 5.6 to 10 K depending on Ln. Each Ln element’s ionic radius plays a significant role in influencing various properties. This specific approach led to a noteworthy outcome where the hole density in the Cu(2)O₂ planes increased. The observed correlation between hole concentration in these planes and the critical temperature adds further importance to these findings.

In our investigation, we have reached the conclusion that the critical temperature (Tc) is significantly influenced by various factors associated with the number of holes in the copper Cu(2)O₂ planes. Among these factors, the ionic size of the rare earth element Ln in YBaSrCu₃O_6+z, as well as its disorder on the site (Sr/Ba), have been found to play a crucial role. Additionally, factors such as the oxygen order in the chains, surface characteristics, atomic distances, heat treatment, and orthorhombicity also have a substantial impact on Tc.

It is worth noting that in our samples, the superconducting behavior is primarily governed by the density of holes present in the Cu(2)O₂ planes. This parameter emerges as a key determinant of the superconducting properties and represents an essential aspect in understanding the overall superconductivity in the system.

The authors declare no conflicts of interest regarding the publication of this paper.

Bellioua, M., El Amel, M.I., Bouzit, F., Errai, M., Soubane, D., Khlifa, A.A., Khenfouch, M., Mouhti, I., Tirbiyine, A., El Yakoubi, E.Y. and Nafidi, A. (2023) Impact of Heat Treatments and Hole Density (p) on the Structural, Electrical, and Superconducting Properties of LnSrBaCu₃O_6+z (Ln = Eu, Sm, Nd) Compounds. Communications and Network, 15, 83-97. https://doi.org/10.4236/cn.2023.154006