Reinforcing Increase of ΔTc in MgB2 Smart Meta-Superconductors by Adjusting the Concentration of Inhomogeneous Phases

Incorporating with inhomogeneous phases with high electroluminescence (EL) intensity to prepare smart meta-superconductors (SMSCs) is an effective method for increasing the superconducting transition temperature (Tc) and has been confirmed in both MgB2 and Bi(Pb)SrCaCuO systems. However, the increase of ΔTc (ΔTc = Tc ‒ Tcpure) has been quite small because of the low optimal concentrations of inhomogeneous phases. In this work, three kinds of MgB2 raw materials, namely, aMgB2, bMgB2, and cMgB2, were prepared with particle sizes decreasing in order. Inhomogeneous phases, Y2O3:Eu3+ and Y2O3:Eu3+/Ag, were also prepared and doped into MgB2 to study the influence of doping concentration on the ΔTc of MgB2 with different particle sizes. Results show that reducing the MgB2 particle size increases the optimal doping concentration of inhomogeneous phases, thereby increasing ΔTc. The optimal doping concentrations for aMgB2, bMgB2, and cMgB2 are 0.5%, 0.8%, and 1.2%, respectively. The corresponding ΔTc values are 0.4, 0.9, and 1.2 K, respectively. This work open a new approach to reinforcing increase of ΔTc in MgB2 SMSCs.


Introduction
According to BCS theory, McMillan theoretically calculated the upper limit of the critical temperature (T c ) of conventional BCS superconductors to be 40 K, which is called the McMillan limit temperature [1,2]. Although the T c of conventional superconductors has an upper limit, the search for high-T c superconducting materials has been continuous. High-temperature superconductors [3,4], iron-based superconductors [5,6], high-pressure superconductors [7][8][9][10], and photo-induced superconductors [11,12] have been gradually studied and discovered. However, these new superconducting materials are not simple conventional superconductors. Breaking the McMillan limit temperature remains a challenge for conventional BCS superconductors. In 2001, the superconductivity of MgB 2 was discovered [13]. The excellent superconductivity, simple preparation process, and especially high T c of MgB 2 quickly aroused great interest in the scientific community and led scholars to believe that the McMillan limit temperature may finally be surpassed [14][15][16][17][18][19]. Various methods have been applied to improve the superconductivity of MgB 2 [20][21][22][23][24], which would not only improve the practical application of MgB 2 but also help transcend the McMillan limit temperature and further elucidate the superconducting mechanism. Chemical doping is often used to study superconductivity. Unfortunately, many experimental results confirm that this method reduces the T c of MgB 2 [25][26][27][28][29][30]. Thus far, no useful strategy for improving the T c of MgB 2 is yet available.
Metamaterial mainly refers to materials made up of two or more media, which can produce new properties that are not found in a single medium. Meta-method is often used to achieve some special properties and provides new ways of improving the T c

Model
Figure 1a-c show the cross-sectional view of MgB 2 SMSCs models prepared using a MgB 2 (Φ a < 30 µm), b MgB 2 (Φ b < 15 µm), and c MgB 2 (Φ c < 5 µm) as raw materials. Φ a , Φ b , and Φ c refer to the particle sizes of a MgB 2 , b MgB 2 , and c MgB 2 powders, which will be described in detail at the experiment section. The brown hexagons represent the MgB 2 particles, and the gray dashed lines represent the flakes of inhomogeneous phase with the surface size of approximately 20 nm and thickness of approximately 2.5 nm [40,45]. The flakes of Y 2 O 3 , Y 2 O 3 :Sm 3+ , Y 2 O 3 :Eu 3+ , and Y 2 O 3 :Eu 3+ /Ag mainly gather on the surfaces of the MgB 2 particles as shown in Figure 1d. Figure 1e-h present the schematics of Y 2 O 3 , Y 2 O 3 :Sm 3+ , Y 2 O 3 :Eu 3+ , and Y 2 O 3 :Eu 3+ /Ag, respectively. The gray flake represents Y 2 O 3 . The yellow, white, and green points represent Sm, Eu, and Ag. Obviously, the introduction of these four dopants inevitably reduces the T c of MgB 2 . This is mainly because the dopants are not superconductors, which is unfavorable for the superconductivity of MgB 2 , like the impurity phase of MgO in MgB 2 . For convenience, the reduction in T c caused by introducing the dopants is referred to as the impurity effect [36][37][38][39][40][41][42] [36][37][38][39][40][41][42]. Incorporating with inhomogeneous phases has already been confirmed to be an effective method of increasing the T c for both MgB 2 and Bi(Pb)SrCaCuO systems. The variation of T c is often associated with the change of electron density. However, in the experiments, the inhomogeneous phases do not react with MgB 2 and the diffusion between the inhomogeneous phases and MgB 2 particles is difficult under the current preparation process and conditions. As a result, the dopants only exist between the MgB 2 particles as shown in Figure 1a-c and cannot change the electron density significantly. Therefore, in principle, the electron density is not the key tuning parameter for the variation of T c . Although the mechanism for this method remains unclear, we intend to interpret this phenomenon in terms of EL of inhomogeneous phases based on the results of our experiments. During the measurements, the applied external electric field forms local electric fields in the superconductor, which could excite the inhomogeneous phase to produce EL. The generated EL excites the electrons to inject energy, which is favorable to strengthen the Cooper pairs and enables the increase in T c . However, the completeness of this interpretation needs further demonstration given that the photons may disrupt Cooper pairs. Anyway, further study is required to build a relatively complete theory, especially for such a new experimental phenomenon. are not superconductors, which is unfavorable for the superconductivity of MgB2, like the impurity phase of MgO in MgB2. For convenience, the reduction in Tc caused by introducing the dopants is referred to as the impurity effect [36][37][38][39][40][41][42]. Non-EL dopants Y2O3 and Y2O3:Sm 3+ can only decrease Tc for the introduction of the impurity effect. Unlike Y2O3 and Y2O3:Sm 3+ , introducing EL Y2O3:Eu 3+ and Y2O3:Eu 3+ /Ag may increase the Tc, which is referred to as the EL exciting effect [36][37][38][39][40][41][42]. Incorporating with inhomogeneous phases has already been confirmed to be an effective method of increasing the Tc for both MgB2 and Bi(Pb)SrCaCuO systems. The variation of Tc is often associated with the change of electron density. However, in the experiments, the inhomogeneous phases do not react with MgB2 and the diffusion between the inhomogeneous phases and MgB2 particles is difficult under the current preparation process and conditions. As a result, the dopants only exist between the MgB2 particles as shown in Figure 1a-c and cannot change the electron density significantly. Therefore, in principle, the electron density is not the key tuning parameter for the variation of Tc. Although the mechanism for this method remains unclear, we intend to interpret this phenomenon in terms of EL of inhomogeneous phases based on the results of our experiments. During the measurements, the applied external electric field forms local electric fields in the superconductor, which could excite the inhomogeneous phase to produce EL. The generated EL excites the electrons to inject energy, which is favorable to strengthen the Cooper pairs and enables the increase in Tc. However, the completeness of this interpretation needs further demonstration given that the photons may disrupt Cooper pairs. Anyway, further study is required to build a relatively complete theory, especially for such a new experimental phenomenon. A distinct competition exists between the impurity effect and EL exciting effect. Tc would be improved (ΔTc > 0) when EL exciting effect dominates; otherwise, introducing the inhomogeneous phase would decrease Tc (ΔTc < 0). During the preparation process, the impurity effect should be reduced as extensively as possible, and the EL exciting effect should be enhanced to obtain samples with a high Tc. The resulting superconductor is called a SMSC, and the Tc of which can be improved and adjusted by incorporating EL inhomogeneous phases [36][37][38][39][40][41][42], which is a new property and cannot be achieved by traditional doping with a second phase. However, the ΔTcs obtained in our previous work through the SMSC method are quite small. The low doping concentrations of inhomogeneous phases greatly hindered the further improvement of Tc. To further improve the ΔTc Figure 1. The models of MgB 2 SMSCs prepared using (a) a MgB 2 (Φ a < 30 µm), (b) b MgB 2 (Φ b < 15 µm), and (c) c MgB 2 (Φ c < 5 µm) as raw materials. Schematic depictions of (d) a particle of A distinct competition exists between the impurity effect and EL exciting effect. T c would be improved (∆T c > 0) when EL exciting effect dominates; otherwise, introducing the inhomogeneous phase would decrease T c (∆T c < 0). During the preparation process, the impurity effect should be reduced as extensively as possible, and the EL exciting effect should be enhanced to obtain samples with a high T c . The resulting superconductor is called a SMSC, and the T c of which can be improved and adjusted by incorporating EL inhomogeneous phases [36][37][38][39][40][41][42], which is a new property and cannot be achieved by traditional doping with a second phase. However, the ∆T cs obtained in our previous work through the SMSC method are quite small. The low doping concentrations of inhomogeneous phases greatly hindered the further improvement of T c . To further improve the ∆T c of MgB 2 , the doping concentration of the inhomogeneous phase must be increased to enhance the EL exciting effect. However, the impurity effect inevitably increases with the increasing doping concentration, as analyzed above. The results of our previous work show that the impurity effect tends to dominate at high concentrations, which is not conducive to the T c of the sample. This phenomenon is principally caused by the agglomeration of excessive inhomogeneous phase flakes, which cannot disperse well in the sample to improve T c at concentrations exceeding the optimal value. A simple strategy to solve this problem is to reduce the particle size of MgB 2 as shown in Figure 1a-c. It can be seen that reducing the particle size would increase the optimal doping concentration of the inhomogeneous phase. The inhomogeneous phase flakes can disperse well in the sample with small particle size and fully exert the EL exciting effect to further increase ∆T c . Such a strategy has already been successfully applied to increase the T c of smart meta-superconductor Bi(Pb)SrCaCuO [42].

Experiment
, and Y 2 O 3 :Eu 3+ /Ag were prepared by a hydrothermal method [40,44]. Briefly, a certain amount of Y 2 O 3 and Eu 2 O 3 were weighed and dissolved in HCl to make a precursor. The precursor was dissolved in benzyl alcohol and stirred with a magnetic stirrer. A certain amount of octylamine and AgNO 3 was added dropwise into the beaker in turn. Then the mixture was transferred to a high-pressure reaction kettle, which was then placed in a drying oven and kept at 250 • C for 24 h. Thereafter, the reaction kettle was naturally cooled to room temperature. The precipitate was washed several times with absolute ethanol to remove impurities and then separated from the solution by centrifugation, precipitation, and drying. The obtained solids were placed in a high-temperature tube furnace and heated at 800 • C for 24 h to form a white powder.  [40,45].
Three types of MgB 2 raw materials marked with a MgB 2 , b MgB 2 , and c MgB 2 were prepared in this work. Φ a , Φ b , and Φ c refer to the particle sizes of a MgB 2 , b MgB 2 , and c MgB 2 powders. A 500-mesh sieve was used to sift MgB 2 powder (99%, 100 mesh, Alfa Aesar) to prepare a MgB 2 , indicating that Φ a < 30 µm. b MgB 2 was prepared by sifting a MgB 2 powder through vacuum filtration with a pore size of about 15 µm, indicating that Φ b < 15 µm. Meanwhile, Mg and nano boron powder sifted through vacuum filtration with the pore size of about 5 µm were applied to prepare MgB 2 powder by the traditional sintering process. The obtained MgB 2 powder was then sifted through vacuum filtration with the pore size of about 5 µm to prepare c MgB 2 , indicating that Φ c < 5 µm. MgB 2 -based superconductors were synthesized by an ex situ preparation process, which is described in detail in our previous work [37,40]. The doping concentrations in this work all refer to the mass percentage.  [44]. Figure 2b-d present the SEM images of the pure MgB 2 samples prepared using three different raw materials. Figure 2b is the SEM image of a MgB 2 , which shows that most of the particle exceeded 1 µm. For b MgB 2 , only a few of the particles exceeded 1 µm as shown in Figure 2c. Figure 2d presents the SEM image of c MgB 2 , which shows that most of particles are below 500 nm. The particle sizes of a MgB 2 , b MgB 2 , and c MgB 2 decrease in order. Figure 2e reveals the XRD patterns of four samples. The black and red curves depict the XRD patterns of a MgB 2 and a MgB 2 + 0.5% Y 2 O 3 :Eu 3+ /Ag, respectively. The blue and magenta curves correspond to the XRD patterns of b MgB 2 + 0.8% Y 2 O 3 :Eu 3+ /Ag and c MgB 2 + 1.2% Y 2 O 3 :Eu 3+ /Ag, respectively. The black vertical lines represent the standard XRD patterns   Figure 3b shows the normalized R-T curves of a MgB2 doped with 0.5% y (y = 0, Y2O3, Y2O3:Sm 3+ , Y2O3:Eu 3+ , Y2O3:Eu 3+ /Ag). The doping concentration was fixed at 0.5% base on our previous work [40]. The Tc values of MgB2 doped with Y2O3, Y2O3:Sm 3+ , Y2O3:Eu 3+ , and Y2O3:Eu 3+ /Ag were 36.8-37.6 K, 36.9-37.7 K, 37.6-38.4 K, and 37.8-38.6 K. The results clearly show that non-EL Y2O3 and Y2O3:Sm 3+ decreased the Tc of MgB2, while EL Y2O3:Eu 3+ and Y2O3:Eu 3+ /Ag increased the Tc of MgB2, as shown in the inset. The Tc values of MgB2 doped with Y2O3:Eu 3+ and Y2O3:Eu 3+ /Ag increased by 0.2 and 0.4 K, respectively, compared with that of a MgB2. This finding is similar to those of our previous studies.   Figure 3b shows the normalized R-T curves of a MgB 2 doped with 0.5% y (y = 0, Y 2 O 3 , Y 2 O 3 :Sm 3+ , Y 2 O 3 :Eu 3+ , Y 2 O 3 :Eu 3+ /Ag). The doping concentration was fixed at 0.5% base on our previous work [40].         Figure 3a, that is, T c first increases and then decreases with the increase of the doping concentration, as shown in the inset figure. The optimal doping concentration is 1.2%, and the corresponding ∆T c is 1.0 K. Figure 4d shows the normalized R-T curves of c MgB 2 doped with 1.2% y (y = 0, Y 2 Figure 5a shows the SEM image of a MgB 2 + 0.5% Y 2 O 3 :Eu 3+ /Ag. Figure 5b-e are the EDS mapping for elements Mg, Y, Eu, and Ag listed in the lower right corner of each figure. Figure 5h shows the SEM image of c MgB 2 + 1.2% Y 2 O 3 :Eu 3+ /Ag. Figure 5g-j are the EDS mapping for elements Mg, Y, Eu, and Ag. Given that the inhomogeneous phase did not react with MgB 2 , the mapping of elements Y, Eu, and Ag can reflect the distribution of the inhomogeneous phase in the sample. It can be seen that Y 2 O 3 :Eu 3+ /Ag is relatively evenly distributed in a MgB 2 . Similarly, the inhomogeneous phase did not generate significant agglomeration in c MgB 2 , even though the optimal concentration was enhanced to 1.2% as the particle size decreased, as shown in Figure 5g-j. Therefore, the inhomogeneous phase was able to fully exert the EL exciting effect to further increase ∆T c at high concentrations. 1.2% as the particle size decreased, as shown in Figure 5g-j. Therefore, the inhomogeneous phase was able to fully exert the EL exciting effect to further increase ΔTc at high concentrations.  For the b MgB2 raw material with a smaller particle size than that of a MgB2, the optimal doping concentration was first explored by changing the concentration of Y2O3:Eu 3+ from 0.5% to 1.0%. The results show that the optimal doping concentration is 0.8%. Subsequently, 0.8% Y2O3:Eu 3+ , and Y2O3:Eu 3+ /Ag were separately  raw material with a smaller particle size than that of a MgB 2 , the optimal doping concentration was first explored by changing the concentration of Y 2 O 3 :Eu 3+ from 0.5% to 1.0%. The results show that the optimal doping concentration is 0.8%. Subsequently, 0.8% Y 2 O 3 :Eu 3+ , and Y 2 O 3 :Eu 3+ /Ag were separately doped into b MgB 2 and the corresponding ∆T c values were 0.8 K and 0.9 K, respectively. Similar results were obtained in the samples prepared using c MgB 2 as the raw material. For c MgB 2 , which has the smallest particle size among the three raw materials, the optimal concentration was enhanced to 1.2%. The ∆T cs for c MgB 2 doped with Y 2 O 3 :Eu 3+ and Y 2 O 3 :Eu 3+ /Ag were 1.0 K and 1.2 K, respectively. These results indicate that reducing the particle size can effectively increase the optimal doping concentration of the inhomogeneous phase, thereby enhancing the ∆T c . In this work, the ∆T c is improved by increasing the optimal doping concentration of inhomogeneous phases through reducing the particle size, however, the T c values of MgB 2 SMSCs are relatively low due to the low T c of the pure MgB 2 sample. As the particle size decreases, the grain boundaries in the sample increase and the connectivity decreases, which are disadvantages to the superconductivity [51][52][53]. One possible solution is to incorporate the inhomogeneous phase into the interior of the particles to overcome the disadvantages caused by the increasing grain boundaries with the doping concentration increasing.

Conclusions
Although the effectiveness of improving the T c of superconducting materials through the SMSC method by doping with EL inhomogeneous phases has been proven in previous works, the ∆T cs obtained are quite small. To further increase ∆T c , three types of MgB 2 raw materials, namely, a MgB 2 , b MgB 2 , and c MgB 2 , were prepared with particle sizes decreasing in order. EL inhomogeneous phases were incorporated into these three raw materials with different concentrations to study the change of ∆T c . The results show that the optimal doping concentrations for a MgB 2 , b MgB 2 , and c MgB 2 are 0.5%, 0.8%, and 1.2%, respectively. The corresponding ∆T cs are 0.4, 0.9, and 1.2 K, respectively. Meanwhile, increasing the EL intensity of the inhomogeneous phase can be considered to further increase ∆T c . This work not only proves the effectiveness of the SMSC method in improving T c but also provides an alternative approach to improving the T c of superconducting materials.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.