Mechanical Properties of Melt Textured Y_1-xPr_xBa₂Cu₃O_7-δ Superconductor (x = 0.00 and 0.05)

ABSTRACT

This work reports the mechanical properties of ab and a(b)c-plane of melt textured Y_1-xPr_xBa₂Cu₃O_7-δ (x = 0.00 and 0.05) superconductor. Y_1-xPr_xBa₂Cu₃O_7-δ have been prepared by top seeding technique. Hardness and elastic modulus were obtained by instrumented indentation. Independent of the plane, the hardness values were around 5.0-7.5 GPa. Young’s modulus was approximately the same for both samples for ab-plane, around 132 GPa at the deepest tip penetration. However, for a(b)c-plane, the value of Young’s modulus for x = 0.05 is higher than observed for x = 0.00 sample.

Keywords:
Superconductor; YBCO; PBCO; Mechanical Properties; Hardness; Elastic modulus

1. Introduction

Since the beginning of studies in high critical temperature superconductors, one undesirable property has been the presence of granularity in sintered YBa₂Cu₃O_7-δ (Y - 123) material. To overcome this problem, a top-seeding melt texture growth (TSMTG) process was introduced¹,². With this process, it was possible to fabricate large single grains without high-angle grain boundaries in the YBa₂Cu₃O_7-δ matrix³, which also contains small dispersed particles Y₂BaCuO₅ (Y - 211)⁴ and usually a small addition of CeO₂⁵,⁶. In melt textured samples, the c-axis direction is well defined, while a- and b-axis directions are highly interchanged because of twinning.

Most of the orthorhombic REBa₂Cu₃O_7-δ (RE = Rare Earth elements) compounds exhibit superconductivity with critical temperature T_C above 90 K. The exceptions to this behavior are the elements Ce, Pr, and Tb. The suppression of superconductivity for Y_1-xPr_xBa₂Cu₃O_7-δ occurs with increasing x, and superconductivity disappears with concomitant loss of metallic conductivity at x > 0.6⁷. For PrBa₂Cu₃O₇ (Pr - 123), the compound is non-metallic and non-superconducting, an antiferromagnetic insulator. Many models have been proposed to explain the disappearance of superconductivity in Pr, such as hole filling, magnetic pair breaking, hole localization, percolation, and so on⁸-¹¹, but the question of non-superconductivity in Pr - 123 is still open.

The interest in the praseodymium-containing YBCO system dated from the 1990s, when studies had already demonstrated the dependence of elastic properties with temperature and the Pr amount in polycrystals¹². Ivanov et al.¹³ studied elastic properties of granular Y_1−xPr_xBa₂Cu₃O_7-δwith 0 > x > 0.45 (superconducting) and x = 0.65 (nonsuperconducting), employing an ultrasonic pulse-echo technique during heating from cryogenic temperatures to the room temperature. The shear velocity $v=\sqrt{G/\rho }$, where G is the shear modulus and ρ the density, decreases with the increasing temperature for the same x, while, for the same temperature, it also decreases with increasing x. They observed anomalies in the shear modulus concerning stoichiometry and temperature. The authors indicated that the study of single crystals could bring insights to explain the observed variations in elastic properties with the Pr concentration in the material¹³. The melt-texturing of REBCO arose as a possible technique for producing large-grain materials on an industrial scale, aiming at applications in engineering devices such as energy-storage systems and motors. However, the mechanical performance was always a concern due to the intrinsic brittleness and high density of crystal defects of the RE-123 system¹⁴.

In this scenario, single crystal study can help understand the basic mechanical behavior of melt textured yttrium-based materials. Variables such as hardness and elastic modulus of insulating/superconducting Y_1-xPr_xBa₂Cu₃O_7-δ are of interest aiming at applications in electronic devices such as superconductor-insulator-superconductor junctions. In this study, we produced and characterized Y_1-xPr_xBa₂Cu₃O_7-δ with different contents of Y and Pr. As a transition occurs from the superconductor state to an antiferromagnetic insulator one at $x\cong$ 0.56, then we decided to produce a sample with a low Pr concentration (around 5%) to avoid undesired effects. The mechanical properties were measured by an instrumented indentation on ab- and a(b)c-planes. All analyzes are based on single samples.

2. Experimental Details

Y_1-xPr_xBa₂Cu₃O_7-δ superconductor pellets (x = 0.00 and x = 0.05) have been prepared by top seeding technique using melt-textured NdBa₂Cu₃O₇ seeds. Firstly, a ceramic sample was prepared by the conventional solid-state reaction method. Appropriate amounts of Y₂O₃, Pr₆O₁₁, BaCO_3, and CuO were mixed and calcinated in the air at 880 ^oC, 900 ^oC, and 920 ^oC for 24 hours and then slowly cooled up to 700 ^oC. For the melt textured samples, the starting composition was 75 wt % Y(Pr)Ba₂Cu₃O_7-δ+ 25 wt % Y₂BaCuO₅ + 1 wt % CeO₂. Commercial powder Y₂BaCuO₅ was employed in the synthesis. Also, it was used CeO₂ addition to avoid the Y₂BaCuO₅ coarsening⁵,⁶. The mixture, in appropriate quantities, was pressed into cylindrical pellets, and a seed crystal of NdBa₂Cu₃O_7-δ was placed on the top of the pellet. Then, the temperature was increased to 920 ⁰C at a rate of 40 ⁰C/h and maintained in this condition for 24 h. After that, the temperature increased above the peritectic temperature, at around 1040 ^oC for x = 0.00 and 1045 ^oC for x = 0.05, and maintained for 3 h. Then, the temperature was quickly decreased in 0.1 h (6 minutes) within a temperature window of approximately 40 ^oC (45 ^oC) for the initiation of sample growth. The next step was the temperature decreasing at 0.5 ^oC/h up 980 ^oC. Then, the temperature was slowly cooled to 700 ^oC up to the ambient temperature. Finally, the melt textured samples were heated in flowing oxygen at 420 ^oC for 120 h. Figure 1 illustrates the temperature ramps, and Figure 2 shows a real photograph of the samples.

Figure 1
Temperature ramp diagram for sample texturing.

Figure 2
Real photograph of samples a) Y_0.95Pr_0.05Ba₂Cu₃O_7-δ and b) YBa₂Cu₃O_7-δ. The samples are about 12 mm in diameter.

The single-phase formation of Y_1-xPr_xBa₂Cu₃O_7-δ was confirmed by X-ray analysis, using a Shimadzu Ultima IV diffractometer with CuK_α radiation in θ-2θ configuration. The X-ray diffraction patterns were collected from 3º < 2θ < 120º with 0.02º steps and 3.5 s counting time. The microstructure and the growth process were analyzed by scanning electron microscopy (SEM) with energy-dispersive spectroscopy (EDS). Before the surface mechanical tests, samples were previously grounded and polished up to 1 μm diamond paste. Nanoindentation tests on Y_1-xPr_xBa₂Cu₃O_7-δ samples were performed using a Nanoindenter XP^TM and a diamond Berkovich-type indenter, with applied loads ranging from 10 to 300 mN in a 5 x 4 indentation matrix parallel and perpendicular to the c-axis. The loading-unloading curves consisted of 10 cycles with a loading time of 10 s and a holding time of 15 s. The distance between each indentation was 50 μm. The indentations were performed in pieces taken from the central region of the sample, thus avoiding regions with excess green phase (Y-211) and other impurities. Care was taken to perform the indentations in a region free of pores and cracks, and the mechanical properties near the surface and inside the grains could be measured. The H and E were determined following the Oliver and Pharr method¹⁵.

3. Results and Discussion

The structure of the samples was investigated using X-ray diffraction. Figure 3 presents the diffractogram of the melt textured superconductor YBa₂Cu₃O_7-δ and Y_0.95Pr_0.05Ba₂Cu₃O_7-δ taken at room temperature. The measurements demonstrate that the pattern for the Y_0.95Pr_0.05Ba₂Cu₃O_7-δ is identical to that of YBa₂Cu₃O_7-δ, showing that the two samples have the same orthorhombic structure. Also, the lattice parameters a, b, c, and V obtained from both samples indicated that the Pr atoms were substituted by Y atoms, in agreement with other studies¹⁶.

Figure 3
X-ray diffractogram of the melt textured YBa₂Cu₃O_7-δ and Y_0.95Pr_0.05Ba₂Cu₃O_7-δ superconductor was taken at room temperature. The corresponding number of PDF card for YBa₂Cu₃O_7-δ is 2101545. (*) corresponds to Y-211 phase.

The microstructure of the (a)-(b) YBa₂Cu₃O_7-δ and (c)-(d) Y_0.95Pr_0.05Ba₂Cu₃O_7-δ superconductor for ab- and a(b)c-planes is shown in Figure 4. From SEM-EDS, it was possible to analyze the composition of the superconducting matrix, the dispersion, and the composition of the Y₂BaCuO₅/Pr₂BaCuO₅ particles (211). It was observed that the superconducting matrix (123 phase) is strongly enriched with yttrium while that 211 particles (around 5 μm sizes) have intermediate quantities. It is known that the solubility of rare earth (RE) ions in the superconducting matrix increase with increasing RE ionic size, while the 211 particles embedded in the matrix will be poor in Pr¹⁷,¹⁸. A random distribution of BaCeO₃ particles between 1 and 5 μm in diameter are homogeneously dispersed within the Y_0.95Pr_0.05Ba₂Cu₃O_7-δ. However, the granular nature and the porosity are clearly shown. Defects such as pores are created during the heating and cooling steps or formed during the oxygenation process. Also, as shown in panels (b) and (d), it was revealed microcracks parallel to (001) planes. The bulk critical temperatures for these samples are 91.7 K and 88.7 K for YBa₂Cu₃O_7-δ and Y_0.95Pr_0.05Ba₂Cu₃O_7-δ superconductors, respectively¹⁹. Further details on the sample preparation and characterization may be found in Reference¹⁹,²⁰.

Figure 4
SEM micrographs of (a-b) YBa₂Cu₃O_7-δ and (c-d) Y_0.95Pr_0.05Ba₂Cu₃O_7-δmelt-textured superconductor for ab- and a(b)c-planes.

Figure 5 shows a SEM image of indentions produced with ten loading cycles, from 10 to 300 mN on the melt textured YBa₂Cu₃O_7-δ superconductor and the corresponding loading curves. At the highest applied load of 300 mN, the maximum depth reached by the tip was around 1500-1700 nm in ab- and a(b)c-planes. For this x = 0.00 sample, curves were continuous, presenting no pop-ins caused by cracks nucleation or pores crushing. No radial cracks emanating from the corners of the indentation were observed. However, in both planes, notably in the ab-plane, it was possible to observe more material displaced around the tip imprint due to the nucleation and propagation of lateral cracks. The material displacement in successive indentation tests is a phenomenon typically observed in lamellar-like materials²¹,²². Generally, when these lateral cracks are nucleated, radial cracks are suppressed. However, the involved mechanisms seem to depend on specific features of the compound.

Figure 5
(a) and (c) Secondary-electrons scanning electron microscopy images of imprints produced with a Berkovich indenter under 300 mN load on the melt textured YBa₂Cu₃O_7-δ superconductor, in the ab- and a(b)c-planes, respectively; in (b) and (d), the corresponding loading-unloading curves related with the imprints shown in (a) and (c).

The analyses of the imprints morphologies shown in Figure 5 suggest that the plastic deformation mechanism is similar to that proposed by Pimentel et al.²¹. They studied the mechanical properties of the highly oriented FeSe_0.5Te_0.5 superconductor compound. The samples’ morphology also consisted of plate-like crystals with a lamellar-like structure and the same behavior of cracking for the ab-plane as observed in this material. According to the authors, as the indenter penetrates in the ab-plane, cracks parallel to the surface are nucleated at the edges of the indenter, lifting material at the tip edges and eventually leading to the surface´s partial detachment (as seen in Figure 5a). In this mechanism, the crack pattern is assumed as perpendicular to the c-axis.

Figure 6 shows SEM images of indentions produced with ten loading cycles, from 10 to 300 mN on the melt textured Y_0.95Pr_0.05Ba₂Cu₃O_7-δ superconductor in the ab- and a(b)c-planes and the corresponding loading curves. At the highest applied load of 300 mN, the maximum depth reached by the tip was around 1450-1750 nm. For the ab-plane, the curve is not continuous, presenting tip incursions in the 1300 nm depth range. During the tests, the indenter is submitted to a triaxial stress distribution, and delamination can occur around the indenter, or lateral cracks can be nucleated, with the material being ejected by these tangential forces parallel to the surface. When this effect occurs, the indenter loss sustentation and penetration depth suddenly increase, reflecting in the loading curves as such discontinuities. In this material, as seen for the YBa₂Cu₃O_7-δ, the material displacement around the tip imprint was also observed due to the nucleation and propagation of these cracks, again with a higher degree for ab-plane. No radial cracks emanating from the corners of the indentation were observed. To sum up, the surfaces morphologies after localized mechanical tests were alike between the x = 0.00 and x = 0.05 samples, although the latter disclosed intensified brittleness under normal loading.

Figure 6
(a) and (c) Secondary-electrons scanning electron microscopy images of imprints produced with a Berkovich indenter under 300 mN load on the melt textured Y_0.95Pr_0.05Ba₂Cu₃O_7-δ superconductor in the ab- and a(b)c-planes, respectively; in (b) and (d), the corresponding loading-unloading curves related with the imprints shown in (a) and (c).

Hardness profiles as a function of penetration depth for ab- and a(b)c-planes are presented in Figure 7 for x = 0.00 and x = 0.05 samples. All curves presented higher hardness values at low penetration depths and then decreased continuously in the analyzed penetration depth. Independent of the investigated plane or sample, the profiles tend to reach a plateau at deeper regions, around 5-7.5 GPa at approximately 1500-1700 nm. The x = 0.05 profile at the ab-plane was the lower one, explained by the fracture-promoted increase in the contact area during indentation, evidenced by tip-incursions as shown in Figure 6b. Note that the profiles are deeper than 200 nm (the tip rounding radius) to avoid errors in the contact area measurement, as well as the indentation size effect²³. Nevertheless, others factors may originate the variation observed in hardness with penetration depth, as outermost plastic deformation layers produced by polishing, microcracking in adjacent lamellae, or the crushing of inner pores. Actually, such decrease was small compared to those observed in other lamellar-like single crystals²¹,²² (it is in the order of the error bars), having little influence in the measurements.

Figure 7
Hardness profiles as a function of penetration depth for ab- and a(b)c-planes of melt textured YBa₂Cu₃O_7-$\delta$ and Y_0.95Pr_0.05Ba₂Cu₃O_7-$\delta$ superconductor.

Studying the indentation hardness H of REBa₂Cu₃O_7-δ, researchers obtained values of 5 + 2 GPa for polycrystalline, 8.0 + 0.5 for single crystals and 9.0 + 0.5 GPa for both ab- and a(b)c-plane in melt-textured superconductor bulks²⁴. The RE corresponds to a natural mixture of rare earth elements (Y – Yb – Dy – Ho – Tm – Lu – Gd – Tb – Sm – Ce – Eu – Nd) extracted from the xenotime mineral. In accordance with the authors, the different values for the hardness are due to the different microstructures present in these materials. The hardness of the polycrystalline REBa₂Cu₃O_7-δ is the lowest because pores collapse under indentation, leading to the tip incursion and the subsequent overestimation of the contact area (since H ∝ A^-1). On the other hand, the highest value observed for the melt textured sample is due to the presence of the 211 precipitates, which are harder and stiffer than the 123 phase. The hardness of the 211 phase is 14 + 2 GPa, while it is about 10-11 GPa for the pure 123 phase. Values of the single crystal with lamellar-like structure, with a small size of approximately 1 mm and 20 μm thick (observed at the lamellar edges), were lower than those of the melt textured samples, explained by the specific deformation features of lamellar-like structures, as discussed previously in this report and in²¹,²².

Figure 8 shows elastic modulus profiles as a function of penetration depth for ab- and a(b)c-planes of melt textured YBa₂Cu₃O_7-δ and Y_0.95Pr_0.05Ba₂Cu₃O_7-δ superconductor. Open and closed symbols, respectively, represent pure and doped samples. The elastic modulus was higher near the surface and decreased with the increasing penetration depth due to the aforementioned artifacts affecting indentation measurements. It is conspicuous that, differently from hardness, the planes present significant variations in elastic modulus. For ab-plane, the elastic modulus is approximately the same for x = 0.00 and x = 0.05 samples, around 132 GPa at the deepest tip penetration. However, for a(b)c-plane, the elastic modulus value for x = 0.05 is higher than that observed for the x = 0.00 sample, i.e., around 183 GPa and 147 GPa, respectively, both at the deepest tip penetration.

Figure 8
Elastic modulus profiles as a function of penetration depth for ab- and a(b)c-planes of melt textured YBa₂Cu₃O_7-δ and Y_0.95Pr_0.05Ba₂Cu₃O_7-δ superconductors.

The ~24% increase in elastic modulus, attained by varying the stoichiometry from YBa₂Cu₃O_7-δ to Y_0.95Pr_0.05Ba₂Cu₃O_7-δ, is possibly a consequence of different interactions experienced by neighboring atoms at the orthorhombic structure. The electrons distributions are Ba = [Xe] 6s² and Pr = [Xe] 4f³6s². Hence, substituting barium for praseodymium in the position of the rare earth atom introduces more electrons in the band structure. The consequences to the lattice parameters were minimal, as inferred from XRD results, shown in Figure 3. On the other hand, T_C varies from 91.7 K for YBa₂Cu₃O_7-δ to 88.7 K for Y_0.95Pr_0.05Ba₂Cu₃O_7-δ¹⁹,²⁰. The potential energy among adjacent atoms also changes locally since the electron screening of the nucleus is stronger in Pr than it is in Ba. Such effect is more noticeable in the c direction, where the atomic density is higher from a RE atom´s point of view. The understanding of the mechanism through which the electron balance affects mechanical properties of the REBa₂Cu₃O_7-$\delta$ material is beyond the scope of this report. Nevertheless, variations in the potential energy U through the c-axis do result in different atomic bonding forces (F = - ∇U) and equilibrium separation r₀ in that direction. As a result, the elastic modulus varies as well, as measured here for the a(b)c-plane, since it strongly depends on bonding. From a simplified approach²⁵,

$E\approx \frac{1}{r_0}{\left|\frac{d^{2}U}{d{r}^2}\right|}_{r=r_0}$ (1)

The elastic module of the pure YBa₂Cu₃O_7-δ sample measured at both planes agrees with literature data²⁴. In REBa₂Cu₃O_7-d superconductor single crystals, Foerster et al.²⁴ obtained 107 GPa for elastic modulus. The low value of E was attributed to the small sample thickness.

The plastic index is a useful correlation to compare mechanical properties of the YBa₂Cu₃O_7-δ and Y_0.95Pr_0.05Ba₂Cu₃O_7-δ. It allows to predict a material´s wear behavior in service through the ratio H / E*, where

$$E*=E/(1-n^2)$$ (2)

is the effective elastic modulus²⁶. The efficiency of such parameters when applied in superconductor single crystals was demonstrated elsewhere²⁷. Plastic indexes, summarized in Table 1, were calculated by assuming the Poisson´s ratio ν = 0.25 for both compounds²⁸, and hardness H and elastic modulus E values inferred at the deepest penetration depths in Figures 7 and 8. In the ab-plane, the x = 0.00 condition disclosed a slightly higher index of plasticity; differently, similar values were obtained for a(b)c-planes of both compounds. Thus, the tribological strength is expected to depend neither the x value nor the single crystal´s plane. Interestingly, according to the Cheng and Cheng²⁶ results, such plastic index values situate Y_1-xPr_xBa₂Cu₃O_7-δ in the same class than metals (H / E* < 0.3), and far from typical brittle materials such as sapphire and fused silica.

Table 1
Microscopic mechanical properties of YBa₂Cu₃O_7-δ and Y_0.95Pr_0.05Ba₂Cu₃O_7-δ compounds obtained from ab- and a(b)c- plane.

Compounds	plane	H (GPa)	E (GPa)	H/E*
YBa2Cu3O7-δ	ab	6.1 ± 1.0	130.8 ± 9.0	0.04 ± 0.01
	a(b)c	6.7 ± 0.4	147.0 ± 7.1	0.04 ± 0.01
Y0.95Pr0.05Ba2Cu3O7-δ	ab	4.9 ± 1.0	132.7 ± 9.0	0.03 ± 0.01
	a(b)c	7.5 ± 0.6	182.8 ± 8.8	0.04 ± 0.01

4. Conclusions

The effects of Pr addition on mechanical properties of ab- and a(b)c-plane of melt textured YBa₂Cu₃O_7-δ superconductor have been studied. The samples were produced by top seeding technique and characterized regarding structural, morphology, and mechanical properties along the ab- and a(b)c-planes. All samples corresponded to the orthorhombic YBa₂Cu₃O_7-δ phase. The hardness of the samples was the same and independent of the plane, with values approximately between 5-7.5 GPa. For ab-plane, the elastic modulus was approximately the same in both samples, around 132 GPa. On the other hand, for a(b)c-plane, the value of elastic modulus for doped sample was higher than that observed for the pure sample, around 147 GPa and 183 GPa, respectively.

5. Acknowledgments

Authors are grateful to Prof. C. M. Lepienski for the use of nanoindenter, and the C-LABMU/UEPG for other characterization facilities. This work was partially financed by CNPq under contract n⁰ 472.746/2013-8.

6. References

• ¹
  Morita M, Takebayashi S, Tanaka M, Kimura K, Miyamoto K, Sawano K. Quench and Melt Growth (QMG) Process for Large Bulk Superconductor Fabrication. Adv Supercond. 1991;3:733.
• ²
  Jin S, Tiefel TH, Sherwood RC, van Dover RB, Davis ME, Kammlott GW, et al. Melt-textured growth of polycrystalline YBa₂Cu₃O_{7 − δ} with high transport J_c at 77 K. Phys Rev B Condens Matter. 1988;37:7850.
• ³
  Jin S, Tiefel TH, Sherwood RC, Davis ME, van Dover RB, Kammlott GW, et al. High critical currents in Y‐Ba‐Cu‐O superconductors. Appl Phys Lett. 1988;52(24):2074-6.
• ⁴
  Mendoza E, Puig T, Varesi E, Carrillo AE, Plain J, Obradors X. Critical current enhancement in YBCO–Ag melt-textured composites: influence of microcrack density. Physica C. 2000;334(1-2):7-14.
• ⁵
  Vilalta N, Sandiumenge F, Pinol S, Obradors X. Precipitate size refinement by CeO₂ and Y₂BaCuO₅ additions in directionally solidified YBa₂Cu₃O₇ J Mater Res. 1997;12(1):38-46.
• ⁶
  Obradors X, Yu R, Sandiumenge F, Martinez B, Vilalta N, Gomis V, et al. Directional solidification of ReBa₂Cu₃O₇ (Re = Y, Nd): microstructure and superconducting properties. Supercond Sci Technol. 1997;10(12):884-90.
• ⁷
  Neumeier JJ, Maple MB. Superconducting critical temperature and electrical resistivity of the system Y_1−xPr_xBa₂Cu₃O_6.95 (0⩽x⩽1). Physica C. 1992;191(1-2):158-66.
• ⁸
  Neumeier JJ, Bjornholm T, Maple MP, Schuller IK. Hole filling and pair breaking by Pr ions in YBa₂Cu₃O_6.95±0.02 Phys Rev B Condens Matter. 1989;63:2516.
• ⁹
  Peng JL, Klavins P, Shelton RN, Radousky HB, Hahn PA, Bernardez L. Upper critical field and normal-state properties of single-phase Y_1−xPr_xBa₂Cu₃O_7−γ compounds. Phys Rev B Condens Matter. 1989;40(7):4517-26.
• ¹⁰
  Fink J, Nucker N, Romberg H, Alexander M, Maple MB, Neumeier JJ, et al. Evidence against hole filling by Pr in YBa₂Cu₃O₇ Phys Rev B Condens Matter. 1990;42(7):4823-6.
• ¹¹
  Infante C, El Mously MK, Dayal R, Husain M, Siddiqi SA, Ganguly P. On the localisation of charge carriers and suppression of superconductivity by praseodymium in systems derived from YBa2Cu3O7−d. Physica C. 1990;167(5-6):640-56.
• ¹²
  Lemmens P, Hunnekes C, Froning P, Ewert S, Passing H, Marbach G, et al. Elastic properties of YBa₂Cu₃O_x, (Y_{1 − y}Pr_y)Ba₂Cu₃O₇ and (BiPb)₂Sr₂Ca₂Cu₃O₁₀ studied by ultrasound. J Less Common Met. 1990;164-165:1129-35.
• ¹³
  Ivanov O, Fossheim K, Balankina E, Cjølmesli S, Nyhus J. Shear elastic properties of the Y_1−xPr_xBa₂Cu₃O _7-δ system: A possible correlation between T_c and a structural instability. Phase Transit. 1999;70(3):147-59.
• ¹⁴
  Lo W. Recent progress in large-grain REBCO melt texturing. J Miner Met Mater Soc. 2000;52(6):18-21.
• ¹⁵
  Oliver WC, Pharr GM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res. 1992;7(6):1564-83.
• ¹⁶
  Radousky HB. A review of the superconducting and normal state properties of Y_{1− x}Pr_xBa₂Cu₃O₇ J Mater Res. 1992;7(7):1917-55.
• ¹⁷
  Krauns C, Sumida M, Tagami M, Yamada Y, Shiohara Y. Solubility of RE elements into Ba–Cu–O melts and the enthalpy of dissolution. Z Phys B. 1994;96(2):207-12.
• ¹⁸
  Qi X, MacManus-Driscoll JL. Liquid-phase epitaxial growth of REBa₂Cu₃O_7−δ (RE=Y, Yb, Er) thick films at reduced temperatures. J Cryst Growth. 2000;213(3-4):312-8.
• ¹⁹
  Opata YA, Monteiro JFHL, Jurelo AR, Siqueira EC. Critical current density in (YBa₂Cu₃O_7−δ)_1-x−–(PrBa₂Cu₃O_7−δ)_x melt-textured composites. Physica C. 2018;549:107-12.
• ²⁰
  Opata YA, Monteiro JFHL, Jurelo AR, Rodrigues P Jr. Fluctuation-induced conductivity in melt-textured Pr-doped YBa₂Cu₃O_{7- δ} composite superconductor. Phase Transit. 2018;91(4):343.
• ²¹
  Pimentel JL Jr, Pureur P, Lopes CS, Serbena FC, Foerster CE, Silva SA, et al. Mechanical properties of highly oriented FeSe_0.5Te_0.5 superconductor. J Appl Phys. 2012;111:033908.
• ²²
  Souza GB, Serbena FC, Jurelo AR, Silva SA, Pinheiro LBLG, Dias FT, et al. On the determination of hardness and elastic modulus in BaFe₂As₂ lamellar-like material. J Mater Res. 2016;31(10):1413-22.
• ²³
  Fisher-Cripps AC. Nanoindentation. New York: Springer-Verlag; 2004.
• ²⁴
  Foerster CE, Serbena FC, Jurelo AR, Ferreira TR, Rodrigues P Jr, Chinelatto AL. Mechanical Properties of REBa₂Cu₃O_7-δ Superconductor With RE Obtained From Xenotime Mineral. IEEE Trans Appl Supercond. 2011;21(2):52-9.
• ²⁵
  Meyers M, Chawla K. Mechanical behavior of materials. 2nd ed. New York: Cambridge University Press; 2009. 145 p.
• ²⁶
  Cheng Y, Cheng C. Scaling, dimensional analysis, and indentation measurements. Mater Sci Eng Rep. 2004;44(4-5):91-149.
• ²⁷
  Souza GB, Jurelo AR, Monteiro JFHL, Oliveira WR, Barcote MV, Siqueira EC. BiS₂-based superconductor presents ductile-like tribo-mechanical behavior. Supercond Sci Technol. 2017;30:075005.
• ²⁸
  Diko P, Fuchs G, Krabbes G. Influence of silver addition on cracking in melt-grown YBCO. Physica C. 2001;363(1):60-6.

Publication Dates

• Publication in this collection
  27 May 2022
• Date of issue
  2022

History

• Received
  16 Dec 2021
• Reviewed
  25 Apr 2022
• Accepted
  11 May 2022