Microhardness studies on 4-Dimethylamino-N-methyl 4-Stilbazolium Tosylate (DAST)

The Vickers and Knoop microhardness studies were carried out on the (001) face of 4-Dimethylamino-N-methyl 4-Stilbazolium Tosylate (DAST) crystals grown by the slope nucleation technique. The Vickers microhardness number (H_v) and the Knoop microhardness number (H_k) were found to dwindle with increasing load. The Meyer's index number (n) and hardness were calculated from H_v. The fracture toughness, brittle index and yield strength were calculated. The Young's modulus was calculated using the Knoop hardness value.     

Microhardness properties of 4-methoxy benzaldehyde N-methyl 4-stilbazolium tosylate

The mechanical properties of crystals are evaluated by mechanical testing which reveals certain mechanical characteristics. The fastest and simplest type of mechanical testing is hardness measurement. The Vickers and Knoop microhardness studies have been carried out on 4-methoxy benzaldehyde N-methyl 4-stilbazolium tosylate crystals grown by a slow evaporation technique over a load range of 10-100 g. The Vickers hardness number (H_v) and the Knoop microhardness number (H_k) were found to increase with the increase in load. The Meyer's index number ‘n’ was calculated from H_v. The Young's modulus was calculated using the Knoop hardness values. Hardness anisotropy has been observed in accordance with the orientation of the crystal.     

Significant Change in Mechanical Properties of YBa2Cu3O7−x Bulk Superconductors Diffused with Sn Nanoparticles

Mechanical behavior of YBa₂Cu₃O_7?x (Y123) superconductors exposed to Sn nanoparticles diffusion is determined by the way of Vickers microhardness (H _v ) conducted at different applied loads (0.245N≤F≤2.940 N). Load dependent microhardness, load independent microhardness, elastic modulus, and yield strength values are estimated from the microhardness curves. Unpredictably, the findings of the H _v values reveal that the undiffused sample and Sn diffused sample prepared at 500 ^°C exhibit reverse indentation size effect (RISE) behavior while the other samples obey indentation size effect (ISE) nature. Further, we extract the load independent (true) microhardness using the Meyer’s law, proportional specimen resistance (PSR), elastic/plastic deformation (EPD), Hays–Kendall (HK) approach and indentation-induced cracking (IIC) model, and compare the true hardness with the apparent hardness.     

Correlation between hardness and elastic moduli of the covalent crystals

From a statistical manner, we collected and correlated experimental bulk (B), shear (G), Young’s modulus (E), and ductility (G/B) with Vickers hardness (H_v) for a number of covalent materials and fitted quantitative and simple H_v–G and H_v–E relationships. Using these experimental formulas and our first-principles calculations, we further predicted the microhardness of some novel potential hard/superhard covalent compounds (BC₂N, AlMgB₁₄, TiO₂, ReC, and PtN₂). It was found that none of them are superhard materials (H_v ? 40 GPa) except BC₂N. The present empirical formula builds up a bridge between Vickers hardness and first-principles calculations that is useful to evaluate and design promising hard/superhard materials.     

Influence of Nano-Ag Addition on the Mechanical Properties of (Cu0.5Tl0.5)-1223 Superconducting Phase

Superconducting samples of type (nano-Ag) _x Cu_0.5Tl_0.5Ba₂Ca₂Cu₃O_10?δ , x=0.0,0.5,1.0,1.5,2.0, and 3.0 wt.% of the total sample’s mass were prepared by a single step solid-state reaction technique. The prepared samples were characterized using X-ray powder diffraction (XRD) and a scanning electron microscope (SEM). The electrical properties of the prepared samples were investigated using the electrical resistivity and I–V measurements. The Vickers microhardness (H _v ) was measured at different applied loads (0.25–3.0 N) for studying the mechanical performance of the prepared samples. All prepared samples exhibited normal indentation size effect (normal ISE) and the H _v number was load dependent. H _v number increases as nano-Ag addition increased. The experimental data of H _v was analyzed using different models; Mayer’s law, Hays–Kendall (H–K) approach, elastic/plastic deformation (EPD) model, proportional specimen resistance (PSR) model, and indentation induced cracking (IIC) model. In addition, the true microhardness (H _o ) values were evaluated through different models. The obtained data has good agreement with the PSR model. Also, Young’s modulus (E), yield strength (Y), fracture toughness (K _f ), and brittle index (B _i ) were calculated.     

Hardness and fracture toughness of thermoelectric La<Subscript>3−<Emphasis Type="Italic">x</Emphasis></Subscript>Te<Subscript>4</Subscript>

Lanthanum telluride (La_3?x Te₄) is a state-of-the-art n-type high temperature thermoelectric material that behaves as a weak and brittle ceramic. Vickers microindentation hardness testing was explored as a rapid analysis technique to characterize the mechanical properties of this material. An indentation size effect was observed with hardness values ranging from 439 ± 31 kgf/mm² (0.01 kgf/10 s contact time) to 335 ± 6 kgf/mm² (0.5 kgf/10 s contact time). The Vickers indentation fracture toughness, K _VIF, based on measurements of crack lengths emanating from the corners of the Vickers indents was 0.70 ± 0.06 MPa m^1/2.     

A comprehensive study on mechanical properties of Bi1.8Pb0.4Sr2MnxCa2.2Cu3.0Oy superconductors

This study manifests the crucial change in the mechanical performances of Bi_1.8Pb_0.4Sr₂Mn_xCa_2.2Cu_3.0O_y superconductor samples (x = 0, 0.03, 0.06, 0.15, 0.3 and 0.6) prepared by conventional solid-state reaction method by use of Vickers microhardness (H_v) measurements carried out at different applied loads, (0.245 N ≤ F ≤ 2.940 N). Load dependent microhardness, load independent microhardness, Young’s (elastic) modulus and yield strength values being account for the potential technological and industrial applications are evaluated from the hardness curves and compared with each other. It is found that the H_v, elastic modulus and yield strength obtained decrease (increase) with the enhancement of the applied load for the undoped (doped) samples. Surprisingly, the results of the H_v values illustrate that the samples doped with x = 0.03, 0.06, 0.15, 0.3 and 0.6 exhibit reverse indentation size effect (RISE) feature whereas the pure sample obeys indentation size effect (ISE) behavior. Furthermore, the experimental results are examined with the aid of the available methods such as Meyer’s law, proportional sample resistance model (PSR), elastic/plastic deformation (EPD), Hays–Kendall (HK) approach and indentation-induced cracking (IIC) model. The results inferred show that the hardness values calculated by PSR and EPD models are far from the values of the plateau region, meaning that these models are not adequate approaches to determine the real microhardness value of the Mn doped Bi-2223 materials. On the other hand, the HK approach is completely successful for the explanation of the ISE nature for the pure sample while the IIC model is obtained to be the best model to describe the hardness values of the doped materials exhibiting the RISE behavior. Additionally, the bulk porosity analysis for the samples reveals that the porosity increases monotonously with the increment in the Mn inclusions inserted in the Bi-2223 system, presenting the degradation of the grain connectivity.     

Change of formation velocity of Bi-2212 superconducting phase with annealing ambient

This exhaustive study enables the researchers to recognize the role of the annealing conditions (temperature and time) on the microstructural, mechanical, electrical and superconducting properties of the Bi-2212 superconducting material with the aid of ρ-T, X-ray diffraction, scanning electron microscopy and Vickers microhardness (H_v) measurements. For this aim, the superconducting samples are elaborated by standard solid-state reaction route at different annealing temperature and different annealing duration. The results show that the annealing temperature of 840 °C and the annealing duration of 72 h are the best for the formation velocity of Bi-2212 superconducting phase. In this study we have focused on microhardness measurements to investigate the mechanical properties. Vickers microhardness, Young’s modulus, fracture toughness and yield strength values are calculated separately for all samples. Experimental results of hardness measurements are analyzed using the some models. Finally, the Hays–Kendall model is determined as the most successful model describing the mechanical properties of our samples.     

Investigation of indentation size effect (ISE) and micro-mechanical properties of Lu added Bi2Sr2CaCu2Oy ceramic superconductors

In this study, we investigated the effect of the Lutetium (Lu) addition on microstructure and mechanical properties of the Bi-2212 superconductors annealed at 840 °C for 50 h. The samples were prepared by the widely used conventional solid-state reaction method. For comparison, undoped sample was prepared in the same conditions. The prepared samples were characterized using X-ray powder diffraction (XRD), scanning electron microscope (SEM), and microhardness measurements (H _v ). The volume fraction and lattice parameters were determined from the XRD measurements. The microstructure, surface morphology and orientation of the grains were investigated by SEM. In this study we have focused on microhardness measurements to investigate the mechanical properties. Vickers microhardness, load independent hardness, Young’s modulus, fracture toughness and yield strength values were calculated separately for doped and undoped samples. Experimental results of hardness measurements were analyzed using the Meyer’s law, proportional sample resistance (PSR)model, modified proportional sample resistance (MPRS) model, Elastic–Plastic deformation model (EPD), and Hays-Kendall (HK) approach. Finally, the Hays-Kendall (HK) approach was determined as the most successful model describing the mechanical properties of our samples. Moreover, lattice parameter c and volume fraction of Bi-2212 phase decreased with increasing Lu content. SEM measurements show that not only the surface morphology and grain connectivity were obtained to degrade but also the grain sizes of the samples were found to decrease with the increase of the Lu addition, as well.     

Variation of Mechanical Properties of Cr Doped Bi-2212 Superconductors

This study shows the influence of Cr inclusions on the mechanical properties of Bi_1.8Sr_2.0Cr _x Ca_1.1Cu_2.1O _y (Bi-2212) superconducting samples (x=0, 0.1, 0.3, 0.5, 0.7, and 1) prepared by conventional solid-state reaction route with the aid of the microhardness (H _v) measurements. Moreover, some characteristics such as Vickers microhardness, Young’s (elastic) modulus (E) and yield strength (Y), being responsible for the potential technological and industrial applications, are theoretically evaluated from the microhardness curves belonging to the samples and compared with each other. It is found that the load dependent microhardness values decrease nonlinearly as the applied load enhances until 2 N beyond, which the curves shift to the saturation region, confirming that all the samples exhibit the indentation size effect (ISE) nature. Further, the elastic modulus and yield strength values observed reduce with the enhancement of the applied load and Cr inclusions in the Bi-2212 matrix. The experimental findings are also analyzed by Meyer’s law, proportional sample resistance model (PSR), modified proportional sample resistance model (MPRS), elastic/plastic deformation model (EPD), and Hays–Kendall (HK) approach. According to the results obtained, the load independent microhardness values calculated by EPD, PSR, and MPSR models are far from the values of the plateau region; however, the HK approach is the most suitable model for the microhardness calculations of the samples prepared in this study.     

The Influence of SnO2 Nano-Particles Addition on the Vickers Microhardness of (Bi, Pb)-2223 Superconducting Phase

The Vickers microhardness of Bi_1.6Pb_0.4Sr₂Ca₂Cu₃O_10+?? superconducting phase with added SnO₂ nano-particles was investigated. The concentration of SnO₂ nano-particles x varied from 0.0 to 2.0 of the sample??s total mass. The experimental data of the Vickers microhardness were analyzed using Meyer??s law, the elastic/plastic deformation model, Hays?CKendall??s approach and the proportional specimen resistance model. The Vickers microhardness number H _v increased as x increased up to 0.4?wt%. The load dependence of H _v exhibited a normal indentation-size effect, H _v increased as the applied load increased. Moreover, this dependence was well fitted with the Hays?CKendall approach rather than the elastic/plastic deformation and proportional specimen resistance models. In addition, we calculated Young modulus, yield strength, fracture toughness and brittleness index as a function of both applied load and SnO₂ nano-particle concentration.     

AFM studies of microindented GaN and InGaN

The microhardness characteristics of GaN and GaN/InGaN films epitaxially grown on (0001) sapphire have been investigated using Vickers and Knoop indenters. The variation of H_V and H_K follows a reverse type of indentation size effect (reverse ISE). The microhardness results have also been analyzed using Meyer's law, Hays-Kendall approach and Proportional specimen resistance (PSR) model. The effect of N⁺ implantation on the microhardness of GaN has also been studied. The implanted sample is more resistant to plastic penetration than the unimplanted one and it is found that implantation enhances the surface hardness. Detailed AFM studies around the indented regions of the GaN and GaN/InGaN give the nature and behavior of the deformation on the surface.     

Mechanical and Electrical Properties of (Cu0.5Tl0.5)-1223 Phase Added with Nano-Fe2O3

Superconducting samples of type (Cu_0.5Tl_0.5)-1223 added with nano-Fe₂O₃ (x=0.0, 0.1, 0.2, 0.4, 0.6 and 1.0 wt.%) were prepared by solid-state reaction technique. The prepared samples were characterized using X-ray powder diffraction (XRD) and scanning electron microscopy (SEM) for phase analysis and microstructure examination. The elemental content of the prepared samples was determined using particle induced X-ray emission (PIXE), whereas the Oxygen-content of these samples was obtained using non Rutherford backscattering spectroscopy at 3 MeV proton beam. It was found that the Oxygen-content of (Cu_0.5Tl_0.5)-1223 phase was not affected with the addition of nano-Fe₂O₃. The electrical resistivity measurements showed that the superconducting transition temperature (T _c ) increases up to x=0.2 wt.%, followed by a systematic decrease for x>0.2 wt.%. In addition, room temperature Vickers microhardness (H _v ) measurements were carried out at different applied loads (0.49–2.94 N) to study the performance of the mechanical properties of samples. The experimental results of H _v were analyzed using different models such as elastic, energy dissipation, energy balance and modified energy balance models. It has been found that the energy dissipation model is in a good agreement with the microhardness data.     

Role of diffusion-annealing time on the superconducting, microstructural and mechanical properties of Cu-diffused bulk MgB2 superconductor

In this study, the effect of various annealing time (0.5, 1, 1.5 and 2 h) on microstructural, mechanical and superconducting properties of the Cu-diffused bulk MgB₂ superconducting samples is investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM), Vickers microhardness (H _v ) and dc resistivity measurements for the first time. The critical transition temperature, grain size, phase purity, lattice parameter, surface morphology, crystallinity and room temperature resistivity values of the bulk samples prepared are compared with each other. Electrical-resistivity measurements show that the sample (annealed at 850 °C for 1 h), exhibiting the highest room temperature resistivity, obtains the maximum zero resistivity transition temperature (T _c ). From the XRD results, all the samples contain MgB₂ as the main phase with a very small amount of Mg₂Cu phase. Moreover, SEM investigations conducted for the microstructural characterization illustrate that not only does the grain size of the samples studied enhance gradually, but the surface morphology and grain connectivity also improve with the increase in the diffusion-annealing time up to 1 h beyond which all the properties obtained start to degrade. Indeed, the worst surface morphology is observed for the Cu-diffused bulk MgB₂ superconductor exposed to 2 h annealing duration. At the same time, Vickers microhardness, elastic modulus, load independent hardness, yield strength, fracture toughness and brittleness index values are calculated separately for the pure and Cu-diffused samples. It is found that the microhardness values depend strongly on the diffusion-annealing time. Furthermore, the diffusion coefficient of the Cu ion in the bulk MgB₂ superconductor is obtained to change from 1.63 × 10^?7 to 2.58 × 10^?7 cm² s^?1. The maximum diffusion coefficient is observed for the sample prepared at 850 °C for 1 h whereas the minimum one is noted for the sample annealed at 850 °C for 2 h, confirming that the annealing-time of 1 h is the best ambient to improve the mechanical, microstructural and superconducting properties of the samples produced.     

Deformation of Mechanical Properties and Failure Behavior of Hays–Kendall Approach in Bi-2223 Superconducting Core After Eu Inclusions

Mechanical features of Bi_1.8Pb_0.4Eu _x Sr₂Ca_2.2Cu₃O _y superconductor samples (x=0, 0.01, 0.03, 0.05, 0.07, 0.1, and 0.3) are elaborated by traditional solid-state reaction route. The deformation of the mechanical properties belonging to the Bi-2223 crystal structure by Eu impurities with the aid of Vickers hardness (H _v ) measurements are conducted at different indentation loads from 0.245 N to 2.940 N for the first time. Further, the H _v values extracted from experimental results are investigated using five different models so as to demonstrate the role of Eu addition on Bi-2223 samples. Based on these results, we observed that the undoped sample reveals the indentation size effect (ISE) feature, whereas the Eu-doped Bi-2223 superconducting core demonstrates the reverse indentation size effect (RISE) nature. Additionally, it is attained that the models (Meyer’s law, EPD, and PSR) fail to determine the estimate of the microhardness with the applied load. Nonetheless, the HK approach is observed to be superior to other models for the pure sample showing the ISE feature, while the IIC model is found to be the most successful model for the explanation of the mechanical characteristics of the Eu impurities in Bi-2223 bulk ceramics obeying RISE nature.     

Investigation of microstructural, Vickers microhardness and superconducting properties of YBa2Cu3−xGdxO7−δ (0 ≤ x ≤ 0.150) superconducting ceramics via experimental and theoretical approaches

This study manifests the change of pinning mechanism, electrical, structural, physical, mechanical and superconducting properties of YBa₂Cu_3?xGd_xO_7?δ superconductors samples prepared by the conventional solid-state reaction method (x = 0, 0.025, 0.050, 0.100 and 0.150) by use of dc resistivity, X-ray analysis (XRD), scanning electron microscopy (SEM) and Vickers microhardness measurements. Zero resistivity transition temperatures (T _c ^offset ) of the samples are deduced from the dc resistivity measurements. Additionally, the lattice parameters are determined from XRD measurements when the microstructure, surface morphology and microhardness of the samples studied are examined by SEM and mechanical measurements, respectively. The results obtained demonstrate that T _c ^offset values of the samples decrease slowly with the increase in the Gd content. The maximum T _c ^offset (92.0 K) is obtained for the pure sample prepared at 940 °C for 20 h in air atmosphere while the minimum value of 83.3 K is found for the sample doped with 0.150 Gd content. Moreover, it is obtained that J _c values reduce from 132 to 34 A/cm² with the enhancement of the Gd level in the crystalline structure. Further, the peak intensities belonging to Y123 (major) phase are obtained to decrease whereas the peak intensities of the minor phases such as BaCuO₂ and Y211 are found to enhance systematically with the increment in the Gd content in the system, illustrating that partial substitution of Cu²⁺ ions by Gd³⁺ ions are carried out successfully. Moreover, SEM images display that the undoped sample obtains the best crystallinity and connectivity between superconducting grains and largest grain size whereas the worst surface morphology is observed for the maximum doped sample (x = 0.150). At the same time, Vickers microhardness, elastic modulus, load independent hardness, yield strength, fracture toughness and brittleness index values, playing important roles on the mechanical properties, are computed for all the samples. The experimental results of the microhardness measurements are examined using the Meyer’s law, PSR (proportional specimen resistance), modified PRS, Elastic–Plastic deformation model (EPD) and Hays–Kendall (HK) approach. The microhardness values obtained increase with the enhancement of the Gd content in the samples. Besides, it is noted that the Hays–Kendall approach is the most successful model explaining the mechanical properties of the samples studied in this work.     

Microhardness studies on calcium hydrogen phosphate (brushite) crystals

Vicker's and Knoop microhardness studies were carried out on grown calcium hydrogen phosphate dihydrate (CaHPO₄·2H₂O) crystals over a load range of 10-50 g. The Vickers (H_V) and Knoop (H_K) microhardness numbers for the above loads were found to be in the range of 94-170 kg/mm² and 28-35 kg/mm² respectively. It was also found that these numbers increased with increase in load. The Mayer's index (n) was found to be greater than 1.6 showing soft-material characteristics. The fracture toughness values (K_c), determined from measurements of crack length, were estimated to be 6 ± 0.5 × 10³ kg m^−3/2 and 4.5 ± 0.5 × 10³ kg m^−3/2 at 25 g and 50 g respectively. The brittleness indices (B_i) were found as 2.3 ± 0.1 × 10⁴ m^−1/2 for 25 g and 3.7 ± 0.1 × 10⁴ m^−1/2 for 50 g. Using Wooster's empirical relation, the elastic stiffness coefficient (c₁₁) has been calculated from Vicker's hardness values as 4.8 ± 0.5 × 10¹⁵ Pa for 10 g, 9.7 ± 0.5 × 10¹⁵ Pa for 25 g and 13.3 ± 0.5 × 10¹⁵ Pa for 50 g. The Young's modulus was calculated as 1.5 ± 0.1 × 10¹⁰ N m⁻² from Knoop microhardness values.     

Influence of diffusion-annealing temperature on physical and mechanical properties of Cu-diffused bulk MgB2 superconductor

This study reports not only the effect of Cu diffusion on physical and mechanical properties of bulk MgB₂ superconductors with the aid of Vickers microhardness (H_v) measurements but also the diffusion coefficient and the activation energy of copper (Cu) in the MgB₂ system using the resistivity measurements for the first time. Cu diffusion is examined over the different annealing temperature such as 650, 700, 750, 800 and 850 °C via the successive removal of thin layers and resistivity measurement of the sample. Further, Vickers microhardness, elastic modulus, yield strength, fracture toughness and brittleness index values of the samples studied are evaluated from microhardness measurements. It is found that all the results obtained depend strongly on the diffusion annealing temperature and applied load. The microhardness values increase with ascending the annealing temperature up to 850 °C owing to the increment in the strength of the bonds between grains but decreasing with the enhancement in the applied load due to Indentation Size Effect behaviour of the bulk samples. Moreover, the diffusion coefficient is observed to enhance from 2.84 × 10^?8 to 3.22 × 10^?7 cm² s^?1 with the increase of the diffusion-annealing temperature, confirming that the Cu diffusion is more dominant at higher temperatures compared to lower ones. Besides, temperature dependence of the Cu diffusion coefficient is described by the Arrhenius relation D = 2.66 × 10^?3 exp(?1.09 ± 0.05 eV/k_BT) and the related activation energy of the Cu ions in the MgB₂ system is obtained to be about 1.09 eV. Based on the relatively low value of activation energy, the migration of the Cu ions primarily proceeds through defects such as pore surfaces and grain boundaries in the polycrystalline structure, resulting in the improvement of the physical and mechanical properties of the bulk MgB₂ samples.