Tetrahedral amorphous boron nitride: A hard material

We generate a tetrahedrally coordinated amorphous boron nitride (BN) model by means of first principles molecular dynamics calculations and report its mechanical and electrical properties in detail. The amorphous configuration is almost free from chemical disorder and consists of about 20% coordination defects, similar to tetrahedral (diamond-like) amorphous carbon. Its theoretical band gap energy is about 2.0 eV, less than 4.85 eV estimated for cubic BN. The bulk modulus and Vickers hardness of tetrahedral amorphous BN are computed as 206 GPa and 28-35 GPa, respectively. Based on these findings, we propose that tetrahedral noncrystalline BN can serve as electronic and hard materials as well.     

Investigating the elastic,mechanical, and thermal properties of polycrystalline Mo2C under high pressure and high temperature

Understanding pressure-induced acoustic velocity-elasticity behavior has extraordinary significance in the fields of materials science and earth science. Herein, we used an advanced high-pressure high-temperature (HPHT) method to synthesize pure-phase β-Mo₂C bulk ceramics. The sound velocity-elasticity behavior, thermodynamic properties, and mechanical behavior of the synthesized β-Mo₂C ceramics were systematically investigated by in-situ high-pressure ultrasonic interferometry and theoretical calculations. The compressive and shear wave velocities, isothermal bulk modulus, shear modulus, Vickers hardness, fracture toughness, Debye temperature, and melting temperature of polycrystalline β-Mo₂C exhibited a monotonic increase with increasing pressure. The experimental and calculation results showed that β-Mo₂C had strong ductile behavior and was a ductile ceramic. Additionally, the temperature-hardness relationship of the as-synthesized polycrystalline β-Mo₂C was investigated by in-situ high-temperature Vickers indentation measurements. The hardness of β-Mo₂C gradually decreased with increasing temperature, and this ceramic still maintained a hardness as high as 12.3 GPa at 500 °C. These results suggest that the intrinsic mechanical and thermodynamic properties of β-Mo₂C are dominated by its unique electronic structure and bonding mode.     

Effect of atomic layer deposited aluminium oxide on mechanical properties of porous silicon carbide

Silicon carbide nanopowder was coated with amorphous alumina by atomic layer deposition (ALD), using trimethylaluminium Al(CH₃)₃ (TMA) and water as precursors. The ALD experiments were carried out at 300 ^°C, using variable cycle count or changing pulse times at constant cycle count. Depending on deposition conditions, hardness averaging at 14.8 GPa and corresponding reduced elastic modulus of 114 GPa were measured. Maximum hardness values and reduced moduli of elasticity reached 25–30 and 134–202 GPa, respectively, improving the mechanical properties of composites. Increased precursor flow had positive effect on mechanical properties – maximum values of hardness and elastic module reached 35–45 and 218–261 GPa, respectively. In the composites, the mechanical properties were improved compared to pure alumina films or silicon carbide and the brittleness characteristic of SiC particle tablets was decreased.     

Mechanical properties and structure of a nanoporous sodium borosilicate glass

The nanohardness (H) and microhardness (H _M) of sodium borosilicate glasses with and without nanopores were studied. From nanoindentation measurements, along with the hardness H, the Young’s modulus E was derived. While both H and H _M varied between ∼10 GPa and ∼7 GPa for the bulk glass, the values for nanoporous specimens were one order of magnitude lower at about 0.5 GPa. The Young’s moduli were found to be ∼82 GPa and ∼5 GPa for bulk and porous glasses, respectively. Cracks and pileups were observed, respectively, arising from microindents and nanoindents in the bulk glass, whereas none of them could be detected in the nanoporous material. The molecular structures of both glasses studied by X-ray diffraction are similar. The text was submitted by the authors in English.     

Preparation,microstructure and mechanical properties of MoAlB-0.15% Si ceramics with superior strength and toughness

MoAlB has been regarded as a promising high-temperature structural ceramic, but the strength and toughness are still insufficient in the practical application. In this work, MoAlB ceramic bulk with superior hardness, strength and toughness has been fabricated by adding 0.15 mol. % Si. The MoAlB-0.15Si bulk is composed of Si-doped MoAlB, Mo(Al, Si)₂ and ultrafine Al₂O₃. The Vickers hardness ranges from 14.2 to 12.5 GPa with the tested load increasing from 10 to 200 N. The Vickers indentation remains the intact tetragonum in spite of the appearance of corner cracks, indicating the excellent damage tolerance. The flexural strength, fracture toughness and compressive strength of MoAlB-0.15Si are 518.46 MPa, 7.01 MPa m^1/2 and 2.62 GPa, respectively, obviously superior to the present MoAlB polycrystalline bulk. Si doping, grain refinement, strengthening effect of ultrafine Al₂O₃ and phase transformation from Al₈Mo₃ to Mo(Al, Si)₂ jointly account for the improvement of comprehensive properties of MoAlB bulk.     

Determination of the elastic properties of amorphous materials: Case study of alkali–silica reaction gel

The gel formed during alkali–silica reaction (ASR) can lead to cracking and deterioration of a concrete structure. The elastic properties of the ASR gel using X-ray absorption and Brillouin spectroscopy measurements are reported. X-ray absorption was used to determine the density of the gel as a function of pressure, and the result yields an isothermal bulk modulus of 33 ± 2 GPa. Brillouin spectroscopy was applied to measure isentropic bulk (24.9–34.0 GPa) and shear moduli (8.7–10.1 GPa) of the gel. The range of values obtained is attributed to the variable composition of samples that were collected under field conditions. Results suggested that amorphous silica becomes expanded and compressible as it absorbs water molecules and alkali ions. This could explain high gel migration rates through the complex pore structures in concrete.     

High‐Pressure Investigation in the System SiO2–GeO2: Mutual Solubility of Si and Ge in Quartz,Coesite and Rutile Phases

Mutual solubilities in crystalline phases in the system SiO₂–GeO₂ have been investigated up to 10 GPa pressure and 1500°C temperature, using a bulk composition of 50 mol% GeO₂. Solid solution of up to 40 mol% GeO₂ into the mineral quartz has been confirmed as well as solubility of Si into GeO₂ rutile (argutite) and Ge into SiO₂ rutile (stishovite) phases and limited Ge into coesite. Solubility of Ge in quartz is very high, and decreases with pressure, with the univariant quartz‐out reaction occurring near 3.4 GPa at 1200°C. The solubility of GeO₂ in coesite is highest at 3.4 GPa (about 8 mol%) and decreases with increasing pressure. Significantly more extensive solubility than previously reported for the rutile phases has been found and measured in detail as a function of pressure and temperature. Extensive solubility of SiO₂ in GeO₂ is found in argutite at 1200°C, increasing strongly with pressure and reaching a maximum of 25.2 mol% SiO₂ in GeO₂ at 9 GPa. At this point coesite (ss) plus argutite (ss) react to form a stishovite phase with 18 mol% GeO₂, and the mutual solubility in both phases decreases above this pressure. At 1500°C, similar solubilities are observed but the maximum SiO₂ solubility in argutite of just over 25 mol% occurs near 10 GPa. All these solid solutions can be recovered to ambient temperature and pressure. Phase diagrams and unit cell information of the phases are presented here. Based on these results, a useful and industrially relevant, application for accurately measuring high pressure is suggested.     

Transition metal diboride-silicon carbide-boron carbide ceramics with super-high hardness and strength

Three phase boride and carbide ceramics were found to have remarkably high hardness values. Six different compositions were produced by hot pressing ternary mixtures of Group IVB transition metal diborides, SiC, and B₄C. Vickers’ hardness at 9.8 N was ~31 GPa for a ceramic containing 70 vol% TiB₂, 15 vol% SiC, and 15 vol% B₄C, increasing to ~33 GPa for a ceramic containing equal volume fractions of the three constituents. Hardness values for the ceramics containing ZrB₂ and HfB₂ were ~30% and 20% lower than the corresponding TiB₂ containing ceramics, respectively. Hardness values also increased as indentation load decreased due to the indentation size effect. At an indentation load of 0.49 N, the hardness of the previously reported ceramic containing equal volume fractions of TiB₂, SiC and B₄C was ~54 GPa, the highest of the ceramics in the present study and higher than the hardness values reported for so-called “superhard” ceramics at comparable indentation loads. The previously reported ceramic containing 70 vol% TiB₂, 15 vol% SiC, and 15 vol% B₄C also displayed the highest flexural strength of ~1.3 GPa and fracture toughness of 5.7 MPa·m^1/2, decreasing to ~0.9 GPa and 4.5 MPa·m^1/2 for a ceramic containing equal volume fractions of the constituents.     

Mechanical and thermal properties of light weight boron-mullite Al5BO9

Al₅BO₉ is a promising thermal sealing material for hypersonic vehicles due to its low density, theoretically predicted low shear modulus, and low thermal conductivity. However, experimental investigations on the mechanical and thermal properties of bulk Al₅BO₉ have not been carried out. Herein, we report the mechanical and thermal properties of bulk Al₅BO₉ prepared by spark plasma sintering of solid-state reaction synthesized Al₅BO₉ powders. The bulk (B), shear (G), and Young's (E) moduli are 148 GPa, 85 GPa, and 214 GPa, respectively, which are close to the theoretical values. The Pugh's ratio G/B is 0.574, indicating its intrinsic damage tolerance, which is also revealed by Hertzian contact test. The Vickers hardness (H_v) is 10.8 GPa, being lower than mullite. The flexural strength, compressive strength, and fracture toughness are, respectively, 277 ± 35 MPa, 814 ± 75 MPa, and 2.4 ± 0.3 MPa·m^1/2, which are close to those of mullite. Al₅BO₉ has anisotropic coefficient of thermal expansion (CTE) in three crystallographic directions, ie α_a = (4.40 ± 0.21) × 10⁻⁶ K⁻¹, α_b = (7.11 ± 0.18) × 10⁻⁶ K⁻¹, α_c = (6.70 ± 0.29) × 10⁻⁶ K⁻¹ from Debye temperature to 1473 K, which are underpinned by its structural feature, ie lower α_a is resulted from the edge-shared AlO₆ octahedron chains along the [100] direction. The average CTE is (6.05 ± 0.06) × 10⁻⁶ K⁻¹. The thermal conductivity declines with temperature as κ = 1336.39/T + 1.97, consisting with predicted trend from Slack's model. The low thermal conductivity and low density guarantee Al₅BO₉ a promising candidate as ceramic wafer in the seal structure for hypersonic vehicles.     

Elastic and thermodynamic properties of Mo2C polymorphs from first principles calculations

Transition metal carbides have unique physical and chemical properties and been widely used in engineering parts that need to work under high temperatures and pressures. o-Mo₂C, h-Mo₂C and t-Mo₂C are three critical molybdenum carbides polymorphs while remaining are largely unknown in their mechanical anisotropy, hardness and thermal properties. In this work, we investigated systematically the mechanical and thermodynamic properties of these three candidate carbides using first principles calculations based on density functional theory. Our results showed that the bonds in these compounds were mainly of metallic and covalent type. The Gibbs free energy analysis showed thermodynamically stable structures for all the three carbides. Their shear moduli were estimated to range from 149.1 to 153.4 GPa and hardnesses were expected to be less than 20 GPa. Young׳s moduli were analyzed to have more anisotropic features than bulk modulus for all the three compounds. In addition, heat capacities were calculated to predominate by phonon excitations at high temperature but electron excitations at low temperatures near 0 K.     

Experimental and DFT insights into elastic,magnetic, electrical,and thermodynamic properties of MAB-phase Fe2AlB2

The elastic, magnetic, electrical, and thermodynamic properties of bulk polycrystalline Fe₂AlB₂ are reported, with further theoretical insights provided through first-principles calculations. DFT simulations, along with an appropriate empirical method to treat magnetic contributions, reproduce well the experimental heat capacity, phonon thermal conductivity, and thermal expansion. The shear, Young's and bulk moduli all decrease linearly from 107.7, 264.5, and 162.4 GPa at 298 K to 91.4, 227.7, and 149.6 GPa at 1273 K, respectively, while the Poisson's ratio shows a weak dependence on temperature, hovering around 0.23-0.26. The mechanical damping, Q⁻¹, is found to be a weak function of temperature up to 973 K, but above this temperature increases sharply, peaking at a specific temperature that becomes higher with increasing resonant frequency. The phonon contribution plays a dominant role in the measured heat capacity from 4.2 to 1000 K, while the magnetic contribution becomes significant around the Curie temperature (301 K). The electronic contribution increases with temperature above 100 K. Furthermore, the standard enthalpy, entropy, and Gibbs free energy are calculated as 16.60 kJ/mol, 92.92 J/(mol·K) and −11.09 kJ/mol, respectively. The thermal conductivity increases linearly with increasing temperature from RT to 1173 K, up to around 13.0 W/(m·K) at 1323 K after hovering at around 7.8 W/(m·K) in the low-temperature range. The electrons play a dominant role in heat conduction, while the phonons contribute only a little to the thermal conductivity. The dilatometric coefficient of thermal expansion of Fe₂AlB₂ is measured as 13.5 × 10⁻⁶ K⁻¹ in the temperature range RT-1348 K.     

Structural characterization of bulk ZrTiO4 and its potential for thermal shock applications

Zirconium titanate, ZrTiO₄, is a well known compound in the field of electroceramics. Furthermore, it shows a large potential as structural material for thermal shock resistance applications, since it presents crystallographic anisotropy in thermal expansion. However, there is no information in the current literature about its thermomechanical behaviour. In this work, single phase zirconium titanate bulk materials have been prepared from well dispersed ZrO₂ and TiO₂ mixed suspensions, combining reaction and conventional sintering processes. The crystal structures of ZrTiO₄ have been studied by the Rietveld method for bulk samples. The structural evolution upon the cooling rate has been unravel, as the b-axis strongly decreases for slow cooled samples when compared to quenched materials. For the first time apparent Young's modulus (≈130 GPa) and Vickers hardness (≈8 GPa) values of a fully dense single phase zirconium titanate material have been evaluated and its potential for thermal shock applications has been analysed in comparison with other thermal shock resistant materials.     

Spark plasma sintering of self-propagating high-temperature synthesized TiC0.7/TiB2 powders and detailed characterization of dense product

In this work, the fabrication of bulk TiC_0.7/TiB₂ nanostructured composites through metastable transformation processing is investigated by taking advantages of two non-conventional powder metallurgy methods. First, the highly metastable TiC_0.7/TiB₂ agglomerated powders are synthesized by the so-called self-propagating high-temperature synthesis (SHS), followed by rapid quenching. Then, the spark plasma sintering (SPS) method is adopted to consolidate the SHSed powders.A bulk ceramic composite with nanocrystalline microstructure characterized by a high-relative density is then obtained. Dwell temperature of 1400 °C, heating time of 3 min, and total processing time equal to 5 min, while applying a mechanical pressure of 20 MPa, are found to be the optimal SPS experimental conditions in order to obtain near-fully densified samples.The obtained TiC_0.7/TiB₂ samples exhibit hardness HV5 as high as 24 GPa, modulus of elasticity of about 400 GPa, fracture toughness of about 5.6 MPa m^1/2, and a compressive strength of about 2.9 GPa. A very low-wear rate (W_v = 3.8 × 10⁻⁶ mm³/(N m)) and a good thermal shock resistance (ΔT_c = 250 °C) are also displayed. In addition, a high-abrasive wear factor (AWF) equal to 1.84 is evaluated on the basis of the achieved mechanical properties. These results make the obtained TiC_0.7/TiB₂ composite suitable for wear resistant parts as well as cutting tool materials.     

Ordered structure and mechanical properties of ternary Sc0.5TM0.5B2 (TM = Ti,V, Zr) alloys under high pressure

The structural and mechanical properties of ScB₂ and Sc_0.5TM_0.5B₂ (TM = Ti, V, Zr) alloys are investigated in the pressure range of 0–150 GPa based on density functional theory. The ground state structures of ScB₂ are screened out by structural substitution, and the P6/mmm is determined as the initial structure of alloying research according to structural stability. The structures of alloy generation and recognition (SAGAR) code combined with first-principles calculations selected the stable structures of Sc_0.5TM_0.5B₂ (TM = Ti, V) and Sc_0.5Zr_0.5B₂ alloys as ordered structure types Ⅰ and Ⅱ, respectively. The formation enthalpy, phonon dispersion and elastic constants demonstrate that Sc_0.5TM_0.5B₂ (TM = Ti, V, Zr) alloys are thermodynamically, dynamically and mechanically stable. In the whole pressure range, the elastic moduli of Sc_0.5TM_0.5B₂ (TM = Ti, V, Zr) increased significantly compared with ScB₂. This indicates that the introduction of TM improves the mechanical properties of ScB₂. The Vickers hardness (H_V) of the ScB₂ ground state is 42.4 GPa, and the H_V of the Sc_0.5TM_0.5B₂ (TM = Ti, V, Zr) alloys are increased to 47.8, 50.3 and 44.8 GPa, respectively. The electronic structures and chemical bonding reveal that the Sc_0.5TM_0.5B₂ (TM = Ti, V, Zr) alloys have stronger B–B, B–TM covalent bonds, charge interaction, and higher valence electron density, which significantly improves the hardness. The results show that ScB₂ and Sc_0.5TM_0.5B₂ (TM = Ti, V, Zr) alloys are potential superhard multifunctional materials.     

Conversion behaviour and resulting mechanical properties of polysilazane-based coatings

Polymer-derived ceramics exhibit a convenient route for the processing of low-dimensional ceramics like coatings or fibres. In previous investigations unfilled and composite coatings have been developed using ammonolysed bis(dichloromethylsilyl)ethane (ABSE) or perhydropolysilazane (PHPS) as precursors and BN, ZrO₂ or glass particles as filler materials. The coating systems provide excellent corrosion and oxidation resistance to underlying metals. This paper reports on the effect of the precursor system and the pyrolysis parameters on the conversion behaviour, shrinkage and mechanical properties, including hardness and Young's modulus, of ABSE- and PHPS-based coatings. Therefore the crosslinking and pyrolysis behaviour as well as the mechanical properties of the coatings were investigated up to pyrolysis temperatures of 1000 °C in nitrogen and in air by ATR-IR, SEM, profilometry and nanoindentation measurements. The coatings pyrolysed at 1000 °C in nitrogen, have hardness values of 13 GPa and Young's moduli up to 155 GPa.     

Mechanical properties of nano-polycrystalline cBN synthesized by direct conversion sintering under HPHT

Using hBN and pBN as starting materials, various types of binderless polycrystalline cBN (BL-PcBN) were synthesized in the pressure range of 8–20 GPa and temperature range of 1300–2400 °C, and their mechanical properties were evaluated. In the synthesis pressure range of 10 GPa and higher, the hardness of BL-PcBN showed a correlation not with the synthesis pressure, but with the synthesis temperature. Binderless polycrystalline cBN synthesized at about 2200 °C exhibited the highest mechanical properties, for both starting materials. Specifically, BL-PcBN(h) (100–300 nm grain size) synthesized from hBN at 10 GPa and 2200 °C showed a hardness of 45 GPa, transverse rupture strength of 1.6 GPa. In contrast, BL-PcBN(p) synthesized from pBN at the same temperature had finer grain size (50–100 nm) and exhibited the same level of hardness but lower strength properties (transverse rupture strength of approx. 1.3 GPa) than BL-PcBN(h). Consequently, the material that exhibited the best mechanical properties was BL-PcBN(h) synthesized at 10 GPa and 2200 °C. A prototype micro ball end mill made of this material was examined in a mirror-like (polished-like) finishing test using high-strength hardened steel. This ball end mill achieved a fine finishing surface with a surface roughness (Ra) of 20 nm or better. The test revealed the high potential of this material for use as a high-precision cutting tool for high strength ferrous materials.     

The thermo-mechanical properties and ferroelastic phase transition of RENbO4 (RE = Y,La, Nd,Sm, Gd,Dy, Yb) ceramics

In this work, RENbO₄ (RE = Y, La, Nd, Sm, Gd, Dy, Yb) ceramics with low density, low Young's modulus, low thermal conductivity, and high thermal expansion have been systematically investigated, the excellent thermo-mechanical properties indicate that RENbO₄ ceramics possess the potential as the new generation of thermal barrier coatings (TBCs) materials. X-ray diffraction and Raman spectroscopy phase structure identification reveal that all dense bulk specimens obtained by high-temperature solid-state reaction belonged to the monoclinic (m) phase with C12/c1 space group. The ferroelastic domains are detected in the specimens, revealing the ferroelastic transformation between tetragonal (t) and monoclinic (m) phases of RENbO₄ ceramics. The Young's modulus and hardness of the RENbO₄ ceramics measured by the NanoBlitz 3D nanoindentation method are discussed in details, and the lower Young's modulus (60-170 GPa) and higher hardness (the maximum value reaches 11.48 GPa) indicating that higher resistance of RENbO₄ ceramics to failure and damage. Lower thermal conductivity (1.42-2.21 W [m k]⁻¹ at 500°C-900°C) and lower density (5.330-7.400 g/cm³) than other typical TBCs materials give RENbO₄ ceramics the unique advantage of being new TBCs materials. Meanwhile, the thermal expansion coefficients of RENbO₄ ceramics reach 9.8-11.6 × 10⁻⁶ k⁻¹ and are comparable or higher than other typical TBCs materials. According to the first-order derivative of the thermal expansion rate, the temperature of the ferroelastic transformation of RENbO₄ ceramics can be observed.     

Structural and mechanical properties of NbN and Nb-Si-N films: Experiment and molecular dynamics simulations

The structural and mechanical properties of NbN and Nb-Si-N films have been investigated both experimentally and theoretically, in their as-deposited and annealed states. The films were deposited using magnetron sputtering at substrate bias (U_B) between 0 and −70 V. While NbN films were found to crystallize in the cubic δ-NbN structure, Nb-Si-N films with Si content of 11–13 at% consisted of a two-phases nanocomposite structure where δ-NbN nanocrystals were embedded in SiN_x amorphous matrix. Films deposited at U_B=0 V were highly (001)-textured. Application of substrate bias potential led to a depletion of light atoms, and caused a grain size refinement concomitantly with the increase of (111) preferred orientations in both films. The maximum hardness was 28 GPa and 32 GPa for NbN and Nb-Si-N films, respectively. NbN and Nb-Si-N films deposited at U_B=−70 V exhibited compressive stress of −3 and −4 GPa, respectively. After vacuum annealing, a decrease in the stress-free lattice parameter was observed for both films, and attributed to alteration of film composition. To obtain insights on interface properties and related mechanical and thermal stability of Nb-Si-N nanocomposite films, first principles molecular dynamics simulations of NbN/SiN_x heterostructures with different structures (cubic and hexagonal) and atomic configurations were carried out. All the hexagonal heterostructures were found to be dynamically stable and weakly dependent on temperature. Calculation of the tensile strain-stress curves showed that the values of ideal tensile strength for the δ-NbN(111)- and ε-NbN(001)-based heterostructures with coherent interfaces and Si₃N₄–like Si₂N₃ interfaces were the highest with values in the range 36–65 GPa, but lower than corresponding values of bulk NbN compound. This suggests that hardness enhancement is likely due to inhibition of dislocation glide at the grain boundary rather than interfacial strengthening due to Si-N chemical bonding.     

High temperature properties of B6O-materials

B₆O is a potential superhard material with a hardness of 45 GPa measured on single crystals. Recently it was found that different oxides can be utilized as an effective sintering additive which allows densification under low pressures. In this work the effect of addition of Y₂O₃/Al₂O₃ on high temperature properties was investigated using impulse excitation technique (IET), hardness measurements and dilatometric measurements. The IET technique reveals the softening of the residual B₂O₃ in the materials without additives at 450 °C; in the materials with Y₂O₃/Al₂O₃ the softening is observed at only about 800 °C. This data agrees with the values found for different borate glasses.The materials showed no pronounced reduction of hardness at these temperatures. This is additional evidence, supporting previous observations that the material consists of pure grain boundaries between B₆O grains. Hardness values (HV5) of up to 17 GPa at 1000 °C were observed.     

Nano- versus macro-hardness of liquid phase sintered SiC

Silicon carbide polycrystalline materials were prepared by liquid phase sintering. Different rare-earth oxides (Y₂O₃, Yb₂O₃, Sm₂O₃) and AlN were used as sintering additives. The final microstructure consists of core–rim structure owing to the incorporation of AlN into the rim of SiC grains by solid solution. Nano- versus macro-hardness of polycrystalline SiC materials were investigated in more details. The nano-hardness of SiC grains was in the range of 32–34 GPa and it depends on the chemical compositions of grains. The harness followed the core–rim chemistry of grains, showing lower values for the rim consisting of SiC–AlN solid solution. The comparison of nano- and macro-hardness showed that nano-hardness is significantly higher, generally by 5–7 GPa. The macro-hardness of tested samples had a larger scatter due to the influence of several factors: hardness of grains (nano-hardness), indentation size effect (ISE), microstructure, porosity, and grain boundary phase. The influence of grain boundary phase on macro-hardness is also discussed.