Mo 0.9 W 1.1 BC and ReWC 0.8 compositions have recently been identified to have exceptional hardness and incompressibility. In this work, these compositions are analyzed via in situ radial X-ray diffraction experiments to comparatively assess lattice strain and texture development. Traditionally, Earth scientists have employed these experiments to enhance understanding of dynamic activity within the deep Earth. However, nonhydrostatic compression experiments provide insight into materials with exceptional mechanical properties, as they help elucidate correlations between structural, elastic, and mechanical properties. Here, analysis of differential strain ( t / G ) and lattice preferred orientation in Mo 0.9 W 1.1 BC suggests that dislocation glide occurs along the (010) plane in orthorhombic Mo 0.9 W 1.1 BC. The (200) and (002) planes support the highest differential strain, while planes which bisect two or three axes, such as the (110) or (191), exhibit relatively lower differential strain. In ReWC 0.8 , which crystallizes in a cubic NaCl-type structure, planar density is correlated to orientation-dependent lattice strain as the low-density (311) plane elastically supports more differential strain than the denser (111), (200), and (220) planes. Furthermore, results indicate that ReWC 0.8 likely supports a higher differential stress t than Mo 0.9 W 1.1 BC and, based on a lack of texture development, bulk plastic yielding is not observed in ReWC 0.8 upon compression to ∼60 GPa.
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Exploring the hardness and high-pressure behavior of osmium and ruthenium-doped rhenium diboride solid solutions
Rhenium diboride (ReB2) exhibits high differential strain due to its puckered boron sheets that impede shear deformation. Here, we demonstrate the use of solid solution formation to enhance the Vickers hardness and differential strain of ReB2. ReB2-structured solid solutions (Re0.98Os0.02B2 and Re0.98Ru0.02B2, noted as “ReOsB2” and “ReRuB2”) were synthesized via arc-melting from the pure elements. In-situ high-pressure radial x-ray diffraction was performed in the diamond anvil cell to study the incompressibility and lattice strain of ReOsB2 and ReRuB2 up to ∼56 GPa. Both solid solutions exhibit higher incompressibility and differential strain than pure ReB2. However, while all lattice planes are strengthened by doping osmium (Os) into the ReB2 structure, only the weakest ReB2 lattice plane is enhanced with ruthenium (Ru). These results are in agreement with the Vickers hardness measurements of the two systems, where higher hardness was observed in ReOsB2. The combination of high-pressure studies with experimentally observed hardness data provides lattice specific information about the strengthening mechanisms behind the intrinsic hardness enhancement of the ReB2 system.
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- Award ID(s):
- 2004616
- NSF-PAR ID:
- 10445668
- Date Published:
- Journal Name:
- APL Materials
- Volume:
- 11
- Issue:
- 3
- ISSN:
- 2166-532X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract This work presents a stabilized formulation for phase‐field fracture of hyperelastic materials near the limit of incompressibility. At this limit, traditional mixed displacement and pressure formulations must satisfy the inf‐sup condition for solution stability. The mixed formulation coupled with the damage field can lead to an inhibition of crack opening as volumetric changes are severely penalized effectively creating a pressure‐bubble. To overcome this bottleneck, we utilize a mixed formulation with a perturbed Lagrangian formulation which enforces the incompressibility constraint in the undamaged material and reduces the pressure effect in the damaged material. A mesh‐dependent stabilization technique based on the residuals of the Euler–Lagrange equations multiplied with a differential operator acting on the weight space is used, allowing for linear interpolation of all field variables of the elastic subproblem. This formulation was validated with three examples at finite deformations: a plane‐stress pure‐shear test, a two‐dimensional geometry in plane‐stress, and a three‐dimensional notched sample. In the last example, we incorporate a hybrid formulation with an additive strain energy decomposition to account for different behaviors in tension and compression. The results show close agreement with analytical solutions for crack tip opening displacements and performs well at the limit of incompressibility.
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Radial X‐Ray Diffraction Study of Superhard Early Transition Metal Dodecaborides under High Pressuremore » « less
Abstract The deformation behavior of the three metal dodecaborides (YB12, ZrB12, and Zr0.5Y0.5B12) is investigated using radial X‐ray diffraction under nonhydrostatic compression up to ≈60 GPa with a goal of understanding how bonding and metal composition control hardness. Zr0.5Y0.5B12, which has the highest Vickers hardness (
Hv = 45.8 ± 1.3 GPa at 0.49 N load), also shows the highest bulk modulus (K 0= 320 ± 5 GPa). The 0.49 N hardness for ZrB12and YB12are both lower and very similar, and both show lower bulk moduli (K 0= 276 ± 7 GPa, andK 0= 238 ± 6 GPa, respectively). Differential stress is then measured to study the strength and strength anisotropy. Zr0.5Y0.5B12supports the highest differential stress, in agreement with its high hardness, a fact that likely arises from atomic size mismatch between Zr and Y combined with the rigid network of boron cages. The (200) plane for all samples supports the largest differential strain, while the (111) plane supports the smallest, consistent with the theoretically predicted slip system of {111} [ ]. Strain softening is also observed for ZrB12. Finally, the full elastic stiffness tensors for ZrB12and YB12are solved. ZrB12is the most isotropic, but the extent of elastic anisotropy for all dodecaborides studied is relatively low due to the highly symmetric boron cage network. -
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A boron-rich boron–carbide material (B4+δC) was synthesized by spark plasma sintering of a ball-milled mixture of high-purity boron powder and graphitic carbon at a pressure of 7 MPa and a temperature of 1930 °C. This high-pressure, high-temperature synthesized material was recovered and characterized by X-ray diffraction, X-ray photoelectron spectroscopy, Raman spectroscopy, Vickers hardness measurements, and thermal oxidation studies. The X-ray diffraction studies revealed a single-phase rhombohedral structure (space group R-3m) with lattice parameters in hexagonal representation as a = 5.609 ± 0.007 Å and c = 12.082 ± 0.02 Å. The experimental lattice parameters result in a value of δ = 0.55, or the composition of the synthesized compound as B4.55C. The high-resolution scans of boron binding energy reveal the existence of a B-C bond at 188.5 eV. Raman spectroscopy reveals the existence of a 386 cm−1 vibrational mode representative of C-B-B linear chain formation due to excess boron in the lattice. The measured Vickers microhardness at a load of 200 gf shows a high hardness value of 33.8 ± 2.3 GPa. Thermal gravimetric studies on B4.55C were conducted at a temperature of 1300 °C in a compressed dry air environment, and its behavior is compared to other high-temperature ceramic materials such as high-entropy transition metal boride. The high neutron absorption cross section, high melting point, high mechanical strength, and thermal oxidation resistance make this material ideal for applications in extreme environments.
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Severe plastic deformation (SPD) is an effective route for the nanocrystallization of multi-principal element alloys (MPEAs). The stability of the refined microstructure is important, considering the high temperature applications of these materials. In the present study, the effect of SPD on the stability of a body-centered cubic (bcc) HfNbTiZr MPEA was investigated. SPD was performed using a high-pressure torsion (HPT) technique by varying the number of turns between ½ and 10. The evolution of phase composition and microstructure was studied near the disk centers and edges where the imposed strain values were the lowest and highest, respectively. Thus, the shear strain caused by HPT varies between 3 (½ turn, near the center) and 340 (10 turns, near the edge). It was found that during annealing up to 1000 K, the bcc HfNbTiZr alloy decomposed into two bcc phases with different lattice constants at 740 K. In addition, at high strains a hexagonal close packed (hcp) phase was formed above 890 K. An inhomogeneous elemental distribution was developed at temperatures higher than 890 K due to the phase decomposition. The scale of the chemical heterogeneities decreased from about 10 µm to 30 nm where the shear strain increased from 3 to 340, which is similar to the magnitude of grain refinement. Anneal-induced hardening was observed in the MPEA after HPT for both low and high strains at 740 K, i.e., the hardness of the HPT-processed samples increased due to heat treatment. At low strain, the hardness remained practically unchanged between 740 and 1000 K, while for the alloy receiving high strains there was a softening in this temperature range.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0135620
