| 1. |
- Alvi, Sajid, et al.
(författare)
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Enhanced mechanical, thermal and electrical properties of high‐entropy HfMoNbTaTiVWZr thin film metallic glass and its nitrides
- 2022
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Ingår i: Advanced Engineering Materials. - : John Wiley & Sons. - 1438-1656 .- 1527-2648. ; 24:9
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Tidskriftsartikel (refereegranskat)abstract
- The inception of high-entropy alloy promises to push the boundaries for new alloy design with unprecedented properties. This work reports entropy stabilisation of an octonary refractory, HfMoNbTaTiVWZr, high-entropy thin film metallic glass, and derived nitride films. The thin film metallic glass exhibited exceptional ductility of ≈60% strain without fracture and compression strength of 3 GPa in micro-compression, due to the presence of high density and strength of bonds. The thin film metallic glass shows thermal stability up to 750 °C and resistance to Ar-ion irradiation. Nitriding during film deposition of HfMoNbTaTiVWZr thin film of strong nitride forming refractory elements results in deposition of nanocrystalline nitride films with compressive strength, hardness, and thermal stability of up to 10 GPa, 18.7 GPa, and 950 °C, respectively. The high amount of lattice distortion in the nitride films leads to its insulating behaviour with electrical conductivity as low as 200 S cm−1 in the as-deposited film. The design and exceptional properties of the thin film metallic glass and derived nitride films may open up new avenues of development of bulk metallic glasses and the application of refractory-based high entropy thin films in structural and functional applications.
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| 2. |
- Alvi, Sajid, et al.
(författare)
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Synthesis and Mechanical Characterization of a CuMoTaWV High-Entropy Film by Magnetron Sputtering
- 2020
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Ingår i: ACS Applied Materials and Interfaces. - : American Chemical Society (ACS). - 1944-8244 .- 1944-8252. ; 12:18, s. 21070-21079
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Tidskriftsartikel (refereegranskat)abstract
- Development of high-entropy alloy (HEA) films is a promising and cost-effective way to incorporate these materials of superior properties in harsh environments. In this work, a refractory high-entropy alloy (RHEA) film of equimolar CuMoTaWV was deposited on silicon and 304 stainless-steel substrates using DC-magnetron sputtering. A sputtering target was developed by partial sintering of an equimolar powder mixture of Cu, Mo, Ta, W, and V using spark plasma sintering. The target was used to sputter a nanocrystalline RHEA film with a thickness of ∼900 nm and an average grain size of 18 nm. X-ray diffraction of the film revealed a body-centered cubic solid solution with preferred orientation in the (110) directional plane. The nanocrystalline nature of the RHEA film resulted in a hardness of 19 ± 2.3 GPa and an elastic modulus of 259 ± 19.2 GPa. A high compressive strength of 10 ± 0.8 GPa was obtained in nanopillar compression due to solid solution hardening and grain boundary strengthening. The adhesion between the RHEA film and 304 stainless-steel substrates was increased on annealing. For the wear test against the E52100 alloy steel (Grade 25, 700–880 HV) at 1 N load, the RHEA film showed an average coefficient of friction (COF) and wear rate of 0.25 (RT) and 1.5 (300 °C), and 6.4 × 10–6 mm3/N m (RT) and 2.5 × 10–5 mm3/N m (300 °C), respectively. The COF was found to be 2 times lower at RT and wear rate 102 times lower at RT and 300 °C than those of 304 stainless steel. This study may lead to the processing of high-entropy alloy films for large-scale industrial applications.
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| 3. |
- Dobryden, Illia, et al.
(författare)
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Local Wear of Catechol-Containing Diblock Copolymer Layers : Wear Volume, Stick-Slip, and Nanomechanical Changes
- 2021
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Ingår i: The Journal of Physical Chemistry C. - : American Chemical Society. - 1932-7447 .- 1932-7455. ; 125:38, s. 21277-21292
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Tidskriftsartikel (refereegranskat)abstract
- Polymers containing catechol groups have gained a large interest, as they mimic an essential feature of mussel adhesive proteins that allow strong binding to a large variety of surfaces under water. This feature has made this class of polymers interesting for surface modification purposes, as layer functionalities can be introduced by a simple adsorption process, where the catechol groups should provide a strong anchoring to the surface. In this work, we utilize an AFM-based method to evaluate the wear resistance of such polymer layers in water and compare it with that offered by electrostatically driven adsorption. We pay particular attention to two block copolymer systems where the anchoring group in one case is an uncharged catechol-containing block and in the other case a positively charged and catechol-containing block. The wear resistance is evaluated in terms of wear volume, and here, we compare with data for similar copolymers with statistical distribution of the catechol groups. Monitoring of nanomechanical properties provides an alternative way of illustrating the effect of wear, and we use modeling to show that the stiffness, as probed by an AFM tip, of the soft layer residing on a hard substrate increases as the thickness of the layer decreases. The stick-slip characteristics are also evaluated. © 2021 The Authors.
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| 4. |
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| 5. |
- Feltrin, Ana Carolina, et al.
(författare)
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Transformation of metastable dual-phase (Ti0.25V0.25Zr0.25Hf0.25)B2 to stable high-entropy single-phase boride by thermal annealing
- 2021
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Ingår i: Applied Physics Letters. - : AIP Publishing LLC. - 0003-6951 .- 1077-3118. ; 119:16
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Tidskriftsartikel (refereegranskat)abstract
- Transition metal borides have a unique combination of high melting point and high chemical stability and are suitable for high temperature applications (>2000 °C). A metastable dual-phase boride (Ti0.25V0.25Zr0.25Hf0.25)B2 with distinct two hexagonal phases and with an intermediate entropy formation ability of 87.9 (eV/atom)−1 as calculated via the density functional theory (DFT) was consolidated by pulsed current sintering. Thermal annealing of the sintered dual-phase boride at 1500 °C promoted the diffusion of metallic elements between the two boride phases leading to chemical homogenization and resulted in the stabilization of a single-phase high-entropy boride. Scanning electron microscopy, in situ high temperature x-ray diffraction, and simultaneous thermal analysis of the as-sintered and annealed high-entropy borides showed the homogenization of a dual-phase to a single-phase. The experimentally obtained single-phase structure was verified by DFT calculations using special quasirandom structures, which were further used for theoretical investigations of lattice distortions and mechanical properties. Experimentally measured mechanical properties of the single-phase boride showed improved mechanical properties with a hardness of 33.2 ± 2.1 GPa, an elastic modulus of 466.0 ± 5.9 GPa, and a fracture toughness of 4.1 ± 0.6 MPa m1/2.
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| 6. |
- Hedman, Daniel, 1989-
(författare)
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A Theoretical Study: The Connection between Stability of Single-Walled Carbon Nanotubes and Observed Products
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Over the past 20 years’ researchers have tried to utilize the remarkable properties of single-walled carbon nanotubes (SWCNTs) to create new high-tech materials and devices, such as strong light-weight composites, efficient electrical wires and super-fast transistors. But the mass production of these materials and devices are still hampered by the poor uniformity of the produced SWCNTs. These are hollow cylindrical tubes of carbon where the atomic structure of the tube wall consists of just a single atomic layer of carbon atoms arranged in a hexagonal grid. For a SWCNT the orientation of the hexagonal grid making up the tube wall is what determines its properties, this orientation is known as the chirality of a SWCNT. As an example, tubes with certain chiralities will be electrically conductive while others having different chiralities will be semiconducting.Today’s large scale methods for producing SWCNTs, commonly known as growth of SWCNTs, gives products with a large spread of different chiralities. A mixture of chiralities will give products with a mixture of different properties. This is one of the major problems holding back the use of SWCNTs in future materials and devices. The ultimate goal is to achieve growth where the resulting product is uniform, meaning that all of the SWCNTs have the same chirality, a process termed chirality-specific growth. To achieve chirality-specific growth of SWCNTs requires us to obtain a better fundamental understanding about how they grow, both from an experimental and a theoretical point of view.This work focuses on theoretical studies of SWCNT properties and how they relate to the growth process, thereby giving us vital new information about how SWCNTs grow and taking us ever closer to achieving the ultimate goal of chirality-specific growth. In this thesis, an introduction to the field is given and the current state of the art experiments focusing on chirality-specific growth of SWCNTs are presented. A brief review of the current theoretical works and computer simulations related to growth of SWCNTs is also presented. The results presented in this thesis are obtained using first principle density functional theory. The first study shows a correlation between the stability of SWCNT-fragments and the observed products from experiments. Calculations confirm that in 84% of the investigated cases the chirality of experimental products matches the chirality of the most stable SWCNT-fragments (within 0.2 eV). Further theoretical calculations also reveal a previously unknown link between the stability of SWCNT-fragments and their length. The calculations show that at specific SWCNT-fragment lengths the most stable chirality changes. Thus, introducing the concept of a switching length for SWCNT stability. How these new results link to the existing understanding of SWCNT growth is discussed at the end of the thesis.
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| 7. |
- Hedman, Daniel, 1989-, et al.
(författare)
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Ab initio aided design of novel quaternary, quinary and senary high-entropy borocarbides
- 2022
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Ingår i: Journal of Materials Science. - : Springer. - 0022-2461 .- 1573-4803. ; 57:1, s. 422-443
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Tidskriftsartikel (refereegranskat)abstract
- High-entropy materials have attracted considerable interest due to their unique, improved properties and large configurational entropy. Out of these, high-entropy ceramics (HECs) are of particular interest since the independent solubility of cations and anions results in increased configurational entropy. However, most HEC research considers only a single element occupying the anion sublattice, which limits the maximum attainable configurational entropy. Here, we expand our previous work on high-entropy borocarbides where both boron and carbon occupy the anion sublattice. By applying an ab initio based screening procedure, we identify six elements Li, Ti, V, Zr, Nb and Hf suitable for forming high-entropy borocarbides. With these elements, we propose six novel HEC compositions, and by computing their entropy forming ability, we identify that three are likely to form single-phase during synthesis. Material properties and lattice distortions for all proposed compositions are studied using density functional theory calculations with special quasirandom structures. The directional lattice distortions, a concept we introduce in this work, show that lattice distortions have an elemental and directional preference for certain HEC compositions. We also show that the novel inclusion of Li improves the mechanical properties of the proposed HECs, the details of which are studied using the electron localization function.
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| 8. |
- Hedman, Daniel, 1989-, et al.
(författare)
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Analytical modelling of single-walled carbon nanotube energies : the impact of curvature, length and temperature
- 2020
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Ingår i: SN Applied Sciences. - : Springer. - 2523-3963 .- 2523-3971. ; 2:3
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Tidskriftsartikel (refereegranskat)abstract
- Recent breakthroughs in the field of single-walled carbon nanotube (SWCNT) growth have been achieved by combining theoretical models with experiments. Theoretical models rely on accurate energies for SWCNTs, obtained via first principle calculations in the form of density functional theory (DFT). Such calculations are accurate, but time and resource intensive which limits the size and number of systems that can be studied. Here, we present a new analytical model consisting of three fundamental energy expressions, parametrized using DFT, for fast and accurate calculation of SWCNT energies at any temperature. Tests against previously published results show our model having excellent accuracy, with an root mean square error in total energies below 2 meV per atom as compared to DFT. We apply the model to study SWCNT growth on Ni catalysts at elevated temperatures by investigating the SWCNT/catalyst interface energy. Results show that the most stable interface shifts towards chiral edges as the temperature increases. The model’s ability to perform calculations at any temperature in combination with its speed and flexibility will allow researcher to study more and larger systems, aiding future research into SWCNT growth
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| 9. |
- Hedman, Daniel, 1989-, et al.
(författare)
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Impact of training and validation data on the performance of neural network potentials : A case study on carbon using the CA-9 dataset
- 2021
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Ingår i: Carbon Trends. - : Elsevier. - 2667-0569. ; 3
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Tidskriftsartikel (refereegranskat)abstract
- The use of machine learning to accelerate computer simulations is on the rise. In atomistic simulations, the use of machine learning interatomic potentials (ML-IAPs) can significantly reduce computational costs while maintaining accuracy close to that of ab initio methods. To achieve this, ML-IAPs are trained on large datasets of images, which are atomistic configurations labeled with data from ab initio calculations. Focusing on carbon, we use deep learning to train neural network potentials (NNPs), a form of ML-IAP, based on the state-of-the-art end-to-end NNP architecture SchNet and investigate how the choice of training and validation data affects the performance of the NNPs. Training is performed on the CA-9 dataset, a 9-carbon allotrope dataset constructed using data obtained via ab initio molecular dynamics (AIMD). Our results show that image generation with AIMD causes a high degree of similarity between the generated images, which has a detrimental effect on the performance of the NNPs. But by carefully choosing which images from the dataset are included in the training and validation data, this effect can be mitigated. We conclude by benchmarking our trained NNPs in applications such as relaxation and phonon calculation, where we can reproduce ab initio results with high accuracy.
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| 10. |
- Hedman, Daniel, 1989-
(författare)
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Linking Stability of Single-Walled Carbon Nanotubes with Growth Products
- 2017
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Many of the envisioned products and technologies using single-walled carbon nanotubes (SWCNTs) are only possible with a uniform product. Thus, control over the chirality during catalytical chemical vapor deposition (CCVD) growth of SWCNTs is necessary. Our highlighted works1,2 focuses on stabilities of SWCNTs and how that relates to growth, in order to reach the ultimate goal of chirality-specific growth. In ref.1 density functional theory (DFT) has been used to calculate the stability of SWCNT-fragments of all chiralities in the (n+m) = 8 to 18 series. The fragment stabilities are compare to the chiralities of actual CCVD products from all properly analysed experiments to date. The results show that in 84% of the cases the experimental products represent chiralities among the most stable SWCNT-fragments (within 0.2 eV) from the calculations. The analysed products from growth experiments show that diameters of SWCNTs are governed by the well-known relation to the size of the catalytic particle and that the specific chirality of SWCNT products are strongly dependent on the stability of the tubes within each series, suggesting thermodynamic control at the early stage of growth. Analysis of the relative energy show that for the lower series 8 to 10, zigzag SWCNTs are the most stable and for the higher series 11 to 18 the most stable chirality changes from zigzag to armchair. This switch in stability between armchair and zigzag chiralities is studied further in ref.2, where DFT was used to calculate the stability of armchair and zigzag SWCNTs and graphene nanoribbons (GNRs) of different lengths. The calculations show that the stability of armchair and zigzag tubes has different linear dependence with regard to their length, with switches in the most stable chirality occurring at specific lengths for each SWCNT-series. These dependencies are explained by competing edge and curvature energies. Within each series armchair nanotubes are the most stable at short lengths, while zigzag nanotubes are the most stable at long lengths, this sheds new light into why armchair and near-armchair tubes are the dominant product from CCVD growth, if templating is not used. Paradoxically, the stability of armchair nanotubes at short lengths favors their growth although zigzag nanotubes are more stable at long lengths, resulting in the production of the least stable SWCNTs.
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| 11. |
- Hedman, Daniel, 1989-
(författare)
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On the Stability of Single-Walled Carbon Nanotubes and how it relates to Growth
- 2017
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Ingår i: CCTN17.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Many envisioned products and technologies using single-walled carbon nanotubes (SWCNTs) are only possible with a uniform product. Thus, control over the chirality during catalytical chemical vapor deposition (CCVD) growth is necessary. Our highlighted works [1,2] focuses on stabilities of SWCNTs and how they relate to growth. In ref. [1] density functional theory (DFT) is used to calculate the stability of SWCNT-fragments of all chiralities in the 8-18 series. The fragment stabilities are compare with chiralities from actual CCVD products. The results show that 84% of the experimental products represent chiralities among the most stable SWCNT-fragments (within 0.2 eV) from the calculations. The analyzed products from growth experiments show that the chirality of SWCNT products are strongly dependent on the stability of the tubes within each series, suggesting thermodynamic control at the early stage of growth. Analysis of the relative energy show that for lower series 8-10, zigzag SWCNTs are the most stable and for higher series 11-18 the most stable chirality changes from zigzag to armchair. This switch in stability is studied further in ref. [2], where DFT is used to calculate the stability of armchair and zigzag SWCNTs and graphene nanoribbons of different lengths. The calculations show that the stability of armchair and zigzag tubes have different linear dependence with regards to their length, with switches in the most stable chirality occurring at specific lengths for each SWCNT-series. These dependencies are explained by competing edge and curvature energies. Within each series armchair nanotubes are most stable at short lengths, while zigzag nanotubes are most stable at long lengths. This sheds new light into why armchair and near-armchair tubes are dominant products from CCVD growth.[1] D. Hedman, H.R Barzegar, A. Rosen, T. Wågberg, J.A Larsson, Sci. Rep., 2015, 5, 16850. [2] D. Hedman, J.A. Larsson, Carbon, 2017, 116, 443.
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| 12. |
- Hedman, Daniel, 1989-
(författare)
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Single-Walled Carbon Nanotubes : A theoretical study of stability, growth and properties
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Since their discovery over 25 years ago, scientists have explored the remarkable properties of single-walled carbon nanotubes (SWCNTs) for use in high-tech materials and devices, such as strong light-weight composites, efficient electrical wires, supercapacitors and high-speed transistors. However, the mass production of such materials and devices is still limited by the capability of producing uniform high-quality SWCNTs. The properties of a SWCNT are determined by the orientation of the hexagonal grid of carbon atoms constituting the tube wall, this is known as the chirality of the SWCNT.Today's large-scale methods for producing SWCNTs, commonly known as growth, give products with a large spread of different chiralities. A mixture of chiralities give products with a mixture of different properties. This is one of the major obstacles preventing large-scale use of SWCNTs in future materials and devices. The goal is to achieve growth where the resulting product is uniform, meaning that all SWCNTs have the same chirality, a process termed chirality-specific growth. To achieve this requires a deep fundamental understanding of how SWCNTs grow, both from an experimental and a theoretical perspective.This work focuses on theoretical studies of SWCNTs and their growth mechanisms. With the goal of achieving a deeper understanding of how chirality arises during growth and how to control it. Thus, taking us ever closer to the ultimate goal of achieving chirality-specific growth. In this thesis, an introduction to the field is given and the current research questions are stated. Followed by chapters on carbon nanomaterials, SWCNTs and computational physics. A review of the state-of-the-art experimental and theoretical works relating to chirality specific growth is also given.The results presented in this thesis are obtained using first principle density functional theory calculations. Results show that the stability of short SWCNT-fragments can be linked to the products observed in experiments. In 84% of the investigate cases, the chirality of experimental products matches the chirality of the most stable SWCNT-fragments (within 0.2 eV). Further studies also reveal a previously unknown link between the stability of SWCNT-fragments and their length. Calculations show that at specific lengths the most stable chirality changes. Thus, introducing the concept of a switching length for SWCNT stabilities.This newly found property of SWCNTs is used in combination with previously published works to create a state-of-the-art analytical model to investigate growth of SWCNTs any temperature. Results from the model show that the most stable chirality obtained is dependent on the diameter, length of the SWCNT, the growth temperature and the composition of the catalyst. Finally, a detailed study on the ability of catalyst metals to sustain SWCNT growth points to Pt as an interesting candidate to achieve growth of rarely seen chiralities. The new knowledge gained from these results takes us even closer to achieving chirality-specific growth.
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| 13. |
- Yusupov, Khabib, et al.
(författare)
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Enhancing the thermoelectric performance of single-walled carbon nanotube-conducting polymer nanocomposites
- 2020
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Ingår i: Journal of Alloys and Compounds. - : Elsevier. - 0925-8388 .- 1873-4669. ; 845
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Tidskriftsartikel (refereegranskat)abstract
- Harnessing energy lost in the form of heat is an important challenge today. Organic thermoelectric materials (TE) can convert lost heat into electricity at relatively low temperature. Single-walled carbon nanotubes (SWCNTs) are known to boost the TE properties of organic-based materials at room temperature (TR). However, the TE performance decreases with the increasing temperature, which restricts the working temperature region of the devices. Here, we present a three steps investigation: initially, the influence of the net of SWCNTs on TE properties of polymer matrix; secondly, creation of hybrid fillers via SWCNTs treatment with gold chloride; lastly, chemical post-treatment of obtained systems in the temperature range 325–410 K. In the process of HAuCl4 aerosolization (gold chloride treatment) on the surface of nanotubes, different ionic conformations (Au and AuCl4−) can be formed. For this reason, we performed a theoretical investigation on the influence of ionic conformations on SWCNTs on the electronic structure. Implementation of SWCNTs net into polymer matrix alongside gold chloride doping and chemical post-treatment successfully increased the power factor of the system in the temperature interval from 300 to 410 K. These results demonstrate the potential of combined approach in creation of hybrid fillers based on organic/inorganic materials with chemical post-treatment in boosting the thermoelectric performance within the whole operating temperature of polymer-based composite alongside the importance of theoretical modeling in tuning the electronic structure of composite systems through a material-by-design approach.
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| 14. |
- Zhang, Hanzhu, 1991-, et al.
(författare)
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A high-entropy B4(HfMo2TaTi)C and SiC ceramic composite
- 2019
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Ingår i: Dalton Transactions. - : Royal Society of Medicine Press. - 1477-9226 .- 1477-9234. ; 48:16, s. 5161-5167
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Tidskriftsartikel (refereegranskat)abstract
- A multicomponent composite of refractory carbides, B4C, HfC, Mo2C, TaC, TiC and SiC, of rhombohedral, face-centered cubic (FCC) and hexagonal crystal structures is reported to form a single phase B4(HfMo2TaTi)C ceramic with SiC. The independent diffusion of the metal and nonmetal atoms led to a unique hexagonal lattice structure of the B4(HfMo2TaTi)C ceramic with alternating layers of metal atoms and C/B atoms. In addition, the classical differences in the crystal structures and lattice parameters among the utilized carbides were overcome. Electron microscopy, X-ray diffraction and calculations using density functional theory (DFT) confirmed the formation of a single phase B4(HfMo2TaTi)C ceramic with a hexagonal close-packed (HCP) crystal structure. The DFT based crystal structure prediction suggests that the metal atoms of Hf, Mo, Ta and Ti are distributed on the (0001) plane in the HCP lattice, while the carbon/boron atoms form hexagonal 2D grids on the (0002) plane in the HCP unit cell. The nanoindentation of the high-entropy phase showed hardness values of 35 GPa compared to the theoretical hardness value estimated based on the rule of mixtures (23 GPa). The higher hardness was contributed by the solid solution strengthening effect in the multicomponent hexagonal structure. The addition of SiC as the secondary phase in the sintered material tailored the microstructure of the composite and offered oxidation resistance to the high-entropy ceramic composite at high temperatures.
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| 15. |
- Zhang, Hanzhu, 1991-, et al.
(författare)
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High Entropy B2(HfMoTaTi)C and SiC Ceramic Composite
- 2019
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Ingår i: XVI Conference and Exhibition of the European Ceramic Society. - : European Ceramic Society (ECerS). ; , s. 338-338
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Konferensbidrag (refereegranskat)abstract
- Refractory carbides HfC, Mo2C, TiC, TaC, B4C, and SiC were mixed with a molar ratio of 2:1:2:2:1:2 to fabricate multicomponent ceramic composite by pulsed current processing (PCP). From the starting materials that consist of face-centered cubic (FCC), hexagonal and rhombohedral crystal structures, the investigated carbide system is reported to form a single phase B2(HfMoTaTi)C high-entropy ceramic (HEC) with SiC. The HEC phase contains uniform distribution of constitutional elements Hf, Mo, Ta, Ti, B and C, according to Energy dispersive X-ray spectroscopy (EDS) and wavelength dispersive X-ray spectroscopy (WDS) results.The fabricated HEC phase displays a hexagonal close-packed (HCP) crystal structure, with a high average lattice distortion of 8.26% (see Figure). The HCP structure was observed by X-ray diffraction and selected area diffraction in transmission electron microscopy (TEM). Density-functional theory (DFT) optimization suggested that the hexagonal close-packed (HCP) crystal structure has alternating layers of metal atoms and carbon/boron atoms, i.e. metal atoms of Hf, Mo, Ta and Ti were distributed on the (0001) plane in the HCP lattice, while the carbon/boron atoms formed hexagonal 2D grids on the (0002) plane in the HCP unit cell. Despite of the vast differences in the crystal structures and lattice parameters among the utilized carbides, the formation of the unique hexagonal lattice structure of B2(HfMoTaTi)C can be a result of independent diffusion of the metal and nonmetal atoms. The sintered HEC ceramic composite exhibits excellent oxidation resistance at mediate temperature, 900 ºC for 50h, and elevated temperature, 2000 ºC for 20 s. Nanoindentation test shows that the HEC phase has a high hardness of 35 GPa. The remarkable improvement compared to the theoretical hardness value estimated based on the rule of mixtures (23 GPa) was contributed by the severe lattice distortion in the HCP structure.
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