Narrow Results

In this paper, we improve Galvin’s Theorem for ultrafilters which are $p$-point limits of $p$-points. This implies that in all the canonical inner models up to a superstrong cardinal, every $\kappa$-complete ultrafilter over a measurable cardinal $\kappa$ satisfies the Galvin property. On the other hand, we prove that supercompact cardinals always carry non-Galvin $\kappa$-complete ultrafilters. Finally, we prove that $♢(\kappa )$ implies the existence of a $\kappa$-complete filter which extends the club filter and fails to satisfy the Galvin property. This answers questions [8, Question 5.22], [4, Question 3.4] and questions, [7, Question 4.5], [6, Question 2.26].

In recent years, the emergence of the ultrawide‐bandgap (UWBG) semiconductor materials that have an extremely large bandgap, exceeding 5eV including AlGaN/AlN, diamond, β-Ga₂O₃, and cubic BN, provides a new opportunity in myriad applications in electronic, optoelectronic and photonics with superior performance matrix than conventional WBG materials. In this review paper, we will focus on high power and high frequency devices based on two most promising UWBG semiconductors, β-Ga₂O₃ and diamond among various UWBG semiconductor devices. These two UWBG semiconductors have gained substantial attention in recent years due to breakthroughs in their growth technique as well as various device engineering efforts. Therefore, we will review recent advances in high power and high frequency devices based on β-Ga₂O₃ and diamond in terms of device performance metrics such as breakdown voltage, power gain, cut off frequency and maximum operating frequency.

We present tight binding molecular dynamics simulations of the diffusion and bonding of hydrogen in bulk diamond. The motion of hydrogen atoms and the resultant structural and electronic energy level changes are investigated. The hydrogen atoms were found to have a tendency to migrate to the surface layer of diamond, resulting in a local deformation of the lattice, creating new energy states above and below the Fermi energy in the bandgap of the diamond density of states. In the diamond bulk, at high hydrogen concentrations, vacancies created by a hydrogen atom are quickly filled with other hydrogen atoms causing a deformation of the diamond lattice, inducing H₂ formation. This creates new energy states above the Fermi energy and reduces the secondary bandgap of the diamond density of states.

Site and bond percolation thresholds are calculated for the face centered cubic, body centered cubic and diamond lattices in four, five and six dimensions. The results are used to study the behavior of percolation thresholds as a functions of dimension. It is shown that the predictions from a recently proposed invariant for percolation thresholds are not satisfactory for these lattices.

We present computational aspects of Molecular Dynamics calculations of thermal properties of diamond using the Brenner potential. Parallelization was essential in order to carry out these calculations on samples of suitable sizes. Our implementation uses MPI on a multi-processor machine such as the IBM SP2. Three aspects of parallelization of the Brenner potential are discussed in depth. These are its long-range nature, the need for different parallelization algorithms for forces and neighbors, and the relative expense of force calculations compared to that of data communication. The efficiency of parallelization is presented as a function of different approaches to these issues as well as of cell size and number of processors employed in the calculation. In the calculations presented here, information from almost half of the atoms were needed by each processor even when 16 processors were used. This made it worthwhile to avoid unnecessary complications by making data from all atoms available to all processors. Superlinear speedup was achieved for four processors (by avoiding paging) with 512 atom samples, and 5ps long trajectories were calculated (for 5120 atom samples) in 53 hours using 16 processors; 514 hours would have been needed to complete this calculation using a serial program. Finally, we discuss and make available a set of routines that enable MPI-based codes such as ours to be debugged on scalar machines.

In this paper, the initial stage of films assembled by energetic C₃₆ fullerenes on diamond (001)–(2 × 1) surface at low-temperature was investigated by molecular dynamics simulation using the Brenner potential. The incident energy was first uniformly distributed within an energy interval 20–50 eV, which was known to be the optimum energy range for chemisorption of single C₃₆ on diamond (001) surface. More than one hundred C₃₆ cages were impacted one after the other onto the diamond surface by randomly selecting their orientation as well as the impact position relative to the surface. The growth of films was found to be in three-dimensional island mode, where the deposited C₃₆ acted as building blocks. The study of film morphology shows that it retains the structure of a free C₃₆ cage, which is consistent with Low Energy Cluster Beam Deposition (LECBD) experiments. The adlayer is composed of many C₃₆-monomers as well as the covalently bonded C₃₆ dimers and trimers which is quite different from that of C₂₀ fullerene-assembled film, where a big polymerlike chain was observed due to the stronger interaction between C₂₀ cages. In addition, the chemisorption probability of C₃₆ fullerenes is decreased with increasing coverage because the interaction between these clusters is weaker than that between the cluster and the surface. When the incident energy is increased to 40–65 eV, the chemisorption probability is found to increased and more dimers and trimers as well as polymerlike-C₃₆ were observed on the deposited films. Furthermore, C₃₆ film also showed high thermal stability even when the temperature was raised to 1500 K.

The main purpose of this work is to present the ESR spectra and calculate the spin Hamiltonian parameters of ¹⁴N and ¹⁵N impurities in natural diamond. The ESR spectra of diamond crystal were measured on ESR spectrometer operating at X-band microwave frequency. The results of ESR spectra show that the diamond has a P1 center. This center gives rise to three strong resonance absorption peaks at θ = 90°, φ = 0° due to hyperfine interaction between electron spin and nuclear spin of ¹⁴N. The ESR spectra of ¹⁵N impurity consist of two satellites at the same rotation angle (φ). The effects of isolated substitution nitrogen on carbon atom produced a symmetric distortion from T_d to C_3V symmetry. According to this symmetry, the resonance magnetic field positions of ESR spectra for the rotation angles of 0°, 90° and 180° are almost overlap. The g-factor values and spin Hamiltonian parameters of ¹⁴N and ¹⁵N are: g = 2.0019, A_⊥ = 29.73, A_‖ = 40.24 and g = 2.0019, A_⊥ = −39.90, A_‖ = −57.05, respectively.

Nanopores formed in insulating solid state membrane is of great importance in many fields such as detection of DNA/RNA molecules in their internal environment, probing and manipulating biopolymers. Here, we present an effective and convenient method to form nanopores in diamond etched by self-assembled Ni or Cu nanoparticles in hydrogen atmosphere. With our method, homogeneous nanopores with lateral size in the range of $0.5$–$1\mu \mathrm{\text{m}}$ were created without using Reactive Ion Etching (RIE) process. In this work, the etching pits of Ni and Cu etched diamond were investigated, respectively. A novel step-like pattern of etching pits was observed on diamond etched by Ni. In order to study the etching process and figure out the etching mechanism of diamond, Scanning Electron Microscopy (SEM) was used to observe the etching morphology. Atomic Force Microscopy (AFM) and Laser Scanning Confocal Microscope (LSCM) were used to visualize the image of diamond etching pits and investigate the step-like pattern. A fixed step height was observed in each pit. Based on these observations and findings, a hypothesis is proposed, which can help to provide a new controllable etching method.

Diamond etching of $〈100〉$ orientation is processed in chemical vapor deposition (CVD) chamber using H₂ as reactive gas. Etching process happens on diamond substrates using a variety of etch mask materials including copper and nickel. Scanning electron microscope (SEM) and atomic force microscope (AFM) show different kinds of diamond etching pattern of two mask materials. It is observed that the etching pit of copper is tetrahedron, while the etching pit of nickel is step structure. This indicates diverse etching mechanism of diamond etched by different metal. Observing the surface etching topography of diamond and analyzing the etching mechanism of different metal can help study the growth of diamond by CVD and controllable etching of diamond.

Self-phase modulation (SPM) induces a varying refractive index of the medium due to the optical Kerr effect. The optical waves propagation (OWP) in a medium with SPM occupied a remarkable area of research in the literature. A model equation to describe OWP in the absence of SPM was proposed very recently by Biswas–Arshed equation (BAE). This work is based on constructing the solutions that describe the waves which arise from soliton-periodic wave collisions. A variety of geometric optical wave structures are observed. Here, a transformation that allows to investigate the multi-geometric structures of OW’s result from soliton-periodic wave collisions is introduced. Chirped, conoidal, breathers, diamond and W-shaped optical waves are shown to propagate in the medium in the absence of SPM. The exact solutions of BAE are obtained by using the unified method, which was presented recently. We mention that the results found here, are completely new.

The detonation of carbon- or nitrogen-containing explosives not only produces powerful shock waves but also provides elemental building blocks and a unique high-pressure and high-temperature physical environment for the construction of various nanostructures. This review highlights the situation and key progresses in the detonation approach towards diamond nanoparticles, graphitic carbon nanotubes, fullerene molecules, and gallium nitride nanocrystals. Further extension of the peaceful-use detonation applications and rational reactor design are also proposed.

Phonon transport in two-dimensional silicon and aluminum films is investigated. The frequency dependent solution of Boltzmann transport equation is obtained numerically to account for the acoustic and optical phonon branches. The influence of film size on equivalent equilibrium temperature distribution in silicon and aluminum films is presented. It is found that increasing film width influences phonon transport in the film; in which case, the difference between the equivalent equilibrium temperature due to silicon and diamond films becomes smaller for wider films than that of the thinner films.

In this paper, diamond single crystals doped with LiH and boron additives were synthesized in ${\mathrm{\text{Fe}}}_{64}{\mathrm{\text{Ni}}}_{36}$–$\mathrm{\text{C}}$ system under high pressure and high temperature. Under the fixed pressure condition, we found that the synthesis temperature increased slightly after the addition of LiH in the synthesis system. The {100}-orientated surface morphology was investigated by scanning electron microscopy (SEM). The nitrogen concentration in the obtained diamond was analyzed and evaluated using Fourier transmission infrared spectroscopy (FTIR). Furthermore, the electrical properties of Ib-type and boron-doped diamond before and after hydrogenation using Hall effect measurement, which suggested that the conductivity of diamond co-doped with hydrogen and boron was obviously enhanced than that of boron-doped diamond.

In this paper, diamond single crystals have been successfully synthesized with potassium berohydride (KBH₄) additive from 0 wt.% to 0.4 wt.% in the NiMnCo–C system at 6 GPa and temperature range of 1300${}^{\circ }$C–1350${}^{\circ }$C by temperature gradient growth (TGG) method. The results of experiments showed that the color of diamond crystals changed from light yellow to dark blue to black, as the KBH₄ content increases from 0 wt.% to 0.4 wt.%. The results of FTIR absorption spectroscopy showed that the peaks of boron-related enhanced with an increase of KBH₄ additive. The XPS results showed that the boron, hydrogen, nitrogen and oxygen coexisted in the diamond crystal. The results of Hall effect measurements indicated that the synthesized diamonds using KBH₄ as additive presented $p$-type semiconductor characterizations. The Hall mobility was nearly equivalent between diamond crystals of with 0.2 wt.% and 0.4 wt.% KBH₄ additive, but which was all extremely low due to scattering causing by N and O defects. While the concentrations of carrier and conductivity of the co-doped diamonds enhanced with increasing KBH₄ additive.

In this work, diamond crystals were synthesized with N–H–O impurities by the temperature gradient method (TGM) under high pressure and high temperature (HPHT) conditions using FeNi alloy as the metal solvent (MS). The results indicated that the spontaneous nucleation rate and proportion, growth characteristics, surface growth texture, and the impurity concentration of diamond crystals changed drastically upon changing the impurity content in the system. Mutual diffusion between the MS and carbon source (CS) was also blocked, which seriously inhibited the growth rate of diamond crystals. X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) analyses corroborated that the zero-valent iron (Fe⁰) and nickel (Ni⁰) contents declined after N–H–O impurities were introduced. The newly formed graphite can be found in the MS, but the ferric carbide disappears. XPS also confirmed shifts in the binding energy of FeNi MS peaks, more iron oxide and nickel oxide were identified in MS, hindering the mass transfer process. CO and NO were absorbed on the surface of MS, which hindered the surface processes of diamond growth. The formation of intermediates (Fe₃C) was impeded during diamond growth and blocked the spontaneous nucleation of diamond. All of these phenomena contributed to a poor growth rate and changed the surface growth process of diamond crystals.

The tetrahedral carbon (ta-C) and boron doped amorphous carbon (a-C:B) thin films have been grown by pulsed laser deposition. The respective effects of diamond percentages by weight in the target (Dwt%) and boron percentages by weight in the camphoric carbon target (Bwt%), on the tetrahedral (sp³) and trihedral (sp²) bonding properties are discussed. The optical gap E_g and electrical resistivity ρ increase with Dwt%, up to 1.6 eV and 5.63 × 10⁷ Ω cm respectively, for the film deposited using target with 50 Dwt%. We found that the Dwt% has modified the sp³ bonds content and the morphology of the carbon films. On the other hand, the E_g of a-C:B films is almost unchanged at about 0.95 eV up to 10 Bwt% and decreases thereafter to 0.6 eV at 16 Bwt%. The ρ increases initially to 2.29 × 10⁶ Ω cm at 2 Bwt%, and decreases thereafter up to 4.58 × 10⁵ and 1.82 × 10⁴ Ω cm at 10 and 16 Bwt%, respectively. The variation of structural properties, E_g and ρ, can be related to the successful doping of B in the a-C films at low content of Bwt% (up to 10 Bwt%), as the structural properties and E_g remain almost unchanged and the ρ decreased. Since both E_g and ρ decreased sharply with higher Bwt%, this phenomenon can be related to graphitization. In this paper, the dependence of sp³ and sp² impurity content on the growth and growth conditions of the films are also studied.

For diamond coating, natural fragile property easily leads to fracture, delamination and peeling, which seriously inhibits the applications in many industrial fields. In order to prolong the lifetime, improving the toughness under impact load is essential for diamond coating. In this work, a novel method was proposed by the conventional CVD diamond technique combining with the particles, with which the nanocrystalline diamond (NCD) coating with W particles (W-NCD) was fabricated to evaluate the impact behavior. The pure NCD coating was also produced for comparison. Repeating impact testing was performed to evaluate the impact resistance of the as-deposited NCD coatings. The results showed that the diamond coating can be fabricated on the substrate with W particles. The indentation scar revealed that the W-NCD coating had the stronger impact resistance than the NCD coating. Ratcheting effect was employed to discuss the impact properties of NCD coating for the first time. The coating integrity played a vital role in ratcheting displacement. Repeating impact can make the NCD and W-NCD coatings soft, and the W particles can accelerate the softening process. Hence, embedding particles can provide a potential and valid method to enhance the impact resistance of diamond coating that was very important for the fragile coating.

We establish the consistency of the failure of the diamond principle on a cardinal $\kappa$ which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of $\kappa$ in a Radin generic extension.

We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension with respect to a measure sequence on $\kappa$, if $\kappa$ is weakly compact, then $♢(\kappa )$ holds. This provides contrast with a well-known theorem of Woodin, who showed that in a certain Radin extension over a suitably prepared ground model relative to the existence of large cardinals, the diamond principle fails at a strongly inaccessible Mahlo cardinal. Refining the analysis of the Radin extensions, we consistently demonstrate a scenario where a compactness principle, stronger than the diagonal stationary reflection principle, holds yet the diamond principle fails at a strongly inaccessible cardinal, improving a result from [O. B. -Neria, Diamonds, compactness, and measure sequences, J. Math. Log. 19(1) (2019) 1950002].

Diamond whiskers were formed by etching diamond thin films using metal clusters as a shadow mask, which were deposited on the diamond film before or during etching. The whiskers were as thin as 100 nm and the density was as high as 10¹⁰/cm². The secondary electron emission yield of the diamond whiskers was significantly reduced as compared to the initial diamond film. The decrease in the yield was more significant if the primary electrons were impinged in parallel direction with the whiskers. We suggest that absorption of the secondary electrons in the narrow gap between the whiskers was the reason for the decreased yield.