The Kinetics of Dissolution of Single Crystal Diamond (100) and (110) in Nickel and Cobalt Films and Vapor-Liquid-Solid Growth of Graphene Ribbons on Single Crystal and Polycrystalline Cu Foils

Department of Materials Science and EngineeringThe kinetics of dissolution of single crystal diamond (with surface orientation of 100 or 110, named as D(100) and D(110)) into nickel or cobalt films was measured, to the best of our knowledge, for the first time. This was possible through our discovery that at sufficiently high partial pressure of water vapor the rate determining step was breaking of C-C bonds at the diamond-metal interfaceat lower partial pressures of water vapor, the rate determining step was found to be removal of carbon from the surface of the metal, rather than C-C bond breaking at the diamond-metal interface. The rate of diffusion from the diamond-metal interface to the surface of the metal film was found to never be rate-limiting. We found that single crystal diamond with surface orientation 111 could not be dissolved in either cobalt (Co) or nickel (Ni) films in the temperature range we studied. The details of this study are provided in Chapter 3. Time-of-flight-secondary ion mass spectrometry depth profiles show a concentration gradient of C from a certain depth into the metal film surface down to the M???D(100) interface, and residual gas analyzer measurements show that the gas products formed in the presence of water vapor by reaction of C atoms diffusing to, and thus present at, the metal surface are CO and H2. As mentioned, we discovered two different regimes (we name them I and II) for the kinetics of dissolution of both D(100) and D(110), in which the rate-determining step was the removal of carbon atoms on the open metal surface (regime I, lower partial pressure of water vapor) or dissolution of diamond at the metal???diamond interface (regime II, higher partial pressure of water vapor) that yielded different Arrhenius parameters. We found that the rate of dissolution of diamond in Co was higher than that in Ni for both D(100) and D(110) and for both regimes I and II, and possible reasons are suggested. As mentioned, we also found that D(111) could not be dissolved at the Ni/D(111) and Co/D(111) interface in the presence of water vapor (over the same range of sample temperatures). The reaction paths for dissolution of C at the M???D(100) or M???D(110) interface and for removal of C from the free surfaces of Ni and Co were assessed through density functional theory modeling at 1273 K by colleagues Yongchul Kim and Prof. Geunsik Lee. In Chapter 4, we describe the bottom-up direct growth of graphene ribbons catalyzed by deliberate introduction of silica particles onto a Cu(111) foil surface, and we ascribe their growth to a combination of vapor-liquid-solid (VLS) growth (longitudinal growth) and vapor-solid (VS) growth (lateral growth onto the already existing ribbon that extends longitudinally from the VLS growth). Micrometer-long single crystal graphene ribbons (tapered when grown above 900 ???, but uniform width when grown in the range 850 to 900 ???, as this latter temperature range is too low for VS growth) using silica particle seeds were synthesized on single crystal Cu(111) foil. We discovered that tapered and uniform-width graphene ribbons grew strictly along the Cu direction on Cu(111) and polycrystalline copper (Cu) foils. Silica particles on both the single crystal and polycrystalline Cu foils formed (semi-)molten Cu-Si-O droplets at growth temperatures, then catalyzed nucleation and drove the longitudinal growth of graphene ribbons. Longitudinal growth is likely by a vapor-liquid-solid (VLS) mechanism, but edge growth (above 900 ???) is due to catalytic activation of ethylene (C2H4) and attachment of C atoms or species (???vapor solid??? or VS growth) at the edges. We found that the taper angle is determined only by the growth temperature and that the growth rates were independent of the particle size. A surface-diffusion vapor-liquid-solid growth model thus seems most appropriate for rationalizing the longitudinal growth. According to our kinetics study, we found the activation enthalpy (1.73 ?? 0.03 eV) for longitudinal ribbon growth on Cu(111) from ethylene is lower than that for VS growth at the edges of the GRs (2.78 eV ?? 0.15 eV) and for the graphene island growth (2.85 ?? 0.07 eV) that occurs concurrently. (That is, the Cu(111) surface has both GRs and hexagonal graphene islands. The graphene islands nucleate and grow on the regions of the Cu(111) surface where there is not a silica particle.ope

Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points

We review the Shimura–Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched at three points. As an application, we produce multiple new examples of Newton polygons that occur for Jacobians of smooth curves in characteristic p. Under certain congruence conditions on p, these include: the supersingular Newton polygon for each genus g with 4 ≤ g ≤ 11; nine non-supersingular Newton polygons with p-rank 0 with 4 ≤ g ≤ 11; and, for all g ≥ 5, the Newton polygon with p-rank g − 5 having slopes 1∕5 and 4∕5

Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points

We review the Shimura–Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched at three points. As an application, we produce multiple new examples of Newton polygons that occur for Jacobians of smooth curves in characteristic p. Under certain congruence conditions on p, these include: the supersingular Newton polygon for each genus g with 4 ≤ g ≤ 11; nine non-supersingular Newton polygons with p-rank 0 with 4 ≤ g ≤ 11; and, for all g ≥ 5, the Newton polygon with p-rank g − 5 having slopes 1∕5 and 4∕5

Newton polygons of cyclic covers of the projective line branched at three points

We review the Shimura-Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched at three points. As an application, we produce multiple new examples of Newton polygons that occur for Jacobians of smooth curves in characteristic $p$. Under certain congruence conditions on $p$, these include: the supersingular Newton polygon for each genus $g$ with $4 \leq g \leq 11$; nine non-supersingular Newton polygons with $p$-rank $0$ with $4 \leq g \leq 11$; and, for all $g \geq 5$, the Newton polygon with $p$-rank $g-5$ having slopes $1/5$ and $4/5$.Comment: to appear in Research Directions in Number Theory, Women in Numbers IV. arXiv admin note: text overlap with arXiv:1805.0691

An Improved Hierarchical Genetic Algorithm for Sheet Cutting Scheduling with Process Constraints

For the first time, an improved hierarchical genetic algorithm for sheet cutting problem which involves n cutting patterns for m non-identical parallel machines with process constraints has been proposed in the integrated cutting stock model. The objective of the cutting scheduling problem is minimizing the weighted completed time. A mathematical model for this problem is presented, an improved hierarchical genetic algorithm (ant colony—hierarchical genetic algorithm) is developed for better solution, and a hierarchical coding method is used based on the characteristics of the problem. Furthermore, to speed up convergence rates and resolve local convergence issues, a kind of adaptive crossover probability and mutation probability is used in this algorithm. The computational result and comparison prove that the presented approach is quite effective for the considered problem