Taras M. Radchenko

Effects of nitrogen-doping configurations with vacancies on conductivity in graphene

Abstract We investigate electronic transport in the nitrogen-doped graphene containing different configurations of point defects: singly or doubly substituting N atoms and nitrogen–vacancy complexes. The results are numerically obtained using the quantum-mechanical Kubo–Greenwood formalism. Nitrogen substitutions in graphene lattice are modelled by the scattering potential adopted from the independent self-consistent ab initio calculations. Variety of quantitative and qualitative changes in the conductivity behaviour are revealed for both graphite- and pyridine-type N defects in graphene. For the most common graphite-like configurations in the N-doped graphene, we also consider cases of correlation and ordering of substitutional N atoms. The conductivity is found to be enhanced up to several times for correlated N dopants and tens times for ordered ones as compared to the cases of their random distributions. The presence of vacancies in the complex defects as well as ordering of N dopants suppresses the electron–hole asymmetry of the conductivity in graphene.

Influence of correlated impurities on conductivity of graphene sheets: Time-dependent real-space Kubo approach

Numerical calculations of the conductivity of graphene sheets with random and correlated distributions of disorders have been performed using the time-dependent real-space Kubo formalism. The disorder was modeled by the long-range Gaussian potential describing screened charged impurities and by the short-range potential describing neutral adatoms both in the weak and strong scattering regimes. Our central result is that correlation in the spatial distribution for the strong short-range scatterers and for the long-range Gaussian potential do not lead to any enhancement of the conductivity in comparison to the uncorrelated case. Our results strongly indicate that the temperature enhancement of the conductivity reported in the recent study [J. Yan and M. S. Fuhrer, Phys. Rev. Lett. 107, 206601 (2011)] and attributed to the effect of dopant correlations was most likely caused by other factors not related to the correlations in the scattering potential.

On adatomic-configuration-mediated correlation between electrotransport and electrochemical properties of graphene

Abstract The electron-transport properties of adatom–graphene system are investigated for different spatial configurations of adsorbed atoms: when they are randomly-, correlatively-, or orderly-distributed over different types of high symmetry sites with various adsorption heights. The results are obtained numerically using the quantum-mechanical Kubo–Greenwood formalism. A band gap may be opened only if ordered adatoms act as substitutional atoms, while there is no band gap opening for adatoms acting as interstitial atoms. The type of adsorption sites strongly affect the conductivity for random and correlated adatoms, but practically does not change the conductivity when they form ordered superstructures with equal periods. Depending on electron density and type of adsorption sites, the conductivity for correlated and ordered adatoms is found to be enhanced in dozens of times as compared to the cases of their random positions. The correlation and ordering effects manifest weaker or stronger depending on whether adatoms act as substitutional or interstitial atoms. The conductivity approximately linearly scales with adsorption height of random or correlated adatoms, but remains practically unchanged with adequate varying of elevation of ordered adatoms. Correlations between electron transport properties and heterogeneous electron transfer kinetics through potassium-doped graphene and electrolyte interface are investigated as well.

A statistical-thermodynamic analysis of stably ordered substitutional structures in graphene

Ordered distributions of carbon and substitutional dopant (A) atoms over the sites of a graphene lattice, i.e. CmA superstructures with dopant contents c=1/(m+1), and problem of their stability are considered theoretically. The ranges of values of interatomic-interaction parameters providing the low-temperature stability of the graphene-based C7A, C3A, and CA superstructures are determined within the framework of both the third-nearest-neighbor Ising model and, more realistically, the all-coordination-shell interaction model. The first model results in the “omission” (instability) of some predicted superstructures, while the second model shows that all predicted superstructures are stable at certain values of interatomic-interaction energies. Even short-range interatomic interactions provide a stability of some superstructures, while only long-range interactions stabilize others.

Effect of charged line defects on conductivity in graphene : Numerical Kubo and analytical Boltzmann approaches

Charge carrier transport in single-layer graphene with one-dimensional charged defects is studied theoretically. Extended charged defects, considered an important factor for mobility degradation in chemically vapor-deposited graphene, are described by a self-consistent Thomas-Fermi potential. A numerical study of electronic transport is performed by means of a time-dependent real-space Kubo approach in honeycomb lattices containing millions of carbon atoms, capturing the linear response of realistic size systems in the highly disordered regime. Our numerical calculations are complemented with a kinetic transport theory describing charge transport in the weak scattering limit. The semiclassical transport lifetimes are obtained by computing scattered amplitudes within the second Born approximation. The transport electron-hole asymmetry found in the semiclassical approach is consistent with the Kubo calculations. In the strong scattering regime, the conductivity is found to be a sublinear function of electronic density and weakly dependent on the Thomas-Fermi screening wavelength. We attribute this atypical behavior to the extended nature of one-dimensional charged defects. Our results are consistent with recent experimental reports.

Statistical Thermodynamics and Kinetics of Long-Range Order in Metal-Doped Graphene

The statistical-thermodynamics and kinetics models of atomic ordering in a metal-doped graphene (binary two-dimensional planar graphene-type crystal lattice) at 1/8, 1/4, and 1/2 stoichiometries are proposed. Impossibility of (completely) atomic-ordered distribution at 1/6 and 1/3 stoichiometries is ascertained in a graphene-type crystal lattice (in case of a short-range interatomic interactions at least). If a graphene is doped by the short-range interacting metal atoms, the superstructures described only by a one LRO parameter are possible; and if it is doped by the long-range interacting metal atoms, the new superstructures with the two or three LRO parameters may appear as well. If stoichiometry is 1/4, the structure has a one long-range order (LRO) parameter is more thermodynamically favorable than those have one or two LRO parameters. It is established that kinetics curves of LRO parameters can be non-monotonic for structures where there are two or three LRO parameters (because graphene-type lattice contains two sublattices, and mixing energy is different for each of them). It is shown that the most ordered is structure with equal atomic fractions of carbon and metal atoms, while the least one is structure with a maximal difference of carbon and metal atoms. Kinetics results confirm statistical-thermodynamic ones: firstly, equilibrium values of LRO parameter coincide within the framework of both models, secondly, equilibrium (and instantaneous) value of LRO parameter in a nonstoichiometric binary graphene-type structure (where atomic fraction of a doping component deviates from the stoichiometry to the side of the higher concentrations) may be higher than it is in a stoichiometric one. The dominance of the same physical mechanisms of atomic ordering in both mixed nanosystems and macrosystems is assumed.

The application of radiation diffuse scattering to the calculation of phase diagrams of F.C.C. substitutional alloys

Abstract By using quantitative information about the radiation diffuse-scattering intensity of the disordered f.c.c. substitutional alloy Me ′ 1- c Me ″ c ( c —concentration) the Fourier component, w ∼ k , of mixing energies of Me ′ and Me ″ atoms may be estimated. We have to use the measurement data of the diffuse-scattering intensities at the corresponding reciprocal-space points k of the disordered phase and then determine the parameter w ∼ ( k ). The statistical thermodynamics of the non-ideal solid solution is determined by these energy parameters { w ∼ ( k )}. Therefore, one can obtain the configuration free energy of an alloy, F=U-TS ( U —internal energy, S —entropy), and then determine its fundamental thermodynamic characteristics, including not only its phase diagram, but also the concentration-dependent order–disorder transformation temperature, temperature and concentration long-range order parameter dependences, chemical activity, heat capacity etc. Some thermodynamic properties are calculated within the framework of the statistical-thermodynamic approach for f.c.c.-Ni–Fe alloy. The diffuse-scattering intensity values are taken from data in the literature.

Conductivity of epitaxial and CVD graphene with correlated line defects

Abstract Transport properties of single-layer graphene with correlated one-dimensional defects are studied theoretically using the computational model within the time-dependent real-space Kubo–Greenwood formalism. Such defects are present in epitaxial graphene, comprising atomic terraces and steps due to the substrate morphology, and in polycrystalline chemically vapor-deposited (CVD) graphene due to the grain boundaries, composed of a periodic array of dislocations, or quasi-periodic nanoripples originated from the metal substrate. The extended line defects are described by the long-range Lorentzian-type scattering potential. The dc conductivity is calculated numerically for different cases of distribution of line defects. This includes a random (uncorrelated) and a correlated distribution with a prevailing direction in the orientation of lines. The anisotropy of the conductivity along and across the line defects is revealed, which agrees with experimental measurements for epitaxial graphene grown on SiC. We performed a detailed study of the conductivity for different defect correlations, introducing the correlation angle α max —the maximum possible angle between any two lines. We find that for a given electron density, the relative enhancement of the conductivity for the case of fully correlated line defects in comparison to the case of uncorrelated ones is larger for a higher defect density. Finally, we, for the first time, study the conductivity of realistic samples where both extended line defects and point-like scatterers such as adatoms and charged impurities are presented.

Statistical Thermodynamics and Ordering Kinetics of D019-Type Phase: Application of the Models for H.C.P.-Ti–Al Alloy

Using the self-consistent field approximation, the static concentration waves approach and the Onsager-type kinetics equations, the descriptions of both the statistical thermodynamics and the kinetics of an atomic ordering of D019 phase are developed and applied for h.c.p.-Ti–Al alloy. The model of order–disorder phase transformation describes the phase transformation of h.c.p. solid solution into the D019 phase. Interatomic-interaction parameters are estimated for both approximations: one supposes temperature-independent interatomic-interaction parameters, while the other one includes the temperature dependence of interchange energies for Ti–Al alloy. The partial Ti–Al phase diagrams (equilibrium compositions of the coexistent ordered α2-phase and disordered α-phase) are evaluated for both cases. The equation for the time dependence of D019- type long-range order (LRO) parameter is analyzed. The curves (showing the LRO parameter evolution) are obtained numerically for both temperature-independent interaction energies and temperature-dependent ones. Temperature dependence of the interatomic-interaction energies accelerates the LRO relaxation and diminishes a spread of the values of instantaneous and equilibrium LRO parameters versus the temperature. Both statistical-thermodynamics and kinetics results show that equilibrium LRO parameter for a non-stoichiometry (where an atomic fraction of alloying component is more than 0.25) can be higher than for a stoichiometry at high temperatures. The experimental phase diagram confirms the predicted (ordered or disordered) states for h.c.p.-Ti– Al.

Atomic-Ordering Kinetics and Diffusivities in Ni–Fe Permalloy

Using the static concentration waves’ method and self-consistent-field approximation, the Onsager-type kinetics equation is solved to describe the L12-type long-range order (LRO) relaxation. To calculate the diffusivities for Permalloy, the experimental diffraction data in respect to LRO-parameter evolution for Ni3Fe are used. Theoretical curves of a time-dependent LRO for Ni– Fe are plotted. Dilution of alloying element (with a deviation from stoichiometry) results in deceleration of the LRO-parameter history (at the initial evolution stage) and in an increase of its relaxation time. Both statistical-thermodynamics and kinetics results show: at high temperatures, equilibrium LRO parameter for non-stoichiometric Permalloys can be higher than for stoichiometric one.