Boris Kozinsky

SECULAR EVOLUTION OF HIERARCHICAL TRIPLE STAR SYSTEMS

We derive octupole-level secular perturbation equations for hierarchical triple systems, using classical Hamiltonian perturbation techniques. Our equations describe the secular evolution of the orbital eccentricities and inclinations over timescales that are long compared to the orbital periods. By extending previous work done to leading (quadrupole) order to octupole level (i.e., including terms of order α3, where α ≡ a1/a2 < 1 is the ratio of semimajor axes), we obtain expressions that are applicable to a much wider range of parameters. In particular, our results can be applied to high-inclination as well as coplanar systems, and our expressions are valid for almost all mass ratios for which the system is in a stable hierarchical configuration. In contrast, the standard quadrupole-level theory of Kozai gives a vanishing result in the limit of zero relative inclination. The classical planetary perturbation theory, while valid to all orders in α, applies only to orbits of low-mass objects orbiting a common central mass, with low eccentricities and low relative inclinations. For triple systems containing a close inner binary, we also discuss the possible interaction between the classical Newtonian perturbations and the general relativistic precession of the inner orbit. In some cases we show that this interaction can lead to resonances and a significant increase in the maximum amplitude of eccentricity perturbations. We establish the validity of our analytic expressions by providing detailed comparisons with the results of direct numerical integrations of the three-body problem obtained for a large number of representative cases. In addition, we show that our expressions reduce correctly to previously published analytic results obtained in various limiting regimes. We also discuss applications of the theory in the context of several observed triple systems of current interest, including the millisecond pulsar PSR B1620-26 in M4, the giant planet in 16 Cygni, and the protostellar binary TMR-1.

Identifying Capacity Limitations in the Li/Oxygen Battery Using Experiments and Modeling

The Li/oxygen battery may achieve a high practical specific energy as its theoretical specific energy is 11,400 Wh/kg Li assuming Li 2 O 2 is the product. To help understand the physics of the Li/oxygen battery we present the first physics-based model that incorporates the major thermodynamic, transport, and kinetic processes. We obtain a good match between porous-electrode experiments and simulations by using an empirical fit to the resistance of the discharge products (which include carbonates and oxides when using carbonate solvents) as a function of thickness that is obtained from flat-electrode experiments. The experiments and model indicate that the discharge products are electronically resistive, limiting their thickness to tens of nanometers and their volume fraction in one of our discharged porous electrodes to a few percent. Flat-electrode experiments, where pore clogging is impossible, show passivation similar to porous-electrode experiments and allow us to conclude that electrical passivation is the dominant capacity-limiting mechanism in our cells. Although in carbonate solvents Li 2 O 2 is not the dominant discharge product, we argue that the implications of this model, (i.e., electrical passivation by the discharge products limits the capacity) also apply if Li 2 O 2 is the discharge product, as it is an intrinsic electronic insulator.

Static dielectric properties of carbon nanotubes from first principles.

We characterize the response of isolated single-wall (SWNT) and multiwall (MWNT) carbon nanotubes and nanotube bundles to static electric fields using first-principles calculations and density-functional theory. The longitudinal polarizability of SWNTs scales as the inverse square of the band gap, while in MWNTs and bundles it is given by the sum of the polarizabilities of the constituent tubes. The transverse polarizability of SWNTs is insensitive to band gaps and chiralities and is proportional to the square of the effective radius; in MWNTs, the outer layers dominate the response. The transverse response is intermediate between metallic and insulating, and a simple electrostatic model based on a scale-invariance relation captures accurately the first-principles results. The dielectric response of nonchiral SWNTs in both directions remains linear up to very high values of applied field.

NbFeSb-based p-type half-Heuslers for power generation applications

We report a peak dimensionless figure-of-merit (ZT) of ∼1 at 700 °C in a nanostructured p-type Nb0.6Ti0.4FeSb0.95Sn0.05 composition. Even though the power factor of the Nb0.6Ti0.4FeSb0.95Sn0.05 composition is improved by 25%, in comparison to the previously reported p-type Hf0.44Zr0.44Ti0.12CoSb0.8Sn0.2, the ZT value is not increased due to a higher thermal conductivity. However, the higher power factor of the Nb0.6Ti0.4FeSb0.95Sn0.05 composition led to a 15% increase in the power output of a thermoelectric device in comparison to a device made from the previous best material Hf0.44Zr0.44Ti0.12CoSb0.8Sn0.2. The n-type material used to make the unicouple device is the best reported nanostructured Hf0.25Zr0.75NiSn0.99Sb0.01 composition with the lowest hafnium (Hf) content. Both the p- and n-type nanostructured samples are prepared by ball milling the arc melted ingot and hot pressing the finely ground powders. Moreover, the raw material cost of the Nb0.6Ti0.4FeSb0.95Sn0.05 composition is more than six times lower compared to the cost of the previous best p-type Hf0.44Zr0.44Ti0.12CoSb0.8Sn0.2. This cost reduction is crucial for these materials to be used in large-scale quantities for vehicle and industrial waste heat recovery applications.

BoltzWann: A code for the evaluation of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis ☆

We present a new code to evaluate thermoelectric and electronic transport properties of extended systems with a maximally-localized Wannier function basis set. The semiclassical Boltzmann transport equations for the homogeneous infinite system are solved in the constant relaxation-time approximation and band energies and band derivatives are obtained via Wannier interpolations. Thanks to the exponential localization of the Wannier functions obtained, very high accuracy in the Brillouin zone integrals can be achieved with very moderate computational costs. Moreover, the analytical expression for the band derivatives in the Wannier basis resolves any issues that may occur when evaluating derivatives near band crossings. The code is tested on binary and ternary skutterudites CoSb3 and CoGe3/2 S-3/2. Program summary Program title: BoltzWann Catalogue identifier: AEQX_v1_0 Program summaiy URL: http://cpc.cs.qub.ac.uk/summaries/AEQX_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 710 810 No. of bytes in distributed program, including test data, etc.: 8 337 000 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any architecture with a Fortran 90 compiler. Operating system: Linux, Windows, Solaris, AIX, Tru64 Unix, OSX. Has the code been vectorized or parallelized?: Yes. RAM: The example requires approximately 10 MB. Classification: 7.3, 7.9. External routines: BLAS and LAPACK (available on http://www.netlib.org/); MPI libraries (optional) for parallel execution Nature of problem: Obtain electronic and thermoelectric transport properties for crystals. Solution method: The Boltzmann transport equations in the constant relaxation-time approximation are used. These equations require the integration of the band velocities over all the Brillouin zone; this is done numerically on a sufficiently dense k grid. Band energies and band derivatives are obtained by interpolation using the maximally-localized Wannier functions basis obtained with a preliminary run of the Wannier90 code. Unusual features: The maximally-localized Wannier functions interpolation scheme allows the use of analytical formulas (instead of finite-difference methods) to obtain the band derivatives. Additional comments: This is a package that is tightly integrated with the Wannier90 code (http://www.wannier.org). The Wannier90 code is included in the distribution package. Running time: The example runs (in its serial version) in less than 2 min

Electrostatics in Periodic-boundary Conditions and Real-space Corrections

We address periodic-image errors arising from the use of periodic boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. The difference between the periodic potential, as straightforwardly obtained from a Fourier transform, and the potential satisfying any other boundary conditions can be characterized analytically. In light of this observation, we present an efficient real-space method to correct periodic-image errors, based on a multigrid solver for the potential difference, and demonstrate that excellent convergence of the energy with respect to cell size can be achieved in practical calculations. Additionally, we derive rapidly convergent expansions for determining the Madelung constants of point-charge assemblies in one, two, and three dimensions.

Electron–Phonon Interactions and the Intrinsic Electrical Resistivity of Graphene

We present a first-principles study of the temperature- and density-dependent intrinsic electrical resistivity of graphene. We use density-functional theory and density-functional perturbation theory together with very accurate Wannier interpolations to compute all electronic and vibrational properties and electron-phonon coupling matrix elements; the phonon-limited resistivity is then calculated within a Boltzmann-transport approach. An effective tight-binding model, validated against first-principles results, is also used to study the role of electron-electron interactions at the level of many-body perturbation theory. The results found are in excellent agreement with recent experimental data on graphene samples at high carrier densities and elucidate the role of the different phonon modes in limiting electron mobility. Moreover, we find that the resistivity arising from scattering with transverse acoustic phonons is 2.5 times higher than that from longitudinal acoustic phonons. Last, high-energy, optical, and zone-boundary phonons contribute as much as acoustic phonons to the intrinsic electrical resistivity even at room temperature and become dominant at higher temperatures.

High-throughput screening of perovskite alloys for piezoelectric performance and thermodynamic stability

We screen a large chemical space of perovskite alloys for systems with optimal properties to accommodate a morphotropic phase boundary (MPB) in their composition-temperature phase diagram, a crucial feature for high piezoelectric performance. We start from alloy end points previously identified in a high-throughput computational search. An interpolation scheme is used to estimate the relative energies between different perovskite distortions for alloy compositions with a minimum of computational effort. Suggested alloys are further screened for thermodynamic stability. The screening identifies alloy systems already known to host an MPB and suggests a few others that may be promising candidates for future experiments. Our method of investigation may be extended to other perovskite systems, e.g., (oxy-)nitrides, and provides a useful methodology for any application of high-throughput screening of isovalent alloy systems.

Role of phonon dispersion in studying phonon mean free paths in skutterudites

Experimental thermal conductivity of bulk materials are often modeled using Debye approximation together with functional forms of relaxation time with fitting parameters. While such models can fit the temperature dependence of thermal conductivity of bulk materials, the Debye approximation leads to large error in the actual phonon mean free path, and consequently, the predictions of the thermal conductivity of the nanostructured materials using the same relaxation time are not correct even after considering additional size effect on the mean free path. We investigate phonon mean free path distribution inside fully unfilled (Co4Sb12) and fully filled (LaFe4Sb12) bulk skutterudites by fitting their thermal conductivity to analytical models which employ different phonon dispersions. We show that theoretical thermal conductivity predictions of the nanostructured samples are in agreement with the experimental data obtained for samples of different grain sizes only when the full phonon dispersion is considered.

Effects of Sublattice Symmetry and Frustration on Ionic Transport in Garnet Solid Electrolytes

We use rigorous group-theoretic techniques and molecular dynamics to investigate the connection between structural symmetry and ionic conductivity in the garnet family of solid Li-ion electrolytes. We identify new ordered phases and order-disorder phase transitions that are relevant for conductivity optimization. Ionic transport in this materials family is controlled by the frustration of the Li sublattice caused by incommensurability with the host structure at noninteger Li concentrations, while ordered phases explain regions of sharply lower conductivity. Disorder is therefore predicted to be optimal for ionic transport in this and other conductor families with strong Li interaction.