Electron-hole asymmetry in the electron-phonon coupling in top-gated phosphorene transistor

Using in situ Raman scattering from phosphorene channel in an electrochemically top-gated field effect transistor, we show that phonons with A(g) symmetry depend much more strongly on concentration of electrons than that of holes, wheras phonons with B-g symmetry are insensitive to doping. With first-principles theoretical analysis, we show that the observed electon-hole asymmetry arises from the radically different constitution of its conduction and valence bands involving pi and sigma bonding states respectively, whose symmetry permits coupling with only the phonons that preserve the lattice symmetry. Thus, Raman spectroscopy is a non-invasive tool for measuring electron concentration in phosphorene-based nanoelectronic devices.

Graphite intercalation compounds under pressure

Motivated by recent experimental work, we use first-principles density functional theory methods to conduct an extensive search for low enthalpy structures of C$_6$Ca under pressure. As well as a range of buckled structures, which are energetically competitive over an intermediate range of pressures, we show that the high pressure system ($\gtrsim 18$ GPa) is unstable towards the formation of a novel class of layered structures, with the most stable compound involving carbon sheets containing five- and eight-membered rings. As well as discussing the energetics of the different classes of low enthalpy structures, we comment on the electronic structure of the high pressure compound and its implications for superconductivity.

La luz del intelecto agente en los principios de la razón práctica según San Alberto Magno

Resumen: La Antigone de Sófocles y el Corpus Hippocraticum delinean ya los rasgos propios del derecho natural. La ética de Aristóteles, luego, ofrece una primera noción explícita del derecho natural, que San Alberto Magno comenta en Super ethica. Sin embargo, en De inventione de Cicerón el teólogo alemán encuentra su definición de derecho natural: “lo que cierta fuerza innata introdujo”. En De bono V q. 1 San Alberto determina los alcances de esta definición y completa una presentación acabada de la noción de derecho natural. También advierte San Alberto que el hombre, con respecto a la ciencia del intelecto práctico, se encuentra doblemente en potencia. Primero, está en potencia de conocer los principios primeros de esta ciencia y, segundo, una vez conocidos éstos, se encuentra en potencia de inferir a partir de ellos las conclusiones de la ciencia práctica. Poseídas estas conclusiones, finalmente, el hombre está en potencia de aplicarlas en la acción práctica. Intrigado por el modo en que los primeros principios son conocidos, San Alberto advierte que el conocimiento de las nociones correspondientes a estos principios sólo accidentalmente debe ser atribuido al descubrimiento o determinación de los nombres con los que llamamos a estos principios. En verdad, es necesaria la intervención de la luz del intelecto agente para llevar al acto el conocimiento de los principios. En este punto el discurso de San Alberto retorna a la definición ciceroniana: aquella fuerza innata que introduce el derecho natural no es otra que la luz del intelecto agente.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.

Los fundamentos teóricos de la ley natural

Resumen: El comentario sobre los fundamentos teóricos trata de la distinción entre un acceso práctico a la ley natural mediante la captación evidente e inmediata de los primeros principios (referidos a los valores fundamentales) por la razón en su función práctica (razón práctica), y la fundamentación teórica y metafísica del contenido de la ley natural con sus primeros principios, realizado ulteriormente por la razón en su función teórica (razón teórica o especulativa). Se aborda de esta manera la patencia de esos valores fundamentales como punto de partida o primera ratio del proceso que realiza la razón práctica y su justificación racional en el plano metafísico como última ratio que realiza la razón teórica o especulativa.

Effect Of Load Triaxiality On Polymorphic Transitions In Zinc Oxide

Molecular dynamics (MD) simulations and first-principles calculations are carried out to analyze the stability of both newly discovered and previously known phases of ZnO under loading of various triaxialities. The analysis focuses on a graphite-like phase (FIX) and a body-centered-tetragonal phase (BCT-4) that were observed recently in [0 1 (1) over bar 0]- and [0 0 0 1]-oriented nanowires respectively under uniaxial tensile loading as well as the natural state of wurtzite (WZ) and the rocksalt (RS) phase which exists under hydrostatic pressure loading. Equilibrium critical stresses for the transformations are obtained. The WZ -> HX transformation is found to be energetically favorable above a critical tensile stress of 10 GPa in [0 1 (1) over tilde 0] nanowires. The BCT-4 phase can be stabilized at tensile stresses above 7 GPa in [0 0 0 1] nanowires. The RS phase is stable at hydrostatic pressures above 8.2 GPa. The identification and characterization of these phase transformations reveal a more extensive polymorphism of ZnO than previously known. A crystalline structure-load triaxiality map is developed to summarize the new understanding. (c) 2007 Elsevier Ltd. All rights reserved.

Efficient Gate-tunable light-emitting device made of defective boron nitride nanotubes: from ultraviolet to the visible

Boron nitride is a promising material for nanotechnology applications due to its two-dimensional graphene-like, insulating, and highly-resistant structure. Recently it has received a lot of attention as a substrate to grow and isolate graphene as well as for its intrinsic UV lasing response. Similar to carbon, one-dimensional boron nitride nanotubes (BNNTs) have been theoretically predicted and later synthesised. Here we use first principles simulations to unambiguously demonstrate that i) BN nanotubes inherit the highly efficient UV luminescence of hexagonal BN; ii) the application of an external perpendicular field closes the electronic gap keeping the UV lasing with lower yield; iii) defects in BNNTS are responsible for tunable light emission from the UV to the visible controlled by a transverse electric field (TEF). Our present findings pave the road towards optoelectronic applications of BN-nanotube-based devices that are simple to implement because they do not require any special doping or complex growth

基于跨尺度模型的界面研究

探索和建立不同尺度理论之间的关联模式是科学研究的重要课题，本文基于跨尺度模型着重探讨了金属陶瓷界面的凝聚能和原子结构问题。本文遵循原始Peierls-Nabarro模型的基本思想，提出了一种处理一维界面失配位错组的新方法。在这个推广的Peierls-Nabarro模型中，本文得到了一个简单而且准确的解析解，此解反映了失配位错的核结构、能量与失配度、剪切模量之间的依赖关系。当界面剪切模量较强而失配度较小时，界面的结构可以用一组奇导师Volterra位错来描述，这与一些原子模拟结果一致。采用这一简单的模型，引入第一原理计算得到的数据，此模型可以估算金属陶瓷界面的凝聚能。一维界面失配位错组的Peierls-Nabarro模型还被解析推广描述一大类较宽的位错。在模型中我们引进了一个参数a，通过控制参数a，我们可以系统地改变失配位错芯的宽度、剪切应力的分布和弹性恢复力。随着a增加，位错宽度增加，同时弹性恢复力和失配位错应力的幅度减少。当界面剪切模量强和失配度小时，失配位错的宽度近似线性反比于弹性恢复力的幅度大小。同时当界面剪切模量和失配度固定时，失配能、弹性能和总的界面能随a的增加而减少。界面能和恢复力律形式密切相关，当界面剪切模量弱和失配度大时，这种依赖关系更强。考虑到界面常常是在晶格两个方向都有失配，本文还引进了描述界面周期失配位错的二维广义Peierls-Nabarro模型，使得我们能够定量地研究界面的结构和能量。文中定量分析了广义堆垛能γ面对界面失配位错的结构和能量的影响，分析了位错网中两种位错组的相互作用。当界面剪切模量τ_0变大和失配度f变小时，随着位错核区占整个界面的比重下降，γ面的形状对界面能量和结构影响减弱，结果两种位错组之间的相互作用也减弱。此外γ面的变化还有可能导致位错网结构的转变，也就是导致界面结构的转变。应用此模型，本文还研究了金属－陶瓷Ag/MgO(100)界面，给出了界面的能量和原子结构。文中得出结论：在Ag/MgO(100)界面将会形成{1/2<110>; <110>}类型的位错网。此外由于界面失配位错的形成，Ag/MgO(100)界面凝聚能的理论值900mJ/m~2将减少214mJ/m~2，最终成为686mJ/m~2。基于第一原理赝势平面波的总能计算，文中给出了金属陶瓷Al/MgO(100)界面弛豫和未弛豫时的广义堆垛能面。然后结合第三章发展的广义二维Peierls-Nabarro模型，详细研究了金属陶瓷Al/MgO(100)界面的原子结构和界面能。文中得出的“在Al/MgO(100)界面将会形成{1/2<110>; <110>}类型位错网”的推论，证实了Vellinga等的猜测；文中还预测了凝聚能的理论是在600mJ/m~2（未弛豫情形）和670mJ/m~2（弛豫情形）之间。这个应用表明此方法能够容易地建立连续介质理论和第一原理计算之间的联系，实现理论上的跨尺度。本文最后提出了一种得到界面原子有效对势的反演方法。通过反演金属－MgO陶瓷界面的第一原理计算的凝聚能曲线，我们得到了一些金属原子和陶瓷离子之间的对势，此对势反映了金属陶瓷键合的特性。本文的反演方法提供了通过第一原理计算数据来拟合界面原子对势的一种可行性途径。这种方法可归结为第一类尺度关联理论，即单向的跨尺度关联模式。

Studies of phonon anharmonicity in solids

Today our understanding of the vibrational thermodynamics of materials at low temperatures is emerging nicely, based on the harmonic model in which phonons are independent. At high temperatures, however, this understanding must accommodate how phonons interact with other phonons or with other excitations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems, and essentially modify the equilibrium and non-equilibrium properties of materials, e.g., thermodynamic stability, heat capacity, optical properties and thermal transport of materials. Despite its great importance, to date the anharmonic lattice dynamics is poorly understood and most studies on lattice dynamics still rely on the harmonic or quasiharmonic models. There have been very few studies on the pure phonon anharmonicity and phonon-phonon interactions. The work presented in this thesis is devoted to the development of experimental and computational methods on this subject.

Modern inelastic scattering techniques with neutrons or photons are ideal for sorting out the anharmonic contribution. Analysis of the experimental data can generate vibrational spectra of the materials, i.e., their phonon densities of states or phonon dispersion relations. We obtained high quality data from laser Raman spectrometer, Fourier transform infrared spectrometer and inelastic neutron spectrometer. With accurate phonon spectra data, we obtained the energy shifts and lifetime broadenings of the interacting phonons, and the vibrational entropies of different materials. The understanding of them then relies on the development of the fundamental theories and the computational methods.

We developed an efficient post-processor for analyzing the anharmonic vibrations from the molecular dynamics (MD) calculations. Currently, most first principles methods are not capable of dealing with strong anharmonicity, because the interactions of phonons are ignored at finite temperatures. Our method adopts the Fourier transformed velocity autocorrelation method to handle the big data of time-dependent atomic velocities from MD calculations, and efficiently reconstructs the phonon DOS and phonon dispersion relations. Our calculations can reproduce the phonon frequency shifts and lifetime broadenings very well at various temperatures.

To understand non-harmonic interactions in a microscopic way, we have developed a numerical fitting method to analyze the decay channels of phonon-phonon interactions. Based on the quantum perturbation theory of many-body interactions, this method is used to calculate the three-phonon and four-phonon kinematics subject to the conservation of energy and momentum, taking into account the weight of phonon couplings. We can assess the strengths of phonon-phonon interactions of different channels and anharmonic orders with the calculated two-phonon DOS. This method, with high computational efficiency, is a promising direction to advance our understandings of non-harmonic lattice dynamics and thermal transport properties.

These experimental techniques and theoretical methods have been successfully performed in the study of anharmonic behaviors of metal oxides, including rutile and cuprite stuctures, and will be discussed in detail in Chapters 4 to 6. For example, for rutile titanium dioxide (TiO₂), we found that the anomalous anharmonic behavior of the B_1g mode can be explained by the volume effects on quasiharmonic force constants, and by the explicit cubic and quartic anharmonicity. For rutile tin dioxide (SnO₂), the broadening of the B_2g mode with temperature showed an unusual concave downwards curvature. This curvature was caused by a change with temperature in the number of down-conversion decay channels, originating with the wide band gap in the phonon dispersions. For silver oxide (Ag₂O), strong anharmonic effects were found for both phonons and for the negative thermal expansion.

Advanced density functional theory methods for materials science

In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description.

Zinc Phosphide (Zn₃P₂) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn₃P₂ and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems.

Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via ’classical’ molecular dynamics where the atomic motion is calculated from Newtonian mechanics with the electronic effects abstracted away into an interatomic potential function. For our purposes, a ’first principles’ approach such as DFT is useful as a classical potential is typically valid for only a portion of the phase diagram (i.e. whatever part it has been fit to). Furthermore, for extremes of temperature and pressure quantum effects become critical to accurately capture an equation of state and are very hard to capture in even complex model potentials. This requires extending the inherently zero temperature DFT to predict the finite temperature response of the system. Statistical modelling and thermodynamic integration is used to extend our results over all phases, as well as phase-coexistence regions which are at the limits of typical DFT validity. We deliver the most comprehensive and accurate equation of state that has been done for Ta. This work also lends insights that can be applied to further equation of state work in many other materials.

Methods for melting temperature calculation

Melting temperature calculation has important applications in the theoretical study of phase diagrams and computational materials screenings. In this thesis, we present two new methods, i.e., the improved Widom's particle insertion method and the small-cell coexistence method, which we developed in order to capture melting temperatures both accurately and quickly.

We propose a scheme that drastically improves the efficiency of Widom's particle insertion method by efficiently sampling cavities while calculating the integrals providing the chemical potentials of a physical system. This idea enables us to calculate chemical potentials of liquids directly from first-principles without the help of any reference system, which is necessary in the commonly used thermodynamic integration method. As an example, we apply our scheme, combined with the density functional formalism, to the calculation of the chemical potential of liquid copper. The calculated chemical potential is further used to locate the melting temperature. The calculated results closely agree with experiments.

We propose the small-cell coexistence method based on the statistical analysis of small-size coexistence MD simulations. It eliminates the risk of a metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Using empirical potentials, we validate the method and systematically study the finite-size effect on the calculated melting points. The method converges to the exact result in the limit of a large system size. An accuracy within 100 K in melting temperature is usually achieved when the simulation contains more than 100 atoms. DFT examples of Tantalum, high-pressure Sodium, and ionic material NaCl are shown to demonstrate the accuracy and flexibility of the method in its practical applications. The method serves as a promising approach for large-scale automated material screening in which the melting temperature is a design criterion.

We present in detail two examples of refractory materials. First, we demonstrate how key material properties that provide guidance in the design of refractory materials can be accurately determined via ab initio thermodynamic calculations in conjunction with experimental techniques based on synchrotron X-ray diffraction and thermal analysis under laser-heated aerodynamic levitation. The properties considered include melting point, heat of fusion, heat capacity, thermal expansion coefficients, thermal stability, and sublattice disordering, as illustrated in a motivating example of lanthanum zirconate (La₂Zr₂O₇). The close agreement with experiment in the known but structurally complex compound La₂Zr₂O₇ provides good indication that the computation methods described can be used within a computational screening framework to identify novel refractory materials. Second, we report an extensive investigation into the melting temperatures of the Hf-C and Hf-Ta-C systems using ab initio calculations. With melting points above 4000 K, hafnium carbide (HfC) and tantalum carbide (TaC) are among the most refractory binary compounds known to date. Their mixture, with a general formula Ta_xHf_1-xC_y, is known to have a melting point of 4215 K at the composition Ta₄HfC₅, which has long been considered as the highest melting temperature for any solid. Very few measurements of melting point in tantalum and hafnium carbides have been documented, because of the obvious experimental difficulties at extreme temperatures. The investigation lets us identify three major chemical factors that contribute to the high melting temperatures. Based on these three factors, we propose and explore a new class of materials, which, according to our ab initio calculations, may possess even higher melting temperatures than Ta-Hf-C. This example also demonstrates the feasibility of materials screening and discovery via ab initio calculations for the optimization of "higher-level" properties whose determination requires extensive sampling of atomic configuration space.

Phase transitions from the solid state of monatomic elements

The principle aims of this thesis include the development of models of sublimation and melting from first principles and the application of these models to the rare gases.

A simple physical model is constructed to represent the sublimation of monatomic elements. According to this model, the solid and gas phases are two states of a single physical system. The nature of the phase transition is clearly revealed, and the relations between the vapor pressure, the latent heat, and the transition temperature are derived. The resulting theory is applied to argon, krypton, and xenon, and good agreement with experiment is found.

For the melting transition, the solid is represented by an anharmonic model and the liquid is described by the Percus-Yevick approximation. The behavior of the liquid at high densities is studied on the isotherms kT/∈ = 1.3, 1.8, and 2.0, where k is Boltzmann's constant, T is the temperature, and e is the well depth of the Lennard-Jones 12-6 pair potential. No solutions of the PercusYevick equation were found for ρσ³ above 1.3, where ρ is the particle density and σ is the radial parameter of the Lennard-Jones potential. The liquid structure is found to be very different from the solid structure near the melting line. The liquid pressures are about 50 percent low for experimental melting densities of argon. This discrepancy gives rise to melting pressures up to twice the experimental values.

Classical and Quantum Effects in Plasmonic Metals

The field of plasmonics exploits the unique optical properties of metallic nanostructures to concentrate and manipulate light at subwavelength length scales. Metallic nanostructures get their unique properties from their ability to support surface plasmons– coherent wave-like oscillations of the free electrons at the interface between a conductive and dielectric medium. Recent advancements in the ability to fabricate metallic nanostructures with subwavelength length scales have created new possibilities in technology and research in a broad range of applications.

In the first part of this thesis, we present two investigations of the relationship between the charge state and optical state of plasmonic metal nanoparticles. Using experimental bias-dependent extinction measurements, we derive a potential- dependent dielectric function for Au nanoparticles that accounts for changes in the physical properties due to an applied bias that contribute to the optical extinction. We also present theory and experiment for the reverse effect– the manipulation of the carrier density of Au nanoparticles via controlled optical excitation. This plasmoelectric effect takes advantage of the strong resonant properties of plasmonic materials and the relationship between charge state and optical properties to eluci- date a new avenue for conversion of optical power to electrical potential.

The second topic of this thesis is the non-radiative decay of plasmons to a hot-carrier distribution, and the distribution’s subsequent relaxation. We present first-principles calculations that capture all of the significant microscopic mechanisms underlying surface plasmon decay and predict the initial excited carrier distributions so generated. We also preform ab initio calculations of the electron-temperature dependent heat capacities and electron-phonon coupling coefficients of plasmonic metals. We extend these first-principle methods to calculate the electron-temperature dependent dielectric response of hot electrons in plasmonic metals, including direct interband and phonon-assisted intraband transitions. Finally, we combine these first-principles calculations of carrier dynamics and optical response to produce a complete theoretical description of ultrafast pump-probe measurements, free of any fitting parameters that are typical in previous analyses.

On the relationship between hidden Markov Models and convex functional transforms for simulating scanning probe Microscopy

Models for simulating Scanning Probe Microscopy (SPM) may serve as a reference point for validating experimental data and practice. Generally, simulations use a microscopic model of the sample-probe interaction based on a first-principles approach, or a geometric model of macroscopic distortions due to the probe geometry. Examples of the latter include use of neural networks, the Legendre Transform, and dilation/erosion transforms from mathematical morphology. Dilation and the Legendre Transform fall within a general family of functional transforms, which distort a function by imposing a convex solution.In earlier work, the authors proposed a generalized approach to modeling SPM using a hidden Markov model, wherein both the sample-probe interaction and probe geometry may be taken into account. We present a discussion of the hidden Markov model and its relationship to these convex functional transforms for simulating and restoring SPM images.©2009 SPIE.

Shifting atomic patterns: on the origin of the different atomic-scale patterns of graphite as observed using scanning tunnelling microscopy.

We present an in-depth study of the myriad atomically resolved patterns observed on graphite using the scanning tunnelling microscope (STM) over the past three decades. Through the use of highly resolved atomic resolution images, we demonstrate how the interactions between the different graphene layers comprising graphite affect the local surface atomic charge density and its resulting symmetry orientation, with particular emphasis on interactions that are thermodynamically unstable. Moreover, the interlayer graphene coupling is controlled experimentally by varying the tip-surface interaction, leading to associated changes in the atomic patterns. The images are corroborated by first-principles calculations, further validating our claim that surface graphene displacement, coming both from lateral and vertical displacement of the top graphene layer, forms the basis of the rich variety of atomic patterns observed in STM experiments on graphite.