Nucleation and stability of defect clusters: New energetic model in the case of substituted wustites

Abstract

For wüstite Fe_1?z O (z < 0.08) an energetic model accounts for the stability of cubic defect clusters (m/n) which are partly ordered in the crystal. The Gibbs energy G_T (N) associated with clusters, including their distorted envelope, is expressed as a sum of a volume term in N ³ and of surface terms in N ⁴; N is the number of bonds characteristic of the cluster size. In the case of a (10/4) type cluster, this energy is negative and minimum for N_m ranging between 4 and 5, when the volume and surface energies range between specific values. Using simple assumptions, a volume energy ?0.80 eV per vacancy is found in accordance with the value of stabilization energy calculated by theorists for the (10/4) cluster. The substitution of Fe²⁺ by Ca²⁺ should lead to a decrease of cluster size; this has been recently suggested by neutron diffraction studies.     

Ranges of implanted atoms under polyatomic cluster bombardment of the Cu (111) surface

A computer simulation of the bombardment of the Cu (111) surface with Cu_N and Au_N polyatomic clusters differing in size (N = 1, 6, and 13) with energies of 0.5 and 5 keV/atom has been performed in the framework of classical molecular dynamics. The spatial distribution of the implanted atoms, their ranges, and range fluctuations (straggling) depending on the size N and energy E/N of the incident cluster has been investigated. It has been shown that an increase in the mean range and range straggling is observed at a fixed energy per incident atom as the cluster size N increases. At the same time, the effect of an increase in the range (at a specified value of E/N) gradually disappears with increasing cluster energy, whereas the effect of an increase in straggling is retained. These tendencies qualitatively agree with the available experimental observations. It has been shown that the dominating contribution to the increase in the atom range of the implanted cluster is made by the so-called clearing-the-way effect, which is weakened with increasing the incident cluster energy. The effect of the range straggling increasing is significantly due to the presence of nonlinear “spike” effects at the bombarded target.     

Finite size scaling for O(N) φ4-theory at the upper critical dimension

A finite size scaling theory for the partition function zeroes and thermodynamic functions of O(N) φ⁴-theory in four dimensions is derived from renormalization group methods. The leading scaling behaviour is mean-field like with multiplicative logarithmic corrections which are linked to the triviality of the theory. These logarithmic corrections are independent of N for odd thermodynamic quantities and associated zeroes and are N dependent for the even ones. Thus a numerical study of finite size scaling in the Ising model serves as a non-perturbative test of triviality of φ⁴₄-theories for all N.     

Tight-binding approach to field desorption: N2 ON Fe(111)

We present a tight-binding cluster calculation including interatomic Coulomb repulsion for field-induced adsorption and desorption. For electric field strengths F up to the desorption threshold $\text{F ～ 1.5}\text{V}\text{A}\text{?}$ for N₂ on Fe(111) we calculate total potential energy surfaces. The variation of the Schottky barrier and of the N₂ vibrational frequency is extracted as a function of F.     

Energy Characteristics of Small Metal Clusters Containing Vacancies

Self-consistent calculations of spatial distributions of electrons, potentials, and energies of dissociation, cohesion, vacancy formation, and electron attachment, as well as the ionization potential of solid Al _N , Na _N clusters (N ≥ 254), and clusters containing a vacancy (N ≥ 12) have been performed using a model of stable jellium. The contribution of a monovacancy to the energy of the cluster, the size dependences of the characteristics, and their asymptotic forms have been considered. The calculations have been performed on the SKIT-3 cluster at the Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine (Rpeak = 7.4 Tflops).     

Check of the scaling procedure of track structures of ionizing radiation in nanometric volumes

In nanodosimetry, the track structure of ionizing radiation is characterized by the probability distribution of the number of ionizations produced by an ionizing particle in a target volume. By Monte-Carlo simulations of the track structure, this so called ionization cluster size distribution can be determined for nanometric cylindrical water targets used as substitute for the radiation sensitive biological target, namely a DNA-segment of about 20 base pairs length. Measurements of ionization cluster size distributions are carried out in an ion-counting nanodosimeter filled with an appropriate working gas at low pressure. A scaling procedure was proposed by Grosswendt (2006) to derive an operating pressure depending on the working gas for which the measured ionization cluster size distribution becomes equivalent to the ionization cluster size distribution within a nanometric target of liquid water. This scaling procedure was previously tested by means of Monte-Carlo simulations and is now tested experimentally.Ionization cluster size distributions produced by mono-energetic proton and alpha particle beams in the energy range between 0.1 MeV and 20 MeV were measured at the accelerator facilities of the PTB. The working gases used in this experiment were C₃H₈ and N₂. According to the NIST databases for stopping power and mean ionization energy (NIST, 2009), equivalent cluster size distributions for protons and alpha particles should be obtained for pressures of 0.25 mbar C₃H₈ and 1.2 mbar N₂. Measurements reveal the best agreement with pressures of 0.425 mbar C₃H₈ and 1.2 mbar N₂ for protons and 0.46 mbar C₃H₈ and 1.2 mbar N₂ for alpha particles.     

Abelian lattice gauge theories in 3 + 1 dimensions: The linked cluster approach

We use the linked cluster expansion methods of Nickel to derive strong couping series for Z_N abelian gauge theories. These new results together with corresponding estimates using the exact linked cluster expansion algorithm are analysed and compared with previously obtained results for U(1) lattice gauge theory in 3 + 1 dimensions. We confirm the phase structure of these theories as found by other techniques. The critical value of N at which the phase structure of Z_N alters is estimated to be N_C = 4.5 ± 0.2. In each case the string tension estimates using the ELCE algorithm are found to be stable in the presence of a roughening transition.     

Structure of Ti N (N = 6–15) titanium cluster isomers

The atomic structures of various isomers of free Ti _N (N = 6–15) titanium clusters have been studied by molecular dynamics using the many-body interaction potential in the tight binding model. The following parameters of the cluster structure have been calculated: average bond length and energy, coordination number, and frequencies (probabilities) of their appearance. An increase in the cluster size N is accompanied by increased values of these parameters. It is established that the frequency of appearance of an isomer with a given N value increases with the bond energy. The most probable structures of clusters with N = 10–15 correspond to maximum values of the atomic structure parameters among all isomers of a given size.     

Quantum-Size Dependence of the Energy for Vacancy Formation in Charged Small Metal Clusters. Drop Model

Self-consistent computations of the monovacancy formation energy are performed for Na _N , Mg _N , and Al _N (12 < N ≤ 168) spherical clusters in the drop model for stable jelly. Scenarios of the Schottky vacancy formation and “bubble vacancy blowing” are considered. It is shown that the asymptotic behavior of the size dependences of the energy for the vacancy formation by these two mechanisms is different and the difference between the characteristics of a charged and neutral cluster is entirely determined by the difference between the ionization potentials of clusters and the energies of electron attachment to them.     

Geometrical string and dual spin systems

We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a two-plaquette gauge hamiltonian. The duality transformation is constructed in geometrical and algebraic language. The dual hamiltonian represents a new type of spin system with local gauge invariance. At each vertex ξ there are d (d − 1) /2 Ising spins ∧_{μ, η} = ∧_{η,μ N}. ≠ P = 1, … , d and one Ising spin Γ on every linkξ ξ + e,). For the frozen spin Γ  1 the dual hamiltonian factorizes into d (d − 1) /2 two-dimensional Ising ferromagnets and into antiferromagnets in the case Γ  −1. For fluctuating F it is a sort of spin-glass system with local gauge invariance. The generalization to p-membranes is given.     

Product state distributions and rotational polarization for the crossed beam reactions of Ca with F2 and NF3

Product state distributions of the CaF products from the thermal crossed beam reactions Ca + F₂ and Ca + NF₃ have been measured using laser induced fluorescence (LIF) techniques. We obtain information about the rotational and vibrational distributions by generating synthetic band profiles and comparing them with those observed. The inverted vibrational distributions indicate direct reaction mechanisms. For Ca + F₂ the fractionf′ of energy is nearly half going into product translation and the remainder being devided nearly equally between product rotation and vibration. For Ca + NF₃ the largest fraction of the available reaction exoergicity goes into vibrational excitation of the newly formed CaF products. In addition, we have probed the rotational polarization of CaF product molecules. This gives direct information on the role of angular momentum alignment in reactive scattering.     

Monte Carlo study of the Yukawa coupled two-spin Ising model

We consider a particular four state spin system composed of two Ising spins (s_x, σ_x) with independent hopping parameters κ₁ κ₂, coupled by a bilinear Yukawa term, ys_xσ_x. The Yukawa term is solely responsible for breaking the global Z₂ × Z₂ symmetry down to Z2. This model is intended as an illustration of general coupled Higgs system where scalars can arise both as composite and elementary excitations. For the Ising example in 2d, we give convincing numerical evidence of the universality of the two-spin system with the one-spin Ising model, by Monte Carlo simulations and finite size scaling analysis. We also show that as we approach the phase transition, universality arises by having a single correlation length that diverges.     

Progress in lattice gauge theory

Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g²-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a $\text{1}\text{N}$ expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed.     

Modeling Aggregation Processes of Lennard-Jones particles Via Stochastic Networks

We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size N onto stochastic networks, computing transition probabilities from the network for an N-particle cluster to the one for \(N+1\), and connecting these networks into a single joint network. The attachment rate is a control parameter. The resulting network representing the aggregation of up to 14 particles contains 6427 vertices. It is not only time-irreversible but also reducible. To analyze its transient dynamics, we introduce the sequence of the expected initial and pre-attachment distributions and compute them for a wide range of attachment rates and three values of temperature. As a result, we find the configurations most likely to be observed in the process of aggregation for each cluster size. We examine the attachment process and conduct a structural analysis of the sets of local energy minima for every cluster size. We show that both processes taking place in the network, attachment and relaxation, lead to the dominance of icosahedral packing in small (up to 14 atom) clusters.     

Study on the relations of sensitivity with energy properties for HMX and HMX-based PBXs by molecular dynamics simulation

Molecular dynamics simulation was applied to study the structure and energy properties of β-HMX (β-cyclotetramethylene tetranitramine) crystal and its composite PBXs (polymer-bonded explosives) with F₂₃₁₁ as a polymer binder under different temperatures and F₂₃₁₁ concentrations. The interface interaction energy of HMX and F₂₃₁₁, the interaction energy E_N–N between N atoms in N–NO₂ trigger bond in HMX molecules, and the cohesive energy density (CED) are presented and analyzed. A meaningful finding is that there exists correlation between E_N–N and the sensitivity of β-HMX and its composites, i.e. the less the E_N–N is, the larger the sensitivity is. Additionally, molecular interactions are inherently disclosed by using pair correlation function (PCF) to analyze the interfacial structure between (1 0 0)HMX crystal surface and F₂₃₁₁ molecular chain.     

Antiferromagnetic Ordering of Magnetic Clusters Units in Nb6F15

We have studied the magnetic cluster compound Nb₆F₁₅ which has an odd number of 15 valence electrons per (Nb₆F₁₂)³⁺ cluster core, as a function of temperature using nuclear magnetic resonance, magnetic susceptibility, electron magnetic resonance and neutron powder diffraction. Nuclear magnetic resonance of the ¹⁹F nuclei shows two lines corresponding to the apical F^a?a nucleus, and to the inner Fⁱ nuclei. The temperature dependence of the signal from the Fⁱ nuclei reveals an antiferromagnetic ordering at T < 5 K, with a hyperfine field of ~2 mT. Magnetic susceptibility exhibits a Curie–Weiss behavior with T _N ~5 K, and μ _eff ~1.57 μ_B close to the expected theoretical value for one unpaired electron (1.73 μ_B). Electron magnetic resonance linewidth shows a transition at 5 K. Upon cooling from 10 to 1.4 K, the neutron diffraction shows a decrease in the intensity of the low-angle diffuse scattering below Q ~0.27 Å^?1. This decrease is consistent with emergence of magnetic order of large magnetic objects (clusters). This study shows that Nb₆F₁₅ is paramagnetic at RT and undergoes a transition to antiferromagnetic order at 5 K. This unique antiferromagnetic ordering results from the interaction between magnetic spins delocalized over each entire (Nb₆F ₁₂ ⁱ )³⁺ cluster core, rather than the common magnetic ordering.