A microscopic view of the Fourier law

The Fourier law of heat conduction describes heat diffusion in macroscopic systems. This physical law has been experimentally tested for a large class of physical systems. A natural question is to know whether it can be derived from the microscopic models using the fundamental laws of mechanics.     

Fractional generalization of Fick's law: a microscopic approach

In the study of transport in inhomogeneous systems it is common to construct transport equations invoking the inhomogeneous Fick law. The validity of this approach requires that at least two ingredients be present in the system. First, finite characteristic length and time scales associated with the dominant transport process must exist. Second, the transport mechanism must satisfy a microscopic symmetry: global reversibility. Global reversibility is often satisfied in nature. However, many complex systems exhibit a lack of finite characteristic scales. In this Letter we show how to construct a generalization of the inhomogeneous Fick law that does not require the existence of characteristic scales while still satisfying global reversibility.     

A possible origin for the Vogel-Fulcher law

The physical origin for the Vogel-Fulcher law in glass-forming supercooled liquids is not clear. We propose the following picture. The liquid has fluctuations in energy with large amplitude. They permit the formation in the system of an infinite cluster of the amorphous phase. The rigid skeleton inside the liquid has a life time which grows according to a Vogel-Fulcher law. Experimentally these fluctuations manifest themselves in physical properties such as viscosity, dielectric relaxation etc.     

Fourier's law based on microscopic dynamics

While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines, the solution to Newton's equations of motion can be obtained with high precision and for a reasonably large number of particles. For simplified model systems, one thereby arrives at a deeper understanding of the microscopic basis for Fourier's law. We report on recent, and not so recent, advances.     

Slow crack growth: Models and experiments

The properties of slow crack growth in brittle materials are analyzed both theoretically and experimentally. We propose a model based on a thermally activated rupture process. Considering a 2D spring network submitted to an external load and to thermal noise, we show that a preexisting crack in the network may slowly grow because of stress fluctuations. An analytical solution is found for the evolution of the crack length as a function of time, the time to rupture and the statistics of the crack jumps. These theoretical predictions are verified by studying experimentally the subcritical growth of a single crack in thin sheets of paper. A good agreement between the theoretical predictions and the experimental results is found. In particular, our model suggests that the statistical stress fluctuations trigger rupture events at a nanometric scale corresponding to the diameter of cellulose microfibrils.     

Doping by large-size-mismatched impurities: the microscopic origin of arsenic- or antimony-doped p-type zinc oxide

Based on first-principles calculations, a model for large-size-mismatched group-V dopants in ZnO is proposed. The dopants do not occupy the O sites as is widely perceived, but rather the Zn sites: each forms a complex with two spontaneously induced Zn vacancies in a process that involves fivefold As coordination. Moreover, an As(Zn)-2V(Zn) complex may have lower formation energy than any of the parent defects. Our model agrees with the recent observations that both As and Sb have low acceptor-ionization energies and that to obtain p-type ZnO requires O-rich growth or annealing conditions.     

Atomic scale origin of crack resistance in brittle fracture

We investigate the physical meaning of the intrinsic crack resistance in the Griffith theory of brittle fracture by means of atomic-scale simulations. By taking cubic SiC as a typical brittle material, we show that the widely accepted identification of intrinsic crack resistance with the free surface energy underestimates the energy-release rate. The strain dependence of the Young modulus and surface energy, as well as allowance for lattice trapping, improve the estimate of the crack resistance. In the smallest scale limit, crack resistance can be fitted by an empirical elastoplastic model.     

Fatigue crack growth in fiber-metal laminates

Fiber-metal laminates(FMLs)consist of three layers of aluminum alloy 2024-T3 and two layers of glass/epoxy prepreg,and it(it means FMLs)is laminated by Al alloy and fiber alternatively.Fatigue crack growth rates in notched fiber-metal laminates under constant amplitude fatigue loading were studied experimentally and numerically and were compared with them in monolithic 2024-T3 Al alloy plates.It is shown that the fatigue life of FMLs is about 17 times longer than monolithic 2024-T3 Al alloy plate;and crack growth rates in FMLs panels remain constant mostly even when the crack is long,unlike in the monolithic 2024-T3 Al alloy plates.The formula to calculate bridge stress profiles of FMLs was derived based on the fracture theory.A program by Matlab was developed to calculate the distribution of bridge stress in FMLs,and then fatigue growth lives were obtained.Finite element models of FMLs were built and meshed finely to analyze the stress distributions.Both results were compared with the experimental results.They agree well with each other.     

The growth statistics of Zipfian ensembles: Beyond Heaps’ law

We consider an evolving ensemble assembled from a set of n different elements via a stochastic growth process in which independent and identically distributed copies of the elements arrive randomly in time, and their statistics are governed by Zipf’s law. The associated “Heaps process” is the stochastic process tracking the fraction of different element copies present in the evolving ensemble at any given time point. For example, the evolving ensemble is a text assembled from a stream of words, and the Heaps process keeps count of the number of different words in the evolving text. A detailed asymptotic statistical analysis of the Heaps process, in the limit n→∞, is conducted. This paper establishes a comprehensive “Heapsian analysis” of the growth statistics of Zipfian ensembles. The analysis presented far extends and generalizes Heaps’ law, which asserts that the number of different words in a text of length l follows a power law in the variable l.     

Interacting particles as neither bosons nor fermions: A microscopic origin for fractional exclusion statistics

We study a quantum liquid of particles interacting via a long-ranged two-body potential in three dimensions where the original particles are supposed to be either bosons or fermions. We show that such liquids exhibit the nature of a quantum liquid with fractional exclusion statistics. In both quantum liquids enlarged pseudo-Fermi surfaces are formed from bosons and fermions, although with different excitations. Hence, we conclude that the microscopic origin of exclusion statistics comes from the nature of long-ranged two-body interactions between the particles.     

Power law growth for the resistance in the Fibonacci model

Many one-dimensional quasiperiodic systems based on the Fibonacci rule, such as the tight-binding HamiltonianH(n)=(n+1)+(n–1)+v(n) (n),n,l ²(),, wherev(n)=[(n+1)]–[n],[x] denoting the integer part ofx and the golden mean , give rise to the same recursion relation for the transfer matrices. It is proved that the wave functions and the norm of transfer matrices are polynomially bounded (critical regime) if and only if the energy is in the spectrum of the Hamiltonian. This solves a conjecture of Kohmoto and Sutherland on the power-law growth of the resistance in a one-dimensional quasicrystal.     

On the understanding of the microscopic origin of the properties of diluted magnetic semiconductors by atom probe tomography

Spintronics, in which both the spin and charge of electrons are used for logic and memory operations, promises to revolutionize the current information technology. Just as silicon supports microelectronics, diluted magnetic semiconductors (DMSs) will be the platform of spintronics. Ideal DMSs should maintain ferromagnetic and semiconducting properties at operating temperatures to realize the spintronic functions. Although many high-temperature Curie temperature DMSs have been reported, the origin of ferromagnetism remains controversial. Currently, this is a major obstacle to the development of spintronic devices. The solution to this problem depends on a more complete understanding of DMS microstructure, especially the distribution of doped magnetic ions at atomic resolution and any defects introduced. Therefore, an analysis technique is required, possessing both high spatial and elemental resolutions, which is beyond the capability of conventional techniques, such as electron microscopy. However, atom probe tomography (APT), which recently has been successfully applied to nanoscale characterization of structural materials, has the potential to provide the unique combination of near atomic spatial and elemental resolutions needed for such an investigation.     

Simulation of crack growth during fracture of heterogeneous materials

A cellular automaton model for describing the fracture of mechanically loaded heterogeneous materials has been constructed. Two extreme scenarios of the fracture process have been revealed, i.e., the dispersion (percolation) scenario, according to which defects accumulate uniformly throughout the volume of the material, and the correlated scenario (growth of predominantly a single source), which have been observed during the fracture of real materials. It has been shown that, in the case of the correlated fracture, a crack grows through the mechanism of ejection of double kinks of its front. In the intermediate case, the process occurs according to both scenarios: first, the slow accumulating (percolation) fracture and, then, the rapid correlated fracture; by the time the latter process begins, a self-organized critical state with a power-law size distribution of cracks typical of it has been formed.     

Novel domain growth law in random magnets

We investigate the kinetics of domain growth in Ising magnets where a fraction 1 - p of the magnetic atoms or ions (spins) are randomly substituted by non-magnetic impurities. We argue that close to the percolation threshold p_c, the statistical self-similarity of the underlying structure gives rise to a novel crossover in the growth law. We propose a method to detect any evidence of this new prediction from the kinetics of domain growth in the dilute Ising model (DIM) during intermediate time scales by carrying out Monte Carlo simulations not at p = p_c but at slightly higher spin concentrations. We analyze the results of our extensive Monte Carlo simulation of the strongly diluted two-dimensional Ising model and find the growth to be consistent with the proposed scenario. We also compare our observations with those in the recent experiments on the kinetics of ordering in Rb₂Co_pMg_1−pF₄.     

Effect of humidity on subcritical crack growth of indentation crack under sustained electric field in PZT ceramics

The effect of humidity on subcritical crack growth of indentation crack in lead zirconate titanate (PZT) ferroelectric ceramics under various sustained electric field has been investigated. The results showed that subcritical crack growth of indentation crack could occur in humid air of 60%RH without electric field but did not in air with RH ≤ 30%. The subcritical crack growth could occur in vacuum under a sustained electric field of E/E_C = 0.14. The incubation time decreased and the amount of the subcritical crack growth increased with increasing the humidity under the sustained field. The threshold electric field for subcritical crack growth decreased with increasing the humidity.     

On the microscopic origin of the kinetic step bunching instability on vicinal Si(0 0 1)

A scanning tunneling microscopy/atomic force microscopy study is presented of a kinetically driven growth instability, which leads to the formation of ripples during Si homoepitaxy on slightly vicinal Si(0 0 1) surfaces miscut in [1 1 0] direction. The instability is identified as step bunching, that occurs under step-flow growth conditions and vanishes both during low-temperature island growth and at high temperatures. We demonstrate, that the growth instability with the same characteristics is observed in two dimensional kinetic Monte Carlo simulation with included Si(0 0 1)-like diffusion anisotropy. The instability is mainly caused by the interplay between diffusion anisotropy and the attachment/detachment kinetics at the different step types on Si(0 0 1) surface. This new instability mechanism does not require any additional step edge barriers to diffusion of adatoms. In addition, the evolution of ripple height and periodicity was analyzed experimentally as a function of layer thickness. A lateral “ripple-zipper” mechanism is proposed for the coarsening of the ripples.