Maximum Likelihood Analysis of Reaction Coordinates during Solidification in Ni

Understanding the underlying mechanism of crystal nucleation during solidification is a fundamental aspect in the prediction and control of materials properties. Classical nucleation theory (CNT) assumes that homogeneous nucleation occurs via random fluctuations within the supercooled liquid, that the structure of the growing clusters resembles the most stable bulk phase, and that the nucleus size is the sole reaction coordinate (RC) of the process. Many materials are, however, known to exhibit multiple steps during crystallization, forming different polymorphs. As a consequence, more complex RCs are often required to capture all relevant information about the process. In this work, we employ transition path sampling together with a maximum likelihood analysis of candidate order parameters to identify suitable reaction coordinates for the nucleation mechanism during solidification in Ni. In contrast to CNT, the analysis of the reweighted path ensemble shows that a pre-structured liquid region that surrounds the crystal cluster is a relevant order parameter that enhances the RC and therefore plays a key role in the description of the growing nucleus and the interfacial free energy. We demonstrate that pre-structured liquid clusters that emerge within the liquid act as precursors of the crystallization in a non-classical two-step mechanism which predetermines the coordination of the polymorphs that are being selected

Diffusion of hydrogen within idealised grains of bcc-Fe: A kinetic Monte Carlo study

Structural defects in materials such as vacancies, grain boundaries, and dislocations may trap hydrogen and a local accumulation of hydrogen at these defects can lead to the degradation of the materials properties. An important aspect in obtaining insight into hydrogen induced embrittlement on the atomistic level is to understand the diffusion of hydrogen in these materials. In our study we employ kinetic Monte Carlo (kMC) simulations to investigate hydrogen diffusion in bcc iron within different microstructures. All input data to the kMC model, such as available sites, solution energies, and diffusion barriers are obtained from first-principles calculations. We find that hydrogen mainly diffuses within the interface region with an overall diffusivity that is lower than in pure bcc-Fe bulk. The concentration dependence of the diffusion coefficient is strongly non-linear and the diffusion coefficient may even decrease with increasing hydrogen concentration. To describe the macroscopic diffusion coefficient we derive an analytic expression as a function of hydrogen concentration and temperature which is in excellent agreement with our numerical results for idealised microstructures

First-principles statistical mechanics study of the stability of a sub-nanometer thin surface oxide in reactive environments: CO oxidation at Pd(100)

We employ a multiscale modeling approach to study the surface structure and composition of a Pd(100) model catalyst in reactive environments. Under gas phase conditions representative of technological CO oxidation (~1 atm, 300-600 K) we find the system on the verge of either stabilizing sub-nanometer thin oxide structures or CO adlayers at the surface. Under steady-state operation this suggests the presence or continuous formation and reduction of oxidic patches at the surface, which could be key to understand the observable catalytic function.Comment: 4 pages including 2 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Higher Mellin moments for charged current DIS

We report on our recent results for deep-inelastic neutrino-proton scattering. We have computed the perturbative QCD corrections to three loops for the harged current structure functions F_2, F_L and F_3 for the combination nu P - nubar P. In leading twist approximation we have calculated the first six odd-integer Mellin moments in the case of F_2 and F_L and the first six even-integer moments in the case of F_3. As a new result we have obtained the coefficient functions to O(alpha_s^3) and we have found the corresponding anomalous dimensions to agree with known results in the literature.Comment: Contribution to the proceedings of the conference DIS 2007, Munich, April 200

First principles characterization of reversible martensitic transformations

Reversible martensitic transformations (MTs) are the origin of many fascinating phenomena, including the famous shape memory effect. In this work, we present a fully ab initio procedure to characterize MTs in alloys and to assess their reversibility. Specifically, we employ ab initio molecular dynamics data to parametrize a Landau expansion for the free energy of the MT. This analytical expansion makes it possible to determine the stability of the high- and low-temperature phases, to obtain the Ehrenfest order of the MT, and to quantify its free energy barrier and latent heat. We apply our model to the high-temperature shape memory alloy Ti-Ta, for which we observe remarkably small values for the metastability region (the interval of temperatures in which the high-and low-temperature phases are metastable) and for the barrier: these small values are necessary conditions for the reversibility of MTs and distinguish shape memory alloys from other materials

Laurent series expansion of a class of massive scalar one-loop integrals up to {\cal O}(\ep^2) in terms of multiple polylogarithms

In a recent paper we have presented results for a set of massive scalar one-loop master integrals needed in the NNLO parton model description of the hadroproduction of heavy flavors. The one--loop integrals were evaluated in n=4-2\ep dimension and the results were presented in terms of a Laurent series expansion up to {\cal O}(\ep^2). We found that some of the \ep^2 coefficients contain a new class of functions which we termed the $L$ functions. The $L$ functions are defined in terms of one--dimensional integrals involving products of logarithm and dilogarithm functions. In this paper we derive a complete set of algebraic relations that allow one to convert the $L$ functions of our previous approach to a sum of classical and multiple polylogarithms. Using these results we are now able to present the \ep^2 coefficients of the one-loop master integrals in terms of classical and multiple polylogarithms.Comment: 32 pages, Latex, references added, matches published versio

Beyond Heavy Top Limit In Higgs Boson Production At LHC

QCD corrections to inclusive Higgs boson production at the LHC are evaluated at next-to-next-to leading order. By performing asymptotic expansion of the cross section near the limit of infinitely heavy top quark we obtained a few first top mass-suppressed terms. The corrections to the hadronic cross sections are found to be small compared to the scale uncertainty, thus justifying the use of heavy top quark approximation in many published results.Comment: Talk at Moriond QCD 2010 conference, La Thuile, March 13-20 201

Neural network based path collective variables for enhanced sampling of phase transformations

We propose a rigorous construction of a 1D path collective variable to sample structural phase transformations in condensed matter. The path collective variable is defined in a space spanned by global collective variables that serve as classifiers derived from local structural units. A reliable identification of local structural environments is achieved by employing a neural network based classification. The 1D path collective variable is subsequently used together with enhanced sampling techniques to explore the complex migration of a phase boundary during a solid-solid phase transformation in molybdenum