arXiv subjects

Paul N. Patrone

Publications and source records attributed to Paul N. Patrone.

21 records · Page 2Linked to original sources

arXiv2016

Towards a high-supersaturation theory of crystal growth: Nonlinear one-step flow model in 1+1 dimensions

Starting with a many-atom master equation of a kinetic, restricted solid-on-solid (KRSOS) model with external material deposition, we investigate nonlinear aspects of the passage to a mesoscale description for a crystal surface in 1+1 dimensions. This latter description focuses on the motion of an atomic line defect (i.e. a step), which is defined via appropriate statistical average over KRSOS microstates. Near thermodynamic equilibrium and for low enough supersaturation, we show that this mesoscale picture is reasonably faithful to the Burton-Cabrera-Frank (BCF) step-flow model. More specifically, we invoke a maximum principle in conjunction with asymptotic error estimates to derive the elements of the BCF model: (i) a diffusion equation for the density of adsorbed adatoms; (ii) a step velocity law; and (iii) a linear relation for the mass flux of adatoms at the step. In this vein, we also provide a criterion by which the adatom flux remains linear in supersaturation, suggesting a range of non-equilibrium conditions under which the BCF model remains valid. Lastly, we make use of kinetic Monte Carlo simulations to numerically study effects that drive the system to higher supersaturations -- e.g. deposition of material onto the surface from above. Using these results, we describe empirical corrections to the BCF model that amount to a nonlinear relation for the adatom flux at the step edge.

cond-mat.mes-hall↗

arXiv2016

Estimation and Uncertainty Quantification of Yield Via Strain Recovery Simulations

In computational materials science, predicting the yield strain of crosslinked polymers remains a challenging task. A common approach is to identify yield via the first critical point of stress-strain curves produced by molecular dynamics simulations. However, the simulated data can be excessively noisy, making it difficult to extract meaningful results. In this work, we discuss an alternate method for identifying yield on the basis of residual strain computations. Notably, the associated raw data produce a sharper signal for yield through a transition in their global behavior. As we show, this transition can be analyzed in terms of simple functions (e.g. hyperbolas) that admit straightforward uncertainty quantification techniques.

cond-mat.soft↗

arXiv2015

From atoms to steps: The microscopic origins of crystal evolution

The BCF theory of crystal growth has been successful in describing a wide range of phenomena in surface physics. Typical crystal surfaces are slightly misoriented with respect to a facet plane; thus, the BCF theory views such systems as composed of staircase-like structures of steps separating terraces. Adsorbed atoms (adatoms), which are represented by a continuous density, diffuse on terraces, and steps move by absorbing or emitting these adatoms. Here we shed light on the microscopic origins of the BCF theory by deriving a simple, one-dimensional (1D) version of the theory from an atomistic, kinetic restricted solid-on- solid (KRSOS) model without external material deposition. We define the time-dependent adatom density and step position as appropriate ensemble averages in the KRSOS model, thereby exposing the non-equilibrium statistical mechanics origins of the BCF theory. Our analysis reveals that the BCF theory is valid in a low adatom-density regime, much in the same way that an ideal gas approximation applies to dilute gasses. We find conditions under which the surface remains in a low-density regime and discuss the microscopic origin of corrections to the BCF model.

cond-mat.mes-hall↗