Andreas Bill

On the origin of logarithmic-normal distributions : An analytical derivation, and its application to nucleation and growth processes

The logarithmic-normal (lognormal) distribution is one of the most frequently observed distributions in nature and describes a large number of physical, biological and even sociological phenomena. The origin of this distribution is therefore of broad interest but a general derivation from basic principles is still lacking. Using random nucleation and growth to describe crystallization processes we derive the time development of grain-size distributions. Our derivation provides, for the first time, an analytical expression of the size distribution in the form of a lognormal type distribution. We apply our results to the grain-size distribution of solid phase crystallized Si-films.

Time-evolution of grain size distributions in random nucleation and growth crystallization processes

We study the time dependence of the grain size distribution

Cascading proximity effects in rotating magnetizations

N(\mathbf{r},t)

The Grain Size Distribution in Crystallization Processes With Anisotropic Growth Rate

during crystallization of a

Electronic Phase Separation and Electron–Phonon Coupling in Cuprate Superconductors

d

Effects from magnetic boundary conditions in superconducting-magnetic proximity systems

-dimensional solid. A partial differential equation, including a source term for nuclei and a growth law for grains, is solved analytically for any dimension

Nonequilibrium grain size distribution with generalized growth and nucleation rates

d

Electronic Inhomogeneities and Pairing from Unscreened Interactions in High- T c Superconductors

. We discuss solutions obtained for processes described by the Kolmogorov-Avrami-Mehl-Johnson model for random nucleation and growth (RNG). Nucleation and growth are set on the same footing, which leads to a time-dependent decay of both effective rates. We analyze in detail how model parameters, the dimensionality of the crystallization process, and time influence the shape of the distribution. The calculations show that the dynamics of the effective nucleation and effective growth rates play an essential role in determining the final form of the distribution obtained at full crystallization. We demonstrate that for one class of nucleation and growth rates, the distribution evolves in time into the logarithmic-normal (lognormal) form discussed earlier by Bergmann and Bill [J. Cryst. Growth 310, 3135 (2008)]. We also obtain an analytical expression for the finite maximal grain size at all times. The theory allows for the description of a variety of RNG crystallization processes in thin films and bulk materials. Expressions useful for experimental data analysis are presented for the grain size distribution and the moments in terms of fundamental and measurable parameters of the model.

Phonon renormalization and symmetry of the superconducting order parameter.

We demonstrate two effects that occur in all diffusive superconducting-magnetic heterostructures with rotating magnetization: the reappearance of singlet correlations deep in the magnetic material and a cascade of s = 1, components (in the two spin- basis ). We do so by examining the order parameter and Josephson current through a multilayer with five mutually perpendicular ferromagnets. The properties of the middle layer determine whether the current is due to m = 0 or contributions. We conclude that so-called long- and short-range components are present across a proximity system with rotating magnetization.

Classical Mechanical Analogies in Wide Dirty SFS Junctions

The grain size distribution allows characterizing quantitatively the microstructure at different stages of crystallization of an amorphous solid. We propose a generalization of the theory we established for spherical grains to the case of grains with ellipsoidal shape. We discuss different anisotropic growth mechanisms of the grains in thin films. An analytical expression of the grain size distribution is obtained for the case where grains grow through a change of volume while keeping their shape invariant. The resulting normalized grain size distribution is shown to be affected by anisotropy through the time-decay of the effective growth rate.