Dr. rer. nat. from the University of Stuttgart Diploma from the École Polytechnique Fédérale de Lausanne (EPFL) Supervisors: E. Sigmund (PhD), P.A. Martin (diploma), and V.Z. Kresin (postdoc) Address: 1250 Bellflower Blvd. Long Beach, CA 90840-9505 USA
The micromorphology of solids impacts in an essential way their mechanical, electronic, optical o... more The micromorphology of solids impacts in an essential way their mechanical, electronic, optical or magnetic properties. Hence, it is an important task to characterize properly the granularity of materials. One central quantity providing such information is the grain size distribution. We propose an analytical derivation of this distribution during the random nucleation and growth crystallization process of a d-dimensional solid (d=1,2,3). We describe how the grain size distribution evolves from early stages of crystallization to its final form when complete crystallization is achieved. We also discuss the remarkable result that for certain classes of nucleation and growth rates the asymptotic limit of large times is a logarithmic-normal (lognormal) type distribution. Finally, we apply the theory to the time-evolution of the grain size distribution during solid-phase crystallization of Si-films.
Physical Review B Condensed Matter and Materials Physics, Jul 4, 2002
Using density-functional methods, we calculated structural and electronic properties of bulk chlo... more Using density-functional methods, we calculated structural and electronic properties of bulk chloroform- and bromoform-intercalated C60,C60.2CHX3 (X=Cl, Br). Both compounds are narrow-band insulator materials with a gap between valence and conduction bands larger than 1 eV. The calculated widths of the valence and conduction bands are 0.4-0.6 eV and 0.3-0.4 eV, respectively. The orbitals of the haloform molecules overlap with the π orbitals of the fullerene molecules, and the p-type orbitals of halogen atoms significantly contribute to the valence and conduction bands of C60.2CHX3. Charging with electrons and holes turns the systems to metals. Contrary to expectation, 10-20 % of the charge is on the haloform molecules and is thus not completely localized on the fullerene molecules. Calculations on different crystal structures of C60.2CHCl3 and C60.2CHBr3 revealed that the density of states at the Fermi energy are sensitive to the orientation of the haloform and C60 molecules. At a charging of three holes, which corresponds to the superconducting phase of pure C60 and C60.2CHX3, the calculated density of states (DOS) at the Fermi energy increases in the sequence DOS (C60)<DOS (C60.2CHCl3)<DOS (C60.2CHBr3).
The logarithmic-normal (lognormal) distribution is one of the most frequently observed distributi... more 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. However, a derivation of this distribution from first principles is lacking. We propose a differential equation governing the time development of grain size distribution in random nucleation and growth processes. The solution of this equation provides an analytical derivation of size distributions that has a form of the lognormal type. The resulting expression is used to discuss the grain size distribution of solid phase crystallized Si-films.
A differential equation involving a third or fourth degree polynomial may be rewritten in terms o... more A differential equation involving a third or fourth degree polynomial may be rewritten in terms of one of three elliptic integrals. These integrals can be inverted to define the Jacobi Elliptic Functions. An application of these functions is to solve non-linear second order differential equations involving circular trigonometric functions sine and cosine. We present solutions of problems in three different areas of physics that have similar Langrangian and associated Euler-Lagrange equations: the bead on a hoop, the Usadel equation of a dirty superconductor and the magnetization twist in a single magnetic layer. We discuss what type of solutions are obtained for these problems and how they relate to each other.
Exchange springs (soft FM/hard FM bilayer) are nowadays implemented as basic elements in magnetic... more Exchange springs (soft FM/hard FM bilayer) are nowadays implemented as basic elements in magnetic recording heads and magnetic random access memories (MRAM). However, it remains a challenge to describe accurately their physics. We present analytical expressions for the magnetization profile of an exchange spring with arbitrary layer thicknesses and material parameters (exchange coupling and anisotropy). This allows us to analyze in detail the mechanisms governing magnetization reversal under an external field. In particular, we show how the interface coupling induces a twist of the hard layer well below its intrinsic reversal field, in agreement with recent experimental observations. We describe in detail the reversible and irreversible parts of the hysteresis loop and identify the barrier between different magnetization states. This allows us to discuss the effect of thermal fluctuations on the magnetization reversal process. Finally, we find a crossover between power-law and exponential behaviour of the coercivity as a function of layer thickness and material parameters.
The micromorphology of solids impacts in an essential way their mechanical, electronic, optical o... more The micromorphology of solids impacts in an essential way their mechanical, electronic, optical or magnetic properties. Hence, it is an important task to characterize properly the granularity of materials. One central quantity providing such information is the grain size distribution. We propose an analytical derivation of this distribution during the random nucleation and growth crystallization process of a d-dimensional solid (d=1,2,3). We describe how the grain size distribution evolves from early stages of crystallization to its final form when complete crystallization is achieved. We also discuss the remarkable result that for certain classes of nucleation and growth rates the asymptotic limit of large times is a logarithmic-normal (lognormal) type distribution. Finally, we apply the theory to the time-evolution of the grain size distribution during solid-phase crystallization of Si-films.
Physical Review B Condensed Matter and Materials Physics, Jul 4, 2002
Using density-functional methods, we calculated structural and electronic properties of bulk chlo... more Using density-functional methods, we calculated structural and electronic properties of bulk chloroform- and bromoform-intercalated C60,C60.2CHX3 (X=Cl, Br). Both compounds are narrow-band insulator materials with a gap between valence and conduction bands larger than 1 eV. The calculated widths of the valence and conduction bands are 0.4-0.6 eV and 0.3-0.4 eV, respectively. The orbitals of the haloform molecules overlap with the π orbitals of the fullerene molecules, and the p-type orbitals of halogen atoms significantly contribute to the valence and conduction bands of C60.2CHX3. Charging with electrons and holes turns the systems to metals. Contrary to expectation, 10-20 % of the charge is on the haloform molecules and is thus not completely localized on the fullerene molecules. Calculations on different crystal structures of C60.2CHCl3 and C60.2CHBr3 revealed that the density of states at the Fermi energy are sensitive to the orientation of the haloform and C60 molecules. At a charging of three holes, which corresponds to the superconducting phase of pure C60 and C60.2CHX3, the calculated density of states (DOS) at the Fermi energy increases in the sequence DOS (C60)<DOS (C60.2CHCl3)<DOS (C60.2CHBr3).
The logarithmic-normal (lognormal) distribution is one of the most frequently observed distributi... more 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. However, a derivation of this distribution from first principles is lacking. We propose a differential equation governing the time development of grain size distribution in random nucleation and growth processes. The solution of this equation provides an analytical derivation of size distributions that has a form of the lognormal type. The resulting expression is used to discuss the grain size distribution of solid phase crystallized Si-films.
A differential equation involving a third or fourth degree polynomial may be rewritten in terms o... more A differential equation involving a third or fourth degree polynomial may be rewritten in terms of one of three elliptic integrals. These integrals can be inverted to define the Jacobi Elliptic Functions. An application of these functions is to solve non-linear second order differential equations involving circular trigonometric functions sine and cosine. We present solutions of problems in three different areas of physics that have similar Langrangian and associated Euler-Lagrange equations: the bead on a hoop, the Usadel equation of a dirty superconductor and the magnetization twist in a single magnetic layer. We discuss what type of solutions are obtained for these problems and how they relate to each other.
Exchange springs (soft FM/hard FM bilayer) are nowadays implemented as basic elements in magnetic... more Exchange springs (soft FM/hard FM bilayer) are nowadays implemented as basic elements in magnetic recording heads and magnetic random access memories (MRAM). However, it remains a challenge to describe accurately their physics. We present analytical expressions for the magnetization profile of an exchange spring with arbitrary layer thicknesses and material parameters (exchange coupling and anisotropy). This allows us to analyze in detail the mechanisms governing magnetization reversal under an external field. In particular, we show how the interface coupling induces a twist of the hard layer well below its intrinsic reversal field, in agreement with recent experimental observations. We describe in detail the reversible and irreversible parts of the hysteresis loop and identify the barrier between different magnetization states. This allows us to discuss the effect of thermal fluctuations on the magnetization reversal process. Finally, we find a crossover between power-law and exponential behaviour of the coercivity as a function of layer thickness and material parameters.
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Papers by Andreas Bill