Heterogenous nucleation and microstructure formation—a scale- and system-bridging approach

Abstract

Scope and aim of this volume.Nucleation and initial microstructure formation play an important role in almost all aspects of materials science [1–5]. The relevance of the prediction and control of nucleation and the subsequent microstructure formation is fully accepted across many areas of modern surface and materials science and technology. One reason is that a large range of material properties, from mechanical ones such as ductility and hardness to electrical and magnetic ones such as electric conductivity and magnetic hardness, depend largely on the specific crystalline structure that forms in nucleation and the subsequent initial microstructure growth. A very demonstrative example for the latter is the so called bamboo structure of an integrated circuit, for which resistance against electromigration [6] , a parallel alignment of grain boundaries vertical to the direction of electricity, is most favorable. Despite the large relevance of predicting and controlling nucleation and the subsequent microstructure formation, and despite significant progress in the experimental analysis of the later stages of crystal growth in line with new theoretical computer simulation concepts [7], details about the initial stages of solidification are still far from being satisfactorily understood. This is in particular true when the nucleation event occurs as heterogenous nucleation.The Priority Program SPP 1296 'Heterogenous Nucleation and Microstructure Formation—a Scale- and System-Bridging Approach' [8] sponsored by the German Research Foundation, DFG, intends to contribute to this open issue via a six year research program that enables approximately twenty research groups in Germany to work interdisciplinarily together following this goal. Moreover, it enables the participants to embed themselves in the international community which focuses on this issue via internationally open joint workshops, conferences and summer schools. An outline of such activities can be found in [8]. Furthermore, the honorable invitation to publish a special issue in Journal of Physics: Condensed Matter dedicated to the Priority Program's topic allows the obtained results to be communicated to relevant international colleagues, which stimulates further interest and encourages future collaborations.The issue comprises the research results of the participants during the first two year period of the Priority Program as well as that of the international referees of the program.Now, what precisely is the research concept of the Priority Program and thus, what are the articles in this special issue dedicated to?Ever since the pioneering work of Volmer and Weber [9], Becker and Döring [10] as well as Turnbull and Fisher [11] nucleation has been modelled more or less phenomenologically. These traditional models describe nucleation by stochastic processes of single atoms, respectively, molecules, which attach at primary droplets. Those thereby growing droplets become stable by reaching a critical size. This concept has largely been em...

Polar liquid crystals in two spatial dimensions: The bridge from microscopic to macroscopic modeling

“…The prefactors are moments of various direct correlation functions and therefore provide the link towards microscopic correlations. This is similar in spirit to PFC models [25,[43][44][45][46]53] for spherical particles.…”

“…The second level which may be called mesoscopic is the phase-field approach where lowest-order gradients of an order-parameter field are considered [41]. This can be performed up to fourthorder gradients in order to describe a stable crystalline state with order-parameter oscillations leading to the seminal PFC model of Elder and co-workers [42][43][44]. The prefactors can be brought into relation with the microscopic DFT approach [25,45].…”

Stability of liquid crystalline phases in the phase-field-crystal model

“…Crystallization and melting processes (see e.g. [1,2]) can be efficiently modelled within the so-called phasefield-crystal (PFC) model [3][4][5] which is basically a Landau-type theory with a conserved position-dependent order parameter which is gradient-expanded up to fourth order. Stable periodic oscillations in the order are interpreted as crystalline density fields.…”

Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model

“…For Brownian particles, the density-functional approach can be generalized towards dynamics [15][16][17] and the dynamics of solidification has been examined in two dimensions [18,19]. Similarly, a more coarse-grained phase-field-crystal model * sven@princeton.edu † cristian.v.achim@gmail.com ‡ hlowen@thphy.uni-duesseldorf.de has been proposed to describe crystal growth [20][21][22][23] and the defect structure and dynamics for various applications; see, e.g., Refs. [24][25][26][27][28][29][30][31][32][33][34].…”