Related papers: Four Lectures on the Physics of Crystal Growth
We consider a model to describe stable configurations in epitaxial growth of crystals in the two dimensional case, and in the regime of linearized elasticity. The novelty is that the model also takes into consideration the adatom density on…
This paper provides an elementary introduction to the basic concepts used in describing epitaxial crystal growth in terms of the thermodynamics and kinetics of atomic steps. Selected applications to morphological instabilities of stepped…
A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales…
The planar front of a growing a crystal is often destroyed by instabilities. In the case of growth from a condensed phase, the most frequent ones are diffusion instabilities, which will be but briefly discussed in simple terms in chapter…
We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…
The nucleation and/or growth of cracks in elastic-brittle solids has been recently described in [14] in terms of a special class of measures and with a variational technique requiring the minimization of a certain energy over classes of…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…
We study the conditions under which and how an imposed cluster of fixed colloidal particles at prescribed positions triggers crystal nucleation from a metastable colloidal fluid. Dynamical density functional theory of freezing and Brownian…
The role of step edge diffusion (SED) in epitaxial growth is investigated. To this end we revisit and extend a recently introduced simple cubic solid-on-solid model, which exhibits the formation and coarsening of pyramid or mound like…
A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter. At a discrete level, the evolution has a "checkerboard" structure and its…
According to classical nucleation theory, a crystal grows from a small nucleus that already bears the symmetry of its end phase - but experiments with colloids now reveal that, from an amorphous precursor, crystallites with different…
We report the results of computer simulations of epitaxial growth in the presence of a large Schwoebel barrier on different crystal surfaces: simple cubic(001), bcc(001), simple hexagonal(001) and hcp(001). We find, that mounds coarse by a…
Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical…
Growth in crystals can be { usually } described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics…
We describe a novel crystal growth instability that enhances the development of thin edges, promoting the formation of plate-like or hollow columnar morphologies. This instability arises when diffusion-limited growth is coupled with…
In this paper, we'll answer several abstract, formal questions about the nature of crack growth and nucleation. Bringing a field theory point of view to fracture illuminates things in what I hope will be an entertaining way. Formally, what…
Classical theories of crystal nucleation and growth from the liquid assume activated processes that are interface limited, with the atoms individually joining the growing interface by jumps that occur at a rate that is determined by the…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
Crystal growth has been widely studied for many years, and, since the pioneering work of Burton, Cabrera and Frank, spirals and target patterns on the crystal surface have been understood as forms of tangential crystal growth mediated by…
This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the…