▪ Abstract Solution phase syntheses and size-selective separation methods to prepare semiconductor and metal nanocrystals, tunable in size from ∼1 to 20 nm and monodisperse to ≤5%, are presented. Preparation of monodisperse samples enables systematic characterization of the structural, electronic, and optical properties of materials as they evolve from molecular to bulk in the nanometer size range. Sample uniformity makes it possible to manipulate nanocrystals into close-packed, glassy, and ordered nanocrystal assemblies (superlattices, colloidal crystals, supercrystals). Rigorous structural characterization is critical to understanding the electronic and optical properties of both nanocrystals and their assemblies. At inter-particle separations 5–100 A, dipole-dipole interactions lead to energy transfer between neighboring nanocrystals, and electronic tunneling between proximal nanocrystals gives rise to dark and photoconductivity. At separations <5 A, exchange interactions cause otherwise insulating ass...

Synthesis and Characterization of Monodisperse Nanocrystals and Close-Packed Nanocrystal Assemblies

https://iopscience.iop.org/article/10.1088/0034-4885/12/1/308/pdf

Theory of the oxidation of metals

The purpose of this article is to describe the basic physical processes involved in the nucleation and growth of thin films of materials on solid surfaces. In this introduction the three modes of crystal growth which are thought to occur on surfaces in the absence of interdiffusion are described, and the relationships between the thermodynamics of adsorption and the kinetics of crystal growth are explored in general terms. This is followed by a brief review of atomistic nucleation theory, explaining the relations of such theories to experimental observables. In the next three sections, recent experimental examples of these three growth modes are given, which are interpreted where possible in terms of nucleation and growth theory. The last section discusses observations on the shapes of growing crystallites and the relation of such observations to nucleation and surface diffusion processes.

https://iopscience.iop.org/article/10.1088/0034-4885/47/4/002/pdf

Nucleation and growth of thin films

Dislocations are common defects in solids, yet all crystals begin as dislocation-free nuclei. The mechanisms by which dislocations form during early growth are poorly understood. When nanocrystalline materials grow by oriented attachment at crystallographically specific surfaces and there is a small misorientation at the interface, dislocations result. Spiral growth at two or more closely spaced screw dislocations provides a mechanism for generating complex polytypic and polymorphic structures. These results are of fundamental importance to understanding crystal growth.

http://science.sciencemag.org/content/sci/281/5379/969.full.pdf

Imperfect Oriented Attachment: Dislocation Generation in Defect-Free Nanocrystals

Level set methods: an overview and some recent results

Parts I and II deal with the theory of crystal growth, parts III and IV with the form (on the atomic scale) of a crystal surface in equilibrium with the vapour. In part I we calculate the rate of advance of monomolecular steps (i.e. the edges of incomplete monomolecular layers of the crystal) as a function of supersaturation in the vapour and the mean concentration of kinks in the steps. We show that in most cases of growth from the vapour the rate of advance of monomolecular steps will be independent of their crystallographic orientation, so that a growing closed step will be circular. We also find the rate of advance for parallel sequences of steps. In part II we find the resulting rate of growth and the steepness of the growth cones or growth pyramids when the persistence of steps is due to the presence of dislocations. The cases in which several or many dislocations are involved are analysed in some detail; it is shown that they will commonly differ little from the case of a single dislocation. The rate of growth of a surface containing dislocations is shown to be proportional to the square of the supersaturation for low values and to the first power for high values of the latter. Volmer & Schultze’s (1931) observations on the rate of growth of iodine crystals from the vapour can be explained in this way. The application of the same ideas to growth of crystals from solution is briefly discussed. Part III deals with the equilibrium structure of steps, especially the statistics of kinks in steps, as dependent on temperature, binding energy parameters, and crystallographic orientation. The shape and size of a two-dimensional nucleus (i.e. an ‘island* of new monolayer of crystal on a completed layer) in unstable equilibrium with a given supersaturation at a given temperature is obtained, whence a corrected activation energy for two-dimensional nucleation is evaluated. At moderately low supersaturations this is so large that a crystal would have no observable growth rate. For a crystal face containing two screw dislocations of opposite sense, joined by a step, the activation energy is still very large when their distance apart is less than the diameter of the corresponding critical nucleus; but for any greater separation it is zero. Part IV treats as a ‘co-operative phenomenon’ the temperature dependence of the structure of the surface of a perfect crystal, free from steps at absolute zero. It is shown that such a surface remains practically flat (save for single adsorbed molecules and vacant surface sites) until a transition temperature is reached, at which the roughness of the surface increases very rapidly (‘ surface melting ’). Assuming that the molecules in the surface are all in one or other of two levels, the results of Onsager (1944) for two-dimensional ferromagnets can be applied with little change. The transition temperature is of the order of, or higher than, the melting-point for crystal faces with nearest neighbour interactions in both directions (e.g. (100) faces of simple cubic or (111) or (100) faces of face-centred cubic crystals). When the interactions are of second nearest neighbour type in one direction (e.g. (110) faces of s.c. or f.c.c. crystals), the transition temperature is lower and corresponds to a surface melting of second nearest neighbour bonds. The error introduced by the assumed restriction to two available levels is investigated by a generalization of Bethe’s method (1935) to larger numbers of levels. This method gives an anomalous result for the two-level problem. The calculated transition temperature decreases substantially on going from two to three levels, but remains practically the same for larger numbers.

The Growth of Crystals and the Equilibrium Structure of their Surfaces

THE theory of nucleation in the formation of liquid or solid phases from the vapour, the most detailed treatment of which in any published work is that by Becker and Doring1,2, is in satisfactory quantitative agreement with experiment with regard to the primary nucleation of liquid droplets1,3, which requires saturation ratios of from 3 to 6 in typical cases. The theory predicts further that the primary nucleation of a crystal from the vapour requires still larger saturation ratios, so that the critical conditions for nucleation of the liquid are reached first, unless working with very low vapour pressures far below the melting point. This is also in agreement with observation.

N. Cabrera

Papers

The Growth of Crystals and the Equilibrium Structure of their Surfaces

Role of Dislocations in Crystal Growth