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Stimulated emission and lasing can be achieved easily in a number of semiconductor nanostructures. This chapter gives an overview of a series of physical mechanisms that were found experimentally to give rise to positive optical gain in quantum wells, quantum wires and nanocrystals. In quantum wells, these are radiative recombination of localized excitons, LO-phonon assisted exciton recombination and electron–hole plasma luminescence. In quantum wires the data are rather scarce; localized excitons and electron–hole plasma appears to be involved in lasing. Separately treated are the cases of nanocrystals dispersed randomly in a matrix and that of heterostructures with ordered quantum dots (grown by Stranski–Krastanow method). Exciton and biexciton mechanisms of optical gain in quantum dots are analyzed. The crucial competing role of Auger recombination is expressed via the filling factor. Prospects of random lasing in semiconductor nanostructures are outlined.

Graphite intercalation compounds (GICs) have unique layered structures where intercalate layers are arranged periodically between graphite layers. This phenomenon is known as staging, and the number of graphite layers between adjacent intercalate layers is known as the stage number n. As the stage number n increases, the separation between adjacent intercalate layers becomes larger. So the interlayer interactions between intercalate layers become weak, leading to a crossover of dimensionality from three-dimensional (3D) to two-dimensional (2D). Because of their intrinsic anisotropy, GICs exhibit a great variety of structural orderings such as staging, in-plane ordering of intercalate layers, and stacking ordering of both graphite and intercalate layers. The stable stage and in-plane ordering of the intercalate layers depend on the relative strength of the intercalate-graphite interaction to the intercalate-intercalate interaction. At low temperatures the intercalate layers form a variety of 2D superlattices resulting from the competing interactions. At elevated temperatures the superlattice undergoes a transition to a 2D liquid. The migration of intercalate atoms is restricted to the 2D gallery between graphite layers. The critical temperature below which the stacking order appears is equal to or lower than the critical temperature below which the in-plane order appears. In this chapter, we review the subject of structures, phase transitions, and kinetics for donor and acceptor GICs. The subject matter of this chapter is organized as follows. Section 3.1 deals with the general structural characteristics of GICs. Sections 3.2 and 3.3 are respectively devoted to descriptions of liquid state and phase transitions of stage-2 alkali metal GICs. Section 3.4 deals with the discommensuration domain model for high-stage alkali metal GICs. Sections 3.5 and 3.6 are devoted to descriptions of liquid-solid transitions in stage-1 K and Rb GIC. In Sections 3.7-3.9, we describe the stage transition, Kirczenow’s model, Hendricks-Teller-type stage disorder, and fractional stage. In Sections 3.10 and 3.11 we describe the phase transitions of acceptor-type GICs (Br2 GIC and SbCl5 GIC). Section 3.12 treats the ordering kinetics in K GIC and SbCl5 GIC.