Epitaxial TiN/NbN superlattices with wavelengths/ranging from 1.6 to 450 nm have been grown by reactive magnetron sputtering on MgO(100). Cross-sectional transmission electron microscopy (XTEM) studies showed well-defined superlattice layers. Voided low-angle boundaries, aligned perpendicular to the film plane, were also present. High-resolution images showed misfit dislocations for Λ = 9.4 nm, but not Λ = 4.6 nm. Up to ninth-order superlattice reflections were observed in diffraction, indicating that the interfaces were relatively sharp. Analysis of the first-order x-ray superlattice reflection intensities indicated that the composition modulation amplitude increased and the coherency strains decreased for Λ increased from 2 to 10 nm. Vickers microhardness H was found to increase rapidly with increasing Λ, from 1700 kg/mm2 for a TiN–NbN alloy (i.e., Λ = 0) to a maximum of 4900 kg/mm2 at Λ = 4.6 nm. H decreased gradually for further increases in Λ above 4.6 nm, to H = 2500 kg/mm2 at Λ = 450 nm. The hardness results are compared with theories for strengthening of multilayers.

Growth, structure, and microhardness of epitaxial TiN/NbN superlattices

Publisher Summary This chapter reviews current theoretical models applicable to concentrated solid solutions. It focuses on concentrated solutions because dilute ones can be considered as special cases and because the interesting effects of clustering and ordering are most apparent at high solute concentrations. The extended ranges of solubility are often found in metallic systems, and for this reason most examples selected will refer to metals and alloys, although the models presented are equally applied to off-stoichiometric compounds, metallic or inorganic, and to amorphous solids. The chapter provides description of the state of the order of the system through suitable averaging procedures. It discusses the internal energy of solutions, from both electronic and elastic standpoints. The chapter presents free energy models, such as generalized Bragg- Williams's model, Landau theory, and cluster variation method. These models are applied to the study of phase equilibrium.

Configurational Thermodynamics of Solid Solutions

The performance of solution processed polymer:fullerene thin film photovoltaic cells is largely determined by the nanoscopic and mesoscopic morphology of these blends that is formed during the drying of the layer. Although blend morphologies have been studied in detail using a variety of microscopic, spectroscopic, and scattering techniques and a large degree of control has been obtained, the current understanding of the processes involved is limited. Hence, predicting the optimized processing conditions and the corresponding device performance remains a challenge. We present an experimental and modeling study on blends of a small band gap diketopyrrolopyrrole- quinquethiophene alternating copolymer (PDPP5T) and [6,6]-phenyl-C 71-butyric acid methyl ester ([70]PCBM) cast from chloroform solution. The model uses the homogeneous Flory-Huggins free energy of the multicomponent blend and accounts for interfacial interactions between (locally) separated phases, based on physical properties of the polymer, fullerene, and solvent. We show that the spinodal liquid-liquid demixing that occurs during drying is responsible for the observed morphologies. The model predicts an increasing feature size and decreasing fullerene concentration in the polymer matrix with increasing drying time in accordance with experimental observations and device performance. The results represent a first step toward a predictive model for morphology formation. © 2013 American Chemical Society.

Predicting Morphologies of Solution Processed Polymer:Fullerene Blends

Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) behaviour of alloys. If the elastic moduli are different in the two phases, the elastic interactions may accelerate, slow down or even stop the phase separation process. If the material is elastically anisotropic, the precipitates can be shaped like plates or needles instead of spheres and can \sps arrange themselves into highly correlated patterns \cs. Tensions or compressions applied externally to the specimen may have a strong effect on the shapes and arrangement of the precipitates. In this paper, we review the main theoretical approaches that have been used to model these effects and we relate them to experimental observations. The theoretical approaches considered are (i) `macroscopic'' models treating the two phases as elastic media separated by a sharp interface (ii) `mesoscopic'' models in which the concentration varies continuously across the interface (iii) `microscopic'' models which use the positions of individual atoms.

Modelling of Phase Separation in Alloys with Coherent Elastic Misfit

Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) of alloys. If the elastic moduli are different in the two phases, the elastic interactions may accelerate, slow down or even stop the phase separation process. If the material is elastically anisotropic, the precipitates can be shaped like plates or needles instead of spheres and can form regular precipitate superlattices. Tensions or compressions applied externally to the specimen may have a strong effect on the shapes and arrangement of the precipitates. In this paper, we review the main theoretical approaches that have been used to model these effects and we relate them to experimental observations. The theoretical approaches considered are (i) `macroscopic' models treating the two phases as elastic media separated by a sharp interface (ii) `mesoscopic' models in which the concentration varies continuously across the interface (iii) `microscopic' models which use the positions of individual atoms.

https://arxiv.org/pdf/math-ph/9811019.pdf

H.E. Cook

Papers

The kinetics of clustering and short-range order in stable solid solutions

The influence of static atomic displacements on the diffuse intensity scattered by solid solutions