Teori för fononexcitationer i substitutionellt oordnade legeringar Theory of phonon excitations in substitutionally disordered alloys The study of elementary excitations (electrons, phonons,magnons) in complex materials having substitutional disorder is one of the emerging areas in computational materials science research as disorder is an important control parameter to tailor materials with target properties. Specifically, phonon spectra are essential for thermodynamic properties and hence phase diagrams. However, first principles calculation of phonon spectra in disordered alloys is a challenging problem due to difficulties in computing the inter-atomic interactions in a random environment. In this proposal, we aim to devise a unique formalism for lattice dynamics in disordered alloys combining first-principles electronic structure methods, physically realistic models of chemical disorder and an analytic mean-field based method for configuration averaging. The effects of short-range order, partial disorder and temperature on the vibrational properties will be studied to interpret the experimental results available for binary metallic alloys, multi-component shape memory alloys, multi-component semiconductor alloys, partially disordered perovskite ferroelectrics and doped multiferroic materials. One of the key objectives will be to build up a database of inter-atomic force constants to serve as a ready reference for the community. This collaboration between Uppsala University and IIT, Guwahati, India involves exchange visits, organization of schools to train young scholars and joint publications. A solid material can be visualized as a rigid crystalline lattice of large number of atoms where the atoms exert forces on one another so as to keep each atom near its equilibrium position. Due to the connections between the atoms, the displacement of one or more atoms from their stable positions will give rise to a set of vibration waves or phonons propagating through the solids. Each phonon is characterized by a wavelength and a frequency. The study of the frequency spectrum of phonons is an important part of solid state physics, because they contribute to the physical properties of materials such as structural stability, thermal and electrical conductivity. For example, propagation of a phonon with a given frequency may disturb the atomic arrangements in a solid significantly leading to an alteration of the crystal structure. Therefore, the stability of a given crystal structure against phonon excitations need be checked first before utilizing the material further. The propagation of phonons is also responsible for heat conduction in insulating materials and the properties of long-wavelength phonons give rise to sound in solids. It, therefore, becomes imperative for a materials scientist to explore the phonon spectra and relate the features with the materials properties. Alloys are materials known from time immortal for their usability in daily life. With the technological advancements, new class of alloys have been attempted to realize new materials with properties that can alter human lives in a significant way. For example, a new class of alloys called shape memory alloys tends to remember their original shapes. Such property has enabled one to use these alloys for various different purposes. Eyeglass frames made out of these alloys can be bent out of shape, yet they return to their parent shape upon heating. A deep fryer made out of these alloys utilizes the thermal sensitivity by lowering the basket into the oil at the correct temperature. Along with metallic alloys, semiconductor alloys too have significant impact on today´s world. It is well known that given the shrinking energy reserves of this planet, new sources of energy have been explored which can be used in a cost-effective manner to benefit the entire humankind. Devising solar cells which convert solar energy into electrical power has been one of the biggest achievements in recent times. The solar cells are made out of semiconductor alloys, for example. It is, however, observed that to increase functionality of the materials, it is necessary to introduce chemical disorder into the parent materials in a controlled way. In a chemically disordered material, a percentage of a certain component is replaced by another element. One example could be in the context of the solar cells with semiconductor materials. A solar cell´s ability to convert sunlight to electric current is limited by the band gap of the semiconductor. For example, semiconductors with wide band gaps respond only to the shorter wavelengths. In order to utilize the full solar spectrum, one therefore has to tune the band gap which can only be done by chemical substitution. Thus, the substitutional disorder must play a key role in the functionalities of the modern materials. This, therefore, leads the materials scientists to first understand the behavior of such materials with various degrees of disorder. The behavior of these materials under phonon excitations must be one of the primary areas one should explore as that is bound to affect the dynamical properties of the materials with target properties as has been explained earlier. In this backdrop, the present proposal carries immense significance as no such elaborate theoretical endeavor has yet been taken up in the community. Arrays of materials with emerging potentials for technological breakthrough have been chosen to match up with the demands of the industry. Our motivation to pinpoint the microscopic origins of the materials behavior by analyz