First-principles based computation of lattice dynamics in substitutionally disordered alloys

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The computation of phonon spectra in disordered alloys in an accurate and reliable way has been a longstanding problem in the area of condensed matter research. Available theoretical tools so far did not have the necessary ingredients to treat the mass, the force-constant and the environmental disorders on an equal footing. In this thesis, we have worked on the development of new first-principles based formalisms to alleviate these problems. Within the framework of first-principles electronic structure formalisms, the disordered alloy is usually modelled by a large supercell, thus making the computation of lattice dynamics prohibitively demanding. In this thesis, we, therefore, have adopted various strategies to model the interatomic force-constants of a disordered alloy based upon the results of computation of dynamical matrices on smaller systems. These are then used in the computation of configurationaveraged quantities by the recently developed Itinerant Coherent Potential Approximation (ICPA), an analytic, self-consistent, translationally invariant formalism which treats the three kinds of disorder relevant for lattice dynamics on equal footing. Thus, we arrive at formalisms which seamlessly integrate the first-principles electronic structure based methodologies with the methods for configuration-averaging with reliable accuracy. Major part of the thesis deals with a modeling strategy based on transferable force constant (TFC) model which suggests that Dforce constant vs bond lengthD relationship for a given chemical bond, which can be obtained from a small number of first-principles calculations, is transferable across different structures. We combine it with the ICPA to propose DFPT-TFC-ICPA, a new first-principles based tool, which is used extensively in this thesis to calculate the complete phonon spectra and associated quantities for a wide variety of alloys which involve magnetic type-II alloys (FexPd1Dx) and alloys with significant mass and size differences among the constituents (CuxPd1Dx, CuxAu1Dx and NixPt1Dx). Our motivations are different in each of these systems. While in FexPd1Dx, the role of force constant disorder among various pairs of species on the phonon spectra is discussed in detail, the focus in Cu0.715Pd0.285 and Cu0.75Au0.25 has been a thorough investigation of the influence of size mismatch of end-point components on the phonon dispersions. In NixPt1Dx alloys, the origin of the experimentally observed anomalous features in the phonon branches is investigated by computing the lattice dynamics for the alloy system at various compositions. Substantial discrepancy between our calculated results and those obtained by the experiments, in case of Ni0.25Pt0.75, however, propelled us to find an alternative modeling strategy which has the ability to treat environmental disorder (e.g short-range order) in a better way. An improved modeling scheme is thereafter realized by adopting the Dspecial quasirandom structureD (SQS) to model the random environment in a disordered alloy. We demonstrate this new formalism, which is a combination of SQS and ICPA, by computing the phonon spectra of Ni0.5Pt0.5. The better agreement of our results with the experiments over previous models of disorder suggests that the SQS+ICPA formalism can serve as a tractable first-principles based computational tool to address the issues in a....
Supervisor: Subhradip Ghosh