Quantifying and Understanding Anharmonicity of Engineering Materials in Real and Reciprocal Space
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The complex interactions between phonon-phonon, phonon-electron, phonon-magnon, and many other collective excitations and quasi-particles are often responsible for deviation of crystalline material from harmonic behavior, and a source of non-harmonic behavior. Understanding this intricate intercommunication within lattice structure is essential to develop/deepen our knowledge of sophisticated compounds with unusual material properties. In this thesis, we have investigated the interplay of different excitations to quantify and better comprehend the non-harmonic dynamics of crystal in both real and reciprocal space for a wide range of engineering materials. To explore the harmonic/non-harmonic behavior of materials in real space, we have developed the 'Phonon Analysis in Real Space' (PARS) package. Using PARS we have analyzed the interatomic force interaction range, the temperature dependence of Born-von Karman force constants, and Kohn anomaly in experimentally measured phonon dispersion of niobium. The results have indicated long range interactions with strong temperature dependence. Moreover, artificial tailoring of Kohn anomaly have revealed that due to the presence of electron-phonon coupling, the electron charge density is localized along the radial vector joining the two atoms. Furthermore, based on thermodynamic principles, we have derived the vibrational non-harmonic behavior from experimental thermal expansion coefficient and inelastic neutron scattering measurements, and have inferred that the inherent interdependence of thermodynamic quantities are affected by lattice anharmonicity in ways that are not entirely understood yet. Within the present framework, we have quantified the harmonic, quasi-harmonic, anharmonic, and dilational vibrational contribution to free energy, internal energy, and entropy of aluminum, tin-selenide, and scandium tri-fluoride to understand the dynamics of various competing thermodynamic forces and the role of phonon-phonon interaction in determining unusual material behavior. These three materials are governed by very different lattice dynamics. While aluminum can be described with quasi-harmonic approximations, orbitally driven lattice instability in tin-selenide, and large negative thermal expansion coefficient in scandium tri-fluoride leads to exceptionally high vibrational anharmonicity. Total vibrational anharmonic contribution to entropy, internal energy, and free energy have been calculated to be ∼ -0.80 K B , -24 meV and 21 meV per unit cell (8 atoms) at 648K in tin-selenide, and ∼ -2 K B , -70 meV and 100 meV per cubic unit cell (4 atoms) at 750K in scandium tri-fluoride. For comparison, in elemental aluminum these values are ∼ -0.16 K B , -6 meV and 3.2 meV per conventional FCC unit cell (4 atoms) at 600K. Additionally, to examine the large difference in thermoelectric performance of two group IV-VI compounds - tin-selenide and tin-sulfide, using experimental inelastic neutron scattering, we have mapped the four dimensional Q-E space in both materials. With detailed analysis in real and reciprocal space of structural configurational, anisotropy, Born-von Karman force constants, Grüneisen parameter tensor, partial and total density of states, we have shown that both tin-selenide and tin-sulfide have qualitatively and quantitatively very similar features, and large differences in thermoelectric performance is primarily related to the presence of heavy and lighter atoms in the two materials. For their computational efficiency, to calculate various material properties at a large length scale ranging from 100 nm to 1000 μm, continuum mechanics based theories have inherent advantage over experimental inelastic neutron/x-ray scattering and first principle calculations. Within the framework of continuum mechanics based consistent skew-symmetric couple stress theory, linear elastic mechanical behavior of cubic crystals at a length scale of 100 nm to 1000 μm can be described using four independent parameters. Three parameters A 11 , A 12 , and A 44 are associated to bulk material properties, while a fourth parameter η defines the characteristic length scale of the material. We have studied the large wavelength phonon dispersion in four cubic single crystals (NaCl, KCl, Cu and CuZn) with ultrasonic excitations, and have reported the length scale parameter l, associated with η, for NaCl, KCl, Cu and CuZn to be ∼ 28 μm, 39 μm, 23 μm, and 16 μm, respectively.