Normal mode decomposition of atomic motion in solids

Decomposition of atomic motion into individual normal modes has led to remarkable success in microscopically understanding thermal properties and thermodynamics in simple solids. We start this chapter with an example of decomposing atomic motion of a simple monatomic linear chain crystal into normal modes followed by a more general, classical normal mode formalism. Different classifications of normal modes such as phonons, propagons, diffusons, and locons are introduced. Finally, heat capacity and thermal conductivity predictions from the normal mode formalism are demonstrated

Propagating elastic vibrations dominate thermal conduction in amorphous silicon

Thermal atomic vibrations in amorphous solids can be distinguished by whether they propagate as elastic waves or do not propagate due to lack of atomic periodicity. In a-Si, prior works concluded that non-propagating waves are the dominant contributors to heat transport, while propagating waves are restricted to frequencies less than a few THz and are scattered by anharmonicity. Here, we present a lattice and molecular dynamics analysis of vibrations in a-Si that supports a qualitatively different picture in which propagating elastic waves dominate the thermal conduction and are scattered by elastic fluctuations rather than anharmonicity. We explicitly demonstrate the propagating nature of vibration with frequency approaching 10 THz using a triggered wave computational experiment. Our work suggests that most heat is carried by propagating elastic waves in a-Si and demonstrates a route to achieve extreme thermal properties in amorphous materials by manipulating elastic fluctuations

Thermal Conduction in Amorphous Materials and the Role of Collective Excitations

The atomic vibrations and thermal properties of amorphous dielectric solids are of fundamental and practical interest. For applications, amorphous solids are widely used as thermal insulators in thermopile and other detectors where low thermal conductivity directly sets the sensitivity of the detector. Amorphous solids are of fundamental interest themselves because the lack of atomic periodicity complicates theoretical development. As a result, the lower limits of thermal conductivity in solids as well as the nature of the vibrational excitations that carry heat remain active topics of research. In this thesis, we use numerical and experimental methods to investigate the thermal conduction in amorphous dielectrics. We begin by using molecular dynamics to investigate the thermal conductivity of amorphous nanocomposites. We find that mismatching the vibrational density of states of constituent materials in the composite is an effective route to achieve exceptionally low thermal conductivity in fully dense solids. We then transition to examining the properties of the atomic vibrations transporting heat in amorphous solids. For decades, normal mode methods have been used extensively to study thermal transport in amorphous solids. These methods naturally assume that normal modes are the fundamental vibrational excitations transporting heat. We examine the predictions from normal mode analysis that are now able to be tested against experiments, and we find that the predictions from these methods do not agree with experimental observations. For instance, normal mode methods predict that the low frequency normal modes are scattered by anharmonic interactions as in single crystalline solids. However, temperature dependent thermal conductivity measurements demonstrate a typical glassy temperature dependence inconsistent with normal modes scattering through anharmonic interactions. These discrepancies suggest that normal modes are not the fundamental heat carriers in amorphous dielectrics. To identify the actual heat carriers, we draw on fundamental concepts from many- body physics and inelastic scattering theory that dictate that the excitation energies of a many-body interacting system are given by the poles of the single-particle Green's function. The imaginary part of this function is proportional to the dynamic structure factor that is directly measured in inelastic scattering experiments. Collective excitations of a given energy and wavevector can thus be identified from peaks in the dynamic structure factor; their damping is given by the broadening of the peak. Using these concepts from many-body physics, the physical picture that emerges is that heat is carried in large part by a gas of weakly interacting collective excitations with a cutoff frequency that depends on the atomic structure and composition of the glass. We test this picture using numerical and experimental inelastic scattering measurements on amorphous silicon, a commonly studied amorphous solid. We observe collective excitations up to 10 THz, well into the thermal spectrum, and far higher than previous inelastic scattering measurements on other glasses. Our numerical and experimental evidence also confirms that the collective excitations are damped by structural disorder rather than anharmonic interactions and that they dominate the thermal conduction in amorphous silicon. Subsequent analysis shows that these high frequency acoustic excitations are supported in amorphous silicon due to a large sound velocity and monatomic composition, suggesting that other monatomic amorphous solids with large sound velocities may also support these thermal excitations. Overall, our results provide strong evidence that the heat carriers in amorphous dielectrics are collective excitations rather than normal modes. This change in physical picture advances our understanding of atomic dynamics in glasses and also provides a foundation for realizing dielectric solids with ultralow thermal conductivity.</p

Sub-amorphous thermal conductivity in amorphous heterogeneous nanocomposites

Pure amorphous solids are traditionally considered to set the lower bound of thermal conductivity due to their disordered atomic structure that impedes vibrational energy transport. However, the lower limits for thermal conductivity in heterogeneous amorphous solids and the physical mechanisms underlying these limits remain unclear. Here, we use equilibrium molecular dynamics to show that an amorphous SiGe nanocomposite can possess thermal conductivity substantially lower than those of the amorphous Si and Ge constituents. Normal mode analysis indicates that the presence of the Ge inclusion localizes vibrational modes with frequency above the Ge cutoff in the Si host, drastically reducing their ability to transport heat. This observation suggests a general route to achieve exceptionally low thermal conductivity in fully dense solids by restricting the vibrational density of states available for transport in heterogeneous amorphous nanocomposites

The Influence Of Mortality Focus On Guilt Advertising Effectiveness

The current research examined the influence of mortality focus on the effectiveness of guilt advertising via two experiments. Mortality focus and type of guilt advertising appeal interacted such that directing the focus of mortality on one’s own death (vs. other) facilitated effectiveness of guilt-lessening (vs. guilt-magnifying) appeals. The mediators of the influences were the motivation to boost self-confidence (vs. manage impression). The findings contribute to the literatures on consumer guilt, mortality salience, and defensive processing, while offering practical implications for guilt advertising management

Atomic dynamics in fluids: Normal mode analysis revisited

Developing microscopic understanding of the thermal properties of liquids is challenging due to their strong dynamic disorder, which prevents characterization of the atomic degrees of freedom. There have been significant research interests in the past few decades to extend the normal mode analysis for solids to instantaneous structures of liquids. However, the nature of normal modes that arise from these unstable structures is still elusive. In this work, we explore the instantaneous eigenmodes of dynamical matrices of various Lennard-Jones argon liquid/gas systems at high temperatures and show that the normal modes can be interpreted as an interpolation of T \to \infty (gas) and T = 0 (solid) mode descriptions. We find that normal modes become increasingly collisional and translational, recovering atomistic gas-like behavior rather than vibrational with increase in temperature, suggesting that normal modes in liquids may be described by both solid-like and gas-like modes

Origin of micron-scale propagation lengths of heat-carrying acoustic excitations in amorphous silicon

The heat-carrying acoustic excitations of amorphous silicon are of interest because their mean free paths may approach micron scales at room temperature. Despite extensive investigation, the origin of the weak acoustic damping in the heat-carrying frequencies remains a topic of debate. Here, we report measurements of the frequency-dependent mean free path in amorphous silicon thin films from ∼0.1−3 THz and over temperatures from 60 - 315 K using picosecond acoustics and transient grating spectroscopy. The mean free paths are independent of temperature and exhibit a Rayleigh scattering trend from ∼0.3−3 THz, below which the trend is characteristic of damping from density fluctuations or two-level systems. The observed trend is inconsistent with the predictions of numerical studies based on normal mode analysis but agrees with diverse measurements on other glasses. The micron-scale MFPs in amorphous Si arise from the absence of Akhiezer and two-level system damping in the sub-THz frequencies, leading to heat-carrying acoustic excitations with room-temperature damping comparable to that of other glasses at cryogenic temperatures

Origin of micron-scale propagation lengths of heat-carrying acoustic excitations in amorphous silicon

The heat-carrying acoustic excitations of amorphous silicon are of interest because their mean free paths may approach micron scales at room temperature. Despite extensive investigation, the origin of the weak acoustic damping in the heat-carrying frequencies remains a topic of debate. Here, we report measurements of the frequency-dependent mean free path in amorphous silicon thin films from ∼0.1−3 THz and over temperatures from 60 - 315 K using picosecond acoustics and transient grating spectroscopy. The mean free paths are independent of temperature and exhibit a Rayleigh scattering trend from ∼0.3−3 THz, below which the trend is characteristic of damping from density fluctuations or two-level systems. The observed trend is inconsistent with the predictions of numerical studies based on normal mode analysis but agrees with diverse measurements on other glasses. The micron-scale MFPs in amorphous Si arise from the absence of Akhiezer and two-level system damping in the sub-THz frequencies, leading to heat-carrying acoustic excitations with room-temperature damping comparable to that of other glasses at cryogenic temperatures