Low-temperature heat capacity data contain information on the physical properties of materials, and new models continue to be developed to aid in the analysis and interpretation of heat capacity data into physically meaningful properties. This work presents the development of two such models and their application to real material systems. Equations describing low-energy vibrational modes with a gap in the density of states (DOS) have been derived and tested on several material systems with known gaps in the DOS, and the origins of such gaps in the DOS are presented. Lattice vacancies have been shown to produce a two-level system that can be modeled with a sum of low-energy Schottky anomalies that produce an overall linear dependence on temperature in the low-temperature heat capacity data. These two models for gaps in the vibrational DOS and the relationship between a linear heat capacity and lattice vacancies and many well-known models have been applied to several systems of materials to test their validity and applicability as well as provide greater information on the systems themselves. A series of bulk and nanoscale Mn-Fe and Co-Fe spinel solid solutions were analyzed using the entropies derived from heat capacity data, and excess entropies of mixing were determined. These entropies show that changes in valence, cation distribution, bonding, and the microstructure between the mixing ions is non-ideal, especially in the nanoparticles. The heat capacity data of ten Al doped TiO2 anatase nanoparticle samples have also been analyzed to show that the Al3+ dopant ions form small regions of short-range order, similar to a glass, within the TiO2 particles, while the overall structure of TiO2 remains unchanged. This has been supported by X-ray diffraction (XRD) and electron energy-loss spectroscopy and provides new insights to the synthesis and characterization of doped materials. The final investigation examines nanocrystalline CuO using heat capacities, magnetization, XRD, and electron microscopy and compares the findings to the known properties of bulk CuO. All of these measurements show transitions between antiferromagnetic and paramagnetic states in the temperature range of about 150-350 K that are greater in number and higher in temperature than the transitions in bulk CuO. These changes are shown to cause an increase in the temperature range of multiferroicity in CuO nanoparticles.

Entropy, first introduced in thermodynamics, is used in a wide range of fields. Chapter 1 discusses some important theoretical and practical aspects of entropy: what is entropy, is it subjective or objective, and how to properly apply it to living organisms. Chapter 2 presents applications of entropy to evolution. Chapter 3 shows how cellulosic biofuel production can be improved. Chapter 4 shows how lattice vacancies influence the thermodynamic properties of materials. To determine the nature of thermodynamic entropy, Chapters 1 and 2 describe the roots, the conceptual history of entropy, as well as its path of development and application. From the viewpoint of physics, thermal entropy is a measure of useless energy stored in a system resulting from thermal motion of particles. Thermal entropy is a non-negative objective property. The negentropy concept, while mathematically correct, is physically misleading. This dissertation hypothesizes that concepts from thermodynamics and statistical mechanics can be used to define statistical measurements, similar to thermodynamic entropy, to summarize the convergence of processes driven by random inputs subject to deterministic constraints. A primary example discussed here is evolution in biological systems. As discussed in this dissertation, the first and second laws of thermodynamics do not translate directly into parallel laws for the biome. But, the fundamental principles on which thermodynamic entropy is based are also true for information. Based on these principles, it is shown that adaptation and evolution are stochastically deterministic. Chapter 3 discusses the hydrolysis of cellulose to glucose, which is a key reaction in renewable energy from biomass and in mineralization of soil organic matter to CO2. Conditional thermodynamic parameters, ΔhydG', ΔhydH', and ΔhydS', and equilibrium glucose concentrations are reported for the reaction C6H10O5(cellulose) + H2O(l) ⇄ C6H12O6(aq) as functions of temperature from 0 to 100°C. Activity coefficients of aqueous glucose solution were determined as a function of temperature. The results suggest that producing cellulosic biofuels at higher temperatures will result in higher conversion. Chapter 4 presents the data and a theory relating the linear term in the low temperature heat capacity to lattice vacancy concentration. The theory gives a quantitative result for disordered vacancies, but overestimates the contribution from ordered vacancies because ordering leads to a decreased influence of vacancies on heat capacity.