Thermodynamic insights and microscopic models for characterizing vibrations in solids

Agne, Matthias Thomas

doi:https://doi.org/10.21985/n2-svh2-3747

Work

Thermodynamic insights and microscopic models for characterizing vibrations in solids

Public

Download PDF

Download All Files (.zip)

Given directives such as the UN Global Goals targeting sustainable development, the research presented herein makes but a small contribution to the advancement of alternative energy technologies. Nevertheless, the present work was largely motivated to address specific points of intrigue within the thermoelectrics community. The general principles demonstrated, however, may be directly applicable to other areas of solid-state research. Thermoelectric materials, which can convert heat to electricity through the Seebeck effect, require a complex optimization of their electronic and thermal properties. For the past 2 decades, great strides have been made to improve their energy conversion efficiency— and many successes in doing so can be attributed to reductions in the thermal conductivity. In the long-standing phonon gas model of thermal transport, where atomic vibrations carry heat in a manner analogous to gas particles, the strategy has been to introduce scattering mechanisms that impede transport. This works well in many materials. Recently, however, we have demonstrated that the thermal conductivity of materials like lead telluride may be engineered by controlling their bulk elastic properties, effectively controlling the speed of the phonons, which is a fundamentally different mechanism than scattering. Another proposed method of reducing thermal conductivity was to utilize phase transitions, with the hope of introducing additional phonon scattering. In fact, there are many reports of reduced thermal conductivity (and improved thermoelectric performance) through both solid-solid and solid-liquid (analogous to ice melting) phase transitions. Here, a reassessment of the underlying thermodynamic relationship between thermal conductivity and thermal diffusivity demonstrates that thermal conductivity is likely underestimated from thermal diffusivity measurements when latent heats from phase transformations are not taken into account. In several well-characterized material systems it is shown that thermal conductivity is not greatly impacted by phase transitions, whereas thermal diffusivity is. This relates to a need for the accurate characterization of the heat capacity of materials at high temperature. For materials not undergoing a phase transition a simple equation was developed to describe high temperature heat capacity that is likely more accurate than experiments in many cases. Although phase transitions may not result in ultralow thermal conductivity, there are materials (and materials still to be discovered) with intrinsically high anharmonicity that results in high phonon scattering rates and low thermal conductivity. Here, anharmonicity is an aspect of bonding in materials that deviates from Hooke’s Law, i.e. there are non-linear interactions between atoms. Anharmonicity is also used to explain thermal expansion. Thus, characterizing anharmonicity has widespread repercussions. Here, it is proposed that the harmonic (e.g. elastic) properties of solids can be thermodynamically related to higher order anharmonic effects of bonding. Specifically, a physical model of thermal expansion is developed by considering that harmonic phonons produce a pressure pushing the solid outwards, while the elasticity of the atomic bonds compensates the phonon pressure to achieve mechanical equilibrium. Besides fundamentally reconsidering the nature of anharmonic behaviors in solids, this simple model provides accessible estimates of thermal expansion and the thermodynamic Grüneisen parameter that may be used for thermodynamic modeling and high-throughput screening of anharmonicity, both necessary for next-generation computational materials design. The desire to reduce thermal conductivity for improved thermoelectric efficiency is summarized well by the "phonon-glass electron-crystal" mantra. Here, the thermal properties of the material are desired to be glass-like (amorphous-like) since glasses are known to exhibit some of the lowest thermal conductivities of all solids. However, glasses are not typically good electronic conductors, and so crystallinity is desirable for this aspect of thermoelectrics optimization. Indeed, this concept has been demonstrated in some solids like semiconductor clathrates, zinc antimonide and skutterudites. Nevertheless, the atomic vibrations in crystals are often only discussed in terms of the phonon gas model. Only recently has it has it been shown that vibrations in crystals and those in glasses can be described in the same mathematical framework, and that crystalline materials can transition to more glass-like behavior under certain circumstances. In this work, a phenomenological model of thermal transport by diffusons (the primary mechanism of heat transport in glasses) is developed for applications to crystalline materials. This study was one of the first to promote a reclassification of vibrations in crystals and gives an estimate of the so-called "minimum" thermal conductivity that can be used to benchmark experimental observations. Specifically, the model gives an estimate for thermal conductivity in the case where all vibrations in the material behave as diffusons. Again, characterizing the fundamental nature of vibrations in solids has far reaching implications for energy materials beyond thermoelectrics. So far, both thermodynamic analysis and microscopic models have been used to characterize the thermal properties of solids. In this work, they were also utilized to assess the stability of materials for device-level operation. In one case, it is shown that there are thermodynamic stability criteria in a subclass of thermoelectric materials called mixed ionic-electronic conductors. Their stability depends on the atomic chemical potential of the mobile atom. Importantly, this means that there is a critical voltage above which the material can decompose. This is related to, but not the same as, the prevalent idea that these materials cannot sustain high current densities. In fact, it is shown experimentally that the superionic material copper sulfide can sustain high current densities when the voltage is kept below the thermodynamic critical voltage of the material. Lastly, an estimate for the fracture toughness of solids is proposed that is based on ideal-strength calculations. Modern computational methods in materials science provide a unique opportunity to investigate fracture at the level of local atomic structures. The integral of the ideal stress-displacement curve is used to approximate the work of fracture. That is, to estimate the total energy required to make new surfaces. This computational method is shown to reproduce the magnitude of experimental results quite well, indicating that the relevant physics of fracture are being captured. This method is easily generalized to defect structures in materials and may be useful for atomic scale materials design. Although this body of work is but a humble offering to the scientific community, when research is coupled with international collaboration and education outreach, great strides can be made in small steps. It is my passion to explore material properties, to build the energy sciences community and to share knowledge with others.

Creator