Using high pressure to study thermal transport and phonon scattering mechanisms

The aerospace industry studies nanocomposites for heat dissipation and moderation of thermal expansion, and the semiconductor industry faces a Joule heating barrier in devices with high power density. Be it for the nanocomposite frame of a satellite's solar panel array, or a miniaturized high-power RF circuit, these industries share similar interests in thermal management in nanostructures. We can improve such designs by better understanding nanoscale heat transport by phonons across and away from material interfaces. The heat flux per unit temperature drop across an interface is quantified by the interface thermal conductance. This conductance is difficult to study, as it is comprised of at least three components: bond stiffness at the interface, non-equilibrium resistance near the interface, and some intrinsic conductance. Away from interfaces, phonon-defect scattering is arguably the most complex, and technologically relevant, thermally resistive scattering mechanism in nonmetallic crystals. My primary experimental tools are the diamond anvil cell (DAC) coupled with time-domain thermoreflectance (TDTR). TDTR is a precise optical method well-suited to measuring thermal conductivities and conductances at the nanoscale and across interfaces. The DAC-TDTR method yields thermal property data as a function of pressure, rather than temperature. This relatively unexplored independent variable can separate the components of thermal conductance and serve as an independent test for phonon-defect scattering models. I studied the effect of non-equilibrium thermal transport at the aluminum-coated surface of an exotic cuprate material Ca$_{9}$La$_{5}$Cu$_{24}$O$_{41}$, which boasts a tenfold enhanced thermal conductivity along one crystalline axis where two-leg copper-oxygen spin-ladder structures carry heat in the form of thermalized magnetic excitations. Highly anisotropic materials are of interest for controlled thermal management applications, and the spin-ladder magnetic heat carriers ("magnons") are not well understood, even as they greatly enhance the thermal conductivity along the ladder axis. I found that below room temperature, the apparent thermal conductivity of Ca$_{9}$La$_{5}$Cu$_{24}$O$_{41}$ depends on the frequency of the applied surface heating in TDTR. This occurs because the thermal penetration depth in the TDTR experiment is comparable to the length-scale for the equilibration of the magnons that are the dominant channel for heat conduction and the phonons that dominate the heat capacity. I applied a two-temperature model to analyze the TDTR data and extracted an effective volumetric magnon-phonon coupling parameter $g$ for Ca$_{9}$La$_{5}$Cu$_{24}$O$_{41}$ at temperatures from 75 K to 300 K; $g$ varies by approximately two orders of magnitude over this range of temperature and has the value $g=10^{15}\mbox{ W m}^{-3}\mbox{ K}^{-1}$ near the peak of the thermal conductivity at $T\approx 180$~K. To examine intrinsic phonon-mediated interface conductance between dissimilar materials, I applied DAC-TDTR to measure the thermal conductance of a series of metal-diamond interfaces as a function of pressure up to 50 GPa. The thermal conductance of interfaces between metals and diamond, which has a comparatively high Debye temperature, is often greater than can be accounted for by two phonon-processes, and the nature of heat transport between such dissimilar materials is central to the thermal design of composite materials. The high pressures achievable in a diamond anvil cell can significantly extend the metal phonon density of states to higher frequencies, and can also suppress extrinsic effects by greatly stiffening interface bonding. I measured the interface thermal conductances of Pb, $\mbox{Au}_{0.95}\mbox{Pd}_{0.05}$, Pt, and Al films deposited on Type 1A natural {[}100{]} and Type 2A synthetic {[}110{]} diamond anvils, from ambient pressure to 50 GPa. In all cases, the thermal conductances increase weakly or saturate to similar values at high pressure. My results suggest that anharmonic conductance at metal-diamond interfaces is controlled by partial transmission processes, where a diamond phonon that inelastically scatters at the interface absorbs or emits a metal phonon. Silicon is a highly studied material, and is known to transition from a semiconducting to several metallic phases at high pressures above 12 GPa. However, the thermal conductivity and absolute electrical resistivity of metallic silicon have not been measured previously. I performed regular and beam-offset TDTR to establish the thermal conductivities of Si and Si$_{0.991}$Ge$_{0.009}$ across the semiconductor-metal phase transition and up to 45 GPa. The thermal conductivities of metallic Si and Si(Ge) are comparable to aluminum and indicative of predominantly electronic heat carriers. Metallic Si and Si(Ge) have a transport anisotropy of approximately 1.4, similar to that of beryllium, due to the primitive hexagonal crystal structure. I used the Wiedemann-Franz law to derive the associated electrical resistivity, and found it consistent with the Bloch-Gr{\"u}neisen model. Not all crystalline point defects are alike in how they scatter phonons and reduce the thermal conductivity of mixed crystals. Heat-carrying phonons in iron (Fe) doped MgO, or [Mg,Fe]O ferropericlase, are known to be resonantly scattered by interaction with a 3.3 THz electronic transition in the high-spin state of the Fe impurities. At sufficiently high pressures, the Fe atoms transition from a high-spin to a low-spin state, which eliminates the resonant interaction and reduces the Fe atoms to simpler point defect phonon scatterers. To study the behavior of phonon-defect scattering with and without this resonant scattering process, I measured the thermal conductivity of Mg$_{0.92}$Fe$_{0.08}$O ferropericlase up to and above the 40-60 GPa spin transition. Fe-doped MgO (ferropericlase) is also a model system relevant to geophysical modeling of the Earth's core-mantle boundary, so data on its thermal transport under pressure is valuable in itself