We report on the thermal conductivity of atomic layer deposition-grown amorphous alumina thin films as a function of atomic density. Using time domain thermoreflectance, we measure the thermal conductivity of the thin alumina films at room temperature. The thermal conductivities vary ∼35% for a nearly 15% change in atomic density and are substrate independent. No density dependence of the longitudinal sound speeds is observed with picosecond acoustics. The density dependence of the thermal conductivity agrees well with a minimum limit to thermal conductivity model that is modified with a differential effective-medium approximation.

The thermal boundary conductance across solid-solid interfaces can be affected by the physical properties of the solid boundary. Atomic composition, disorder, and bonding between materials can result in large deviations in the phonon scattering mechanisms contributing to thermal boundary conductance. Theoretical and computational studies have suggested that the mixing of atoms around an interface can lead to an increase in thermal boundary conductance by creating a region with an average vibrational spectra of the two materials forming the interface. In this paper, we experimentally demonstrate that ion irradiation and subsequent modification of atoms at solid surfaces can increase the thermal boundary conductance across solid interfaces due to a change in the acoustic impedance of the surface. We measure the thermal boundary conductance between thin aluminum films and silicon substrates with native silicon dioxide layers that have been subjected to proton irradiation and post-irradiation surface cleaning procedures. The thermal boundary conductance across the Al/native oxide/Si interfacial region increases with an increase in proton dose. Supported with statistical simulations, we hypothesize that ion beam mixing of the native oxide and silicon substrate within $\sim 2.2\mathrm{nm}$ of the silicon surface results in the observed increase in thermal boundary conductance. This ion mixing leads to the spatial gradation of the silicon native oxide into the silicon substrate, which alters the acoustic impedance and vibrational characteristics at the interface of the aluminum film and native oxide/silicon substrate. We confirm this assertion with picosecond acoustic analyses. Our results demonstrate that under specific conditions, a “more disordered and defected” interfacial region can have a lower resistance than a more “perfect” interface.

We employ the theory of {topological phase transitions}, of the Berezinski\u{i}-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial dimensions that is characterized by a {quaternion} $n-$vector (i.e., $n=4$) order parameter. Due to the dimensionality of the quaternion $n-$vector order parameter, the development of orientational order for systems that exist in four spatial dimensions must be viewed within the context of ordering in {restricted dimensions}. At finite temperatures, despite the development of a well-defined amplitude of the $n-$vector order parameter within separate regions, ordered systems that exist in restricted dimensions are prevented from developing global orientational phase-coherence as a consequence of misorientational fluctuations throughout the system. In four dimensions, this gas of misorientational fluctuations takes the form of spontaneously generated topological point defects that belong to the third homotopy group. These topological point defects must become topologically ordered in order to obtain a ground state of aligned order parameters at zero Kelvin; we argue that this topological transition belongs to the BKT universality class. We use standard `Metropolis' Monte Carlo simulations to estimate the thermodynamic response functions, susceptibility and heat capacity, in the vicinity of the transition towards the ground state of perfectly aligned order parameters in our four-dimensional quaternion $n-$vector ordered model system. On lowering the temperature below a critical value, we identify a transition that results from the minimization of misorientations in the scalar phase angles throughout the system. The thermodynamic response functions obtained by Monte Carlo simulations show characteristic behavior of a topological ordering phase transition.

Herein, fundamentals of topology and symmetry breaking are used to understand crystallization and geometrical frustration in topologically close-packed structures. This frames solidification from a new perspective that is unique from thermodynamic discussions. Crystallization is considered as developing from undercooled liquids, in which orientational order is characterized by a surface of a sphere in four-dimensions (quaternion) with the binary polyhedral representation of the preferred orientational order of atomic clustering inscribed on its surface. As a consequence of the dimensionality of the quaternion orientational order parameter, crystallization is seen as occurring in “restricted dimensions.” Homotopy theory is used to classify all topologically stable defects, and third homotopy group defect elements are considered to be generalized vortices that are available in superfluid ordered systems. This topological perspective approaches the liquid-to-crystalline solid transition in three-dimensions from fundamental concepts of: Bose-Einstein condensation, the Mermin-Wagner theorem and Berezinskii-Kosterlitz-Thouless (BKT) topological-ordering transitions. In doing so, in this article, concepts that apply to superfluidity in “restricted dimensions” are generalized to consider the solidification of crystalline solid states.