Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Surface Insulation Resistance Degradation and Electrochemical Migration on Printed Circuit Boards

Widespread adoption of lead-free materials and processing for printed circuit board (PCB) assembly has raised reliability concerns regarding surface insulation resistance (SIR) degradation and electrochemical migration (ECM). As PCB conductor spacings decrease, electronic products become more susceptible to these failures mechanisms, especially in the presence of surface contamination and flux residues which might remain after no-clean processing. Moreover, the probability of failure due to SIR degradation and ECM is affected by the interaction between physical factors (such as temperature, relative humidity, electric field) and chemical factors (such as solder alloy, substrate material, no-clean processing). Current industry standards for assessing SIR reliability are designed to serve as short-term qualification tests, typically lasting 72 to 168 hours, and do not provide a prediction of reliability in long-term applications. The risk of electrochemical migration with lead-free assemblies has not been adequately investigated. Furthermore, the mechanism of electrochemical migration is not completely understood. For example, the role of path formation has not been discussed in previous studies. Another issue is that there are very few studies on development of rapid assessment methodologies for characterizing materials such as solder flux with respect to their potential for promoting ECM. In this dissertation, the following research accomplishments are described: 1). Long-term temp-humidity-bias (THB) testing over 8,000 hours assessing the reliability of printed circuit boards processed with a variety of lead-free solder pastes, solder pad finishes, and substrates. 2). Identification of silver migration from Sn3.5Ag and Sn3.0Ag0.5Cu lead-free solder, which is a completely new finding compared with previous research. 3). Established the role of path formation as a step in the ECM process, and provided clarification of the sequence of individual steps in the mechanism of ECM: path formation, electrodeposition, ion transport, electrodeposition, and filament formation. 4). Developed appropriate accelerated testing conditions for assessing the no-clean processed PCBs' susceptibility to ECM: a). Conductor spacings in test structures should be reduced in order to reflect the trend of higher density electronics and the effect of path formation, independent of electric field, on the time-to-failure. b). THB testing temperatures should be modified according to the material present on the PCB, since testing at 85oC can cause the evaporation of weak organic acids (WOAs) in the flux residues, leading one to underestimate the risk of ECM. 5). Correlated temp-humidity-bias testing with ion chromatography analysis and potentiostat measurement to develop an efficient and effective assessment methodology to characterize the effect of no-clean processing on ECM.