Unrecognized metamorphic complexities can produce erroneous interpretations when using equilibrium thermodynamics and isotope geochronology. Universally employed methods for determining pressure-temperature conditions during regional metamorphism are based on the assumption of chemical equilibrium, and geochronology in metamorphic rocks can suffer from cryptic redistribution of isotopes. In this research, the scales of disequilibrium in regionally metamorphosed rocks and the effects of garnet resorption on Lu-Hf garnet ages were examined through numerical simulations of these processes. Concerning scales of disequilibrium, thirteen porphyroblastic datasets, previously measured using X-ray computed tomography, were examined by numerically simulating diffusion-controlled nucleation and growth of garnet while tracking chemical potential gradients to determine reaction affinity Ar (-[Delta]rG). Maximum nucleation rates are 10⁻¹³̇⁶-10⁻⁹̇⁸ nuclei cm⁻³ s⁻¹, interfacial energies are 0.004-0.14 J m⁻² assuming shape factors of 0.1-1.0, and Al intergranular diffusion (QD = 140 kJ/mol⁻¹) is 10⁻¹⁴̇⁴-10⁻¹¹̇¹ m² s⁻¹ at 600 °C. Limitations in determining crystallization kinetics arise from difficulties in constraining rock-specific properties (e.g., porosity and Al solubility). Ar at the time and location of nucleation is 0.4-5.9 kJ/mol⁻¹ of 12-oxygen garnet ([Delta]T = 4.0-62.0 °C) for the earliest nuclei, and 5.3-29.0 kJ/mol⁻¹ ([Delta]T = 50-125 °C) for nucleation at maximum Ar. The results demonstrate potential for delayed nucleation and metastability that can generate spurious interpretations. The timing of metamorphic events is also critical for understanding geologic history. In the Makhavinekh Lake Pluton aureole, Labrador, garnet resorption caused redistribution of Lu and loss of Hf from consumed rims, creating spuriously young ages. Garnet-ilmenite Lu-Hf geochronology using bulk separates yields apparent ages that young toward the contact from 1876 ± 21 Ma (4025 m) to 1396 ± 8 Ma (450 m). Toward the contact, garnet crystals are progressively more resorbed. Numerical modeling was used to test retention of Lu and loss of Hf during resorption as the dominant control on age. More resorption and Lu retention produce younger apparent ages (false ages). Application of the model to the aureole yields model ages from 1850 Ma to 1374 Ma, younging toward the contact. Thus, Lu-Hf geochronology applied to resorbed garnets requires careful examination of Lu zoning. / text

Chemical reactions can have a staggering amount of molecular complexity. Reaction mechanisms have been proposed with over one hundred elementary reaction steps that occur in the same system simultaneously. While several methods exist to simplify and make sense of the pathways and kinetics via which these reactions proceed, e.g., reaction graphs, sensitivity or flux analysis, microkinetic analysis, and comparison of energy landscapes, etc., these methods all have limitations and are often not able to capture a comprehensive picture of the kinetics of system. It has been found useful to view these mechanisms as a network, i.e., a reaction graph. These graphs enable the visualization of the pathways of the reaction and can provide an analytical tool for pathway and kinetic analysis. However, many of the specific graph-theoretic approaches in the literature are not the most suitable for kinetic analysis of complex mechanisms; as they are simply not based on rules that are rigorous enough to fully enumerate all the pathways or provide quantitative analysis of the reaction rates. Our Reaction Route (RR) Graph approach is different in that it depicts the mechanism by a graph that is consistent with all physical and chemical laws associated with reaction networks, particularly being consistent with mass and energy conservation, i.e., Kirchoff’s Flux Law (KFL) and Kirchoff’s Potential Law (KPL). Because of their adherence to these laws, RR Graphs are able to provide an accurate graph-theoretical tool not only for depicting all reactions routes as walks (hence the name RR Graph) but also for pruning mechanisms and allowing a simplified but accurate quantitative description of reaction rates. This adherence to KFL and KPL does mean that the construction and implementation of these graphs can be prohibitively difficult for large mechanisms. For large reaction systems,especially nonlinear mechanisms, it is not realistic to generate these graphs by hand. And although there exists an analytical solution to find a determinant matrix for the RR Graph of a mechanism, the process involves an exhaustive search for a solution which experiences a combinatorial explosion as the number of steps gets very large. This leads to the idea of developing an algorithm for a computer program that can determine how to generate these graphs automatically. Unfortunately, the same combinatorial explosion is present such that for a moderately sized twenty step mechanism, it could take an average computational processor over a decade to find a solution. We have determined, however, that this brute force combinatorial approach can be avoided if heuristics could be developed to bridge gaps in our knowledge of how these graphs are constructed. Thus, developing a better analytical approach and/or a tighter set of heuristics for a computer algorithm are the overarching goals of this work. To make progress toward developing such heuristics, a set of microkinetic mechanisms were analyzed with the notion that the realization of the RR Graphs would highlight a better approach to their construction and usage. In particular, a very large linear reaction system, a smaller linear system and two non-linear reaction systems were analyzed to develop insights into how each graph is manually constructed and analyzed. Furthermore, kinetic analysis was done for these mechanisms and compared to experimental data and other analytical tools to prove not only the validity of the RR Graphs, but also how they are a significant improvement over more commonly used approaches for mechanistic and kinetic analysis. Based on the lessons learned through a consideration of these examples, a set of heuristics are established and enumerated with the ultimate goal of developing an intuitive algorithm that can help automate drawing and kinetic analysis via RR Graphs of complex mechanisms.