Coupled Nonlinear Ginzburg-Landau and Mechanics Model for Martensitic Transformations in Polycrystals

Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedades destacables como alta resistencia mecánica, memoria de forma, efectos de superelasticidad o funcionalidades ferroicas como la piezoelectricidad, electro y magneto-estricción etc. Varios modelos/teorías se han desarrollado en sinergia con el desarrollo de la física del estado sólido para entender por qué las MT generan microstructuras muy variadas y ricas que muestran propiedades muy interesantes. Entre las teorías mejor aceptadas se encuentra la Teoría Fenomenológica de la Cristalografía Martensítica (PTMC, por sus siglas en inglés) que predice el plano de hábito y las relaciones de orientación entre la austenita y la martensita. La reinterpretación de la teoría PTMC en un entorno de mecánica del continuo (CM-PTMC) explica la formación de los dominios de estructuras multivariantes, mientras que la teoría de Landau con dinámica de inercia desentraña los mecanismos físicos de los precursores y otros comportamientos dinámicos. La dinámica de red cristalina desvela la reducción de la dureza acústica de las ondas de tensión de red que da lugar a transformaciones débiles de primer orden en el desplazamiento. A pesar de las diferencias entre las teorías estáticas y dinámicas dado su origen en diversas ramas de la física (por ejemplo mecánica continua o dinámica de la red cristalina), estas teorías deben estar inherentemente conectadas entre sí y mostrar ciertos elementos en común en una perspectiva unificada de la física. No obstante las conexiones físicas y diferencias entre las teorías/modelos no se han tratado hasta la fecha, aun siendo de importancia crítica para la mejora de modelos de MT y para el desarrollo integrado de modelos de transformaciones acopladas de desplazamiento-difusión. Por lo tanto, esta tesis comenzó con dos objetivos claros. El primero fue encontrar las conexiones físicas y las diferencias entre los modelos de MT mediante un análisis teórico detallado y simulaciones numéricas. El segundo objetivo fue expandir el modelo de Landau para ser capaz de estudiar MT en policristales, en el caso de transformaciones acopladas de desplazamiento-difusión, y en presencia de dislocaciones. Comenzando con un resumen de los antecedente, en este trabajo se presentan las bases físicas de los modelos actuales de MT. Su capacidad para predecir MT se clarifica mediante el ansis teórico y las simulaciones de la evolución microstructural de MT de cúbicoatetragonal y cúbicoatrigonal en 3D. Este análisis revela que el modelo de Landau con representación irreducible de la deformación transformada es equivalente a la teoría CM-PTMC y al modelo de microelasticidad para predecir los rasgos estáticos durante la MT, pero proporciona una mejor interpretación de los comportamientos dinámicos. Sin embargo, las aplicaciones del modelo de Landau en materiales estructurales están limitadas por su complejidad. Por tanto, el primer resultado de esta tesis es el desarrollo del modelo de Landau nolineal con representación irreducible de deformaciones y de la dinámica de inercia para policristales. La simulación demuestra que el modelo propuesto es consistente fcamente con el CM-PTMC en la descripción estática, y también permite una predicción del diagrama de fases con la clásica forma ’en C’ de los modos de nucleación martensítica activados por la combinación de temperaturas de enfriamiento y las condiciones de tensión aplicada correlacionadas con la transformación de energía de Landau. Posteriomente, el modelo de Landau de MT es integrado con un modelo de transformación de difusión cuantitativa para elucidar la relajación atómica y la difusión de corto alcance de los elementos durante la MT en acero. El modelo de transformaciones de desplazamiento y difusión incluye los efectos de la relajación en borde de grano para la nucleación heterogenea y la evolución espacio-temporal de potenciales de difusión y movilidades químicas mediante el acoplamiento de herramientas de cálculo y bases de datos termo-cinéticos de tipo CALPHAD. El modelo se aplica para estudiar la evolución microstructural de aceros al carbono policristalinos procesados por enfriamiento y partición (Q&P) en 2D. La microstructura y la composición obtenida mediante la simulación se comparan con los datos experimentales disponibles. Los resultados muestran el importante papel jugado por las diferencias en movilidad de difusión entre la fase austenita y martensita en la distibución de carbono en las aceros. Finalmente, un modelo multi-campo es propuesto mediante la incorporación del modelo de dislocación en grano-grueso al modelo desarrollado de Landau para incluir las diferencias morfológicas entre aceros y aleaciones con memoria de forma con la misma ruptura de simetría. La nucleación de dislocaciones, la formación de la martensita ’butterfly’, y la redistribución del carbono después del revenido son bien representadas en las simulaciones 2D del estudio de la evolución de la microstructura en aceros representativos. Con dicha simulación demostramos que incluyendo las dislocaciones obtenemos para dichos aceros, una buena comparación frente a los datos experimentales de la morfología de los bordes de macla, la existencia de austenita retenida dentro de la martensita, etc. Por tanto, basado en un modelo integral y en el desarrollo de códigos durante esta tesis, se ha creado una herramienta de modelización multiescala y multi-campo. Dicha herramienta acopla la termodinámica y la mecánica del continuo en la macroescala con la cinética de difusión y los modelos de campo de fase/Landau en la mesoescala, y también incluye los principios de la cristalografía y de la dinámica de red cristalina en la microescala. ABSTRACT Martensitic transformation (MT), in a narrow sense, is defined as the change of the crystal structure to form a coherent phase, or multi-variant domain structures out from a parent phase with the same composition, by small shuffles or co-operative movements of atoms. Over the past century, MTs have been discovered in different materials from steels to shape memory alloys, ceramics, and smart materials. They lead to remarkable properties such as high strength, shape memory/superelasticity effects or ferroic functionalities including piezoelectricity, electro- and magneto-striction, etc. Various theories/models have been developed, in synergy with development of solid state physics, to understand why MT can generate these rich microstructures and give rise to intriguing properties. Among the well-established theories, the Phenomenological Theory of Martensitic Crystallography (PTMC) is able to predict the habit plane and the orientation relationship between austenite and martensite. The re-interpretation of the PTMC theory within a continuum mechanics framework (CM-PTMC) explains the formation of the multivariant domain structures, while the Landau theory with inertial dynamics unravels the physical origins of precursors and other dynamic behaviors. The crystal lattice dynamics unveils the acoustic softening of the lattice strain waves leading to the weak first-order displacive transformation, etc. Though differing in statics or dynamics due to their origins in different branches of physics (e.g. continuum mechanics or crystal lattice dynamics), these theories should be inherently connected with each other and show certain elements in common within a unified perspective of physics. However, the physical connections and distinctions among the theories/models have not been addressed yet, although they are critical to further improving the models of MTs and to develop integrated models for more complex displacivediffusive coupled transformations. Therefore, this thesis started with two objectives. The first one was to reveal the physical connections and distinctions among the models of MT by means of detailed theoretical analyses and numerical simulations. The second objective was to expand the Landau model to be able to study MTs in polycrystals, in the case of displacive-diffusive coupled transformations, and in the presence of the dislocations. Starting with a comprehensive review, the physical kernels of the current models of MTs are presented. Their ability to predict MTs is clarified by means of theoretical analyses and simulations of the microstructure evolution of cubic-to-tetragonal and cubic-to-trigonal MTs in 3D. This analysis reveals that the Landau model with irreducible representation of the transformed strain is equivalent to the CM-PTMC theory and microelasticity model to predict the static features during MTs but provides better interpretation of the dynamic behaviors. However, the applications of the Landau model in structural materials are limited due its the complexity. Thus, the first result of this thesis is the development of a nonlinear Landau model with irreducible representation of strains and the inertial dynamics for polycrystals. The simulation demonstrates that the updated model is physically consistent with the CM-PTMC in statics, and also permits a prediction of a classical ’C shaped’ phase diagram of martensitic nucleation modes activated by the combination of quenching temperature and applied stress conditions interplaying with Landau transformation energy. Next, the Landau model of MT is further integrated with a quantitative diffusional transformation model to elucidate atomic relaxation and short range diffusion of elements during the MT in steel. The model for displacive-diffusive transformations includes the effects of grain boundary relaxation for heterogeneous nucleation and the spatio-temporal evolution of diffusion potentials and chemical mobility by means of coupling with a CALPHAD-type thermo-kinetic calculation engine and database. The model is applied to study for the microstructure evolution of polycrystalline carbon steels processed by the Quenching and Partitioning (Q&P) process in 2D. The simulated mixed microstructure and composition distribution are compared with available experimental data. The results show that the important role played by the differences in diffusion mobility between austenite and martensite to the partitioning in carbon steels. Finally, a multi-field model is proposed by incorporating the coarse-grained dislocation model to the developed Landau model to account for the morphological difference between steels and shape memory alloys with same symmetry breaking. The dislocation nucleation, the formation of the ’butterfly’ martensite, and the redistribution of carbon after tempering are well represented in the 2D simulations for the microstructure evolution of the representative steels. With the simulation, we demonstrate that the dislocations account for the experimental observation of rough twin boundaries, retained austenite within martensite, etc. in steels. Thus, based on the integrated model and the in-house codes developed in thesis, a preliminary multi-field, multiscale modeling tool is built up. The new tool couples thermodynamics and continuum mechanics at the macroscale with diffusion kinetics and phase field/Landau model at the mesoscale, and also includes the essentials of crystallography and crystal lattice dynamics at microscale.

Theodicies, Utilitarianism, and Respect for Persons

Most theodicy responses to the problem of evil have in common the claim that God legitimately allows some evil such that greater good may come. This response is puzzling because the seemingly overwhelming consensus (at least amongst Christian apologists) is that 1) morality is deontological in nature (e.g. our duty of obedience to God’s commands, or acting in accordance with God’s purpose), and 2) relatedly, that humans are made in God’s image (i. e. are rational beings) and thus are worthy of respect. I shall argue that theodicy defenses that claim that God allows some evil such that greater good may come are untenable because they either unnecessarily bifurcate Christian morality in an ad hoc manner, or entail that God cannot have respect for persons.

Comparing in vitro, in situ, and in vivo experimental data in a three-dimensional model of mammalian cochlear mechanics

Normal mammalian hearing is refined by amplification of the motion of the cochlear partition. This partition, comprising the organ of Corti sandwiched between the basilar and tectorial membranes, contains the outer hair cells that are thought to drive this amplification process. Force generation by outer hair cells has been studied extensively in vitro and in situ, but, to understand cochlear amplification fully, it is necessary to characterize the role played by each of the components of the cochlear partition in vivo. Observations of cochlear partition motion in vivo are severely restricted by its inaccessibility and sensitivity to surgical trauma, so, for the present study, a computer model has been used to simulate the operation of the cochlea under different experimental conditions. In this model, which uniquely retains much of the three-dimensional complexity of the real cochlea, the motions of the basilar and tectorial membranes are fundamentally different during in situ- and in vivo-like conditions. Furthermore, enhanced outer hair cell force generation in vitro leads paradoxically to a decrease in the gain of the cochlear amplifier during sound stimulation to the model in vivo. These results suggest that it is not possible to extrapolate directly from experimental observations made in vitro and in situ to the normal operation of the intact organ in vivo.

From ab initio quantum mechanics to molecular neurobiology: A cation–π binding site in the nicotinic receptor

The nicotinic acetylcholine receptor is the prototype ligand-gated ion channel. A number of aromatic amino acids have been identified as contributing to the agonist binding site, suggesting that cation–π interactions may be involved in binding the quaternary ammonium group of the agonist, acetylcholine. Here we show a compelling correlation between: (i) ab initio quantum mechanical predictions of cation–π binding abilities and (ii) EC50 values for acetylcholine at the receptor for a series of tryptophan derivatives that were incorporated into the receptor by using the in vivo nonsense-suppression method for unnatural amino acid incorporation. Such a correlation is seen at one, and only one, of the aromatic residues—tryptophan-149 of the α subunit. This finding indicates that, on binding, the cationic, quaternary ammonium group of acetylcholine makes van der Waals contact with the indole side chain of α tryptophan-149, providing the most precise structural information to date on this receptor. Consistent with this model, a tethered quaternary ammonium group emanating from position α149 produces a constitutively active receptor.

The importance of reactant positioning in enzyme catalysis: A hybrid quantum mechanics/molecular mechanics study of a haloalkane dehalogenase

Hybrid quantum mechanics/molecular mechanics calculations using Austin Model 1 system-specific parameters were performed to study the SN2 displacement reaction of chloride from 1,2-dichloroethane (DCE) by nucleophilic attack of the carboxylate of acetate in the gas phase and by Asp-124 in the active site of haloalkane dehalogenase from Xanthobacter autotrophicus GJ10. The activation barrier for nucleophilic attack of acetate on DCE depends greatly on the reactants having a geometry resembling that in the enzyme or an optimized gas-phase structure. It was found in the gas-phase calculations that the activation barrier is 9 kcal/mol lower when dihedral constraints are used to restrict the carboxylate nucleophile geometry to that in the enzyme relative to the geometries for the reactants without dihedral constraints. The calculated quantum mechanics/molecular mechanics activation barriers for the enzymatic reaction are 16.2 and 19.4 kcal/mol when the geometry of the reactants is in a near attack conformer from molecular dynamics and in a conformer similar to the crystal structure (DCE is gauche), respectively. This haloalkane dehalogenase lowers the activation barrier for dehalogenation of DCE by 2–4 kcal/mol relative to the single point energies of the enzyme's quantum mechanics atoms in the gas phase. SN2 displacements of this sort in water are infinitely slower than in the gas phase. The modest lowering of the activation barrier by the enzyme relative to the reaction in the gas phase is consistent with mutation experiments.

How can statistical mechanics contribute to social science?

A model of interdependent decision making has been developed to understand group differences in socioeconomic behavior such as nonmarital fertility, school attendance, and drug use. The statistical mechanical structure of the model illustrates how the physical sciences contain useful tools for the study of socioeconomic phenomena.

Molecular mechanics calculations of the riboacetal internucleotide linkage in double and triple helices.

Structures of Watson-Crick base paired 15-nucleobase oligomer strands in A-type or B-type conformation in which one strand [a strand of alternating nucleotide and riboacetal thymidine nucleoside (RT) units, RP] is DNA and the other is composed of alternating nucleotides and riboacetal nucleosides have been studied by molecular mechanics. Analogously, oligomer strands of RNA in place of DNA have been modeled. The calculations indicate that the RP strand is more stable when complexed in an A-type duplex relative to a B-type form and that this conformational preference is presumably due to the more uniform nature of the former. Nearly planar ribose rings were more commonly observed in the minimized structures of the B-type DNA.RP duplexes as compared with A-type duplexes, despite the fact that planar ribofuranose rings are known to be energetically unfavorable in oligonucleotides. Computed relative stabilities of all duplexes containing the RP strand suggest that such heteroduplexes are less stable than the corresponding double-stranded DNA and double-stranded RNA species. These findings are in agreement with experimental results which show, when equivalent sequences were compared, that a DNA.RNA control forms a more stable duplex than RP hound to a complementary single-stranded RNA strand. In contrast, molecular mechanics studies of complementary triple-helical (DNA)2.RP, (DNA)2.DNA, and (DNA)2.RNA structures indicate that the binding of RP as a Hoogsteen strand stabilizes the underlying duplex to a greater extent compared with native oligonucleotides. These calculations suggest that puckering of the ribose ring in the riboacetal linkage leads to a more favorable interaction with a complementary nucleic acid target than the proposed planar geometry and that this puckering may account for the enhanced binding of RP to a double-stranded target.

New Approaches for Teaching Soil and Rock Mechanics Using Information and Communication Technologies

Soil and rock mechanics are disciplines with a strong conceptual and methodological basis. Initially, when engineering students study these subjects, they have to understand new theoretical phenomena, which are explained through mathematical and/or physical laws (e.g. consolidation process, water flow through a porous media). In addition to the study of these phenomena, students have to learn how to carry out estimations of soil and rock parameters in laboratories according to standard tests. Nowadays, information and communication technologies (ICTs) provide a unique opportunity to improve the learning process of students studying the aforementioned subjects. In this paper, we describe our experience of the incorporation of ICTs into the classical teaching-learning process of soil and rock mechanics and explain in detail how we have successfully developed various initiatives which, in summary, are: (a) implementation of an online social networking and microblogging service (using Twitter) for gradually sending key concepts to students throughout the semester (gradual learning); (b) detailed online virtual laboratory tests for a delocalized development of lab practices (self-learning); (c) integration of different complementary learning resources (e.g. videos, free software, technical regulations, etc.) using an open webpage. The complementary use to the classical teaching-learning process of these ICT resources has been highly satisfactory for students, who have positively evaluated this new approach.

Abandoned and forgotten: the sad story of Kenya's internally displaced persons

This documentary is about the internal displacement of ethnic minorities brought about by politically instigated post-election violence towards ethnic minorities in all eight provinces, namely, Coast, Rift Valley, Western, Eastern, North Eastern, Central Kenya, Nairobi, and Nyanza. During the years of 1991 to 1996, over 15,000 people died and almost 300,000 were displaced in the Rift Valley, Central, Nyanza and Western provinces. Before the 1997 elections, violence erupted. Again, following the disputed presidential elections in December 2007 politically and ethnically instigated displacements resulted in human rights violations against 600,000 people in 8 provinces of Kenya.

An Act of Assembly of Barbadoes to regulate sales at outcry and the proceedings of persons executing the office of Provost Marshall General ofthe said island and their under officers, 1763

An Act of Assembly of Barbadoes to regulate sales at outcry and the proceedings of persons executing the office of Provost Marshall General of the said island and their under officers (leaf 1) ; A state of some matters relative to the office of Provost Marshall, and to the passing of this bill (leaf 9) ; Observations drawn up by Jonathan Blenman Esq. his Majestys Atty. Gen. in Barbadoes ... on the Act as it had been first brought in 1761 (leaf 13) ; and two leaves laid in ; Power of attorney, granted to Christopher Scandrett, signed by Francis Reynolds and his son Thomas (25 April 1766) ; Petition of Francis Reynolds to the Lords Commissioners of Trade and Plantations (1766).