RT Dissertation/Thesis
T1 Discrete models of dislocations in crystal lattices: formulation, analysis and applications
T2 Modelos discretos de dislocaciones en redes cristalinas: formulación, análisis y aplicaciones
A1 Plans Beriso, Ignacio
AB Real crystal lattices are not perfect. They have defects such asdislocations, vacancies, and cracks that control the mechanicalproperties of materials, including crystal plasticity, creep, fatigue,ductility, brittleness, hardness and friction. Crystal growth, radiationdamage of materials, and their optical and electronicproperties are also strongly affected by defects, particularly dislocations.Why is it so important to understand the behavior of defectsin crystal lattices? An accurate description of defect dynamicsmay help to optimize the design and manufacture of importantnanoelectronic devices such as those based on self-assembledquantum dots [2, 3] or superlattices [4]. Moreover, assessing howand under which conditions dislocations nucleate may become anessential issue, since they act as scattering centers, degradingcharge transport properties in opto-electronic devices. But at thepresent time, even the homogeneous nucleation of dislocations isnot completely understood. While there is a widespread feelingthat it is related to some bifurcation occurring once a dislocationfreestate becomes unstable, no precise analysis and calculation ofthis bifurcation has been reported [5, 6].Think of another example: to build up a superlattice, heteroepitaxialstructures of alternate slices of semiconductors havingdifferent lattice spacings are grown. But layers with quite differentlattice parameters do not fit seamlessly! This typically results inthe formation of misfit dislocations at the interfaces that separatedifferent materials. Therefore, it is crucial to compute thresholdvalues for the formation of dislocations in many important experiments:the critical shear stress for homogeneous nucleationof dislocations, the critical thickness of a thin film (and also thecritical discrepancy between their lattice constants -the criticalmisfit-) in heteroepitaxial growth for interfacial misfit dislocations1formation, the critical stresses leading to dislocation nucleationfrom cracks or from nanoindentor tips, and so on.The goal of this thesis is to provide some insight in the aforementionedissues. But, tackling these problems is not simple!Dislocations may affect phenomena such as the strength of materialsoccurring over many different scales of length and timeand the properties at each scale are influenced by the others. Atthe present time there are different attempts to bridge the gapsbetween disparate scales by using detailed microscopic calculationssuch as molecular dynamics in small regions near defectcores and linear elasticity in the far field [7, 8, 9]. In this thesis,we have chosen to model dislocation dynamics at the nanoscaleby versions of discrete elasticity that become the proper linearanisotropic elasticity of cubic crystals in the far field and allowmotion of dislocations in a natural manner. One important advantageof these models is that they are amenable to analysisusing bifurcation theory and numerical continuation methods.We have used these methods to study very simple scalar versionsof discrete elasticity models for two-dimensional edge dislocations.Within these limitations, we have analyzed homogeneousnucleation of dislocations in sheared materials, misfit dislocations,nanoindentations and cracks. The simplicity of the modelsallows us to find a more precise picture of these phenomena thatmay be useful in the nanoscale. Whether these models can beused as part of multiscale/multiphysics calculations at largerscales, remains as a challenging task for future work.____________________________________________
AB La comprensión del comportamiento de los defectos presentesen las redes cristalinas es esencial para el diseño y fabricaciónde dispositivos nanoelectrónicos porque afectan fuertemente suspropiedades electrónicas, ópticas y magnéticas. Asimismo, defectoscomo las dislocaciones son esenciales para el proceso decrecimiento de estructuras heteroepitaxiales, para entender lapropagación de fisuras o en experimentos de nanoindentaciónque tratan de aclarar el comienzo de la plasticidad.En la presente tesis doctoral se formulan modelos discretosde dislocaciones en redes cristalinas del sistema cúbico (simple,centrado en las caras o centrado en el cuerpo, con la posibilidadde incluir una base de varios átomos en cada nodo de la red) querecuperan la elasticidad lineal anisotrópa en su límite continuo.En la tesis se analiza la nucleación homogénea de dislocacionesen un cristal bidimensional sujeto a tensiones de cizalladura yse concluye que los estados con dislocaciones aparecen comobifurcaciones subcríticas del estado estacionario sin dislocaciones.Las ramas bifurcadas multiestables se calculan por métodos decontinuación numérica y se estudia su selección mediante rampingde la tensión de cizalla. También se calculan valores críticospara la formación de dislocaciones en sistemas heteroepitaxiales,así como en fisuras y experimentos de nanoindentación.
YR 2007
FD 2007-07
LK https://hdl.handle.net/10016/2383
UL https://hdl.handle.net/10016/2383
LA eng
LA eng
DS e-Archivo
RD 1 jun. 2024