Supervised research experience, open only to senior materials science majors. Starting with an open-ended topic, students will plan and execute a project in materials science and engineering that includes written and oral reports based upon actual results, synthesizing topics from their course work. Only the first term may be taken pass/fail.
Materials Science Laboratory
An introductory laboratory in relationships between the structure and properties of materials. Experiments involve materials processing and characterization by X-ray diffraction, scanning electron microscopy, and optical microscopy. Students will learn techniques for measuring mechanical and electrical properties of materials, as well as how to optimize these properties through microstructural and chemical control. Independent projects may be performed depending on the student's interests and abilities.
Advanced Work in Materials Science
The staff in materials science will arrange special courses or problems to meet the needs of students working toward the M.S. degree or of qualified undergraduate students. Graded pass/fail for research and reading.
States of Matter
Thermodynamics and statistical mechanics, with emphasis on gases, liquids, materials, and condensed matter. Effects of heat, pressure, and fields on states of matter are presented with both classical thermodynamics and with statistical mechanics. Conditions of equilibrium in systems with multiple degrees of freedom. Applications include ordered states of matter and phase transitions. The three terms cover, approximately, thermodynamics, statistical mechanics, and phase transitions.
Materials Research Lectures
A seminar course designed to introduce advanced undergraduates and graduate students to modern research in materials science.
Examines the Earth's resources including fresh water, nitrogen, carbon and other biogeochemical cycles that impose planetary constraints on engineering; systems approaches to sustainable development goals; fossil fuel formation, chemical composition, production and use; engineering challenges and opportunities in decarbonizing energy, transportation and industry; global flows of critical elements used in zero-carbon energy systems; food-water-energy nexus; analysis of regional and local systems to model effects of human activities on air, water and soil.
Fundamentals of Materials Science
An introduction to the structure and properties of materials and the processing routes utilized to optimize properties. All major classes of materials are covered, including metals, ceramics, electronic materials, composites, and polymers. The relationships between chemical bonding, crystal structure, defects, thermodynamics, phase equilibria, microstructure, and properties are described.
Mechanical Behavior of Materials
Introduction to the mechanical behavior of solids, emphasizing the relationships between microstructure, architecture, defects, and mechanical properties. Elastic, inelastic, and plastic properties of crystalline and amorphous materials. Relations between stress and strains for different types of materials. Introduction to dislocation theory, motion and forces on dislocations, strengthening mechanisms in crystalline solids. Nanomaterials: properties, fabrication, and mechanics. Architected solids: fabrication, deformation, failure, and energy absorption. Biomaterials: mechanical properties of composites, multi-scale microstructure, biological vs. synthetic, shear lag model. Fracture in brittle solids and linear elastic fracture mechanics.
Laboratory Research Methods in Materials Science
Introduction to experimental methods and approaches for the analysis of structure, dynamics, and properties of materials. Staff members with expertise in various areas including mechanical testing, calorimetry, X-ray diffraction, scanning and transmission electron microscopy, solid state NMR and electrochemistry will introduce and supervise experiments in their specialty. As the situation permits, students are given a choice in selecting experiments. Not offered 2022-23.
Diffraction, Imaging, and Structure
Experimental methods in transmission electron microscopy of inorganic materials including diffraction, spectroscopy, conventional imaging, high resolution imaging and sample preparation. Weekly laboratory exercises to complement material in MS 132.
Advanced Transmission Electron Microscopy
Diffraction contrast analysis of crystalline defects. Phase contrast imaging. Physical optics approach to dynamical electron diffraction and imaging. Microbeam methods for diffraction and imaging. Chemical analysis by energy dispersive X-ray spectrometry and electron energy loss spectrometry. Not offered 2022-23.
Structure and Bonding in Materials
Electronic structure and orbitals in atoms. Structure and symmetry of crystals. Reciprocal space and Brillouin zone. Born-Oppenheimer approximation. Bloch states and band theory. Tight binding and plane-waves. Lattice vibrations and lattice waves. Total energy, entropy, and Gibbs free energy in solids. Stability criteria. Bonding and electronic structure in metals, semiconductors, ionic crystals, and transition metal oxides. Point and line defects. Introduction to surfaces and amorphous materials.
Diffraction and Structure
Principles of electron, X-ray, and neutron diffraction with applications to materials characterization. Imaging with electrons, and diffraction contrast of crystal defects. Kinematical theory of diffraction: effects of strain, size, disorder, and temperature. Correlation functions in solids, with introduction to space-time correlation functions.
Kinetic Processes in Materials
Kinetic master equation, uncorrelated and correlated random walk, diffusion. Mechanisms of diffusion and atom transport in solids, liquids, and gases. Coarsening of microstructures. Nonequilibrium processing of materials.
Introduction to Computational Methods for Science and Engineering
A broad introduction to scientific computing using the Python language. Introduction to Python and its packages Matplotlib, Numpy and SciPy. Numerical precision and sources of error. Root-finding and optimization. Numerical differentiation and integration. Introduction to numerical methods for linear systems and eigenvalue problems. Numerical methods for ordinary differential equations. Finite-difference methods for partial differential equations. Discrete Fourier transforms. Introduction to data-driven and machine learning methods. Singular value decomposition. Deep learning with PyTorch and Keras. Students will develop numerical calculations in the homework and in a final project.
Application of Diffraction Techniques in Materials Science
Applications of X-ray and neutron diffraction methods to the structural characterization of materials. Emphasis is on the analysis of polycrystalline materials but some discussion of single crystal methods is also presented. Techniques include quantitative phase analysis, crystalline size measurement, lattice parameter refinement, internal stress measurement, quantification of preferred orientation (texture) in materials, Rietveld refinement, and determination of structural features from small angle scattering. Homework assignments will focus on analysis of diffraction data. Samples of interest to students for their thesis research may be examined where appropriate. Not offered 2022-23.
Topics in Materials Science
Content will vary from year to year, but will be at a level suitable for advanced undergraduate or graduate students. Topics are chosen according to the interests of students and faculty. Visiting faculty may present portions of the course.
Imperfections in Crystals
The relation of lattice defects to the physical and mechanical properties of crystalline solids. Introduction to point imperfections and their relationships to transport properties in metallic, covalent, and ionic crystals. Kroeger-Vink notation. Introduction to dislocations: geometric, crystallographic, elastic, and energetic properties of dislocations. Dislocation reactions and interactions including formation of locks, stacking faults, and surface effects. Relations between collective dislocation behavior and mechanical properties of crystals. Introduction to computer simulations of dislocations. Grain boundaries. The structure and properties of interfaces in solids. Emphasis on materials science aspects of role of defects in electrical, morphological, optical, and mechanical properties of solids.
An overview of the relationships between chemical, structural, and symmetry properties of prominent material systems with optoelectronic functionalities. Content will be presented through discussions on synthesis and fabrication approaches, core functionalities, and current research frontiers, with a focus on group IV, III-V, and II-VI semiconductors, oxides, two-dimensional materials, dielectrics and mesoscopic systems.
Fracture of Brittle Solids
The mechanical response of brittle materials (ceramics, glasses and some network polymers) will be treated using classical elasticity, energy criteria, and fracture mechanics. The influence of environment and microstructure on mechanical behavior will be explored. Transformation toughened systems, large-grain crack-bridging systems, nanostructured ceramics, porous ceramics, anomalous glasses, and the role of residual stresses will be highlighted. Strength, flaw statistics and reliability will be discussed. Not offered 2022-23.
Inelastic Scattering of Materials, Molecules, and Condensed Matter
Review of Patterson function and memory function for space or time correlations. Van Hove function for correlated dynamics in space and time, especially for materials with thermal energy. Dynamical structure factors for coherent scattering from solids and liquids. Measurements of energy and momentum of dispersive excitations in crystals using neutrons, x-rays, and electrons. Additional topics to be selected from the following list: incoherent inelastic scattering and the thermodynamic partition function, transport of thermal energy, fluctuation-dissipation theorem, quasielastic scattering, sideband information in coherent inelastic scattering, transition from quantum to classical scattering.
Advanced Work in Materials Science
The staff in materials science will arrange special courses or problems to meet the needs of advanced graduate students.
Mechanics and Materials Aspects of Fracture
Analytical and experimental techniques in the study of fracture in metallic and nonmetallic solids. Mechanics of brittle and ductile fracture; connections between the continuum descriptions of fracture and micromechanisms. Discussion of elastic-plastic fracture analysis and fracture criteria. Special topics include fracture by cleavage, void growth, rate sensitivity, crack deflection and toughening mechanisms, as well as fracture of nontraditional materials. Fatigue crack growth and life prediction techniques will also be discussed. In addition, "dynamic" stress wave dominated, failure initiation growth and arrest phenomena will be covered. This will include traditional dynamic fracture considerations as well as discussions of failure by adiabatic shear localization. Not offered 2022-23.
Effective properties of heterogenous and meta-materials
Heterogenous materials. Notion of effective properties. Homogenization theory and applications to linear conductivity, elasticity and viscoelasticity. Effective properties in non-linear setting and instabilities. Wave propagation and meta-materials. Bandgaps.
Multiscale view of materials and different approaches of introducing functionality; Electronic aspects and multiferroic materials; Symmetry breaking phase transformations, microstructure: shape-memory alloys, ferroelectrics, liquid crystal elastomers; Composite materials and metamaterials: multifunctional structures. Not offered 2022-23.
Computational Solid State Physics and Materials Science
The course will cover first-principles computational methods to study electronic structure, lattice vibrations, optical properties, and charge and heat transport in materials. Topics include: Theory and practice of Density Functional Theory (DFT) and the total-energy pseudopotential method. DFT calculations of total energy, structure, defects, charge density, bandstructures, density of states, ferroelectricity and magnetism. Lattice vibrations using the finite-difference supercell and Density Functional Perturbation Theory (DFPT) methods. Electron-electron interactions, screening, and the GW method. GW bandstructure calculations. Optical properties, excitons, and the GW-Bethe Salpeter equation method. Ab initio Boltzmann transport equation (BTE) for electrons and phonons. Computations of heat and charge transport within the BTE framework. If time permits, selected advanced topics will be covered, including methods to treat vander Waals bonds, spin-orbit coupling, correlated materials, and quantum dynamics. Several laboratories will give students direct experience with running first-principles calculations. Not offered 2022-23.