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6.730 Physics for Solid-State Applications (MIT) 6.730 Physics for Solid-State Applications (MIT)

Description

This course examines classical and quantum models of electrons and lattice vibrations in solids, emphasizing physical models for elastic properties, electronic transport, and heat capacity. Topics covered include: crystal lattices, electronic energy band structures, phonon dispersion relatons, effective mass theorem, semiclassical equations of motion, and impurity states in semiconductors, band structure and transport properties of selected semiconductors, and connection of quantum theory of solids with quasifermi levels and Boltzmann transport used in device modeling. This course examines classical and quantum models of electrons and lattice vibrations in solids, emphasizing physical models for elastic properties, electronic transport, and heat capacity. Topics covered include: crystal lattices, electronic energy band structures, phonon dispersion relatons, effective mass theorem, semiclassical equations of motion, and impurity states in semiconductors, band structure and transport properties of selected semiconductors, and connection of quantum theory of solids with quasifermi levels and Boltzmann transport used in device modeling.Subjects

physics | physics | solid state application | solid state application | quantum model | quantum model | electron | electron | lattice vibration | lattice vibration | electronic transport | electronic transport | heat capacity | heat capacity | elastic properties | elastic properties | cystal lattice | cystal lattice | electronic energy band | electronic energy band | phonon dispersion relatons | phonon dispersion relatons | effective mass theorem | effective mass theorem | motion equation | motion equation | impurity state | impurity state | semiconductor | semiconductor | band structure | band structure | transport properties | transport properties | quantum theory of solids | quantum theory of solids | quasifermi | quasifermi | Boltzmann transport | Boltzmann transport | device modeling | device modelingLicense

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See all metadata8.231 Physics of Solids I (MIT) 8.231 Physics of Solids I (MIT)

Description

This course offers an introduction to the basic concepts of the quantum theory of solids. This course offers an introduction to the basic concepts of the quantum theory of solids.Subjects

periodic structure | periodic structure | symmetry of crystals | symmetry of crystals | diffraction | diffraction | reciprocal lattice | reciprocal lattice | chemical bonding | chemical bonding | lattice dynamics | lattice dynamics | phonons | phonons | thermal properties | thermal properties | free electron gas | free electron gas | model of metals | model of metals | Bloch theorem | Bloch theorem | band structure | band structure | nearly free electron approximation | nearly free electron approximation | tight binding method | tight binding method | Fermi surface | Fermi surface | semiconductors | semiconductors | electrons | electrons | holes | holes | impurities | impurities | optical properties | optical properties | excitons | excitons | magnetism. | magnetism.License

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See all metadata8.511 Theory of Solids I (MIT) 8.511 Theory of Solids I (MIT)

Description

This is the first term of a theoretical treatment of the physics of solids. Topics covered include crystal structure and band theory, density functional theory, a survey of properties of metals and semiconductors, quantum Hall effect, phonons, electron phonon interaction and superconductivity. This is the first term of a theoretical treatment of the physics of solids. Topics covered include crystal structure and band theory, density functional theory, a survey of properties of metals and semiconductors, quantum Hall effect, phonons, electron phonon interaction and superconductivity.Subjects

physics of solids | physics of solids | elementary excitations | elementary excitations | symmetry | symmetry | theory of representations | theory of representations | energy bands | energy bands | excitons | excitons | critical points | critical points | response functions | response functions | interactions in the electron gas | interactions in the electron gas | electronic structure of metals | semimetals | electronic structure of metals | semimetals | semiconductors | semiconductors | insulators | insulators | Free electron model | Free electron model | Crystalline lattice | Crystalline lattice | Debye Waller factor | Debye Waller factor | Bravais lattice | Bravais lattice | Pseudopotential | Pseudopotential | van Hove singularity | van Hove singularity | Bloch oscillation | Bloch oscillation | quantization of orbits | quantization of orbits | de Haas-van Alphen effect | de Haas-van Alphen effect | Quantum Hall effect | Quantum Hall effect | Electron-electron interaction | Electron-electron interaction | Hartree-Fock approximation | Hartree-Fock approximation | Exchange energy for Jellium | Exchange energy for Jellium | Density functional theory | Density functional theory | Hubbard model | Hubbard model | Electron-phonon coupling | Electron-phonon coupling | phonons | phononsLicense

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See all metadata2.57 Nano-to-Macro Transport Processes (MIT) 2.57 Nano-to-Macro Transport Processes (MIT)

Description

This course provides parallel treatments of photons, electrons, phonons, and molecules as energy carriers, aiming at fundamental understanding and descriptive tools for energy and heat transport processes from nanoscale continuously to macroscale. Topics include the energy levels, the statistical behavior and internal energy, energy transport in the forms of waves and particles, scattering and heat generation processes, Boltzmann equation and derivation of classical laws, deviation from classical laws at nanoscale and their appropriate descriptions, with applications in nano- and microtechnology. This course provides parallel treatments of photons, electrons, phonons, and molecules as energy carriers, aiming at fundamental understanding and descriptive tools for energy and heat transport processes from nanoscale continuously to macroscale. Topics include the energy levels, the statistical behavior and internal energy, energy transport in the forms of waves and particles, scattering and heat generation processes, Boltzmann equation and derivation of classical laws, deviation from classical laws at nanoscale and their appropriate descriptions, with applications in nano- and microtechnology.Subjects

nanotechnology | nanotechnology | nanoscale | nanoscale | transport phenomena | transport phenomena | photons | photons | electrons | electrons | phonons | phonons | energy carriers | energy carriers | energy transport | energy transport | heat transport | heat transport | energy levels | energy levels | statistical behavior | statistical behavior | internal energy | internal energy | waves and particles | waves and particles | scattering | scattering | heat generation | heat generation | Boltzmann equation | Boltzmann equation | classical laws | classical laws | microtechnology | microtechnology | crystal | crystal | lattice | lattice | quantum oscillator | quantum oscillator | laudaurer | laudaurer | nanotube | nanotube | Louiville equation | Louiville equation | X-ray | X-ray | blackbody | blackbody | quantum well | quantum well | Fourier | Fourier | Newton | Newton | Ohm | Ohm | thermoelectric effect | thermoelectric effect | Brownian motion | Brownian motion | surface tension | surface tension | van der Waals potential. | van der Waals potential. | van der Waals potential | van der Waals potentialLicense

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See all metadata5.069 Crystal Structure Analysis (MIT) 5.069 Crystal Structure Analysis (MIT)

Description

This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scatteringLicense

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See all metadata18.312 Algebraic Combinatorics (MIT) 18.312 Algebraic Combinatorics (MIT)

Description

This course analyzes the applications of algebra to combinatorics and conversely. The topics discussed include enumeration methods, partially ordered sets and lattices, matching theory, partitions and tableaux, algebraic graph theory, and combinatorics of polytopes. This course analyzes the applications of algebra to combinatorics and conversely. The topics discussed include enumeration methods, partially ordered sets and lattices, matching theory, partitions and tableaux, algebraic graph theory, and combinatorics of polytopes.Subjects

Applications of algebra to combinatorics and conversely | Applications of algebra to combinatorics and conversely | enumeration methods | enumeration methods | partially ordered sets and lattices | partially ordered sets and lattices | matching theory | matching theory | partitions and tableaux | partitions and tableaux | algebraic graph theory | algebraic graph theory | combinatorics of polytopes | combinatorics of polytopesLicense

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This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scatteringLicense

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Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles. Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles.Subjects

Thermodynamics | Thermodynamics | entropy. mehanics | entropy. mehanics | microcanonical distributions | microcanonical distributions | canonical distributions | canonical distributions | grand canonical distributions; lattice vibrations | grand canonical distributions; lattice vibrations | ideal gas | ideal gas | photon gas. | photon gas. | quantum statistical mechanics; Fermi systems | quantum statistical mechanics; Fermi systems | Bose systems | Bose systems | cluster expansions | cluster expansions | van der Waal's gas | van der Waal's gas | mean-field theory. | mean-field theory.License

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See all metadata8.231 Physics of Solids I (MIT) 8.231 Physics of Solids I (MIT)

Description

The topics covered in this course include:Periodic Structure and Symmetry of CrystalsDiffraction, Reciprocal LatticeChemical BondingLattice DynamicsPhononsThermal PropertiesFree Electron GasModel of MetalsBloch Theorem and Band StructureNearly Free Electron ApproximationTight Binding MethodFermi SurfaceSemiconductorsElectronsHolesImpuritiesOptical PropertiesExcitons andMagnetism The topics covered in this course include:Periodic Structure and Symmetry of CrystalsDiffraction, Reciprocal LatticeChemical BondingLattice DynamicsPhononsThermal PropertiesFree Electron GasModel of MetalsBloch Theorem and Band StructureNearly Free Electron ApproximationTight Binding MethodFermi SurfaceSemiconductorsElectronsHolesImpuritiesOptical PropertiesExcitons andMagnetismSubjects

periodic structure and symmetry of crystals | periodic structure and symmetry of crystals | diffraction | diffraction | reciprocal lattice | reciprocal lattice | chemical bonding | chemical bonding | phonons | phonons | thermal properties | thermal properties | free electron gas | free electron gas | model of metals | model of metals | Bloch theorem and band structure | Bloch theorem and band structure | nearly free electron approximation | nearly free electron approximation | tight binding method | tight binding method | Fermi surface | Fermi surface | semiconductors | semiconductors | electrons | electrons | holes | holes | impurities | impurities | optical properties | optical properties | excitons | excitons | magnetism | magnetismLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata3.014 Materials Laboratory (MIT) 3.014 Materials Laboratory (MIT)

Description

This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degre This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degreSubjects

electron | electron | electronic properties | electronic properties | magnetism | magnetism | magentic properties | magentic properties | structure | structure | crystal | crystal | lattice | lattice | energy | energy | thermodynamics | thermodynamics | differential scanning calorimetry (DSC) | differential scanning calorimetry (DSC) | x-ray diffraction (XRD) | x-ray diffraction (XRD) | scanning probe microscopy (AFM | scanning probe microscopy (AFM | STM) | STM) | scanning electron microscopy (SEM) | scanning electron microscopy (SEM) | UV/Vis | UV/Vis | Raman spectroscopy | Raman spectroscopy | FTIR spectroscopy | FTIR spectroscopy | x-ray photoelectron spectroscopy (XPS) | x-ray photoelectron spectroscopy (XPS) | vibrating sample magnetometry (VSM) | vibrating sample magnetometry (VSM) | dynamic light scattering (DLS) | dynamic light scattering (DLS) | phonon | phonon | quantum | quantum | quantum mechanics | quantum mechanics | radiation | radiation | battery | battery | fuel cell | fuel cell | ferromagnetism | ferromagnetism | ferromagnetic | ferromagnetic | polymer | polymer | glass | glass | corrosion | corrosionLicense

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See all metadata16.100 Aerodynamics (MIT) 16.100 Aerodynamics (MIT)

Description

This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .tar files found on this course site. MATLAB This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .tar files found on this course site. MATLABSubjects

aerodynamics | aerodynamics | airflow | airflow | air | air | body | body | aircraft | aircraft | aerodynamic modes | aerodynamic modes | aero | aero | forces | forces | flow | flow | computational | computational | CFD | CFD | aerodynamic analysis | aerodynamic analysis | lift | lift | drag | drag | potential flows | potential flows | imcompressible | imcompressible | supersonic | supersonic | subsonic | subsonic | panel method | panel method | vortex lattice method | vortex lattice method | boudary layer | boudary layer | transition | transition | turbulence | turbulence | inviscid | inviscid | viscous | viscous | euler | euler | navier-stokes | navier-stokes | wind tunnel | wind tunnel | flow similarity | flow similarity | non-dimensional | non-dimensional | mach number | mach number | reynolds number | reynolds number | integral momentum | integral momentum | airfoil | airfoil | wing | wing | stall | stall | friction drag | friction drag | induced drag | induced drag | wave drag | wave drag | pressure drag | pressure drag | fluid element | fluid element | shear strain | shear strain | normal strain | normal strain | vorticity | vorticity | divergence | divergence | substantial derviative | substantial derviative | laminar | laminar | displacement thickness | displacement thickness | momentum thickness | momentum thickness | skin friction | skin friction | separation | separation | velocity profile | velocity profile | 2-d panel | 2-d panel | 3-d vortex | 3-d vortex | thin airfoil | thin airfoil | lifting line | lifting line | aspect ratio | aspect ratio | twist | twist | camber | camber | wing loading | wing loading | roll moments | roll moments | finite volume approximation | finite volume approximation | shocks | shocks | expansion fans | expansion fans | shock-expansion theory | shock-expansion theory | transonic | transonic | critical mach number | critical mach number | wing sweep | wing sweep | Kutta condition | Kutta condition | team project | team project | blended-wing-body | blended-wing-body | computational fluid dynamics | computational fluid dynamics | Incompressible | IncompressibleLicense

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See all metadata8.851 Strong Interactions (MIT) 8.851 Strong Interactions (MIT)

Description

Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects. Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects.Subjects

matching | matching | renormalization | renormalization | the operator product expansion | the operator product expansion | power counting | power counting | heavy quark decays | heavy quark decays | CP violation | CP violation | factorization in hard processes | factorization in hard processes | non-relativistic bound states in field theory (QED and QCD) | non-relativistic bound states in field theory (QED and QCD) | chiral perturbation theory | chiral perturbation theory | few-nucleon systems | few-nucleon systems | strong force | strong force | quarks | quarks | relativistic quantum field theory | relativistic quantum field theory | quantum chromodynamics | quantum chromodynamics | QCD | QCD | QCD Langrangian | QCD Langrangian | asymptotic freedom | asymptotic freedom | deep inelastic scattering | deep inelastic scattering | jets | jets | QCD vacuum | QCD vacuum | instantons | instantons | U(1) proglem | U(1) proglem | lattice gauge theory | lattice gauge theory | strong interactions | strong interactions | standard model | standard model | operator product expansion | operator product expansion | factorization | factorization | hard processes | hard processes | exclusive processes | exclusive processes | non-relativistic bound states | non-relativistic bound states | QED | QED | massive particles | massive particles | effective field theory | effective field theory | soft-collinear effective theory | soft-collinear effective theoryLicense

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See all metadata8.333 Statistical Mechanics (MIT) 8.333 Statistical Mechanics (MIT)

Description

8.333 is the first course in a two-semester sequence on statistical mechanics. Basic principles are examined in 8.333: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, micro canonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory. 8.333 is the first course in a two-semester sequence on statistical mechanics. Basic principles are examined in 8.333: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, micro canonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory.Subjects

hermodynamics | hermodynamics | entropy | entropy | mehanics | mehanics | microcanonical distributions | microcanonical distributions | canonical distributions | canonical distributions | grand canonical distributions | grand canonical distributions | lattice vibrations | lattice vibrations | ideal gas | ideal gas | photon gas | photon gas | quantum statistical mechanics | quantum statistical mechanics | Fermi systems | Fermi systems | Bose systems | Bose systems | cluster expansions | cluster expansions | van der Waal's gas | van der Waal's gas | mean-field theory | mean-field theoryLicense

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See all metadata3.014 Materials Laboratory (MIT) 3.014 Materials Laboratory (MIT)

Description

This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degre This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degreSubjects

electron | electron | electronic properties | electronic properties | magnetism | magnetism | magentic properties | magentic properties | structure | structure | crystal | crystal | lattice | lattice | energy | energy | thermodynamics | thermodynamics | differential scanning calorimetry (DSC) | differential scanning calorimetry (DSC) | x-ray diffraction (XRD) | x-ray diffraction (XRD) | scanning probe microscopy (AFM | scanning probe microscopy (AFM | STM) | STM) | scanning electron microscopy (SEM) | scanning electron microscopy (SEM) | UV/Vis | UV/Vis | Raman spectroscopy | Raman spectroscopy | FTIR spectroscopy | FTIR spectroscopy | x-ray photoelectron spectroscopy (XPS) | x-ray photoelectron spectroscopy (XPS) | vibrating sample magnetometry (VSM) | vibrating sample magnetometry (VSM) | dynamic light scattering (DLS) | dynamic light scattering (DLS) | phonon | phonon | quantum | quantum | quantum mechanics | quantum mechanics | radiation | radiation | battery | battery | fuel cell | fuel cell | ferromagnetism | ferromagnetism | ferromagnetic | ferromagnetic | polymer | polymer | glass | glass | corrosion | corrosionLicense

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This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity. This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity.Subjects

crystallography | crystallography | rotation | rotation | translation | translation | lattice | lattice | plane | plane | point group | point group | space group | space group | motif | motif | glide plane | glide plane | mirror plane | mirror plane | reflection | reflection | spherical trigonometry | spherical trigonometry | binary compound | binary compound | coordination number | coordination number | ion | ion | crystal structure | crystal structure | tetrahedral | tetrahedral | octahedral | octahedral | packing | packing | monoclinic | monoclinic | triclinic | triclinic | orthorhombic | orthorhombic | cell | cell | screw axis | screw axis | eigenvector | eigenvector | stress | stress | strain | strain | anisotropy | anisotropy | anisotropic | anisotropic | piezoelectric | piezoelectricLicense

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See all metadata3.20 Materials at Equilibrium (SMA 5111) (MIT) 3.20 Materials at Equilibrium (SMA 5111) (MIT)

Description

Material covered in this course includes the following topics: Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams Computation of phase diagrams Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions Applications to phase stability and properties of mixtures Computational modeling Interfaces This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5111 (Materials at Equilibrium). Material covered in this course includes the following topics: Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams Computation of phase diagrams Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions Applications to phase stability and properties of mixtures Computational modeling Interfaces This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5111 (Materials at Equilibrium).Subjects

thermodynamics | thermodynamics | mechanical | mechanical | electromagnetic and electrochemical systems | electromagnetic and electrochemical systems | phase diagrams | phase diagrams | Statistical thermodynamics | Statistical thermodynamics | microscopic and macroscopic properties | microscopic and macroscopic properties | ensembles | ensembles | gases | gases | crystal lattices | crystal lattices | phase transitions | phase transitions | phase stability | phase stability | properties of mixtures | properties of mixtures | Computational modeling | Computational modeling | Interfaces | Interfaces | mechanical | electromagnetic and electrochemical systems | mechanical | electromagnetic and electrochemical systems | Computational modeling; Interfaces | Computational modeling; Interfaces | mechanical systems | mechanical systems | electromagnetic systems | electromagnetic systems | electrochemical systems | electrochemical systems | laws of thermodynamics | laws of thermodynamics | solutions | solutions | microscopic properties | microscopic properties | macroscopic properties | macroscopic propertiesLicense

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See all metadata2.23 Hydrofoils and Propellers (MIT) 2.23 Hydrofoils and Propellers (MIT)

Description

This course develops the theory and design of hydrofoil sections, including lifting and thickness problems for sub-cavitating sections, unsteady flow problems, and computer-aided design of low drag cavitation-free sections. It also covers lifting line and lifting surface theory with applications to hydrofoil craft, rudder, control surface, propeller and wind turbine rotor design. Other topics include computer-aided design of wake adapted propellers; steady and unsteady propeller thrust and torque; performance analysis and design of wind turbine rotors in steady and stochastic wind; and numerical principles of vortex lattice and lifting surface panel methods. Projects illustrate the development of computational methods for lifting, propeller and wind turbine flows, and use of state-of-the-a This course develops the theory and design of hydrofoil sections, including lifting and thickness problems for sub-cavitating sections, unsteady flow problems, and computer-aided design of low drag cavitation-free sections. It also covers lifting line and lifting surface theory with applications to hydrofoil craft, rudder, control surface, propeller and wind turbine rotor design. Other topics include computer-aided design of wake adapted propellers; steady and unsteady propeller thrust and torque; performance analysis and design of wind turbine rotors in steady and stochastic wind; and numerical principles of vortex lattice and lifting surface panel methods. Projects illustrate the development of computational methods for lifting, propeller and wind turbine flows, and use of state-of-the-aSubjects

turbine | turbine | rotor | rotor | computer-aided design | computer-aided design | propulsion | propulsion | lifting line | lifting line | thrust | thrust | torque | torque | vortices | vortices | boundary layers | boundary layers | wake adaptation | wake adaptation | cavitation | cavitation | fluid flow | fluid flow | fluid dynamics | fluid dynamics | lifting surface panel method | lifting surface panel method | vortex lattice method | vortex lattice method | lifting flow | lifting flowLicense

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See all metadata5.069 Crystal Structure Analysis (MIT) 5.069 Crystal Structure Analysis (MIT)

Description

This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scatteringLicense

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See all metadata8.325 Relativistic Quantum Field Theory III (MIT) 8.325 Relativistic Quantum Field Theory III (MIT)

Description

This course is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physics of the standard model. Topics include: quantum chromodynamics; the Higgs phenomenon and a description of the standard model; deep-inelastic scattering and structure functions; basics of lattice gauge theory; operator products and effective theories; detailed structure of the standard model; spontaneously broken gauge theory and its quantization; instantons and theta-vacua; topological defects; introduction to supersymmetry. This course is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physics of the standard model. Topics include: quantum chromodynamics; the Higgs phenomenon and a description of the standard model; deep-inelastic scattering and structure functions; basics of lattice gauge theory; operator products and effective theories; detailed structure of the standard model; spontaneously broken gauge theory and its quantization; instantons and theta-vacua; topological defects; introduction to supersymmetry.Subjects

gauge symmetry | gauge symmetry | confinement | confinement | renormalization | renormalization | asymptotic freedom | asymptotic freedom | anomalies | anomalies | instantons | instantons | zero modes | zero modes | gauge boson and Higgs spectrum | gauge boson and Higgs spectrum | fermion multiplets | fermion multiplets | CKM matrix | CKM matrix | unification in SU(5) and SO(10) | unification in SU(5) and SO(10) | phenomenology of Higgs sector | phenomenology of Higgs sector | lepton and baryon number violation | lepton and baryon number violation | nonperturbative (lattice) formulation | nonperturbative (lattice) formulationLicense

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See all metadata8.325 Relativistic Quantum Field Theory III (MIT) 8.325 Relativistic Quantum Field Theory III (MIT)

Description

This is the third and last term of the quantum field theory sequence. The course is devoted to the standard model of particle physics, including both its conceptual foundations and its specific structure, and to some current research frontiers that grow immediately out of it. This is the third and last term of the quantum field theory sequence. The course is devoted to the standard model of particle physics, including both its conceptual foundations and its specific structure, and to some current research frontiers that grow immediately out of it.Subjects

gauge symmetry | gauge symmetry | confinement | confinement | renormalization | renormalization | asymptotic freedom | asymptotic freedom | anomalies | anomalies | instantons | instantons | zeromodes | zeromodes | gauge boson and Higgs spectrum | gauge boson and Higgs spectrum | fermion multiplets | fermion multiplets | CKM matrix | CKM matrix | unification in SU(5) andSO(10) | unification in SU(5) andSO(10) | phenomenology of Higgs sector | phenomenology of Higgs sector | lepton andbaryon number violation | lepton andbaryon number violation | nonperturbative (lattice)formulation | nonperturbative (lattice)formulationLicense

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See all metadata12.108 Structure of Earth Materials (MIT) 12.108 Structure of Earth Materials (MIT)

Description

This course provides a comprehensive introduction to crystalline structure, crystal chemistry, and bonding in rock-forming minerals. It introduces the theory relating crystal structure and crystal symmetry to physical properties such as refractive index, elastic modulus, and seismic velocity. It surveys the distribution of silicate, oxide, and metallic minerals in the interiors and on the surfaces of planets, and discusses the processes that led to their formation. It also addresses why diamonds are hard and why micas split into thin sheets. This course provides a comprehensive introduction to crystalline structure, crystal chemistry, and bonding in rock-forming minerals. It introduces the theory relating crystal structure and crystal symmetry to physical properties such as refractive index, elastic modulus, and seismic velocity. It surveys the distribution of silicate, oxide, and metallic minerals in the interiors and on the surfaces of planets, and discusses the processes that led to their formation. It also addresses why diamonds are hard and why micas split into thin sheets.Subjects

Crystal Symmetry | Crystal Symmetry | Point Groups | Point Groups | Space Groups | Space Groups | Crystal Chemistry | Crystal Chemistry | Bonding | Bonding | Electron Diffraction | Electron Diffraction | Crystal lattices | Crystal lattices | Tensor Analysis | Tensor Analysis | Optical Properties | Optical Properties | Elastic Properties | Elastic Properties | Magnetic Properties | Magnetic Properties | Stress | Stress | Strain | StrainLicense

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See all metadata16.100 Aerodynamics (MIT) 16.100 Aerodynamics (MIT)

Description

This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem.Subjects

aerodynamics | aerodynamics | airflow | airflow | air | air | body | body | aircraft | aircraft | aerodynamic modes | aerodynamic modes | aero | aero | forces | forces | flow | flow | computational | computational | CFD | CFD | aerodynamic analysis | aerodynamic analysis | lift | lift | drag | drag | potential flows | potential flows | imcompressible | imcompressible | supersonic | supersonic | subsonic | subsonic | panel method | panel method | vortex lattice method | vortex lattice method | boudary layer | boudary layer | transition | transition | turbulence | turbulence | inviscid | inviscid | viscous | viscous | euler | euler | navier-stokes | navier-stokes | wind tunnel | wind tunnel | flow similarity | flow similarity | non-dimensional | non-dimensional | mach number | mach number | reynolds number | reynolds number | integral momentum | integral momentum | airfoil | airfoil | wing | wing | stall | stall | friction drag | friction drag | induced drag | induced drag | wave drag | wave drag | pressure drag | pressure drag | fluid element | fluid element | shear strain | shear strain | normal strain | normal strain | vorticity | vorticity | divergence | divergence | substantial derivative | substantial derivative | laminar | laminar | displacement thickness | displacement thickness | momentum thickness | momentum thickness | skin friction | skin friction | separation | separation | velocity profile | velocity profile | 2-d panel | 2-d panel | 3-d vortex | 3-d vortex | thin airfoil | thin airfoil | lifting line | lifting line | aspect ratio | aspect ratio | twist | twist | camber | camber | wing loading | wing loading | roll moments | roll moments | finite volume approximation | finite volume approximation | shocks | shocks | expansion fans | expansion fans | shock-expansion theory | shock-expansion theory | transonic | transonic | critical mach number | critical mach number | wing sweep | wing sweep | Kutta condition | Kutta condition | team project | team project | blended-wing-body | blended-wing-body | computational fluid dynamics | computational fluid dynamicsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.786 Topics in Algebraic Number Theory (MIT) 18.786 Topics in Algebraic Number Theory (MIT)

Description

This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants. This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.Subjects

number fields | number fields | dedekind domain | dedekind domain | prime ideal | prime ideal | class group | class group | lattice method | lattice methodLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.318 Topics in Algebraic Combinatorics (MIT) 18.318 Topics in Algebraic Combinatorics (MIT)

Description

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings. The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.Subjects

algebraic combinatorics | algebraic combinatorics | matrix-tree theorem | matrix-tree theorem | linear algebra | linear algebra | commutative algebra | commutative algebra | exterior algebra | exterior algebra | counting faces of simplicial complexes | counting faces of simplicial complexes | tilings | tilings | Young's lattice | Young's lattice | Shannon capacity | Shannon capacity | Fisher inequality | Fisher inequality | Hadamard matrices | Hadamard matrices | f-vectors | f-vectors | Sperner Property | Sperner Property | -Binomial Coeffcients | -Binomial CoeffcientsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This is a graduate-level course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids. This is a graduate-level course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids.Subjects

Combinatorial Theory | Combinatorial Theory | Hyperplane Arrangements | Hyperplane Arrangements | Intersection Poset | Intersection Poset | Matroids | Matroids | Geometric Lattices | Geometric Lattices | Broken Circuits | Broken Circuits | Modular Elements | Modular Elements | Supersolvability | Supersolvability | Finite Fields | Finite Fields | Hyperplane | Hyperplane | Arrangements | Arrangements | intersection poset | intersection poset | geometric lattices | geometric lattices | Broken circuits | Broken circuits | modular elements | modular elements | supersolvability | supersolvability | Finite fields | Finite fieldsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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