The document discusses graphene and its potential applications. It covers 5 topics:
1) Computational modeling of defects in materials and devices.
2) Local structure of metal alloys using diffusion scattering and atomic displacements.
3) Defects in semiconductors like GaN, SiC, and AlSb and their device behavior.
4) Functional materials issues for memristors using TiO2 and ZnO.
5) Graphene as a future material and searching for application niches.
This homework assignment covers several topics in thermodynamics and statistical mechanics. It includes 6 problems related to thermal equilibrium of isolated systems (problem 4), deriving the escape velocity of Earth (problem 7), applying the equipartition theorem to model thermal fluctuations in a spring balance (problem 8), and reviewing probability distributions and average energy as a function of temperature (problems 9-10). Key steps are outlined for some problems, such as using a Taylor expansion to approximate a probability distribution as Gaussian near its maximum for problem 4.
Slides of the talk on Koide Formula. Video should be available at http://viavca.in2p3.fr/alejandro_rivero.html
or directly al flv
http://viavca.in2p3.fr/video/alejandro_rivero.flv
This document provides examples and explanations for proving triangle congruence using the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates. It begins with definitions of key vocabulary like included angle. Example 1 uses SSS to prove two triangles congruent by showing that corresponding sides are congruent. Example 2 has students graph triangles on a coordinate plane and determine if they are congruent. Example 3 uses the midpoint theorem and vertical angles theorem to prove triangles congruent via SAS. The document concludes with practice problems for students.
This talk reviews recent results from Belle regarding charmonia, bottomonia, and exotic states. Measurements include properties of XYZ states like the X(3872), discovery of new bottomonium-like states Y(nS), and evidence for the ηb(2S). Analyses of e+e- → ηJ/ψ via ISR, B → χc1,2γK, B0 → J/ψKπ+, and Y(nS)π+π- provide insights into exotic states and help understand heavy quarkonium spectroscopy.
4.7 use isosceles and equilateral trianglesdetwilerr
1. The document discusses classifying triangles by their sides as equilateral, isosceles, or scalene. It also covers properties of equilateral triangles including that all angles are 60 degrees.
2. Examples show using congruence postulates like SAS and AAS to prove triangles are congruent or find missing angle measures. The base angles theorem is also used.
3. One example involves finding missing side lengths of an isosceles triangle and using properties that the base angles are congruent.
Is Gravitation A Result Of Asymmetric Coulomb Charge Interactions?Jeffrey Gold
Journal of Undergraduate Research (JUR), University of Utah (1992), Vol. 3, No. 1, pp. 56-61.
Jeffrey F. Gold
Department of Physics, Department of Mathematics
University of Utah
Abstract
Many attempts have been made to equate gravitational forces with manifestations of other phenomena. In these remarks we explore the consequences of formulating gravitational forces as asymmetric Coulomb charge interactions. This is contrary to some established theories, for the model predicts differential accelerations dependent on the elemental composition of the test mass. The
predicted di erentials of acceleration of various elemental masses are compared to those differentials that have been obtained experimentally. Although the model turns out to fail, the construction of this model is a useful intellectual and pedagogical exercise.
This document discusses properties of parallelograms. It defines a parallelogram as a quadrilateral with two pairs of parallel sides. The document lists properties of parallelograms, including: opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; if one angle is a right angle, all angles are right angles. It also states that the diagonals of a parallelogram bisect each other and divide the parallelogram into two congruent triangles. Examples demonstrate using these properties to find missing measures and intersection points of diagonals.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
This homework assignment covers several topics in thermodynamics and statistical mechanics. It includes 6 problems related to thermal equilibrium of isolated systems (problem 4), deriving the escape velocity of Earth (problem 7), applying the equipartition theorem to model thermal fluctuations in a spring balance (problem 8), and reviewing probability distributions and average energy as a function of temperature (problems 9-10). Key steps are outlined for some problems, such as using a Taylor expansion to approximate a probability distribution as Gaussian near its maximum for problem 4.
Slides of the talk on Koide Formula. Video should be available at http://viavca.in2p3.fr/alejandro_rivero.html
or directly al flv
http://viavca.in2p3.fr/video/alejandro_rivero.flv
This document provides examples and explanations for proving triangle congruence using the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates. It begins with definitions of key vocabulary like included angle. Example 1 uses SSS to prove two triangles congruent by showing that corresponding sides are congruent. Example 2 has students graph triangles on a coordinate plane and determine if they are congruent. Example 3 uses the midpoint theorem and vertical angles theorem to prove triangles congruent via SAS. The document concludes with practice problems for students.
This talk reviews recent results from Belle regarding charmonia, bottomonia, and exotic states. Measurements include properties of XYZ states like the X(3872), discovery of new bottomonium-like states Y(nS), and evidence for the ηb(2S). Analyses of e+e- → ηJ/ψ via ISR, B → χc1,2γK, B0 → J/ψKπ+, and Y(nS)π+π- provide insights into exotic states and help understand heavy quarkonium spectroscopy.
4.7 use isosceles and equilateral trianglesdetwilerr
1. The document discusses classifying triangles by their sides as equilateral, isosceles, or scalene. It also covers properties of equilateral triangles including that all angles are 60 degrees.
2. Examples show using congruence postulates like SAS and AAS to prove triangles are congruent or find missing angle measures. The base angles theorem is also used.
3. One example involves finding missing side lengths of an isosceles triangle and using properties that the base angles are congruent.
Is Gravitation A Result Of Asymmetric Coulomb Charge Interactions?Jeffrey Gold
Journal of Undergraduate Research (JUR), University of Utah (1992), Vol. 3, No. 1, pp. 56-61.
Jeffrey F. Gold
Department of Physics, Department of Mathematics
University of Utah
Abstract
Many attempts have been made to equate gravitational forces with manifestations of other phenomena. In these remarks we explore the consequences of formulating gravitational forces as asymmetric Coulomb charge interactions. This is contrary to some established theories, for the model predicts differential accelerations dependent on the elemental composition of the test mass. The
predicted di erentials of acceleration of various elemental masses are compared to those differentials that have been obtained experimentally. Although the model turns out to fail, the construction of this model is a useful intellectual and pedagogical exercise.
This document discusses properties of parallelograms. It defines a parallelogram as a quadrilateral with two pairs of parallel sides. The document lists properties of parallelograms, including: opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; if one angle is a right angle, all angles are right angles. It also states that the diagonals of a parallelogram bisect each other and divide the parallelogram into two congruent triangles. Examples demonstrate using these properties to find missing measures and intersection points of diagonals.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
1. The document discusses arithmetic progressions (AP) and geometric progressions (GP). An AP is a sequence where each term after the first is calculated by adding a constant to the previous term. A GP is a sequence where each term is calculated by multiplying the previous term by a constant.
2. Formulas are provided for calculating terms of APs and GPS, including formulas for the nth term, the sum of the first n terms, and identifying whether a set of numbers are in AP or GP.
3. The document concludes with 30 multiple choice questions testing understanding of APs and GPS.
This document contains an unsolved chemistry practice paper from 2008 for IITJEE (Indian Institute of Technology Joint Entrance Examination). It has four sections testing different chemistry concepts through multiple choice questions. Section I has 9 objective questions testing concepts like IUPAC names, compound identification, hybridization, and solubility products. Section II has 4 reasoning questions requiring understanding of statements. Section III has 3 linked comprehension questions about reaction mechanisms. Section IV contains 3 matrix-match questions testing relationships between concepts.
Here are the electron configurations (full and condensed) for the requested elements:
B 1s2 2s2 2p1 or [He] 2s2 2p1
F 1s2 2s2 2p5 or [He] 2s2 2p5
Ca 1s2 2s2 2p6 3s2 3p6 4s2 or [Ar] 4s2
P 1s2 2s2 2p6 3s2 3p3 or [Ne] 3s2 3p3
S 1s2 2s2 2p6 3s2 3p4 or [Ne] 3s2 3p4
As 1s2 2s2 2
The document discusses using the VSEPR model to predict the molecular geometry of O3 and SnCl3-. It explains that for O3, the central O atom has three electron domains in a trigonal planar arrangement, giving it a bent molecular geometry. For SnCl3-, the central Sn atom has four electron domains in a tetrahedral arrangement due to one lone pair, giving it a trigonal pyramidal molecular geometry.
This document summarizes a method called transplantation that can be used to show two planar domains have the same spectrum and are therefore isospectral. Transplantation takes a Dirichlet eigenfunction on one domain and constructs a corresponding eigenfunction on the other domain with the same eigenvalue. This is done by dividing the domains into congruent triangles and piecing together the restrictions of the eigenfunction in a way that satisfies continuity and boundary conditions. Numerical computation of the discretized Laplacian spectrum on sample isospectral domains verifies the transplanted eigenfunctions have identical eigenvalues, demonstrating the domains are isospectral.
1. The document provides definitions and properties of kites and trapezoids, including that a kite has two pairs of congruent consecutive sides and a trapezoid has one pair of parallel sides.
2. Two examples show using properties of kites and trapezoids to solve problems, such as finding missing angle measures in a kite and finding side lengths in isosceles trapezoids.
3. The trapezoid midsegment theorem states that the midsegment of a trapezoid is half the sum of the legs, and this is used to find a missing side length in one example.
This document summarizes the following:
(1) The author proves local existence and a blow-up criterion for solutions to the Euler equations in Besov spaces.
(2) As a corollary, for 2D Euler equations with initial velocity in Besov spaces, the author obtains persistence of Besov space regularity.
(3) The blow-up criterion improves previous criteria by replacing the BMO norm of vorticity with the weaker B∞,∞ norm.
- Rainbows are caused by the scattering and reflection of light inside raindrops, which causes the sky to appear brighter at certain angles depending on the path the light takes.
- The primary rainbow results from one internal reflection and appears at an angle of around 42 degrees. The colors are ordered from red on the outside to violet on the inside due to their different refractive indices.
- Additional rainbows can result from further internal reflections, with the secondary rainbow appearing inverted at around 52 degrees from two reflections. Higher order rainbows appear at increasing angles but are harder to see.
The document discusses the Hinge Theorem and its converse for comparing sides and angles of triangles. It provides examples of applying the Hinge Theorem and its converse to determine if one side or angle is greater than the other. It also gives an example problem of proving that one side is less than the other using the Hinge Theorem and properties of alternate interior angles for parallel lines cut by a transversal. The document concludes with assigning practice problems related to applying the Hinge Theorem and its converse.
I am Terry K . I am a Semiconductor Assignment Expert at eduassignmenthelp.com. I hold a Ph.D. in Semiconductor, from the University of Chicago, USA. I have been helping students with their homework for the past 8 years. I solve assignments related to Semiconductor.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Semiconductor Assignments.
The document discusses the calculation of vacuum polarization corrections to the energy levels of hydrogen atom. It presents numerical calculations of the one-photon vacuum polarization corrections to the 1s, 2s, 2p, 3s, 3p and 3d energy levels of hydrogen using the Uehling potential. The contribution of this correction decreases with increasing principal quantum number n and orbital quantum number l. It also calculates the relativistic effects on the 1s, 2s, 2p1/2 and 2p3/2 levels using Dirac wave functions. The results show the vacuum polarization effect is largest near the nucleus and decreases with n.
The document provides information on anomalous electron configurations of some elements, where the actual electron configuration differs from what is expected based on the Aufbau principle. It notes that stable configurations occur for half-filled or completely filled d or f orbitals. Examples are given of elements like Chromium, Copper, Silver, and Gold that have these anomalous configurations due to having superior stability from half-filled or filled d or f orbitals compared to nearly filled orbitals. The exceptions are said to occur more for larger elements where orbital energies are similar.
This document discusses probabilistic diameter and its properties. It defines probabilistic diameter (DA) as a distribution function that represents the probability that the distance between any two points in a set A is less than some value t. It presents several properties of probabilistic diameter including: (1) DA is a distribution function; (2) DA = H if A contains a single point; and (3) if A is a subset of B, then DA ≥ DB. It also defines probabilistic distance between two sets A and B as another distribution function (FAB) and establishes some of its properties.
5.1 midsegment theorem and coordinate proofdetwilerr
This document discusses using the midsegment theorem and coordinate proofs to find lengths and midpoints of line segments in triangles and rectangles. It provides examples of placing shapes like triangles and rectangles in a coordinate plane to find side lengths and midpoints using the distance and midpoint formulas. It also includes practice problems asking students to find side lengths, midpoints, and perimeters of shapes by using properties of midsegments or coordinates of vertices.
The document discusses the electronic band structure of graphene. It presents the tight-binding model and shows that graphene has a linear dispersion relation around the Dirac points, resulting in massless Dirac fermions. The tight-binding parameters t and t' are defined, and their effects on the band structure are described.
The document studies small excitonic complexes in a disk-shaped quantum dot using the Bethe-Goldstone equation. It examines systems with up to 12 electron-hole pairs. For symmetric configurations where the number of electrons equals the number of holes, it finds:
1) The triexciton and four-exciton system show weak binding or possible unbinding in the weak confinement regime.
2) Higher complexes beyond four pairs exhibit binding in the weak confinement regime.
3) The Bethe-Goldstone approach provides better energies than the BCS variational method in the weak confinement regime.
I am Peterson N. I am a Physical Chemistry Assignment Expert at eduassignmenthelp.com. I hold a Ph.D. in Physical Chemistry, University of Melbourne, Australia. I have been helping students with their homework for the past 8 years. I solve assignments related to Physical Chemistry.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Physical Chemistry Assignments.
FINAL 2014 Summer QuarkNet Research – LHCb PaperTheodore Baker
The document summarizes the author's 2014 summer research analyzing decay data from the LHCb detector. The author analyzed several decay channels including Λ c → Ξ− K+ π+, Ω b
−
→ Ω− J/ψ, and D s
+ → K− K+ π+. For the Λ c decay, the author found evidence of a Ξ0 resonance. For the Ω b decay, the author measured the mass but found the lifetime fit was off. For the D s decay, the author observed decays through φ(1020) and K*(892) resonances. The author was unable to find evidence of the hypothesized Ω cb
0 baryon due
1) The document discusses the electronic configuration of atoms, including the development of wave mechanics and quantum theory to explain the structure of atoms. It introduces concepts like the de Broglie wavelength, quantum numbers, atomic orbitals and shapes, Pauli's exclusion principle, and Hund's rule for electron configuration.
2) Key scientists discussed include de Broglie, Heisenberg, Schrodinger, Pauli, and their contributions to developing models of the atom and allowing prediction of electron configurations.
3) The document provides examples of writing out electron configurations for elements and explaining the rules for filling atomic orbitals in the Aufbau principle.
The document discusses the effective mass approximation in quantum mechanics. It begins by defining the effective mass as inversely proportional to the curvature of energy bands. Having a effective mass allows electrons in crystals to be treated similarly to classical particles, with the crystal forces and quantum properties accounted for in the mass. The effective mass can be a tensor and depends on the crystal direction. It then discusses measuring the effective mass using cyclotron resonance and how it varies by crystallographic direction. In general, the effective mass incorporates the quantum mechanical behavior of electrons in crystals to allow a classical particle treatment.
This document discusses how catastrophe theory can be applied to physical systems using manifolds. It describes how potential functions from catastrophe theory can influence manifolds that are locally like 4D Euclidean space. Seven catastrophes from Thom's theory are structurally stable. In addition to catastrophe manifolds, other manifolds can arise without polar singularities or with a diagonal metric. Complex numbers, quaternions, and octonions can be added to the 4D space. Applications to bifurcations, measuring frames, particles, and effects on systems are discussed.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
1. The document discusses arithmetic progressions (AP) and geometric progressions (GP). An AP is a sequence where each term after the first is calculated by adding a constant to the previous term. A GP is a sequence where each term is calculated by multiplying the previous term by a constant.
2. Formulas are provided for calculating terms of APs and GPS, including formulas for the nth term, the sum of the first n terms, and identifying whether a set of numbers are in AP or GP.
3. The document concludes with 30 multiple choice questions testing understanding of APs and GPS.
This document contains an unsolved chemistry practice paper from 2008 for IITJEE (Indian Institute of Technology Joint Entrance Examination). It has four sections testing different chemistry concepts through multiple choice questions. Section I has 9 objective questions testing concepts like IUPAC names, compound identification, hybridization, and solubility products. Section II has 4 reasoning questions requiring understanding of statements. Section III has 3 linked comprehension questions about reaction mechanisms. Section IV contains 3 matrix-match questions testing relationships between concepts.
Here are the electron configurations (full and condensed) for the requested elements:
B 1s2 2s2 2p1 or [He] 2s2 2p1
F 1s2 2s2 2p5 or [He] 2s2 2p5
Ca 1s2 2s2 2p6 3s2 3p6 4s2 or [Ar] 4s2
P 1s2 2s2 2p6 3s2 3p3 or [Ne] 3s2 3p3
S 1s2 2s2 2p6 3s2 3p4 or [Ne] 3s2 3p4
As 1s2 2s2 2
The document discusses using the VSEPR model to predict the molecular geometry of O3 and SnCl3-. It explains that for O3, the central O atom has three electron domains in a trigonal planar arrangement, giving it a bent molecular geometry. For SnCl3-, the central Sn atom has four electron domains in a tetrahedral arrangement due to one lone pair, giving it a trigonal pyramidal molecular geometry.
This document summarizes a method called transplantation that can be used to show two planar domains have the same spectrum and are therefore isospectral. Transplantation takes a Dirichlet eigenfunction on one domain and constructs a corresponding eigenfunction on the other domain with the same eigenvalue. This is done by dividing the domains into congruent triangles and piecing together the restrictions of the eigenfunction in a way that satisfies continuity and boundary conditions. Numerical computation of the discretized Laplacian spectrum on sample isospectral domains verifies the transplanted eigenfunctions have identical eigenvalues, demonstrating the domains are isospectral.
1. The document provides definitions and properties of kites and trapezoids, including that a kite has two pairs of congruent consecutive sides and a trapezoid has one pair of parallel sides.
2. Two examples show using properties of kites and trapezoids to solve problems, such as finding missing angle measures in a kite and finding side lengths in isosceles trapezoids.
3. The trapezoid midsegment theorem states that the midsegment of a trapezoid is half the sum of the legs, and this is used to find a missing side length in one example.
This document summarizes the following:
(1) The author proves local existence and a blow-up criterion for solutions to the Euler equations in Besov spaces.
(2) As a corollary, for 2D Euler equations with initial velocity in Besov spaces, the author obtains persistence of Besov space regularity.
(3) The blow-up criterion improves previous criteria by replacing the BMO norm of vorticity with the weaker B∞,∞ norm.
- Rainbows are caused by the scattering and reflection of light inside raindrops, which causes the sky to appear brighter at certain angles depending on the path the light takes.
- The primary rainbow results from one internal reflection and appears at an angle of around 42 degrees. The colors are ordered from red on the outside to violet on the inside due to their different refractive indices.
- Additional rainbows can result from further internal reflections, with the secondary rainbow appearing inverted at around 52 degrees from two reflections. Higher order rainbows appear at increasing angles but are harder to see.
The document discusses the Hinge Theorem and its converse for comparing sides and angles of triangles. It provides examples of applying the Hinge Theorem and its converse to determine if one side or angle is greater than the other. It also gives an example problem of proving that one side is less than the other using the Hinge Theorem and properties of alternate interior angles for parallel lines cut by a transversal. The document concludes with assigning practice problems related to applying the Hinge Theorem and its converse.
I am Terry K . I am a Semiconductor Assignment Expert at eduassignmenthelp.com. I hold a Ph.D. in Semiconductor, from the University of Chicago, USA. I have been helping students with their homework for the past 8 years. I solve assignments related to Semiconductor.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Semiconductor Assignments.
The document discusses the calculation of vacuum polarization corrections to the energy levels of hydrogen atom. It presents numerical calculations of the one-photon vacuum polarization corrections to the 1s, 2s, 2p, 3s, 3p and 3d energy levels of hydrogen using the Uehling potential. The contribution of this correction decreases with increasing principal quantum number n and orbital quantum number l. It also calculates the relativistic effects on the 1s, 2s, 2p1/2 and 2p3/2 levels using Dirac wave functions. The results show the vacuum polarization effect is largest near the nucleus and decreases with n.
The document provides information on anomalous electron configurations of some elements, where the actual electron configuration differs from what is expected based on the Aufbau principle. It notes that stable configurations occur for half-filled or completely filled d or f orbitals. Examples are given of elements like Chromium, Copper, Silver, and Gold that have these anomalous configurations due to having superior stability from half-filled or filled d or f orbitals compared to nearly filled orbitals. The exceptions are said to occur more for larger elements where orbital energies are similar.
This document discusses probabilistic diameter and its properties. It defines probabilistic diameter (DA) as a distribution function that represents the probability that the distance between any two points in a set A is less than some value t. It presents several properties of probabilistic diameter including: (1) DA is a distribution function; (2) DA = H if A contains a single point; and (3) if A is a subset of B, then DA ≥ DB. It also defines probabilistic distance between two sets A and B as another distribution function (FAB) and establishes some of its properties.
5.1 midsegment theorem and coordinate proofdetwilerr
This document discusses using the midsegment theorem and coordinate proofs to find lengths and midpoints of line segments in triangles and rectangles. It provides examples of placing shapes like triangles and rectangles in a coordinate plane to find side lengths and midpoints using the distance and midpoint formulas. It also includes practice problems asking students to find side lengths, midpoints, and perimeters of shapes by using properties of midsegments or coordinates of vertices.
The document discusses the electronic band structure of graphene. It presents the tight-binding model and shows that graphene has a linear dispersion relation around the Dirac points, resulting in massless Dirac fermions. The tight-binding parameters t and t' are defined, and their effects on the band structure are described.
The document studies small excitonic complexes in a disk-shaped quantum dot using the Bethe-Goldstone equation. It examines systems with up to 12 electron-hole pairs. For symmetric configurations where the number of electrons equals the number of holes, it finds:
1) The triexciton and four-exciton system show weak binding or possible unbinding in the weak confinement regime.
2) Higher complexes beyond four pairs exhibit binding in the weak confinement regime.
3) The Bethe-Goldstone approach provides better energies than the BCS variational method in the weak confinement regime.
I am Peterson N. I am a Physical Chemistry Assignment Expert at eduassignmenthelp.com. I hold a Ph.D. in Physical Chemistry, University of Melbourne, Australia. I have been helping students with their homework for the past 8 years. I solve assignments related to Physical Chemistry.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Physical Chemistry Assignments.
FINAL 2014 Summer QuarkNet Research – LHCb PaperTheodore Baker
The document summarizes the author's 2014 summer research analyzing decay data from the LHCb detector. The author analyzed several decay channels including Λ c → Ξ− K+ π+, Ω b
−
→ Ω− J/ψ, and D s
+ → K− K+ π+. For the Λ c decay, the author found evidence of a Ξ0 resonance. For the Ω b decay, the author measured the mass but found the lifetime fit was off. For the D s decay, the author observed decays through φ(1020) and K*(892) resonances. The author was unable to find evidence of the hypothesized Ω cb
0 baryon due
1) The document discusses the electronic configuration of atoms, including the development of wave mechanics and quantum theory to explain the structure of atoms. It introduces concepts like the de Broglie wavelength, quantum numbers, atomic orbitals and shapes, Pauli's exclusion principle, and Hund's rule for electron configuration.
2) Key scientists discussed include de Broglie, Heisenberg, Schrodinger, Pauli, and their contributions to developing models of the atom and allowing prediction of electron configurations.
3) The document provides examples of writing out electron configurations for elements and explaining the rules for filling atomic orbitals in the Aufbau principle.
The document discusses the effective mass approximation in quantum mechanics. It begins by defining the effective mass as inversely proportional to the curvature of energy bands. Having a effective mass allows electrons in crystals to be treated similarly to classical particles, with the crystal forces and quantum properties accounted for in the mass. The effective mass can be a tensor and depends on the crystal direction. It then discusses measuring the effective mass using cyclotron resonance and how it varies by crystallographic direction. In general, the effective mass incorporates the quantum mechanical behavior of electrons in crystals to allow a classical particle treatment.
This document discusses how catastrophe theory can be applied to physical systems using manifolds. It describes how potential functions from catastrophe theory can influence manifolds that are locally like 4D Euclidean space. Seven catastrophes from Thom's theory are structurally stable. In addition to catastrophe manifolds, other manifolds can arise without polar singularities or with a diagonal metric. Complex numbers, quaternions, and octonions can be added to the 4D space. Applications to bifurcations, measuring frames, particles, and effects on systems are discussed.
Using resonant ultrasound spectroscopy (RUS), the author will determine the complete elastic constant matrices of two thermoelectric single crystal samples, Ce.75Fe3CoSb12 and CeFe4Sb12. RUS involves measuring the resonant frequencies of a sample's vibrations, which depend on the sample's elastic constants, shape, orientation, and density. The author aims to obtain the elastic moduli from a single RUS spectrum for each sample. Understanding the elastic properties may help identify better thermoelectric materials by correlating low elastic stiffness with low thermal conductivity and higher thermoelectric efficiency. The author will compute the resonant frequencies using the samples' properties and compare to measurements.
A theoretical Investigation of hyperpolarizability for small GanAsm clustersLuan Feitoza
This document summarizes a theoretical investigation of the second- and third-order hyperpolarizabilities of small GanAsm (n+m = 4-10) clusters using time-dependent density functional theory and sum-over-states methods. The study finds that the two-level term makes a significant contribution to the static second-order polarizability for most clusters, except Ga3As4. For the static third-order polarizabilities, the positive channel contributes more than the negative channel. Similar to bulk GaAs, the small GanAsm clusters exhibit large second-order (1x10-6 esu) and third-order (5x10-11 esu) susceptibilities, indicating they may
George Green's Contribution to MRI, Roger Bowley, 21 October 2014uazkjs
Slides to accompany the lunchtime talk given by Professor Roger Bowley of the School of Physics and Astronomy, The University of Nottingham, at the Djanogly Theatre, Nottingham Lakeside Arts, on Tuesday 21 October 2014.
This document summarizes elementary particles in physics. It describes how particles are classified into leptons and hadrons. Leptons include electrons, muons, taus and their neutrinos. Hadrons include baryons like protons and neutrons, and mesons. Interactions are also classified, including the electromagnetic, weak, and strong interactions. The electromagnetic interaction between charged leptons and photons is described based on local gauge invariance, resulting in a theory of quantum electrodynamics that agrees well with experiments.
Deep Inelastic Scattering at HERA (Hadron-Electron Ring Acceleartor)SubhamChakraborty28
A review presentation about the research and experiments done at HERA related to Deep Inelastic Scattering, High Energy Physics and Quantum Chromodynamics
Quantum Theory. Wave Particle Duality. Particle in a Box. Schrodinger wave equation. Quantum Numbers and Electron Orbitals. Principal Shells and Subshells. A Fourth Quantum Number. Effective nuclear charge
This document discusses principles of relative and absolute dating of geologic events.
[1] Relative dating involves determining the sequence of events without knowing exact ages, by applying principles like superposition, cross-cutting relationships, and inclusion. Absolute dating determines exact ages in years using radiometric dating techniques that rely on radioactive decay of isotopes like carbon-14 and uranium-238.
[2] Five diagrams are presented and labeled for practice determining the sequence of rock layers, faults, and unconformities using relative dating principles. Radiometric dating equations are also shown relating radioactive parents and stable daughter isotopes to calculate the time since a rock formed.
The paper discusses using renormalization group theory to understand critical phenomena in ferromagnets. It casts the Kadanoff scaling theory for the Ising model in differential form, with the resulting equations being an example of the renormalization group differential equations. It is shown that the usual scaling laws arise naturally from the equations if the coefficients are analytic at the critical point. A generalization involving an "irrelevant" variable is also considered, where the scaling laws only result if the solution asymptotically approaches a fixed point.
This document summarizes an experiment that slowed the speed of light propagation to 38 mph using a technique involving two closely spaced spectral lines in sodium vapor. The experiment works by "pumping" one of the spectral lines into an inverted population, effectively changing its damping constant. This allows light of a frequency near the spectral lines to propagate without attenuation. The document derives an expression for the light's group velocity in this medium based on its index of refraction and shows the group velocity is reduced based on the density of the sodium vapor. Plugging in parameters from the experiment yields a group velocity consistent with what was measured.
In this paper we study the effect of temperature, magnetic field, and exchange coupling on the thermal entanglement in a spin chain which consist of two qubits and one qutrit. We use negativity as a measure of entanglement in our study. We apply magnetic field, uniform and nonuniform field, on it. The results show that the entanglement decreases with increase in temperature. Also, we have found that under a magnetic field, either uniform or nonuniform, in constant temperature, the entanglement decreases. We have found that increasing exchange coupling of any two particles decreases the entanglement of the other two particles. Finally, we have compared our system with a two-particle system and found that in presence of a magnetic field the increase in number of particles leads to the decrease in the entanglement.
This document presents a new intensity formula for optical emission spectroscopy that has been applied to stellar spectra. The formula relates spectral line intensity to wavelength, frequency, electron temperature, and ionization energies. The author analyzed spectra from the literature for 17 elements and 11 ions and found linear relationships between the logarithm of intensity and the inverse of frequency times ionization energies, supporting the new formula. Stellar spectra from classes O-M were also analyzed and found to follow similar linear relationships, allowing the determination of electron temperatures, mean ionization energies, and effective temperatures for different stellar classes. Intensity ratios of Balmer lines from various stars correlated well between theoretical predictions using the formula and experimental measurements.
This document summarizes research on Casimir torque in the weak coupling approximation. It examines manifestations of Casimir torque between planar objects characterized by delta function potentials. The key findings are:
1) An exact calculation of the Casimir torque between a finite rectangular plate above a semi-infinite plate is presented and agrees well with the proximity force approximation when the plate separation is small compared to their sizes.
2) Cusps in the torque arise when the corners of the finite plate pass over the edge of the semi-infinite plate.
3) A similar calculation is done for a disk above a semi-infinite plate, again finding good agreement with the proximity force approximation.
This document discusses materials informatics and data mining in materials science. It provides an overview of data mining tasks like classification and visualization and examples of large data sets produced in materials science simulations. It also lists several existing materials informatics tools and databases. Python is discussed as a useful programming language for materials informatics applications due to its ease of use, popularity in science, and capabilities for tasks like array manipulation and linear algebra.
The document discusses the use of lightweight aluminum alloys in the automotive industry. Stricter CO2 emission limits by 2020 are driving new trends toward lighter vehicles. Using aluminum alloys can help reduce vehicle weight by up to 100 kg for every 0.5 L/km reduction in fuel consumption. Aluminum meets requirements as it is light yet strong, low-cost, and highly recyclable. Popular aluminum-bodied vehicles include the Audi A2 and A8, Jaguar XJ, and Mercedes Benz SL.
This document describes an ab initio mean field theory approach to modeling site occupation in binary sigma phases. The theory uses a total energy expansion and the coherent potential approximation (CPA) to determine effective chemical potentials and site occupancies as a function of composition and temperature. It is applied to model the magnetic state effect, structural variations, and final site distributions in FeCr sigma phase as well as other binary systems like ReW, CoCr, and FeV. The goal is to provide accurate predictions of atomic distributions in substitutionally disordered sigma phases where experimental determination is challenging.
Ab initio temperature phonons group theorySergey Sozykin
1. The document discusses using ab initio methods to model materials at different temperatures, including calculating phonons and predicting phase transitions.
2. Group theory analysis and phonon calculations for high symmetry phases can identify soft modes and possible low symmetry phase subgroups responsible for second-order phase transitions.
3. Phonon calculations for predicted low symmetry phases then determine the most stable phase as temperature decreases.
The document summarizes research into the mechanism that stabilizes the misfit layer compound (PbS)1.14TaS2. Through density functional theory calculations and analysis of atomic and electronic structures, the researchers found that nonstoichiometry, with Ta atoms substituting into the PbS layers, strongly stabilizes the compound. This allows charge transfer that restores the insulating character of the PbS layers. In contrast, metal cross-substitution alone does not provide sufficient stabilization. The calculations match experimental measurements of core level shifts and formation energies, validating the identified mechanism of nonstoichiometry.
1. The presenter discussed their modeling of defect properties in d-metal oxides like SrTiO3 using ab initio methods.
2. Specific examples included modeling the Jahn-Teller effect of iron and oxygen vacancy defects, and calculating formation energies of oxygen vacancies with and without including phonon contributions.
3. Preliminary results were also presented on modeling the formation energy of oxygen vacancies in ultrathin films of SrTiO3 surfaces.
This document outlines the key steps in analyzing data from gravitational-wave detector networks to search for transient gravitational-wave signals like those produced by compact binary coalescences (CBCs). The analysis pipeline involves: (1) applying data quality checks and vetoes, (2) filtering the data using template waveforms to identify triggers, (3) ranking triggers based on a detection statistic, (4) estimating the background rate of accidental triggers through time shifts, and (5) comparing the loudest triggers to the background to identify potential detections or set upper limits. The document then provides an example outline of a paper searching for CBC signals in data from the LIGO and Virgo detectors.
лекция 3 дефекты в полупроводниках ga n alsbSergey Sozykin
1. DFT calculations identify hydrogenated gallium vacancies and oxygen-related defects as promising candidates to explain hot electron degradation in AlGaN/GaN HEMTs.
2. Monte Carlo simulations show a peak in electron concentration and energy near 1.5 eV below the conduction band minimum, matching the activation energy of hydrogenated defects.
3. A model combining DFT defect formation energies and densities with Monte Carlo transport simulations can reproduce experimentally observed shifts in pinch-off voltage over time under electrical stress.
лекция 2 атомные смещения в бинарных сплавах Sergey Sozykin
This document discusses the use of diffuse x-ray scattering to study short-range order and atomic displacements in alloys. Three key points:
1) Diffuse scattering patterns provide information about correlations between atoms over short lengths scales, revealing phenomena like chemical ordering, clustering, and thermal vibrations.
2) Experiments using synchrotron sources and advanced analysis allow direct comparison of diffuse scattering data to first-principles calculations, providing new insights into phase stability and properties like magnetostriction.
3) A study of Fe-Ga alloys found that slow cooling produces longer-range chemical ordering compared to quenching, and correlations depend strongly on composition, with anisotropic increases in correlation length influencing magnet
лекция 1 обзор методов вычислительной физикиSergey Sozykin
The document discusses multi-scale modeling of radiation effects in dielectric materials. It summarizes:
1. First-principles quantum mechanical methods are used to simulate defect formation and electronic structure changes at the atomic scale.
2. A quantum transport model calculates current-voltage characteristics based on the defect states. This shows good agreement with experimental I-V curves.
3. A percolation model extends the simulations to larger device scales by parameterizing the defect properties from the smaller scale calculations. This allows modeling transient current behavior over nanosecond timescales.
The multi-scale approach combines atomic-scale simulations with mesoscale modeling to directly compare with experimental measurements of device leakage currents.
2. 1.
Обзор
методов
вычислительной
физики
Много-‐масштабное
моделирование:
от
дефектов
к
ошибкам
в
приборах
2.
Локальная
структура
металлических
сплавов:
диффузионное
рассеяние
и
атомные
смещения.
3.
Дефекты
в
полупроводниках
и
поведение
приборов:
GaN,
SiC
и
AlSb.
4.
Проблемы
функциональности
материалов
для
мемристора
TiO2
и
ZnO.
5.
Графен,-‐
материал
будущего
или
поиск
ниши
для
применения.
3. Saito, R., M. lower ͑ Dresselhaus, is M. S. from Eq.
minus sign the Fujita, G. ͒ band. Itand clear Dresselhaus, ͑6͒
that Tight
bspectrum is Lett. 60, 2204. around zero energy if tЈ
lectronic propertiespproximaIon
the inding
a of graphene
1992a, Appl. Phys. symmetric
Saito,finite values graphite”
by
Wallace
Phys.
Rev.
LeT.
71,
622,
1947
is
= 0. For
“The
band
theory
of
R., M. Fujita, of tЈ, the electron-hole symmetry
G. Dresselhaus, and M. S. Dresselhaus,
broken and theRev.and 1804.
, 1992b, Phys.
B 46, * bands become 1asymmetric. In
San-Jose, P., E. Prada, and D. Golubev,k2007,bPhys. Rev. B 76,
-
Fig. 3, we show theAfullBband structure of graphene with y
195445.
,
both t and S.,. 2007, Phys. Rev.figure, we also show a zoom in
Saremi, tЈ δ 3 the1 same B 76, 184430.
In δ K
,
of the band D., E. H. Hwang, and W. K.ofΓ the Dirac points ͑at
Sarma, S. structure close to one Tse, 2007, Phys. Rev. B
s
the K or KЈ a 1
75, 121406. pointδ 2in the BZ͒. This dispersion can be M kx
c Schakel, A. M.2J., 1991, the full band structure, Eq. ͑6͒,
obtained by expanding Phys. Rev. D 43, 1428.
a
K’
t
close to the K ͑orGeim, vector, Eq. ͑3͒, as kE. H. + q, P.
Schedin, F., A. K. KЈ͒ S. V. Morozov, D. Jiang, = K Hill, with
b2
a Blake, and K. S. Novoselov, 2007, Nature Mater. 6, 652.
͉q ͉ Ӷ ͉K͉ ͑Wallace, 1947͒,
n Schomerus, H., 2007, Phys. Rev. B 76, 045433.
- Schroeder,͑ColorM. + O͓͑q/K͒2͔, and A. Javan, 1968, Phys. ͑7͒
FIG. 2. online͒ Honeycomb lattice and its Brillouin
E±͑q͒ Ϸ P. R., ͉q͉ S. Dresselhaus,
± vF
; zone.Lett. 20, 1292.structure of graphene, made out of two in-
Rev. Left: lattice
Semenoff, G. momentumRev. ͑a1 53, a2 are
where q is theW.,triangular latticesLett. and 2449. the latticethe
terpenetrating 1984, Phys. measured relatively to unit
- Sengupta, and ␦i G. 1 , 2the are the nearest-neighbor by vF
vectors, and
Dirac pointsK., and, viF=Baskaran, 2008, Phys. Rev. B given vectors͒.
is , 3 Fermi velocity, 77, 045417.
Seoanez, C., a value vandf
1raphene”
The This result are lo-
“The
electronic
properIes
o A. H. Castro Neto, 2007, Phys.
F. Guinea, Ӎ g ϫ 106 m / s. Dirac cones was
Right: corresponding Brillouin zone.
= 3ta / 2,.
Castro
Neto
Rev.
Mod.
Phys.
81,
109
2009
- A.
H with 125427. KЈ F
catedB 76, K and
Rev. at the points.
first obtained by Wallace ͑1947͒.
-
4. form Left: energy spectrum ͑in units of t͒ for finite values of
lattice. ͑Wallace, 1947͒
t and tЈ, with t = 2.7 eV and tЈ = −0.2t. Right: zoom in of the
E±͑k͒ = ± tͱ3 + f͑k͒ − tЈf͑k͒,
energy bands close to one of the Dirac points.
1
f͑k͒ = 2 of tЈ is not 4 cos ͩ ͪ ͩ ͪ
ͱ3
ky cos kxa
3
The valuecos͑ͱ3kya͒ + well knownabut ab initio , calcula
͑6͒
͑Reich et al., 2002͒ find 0.02t Շ tЈ2 0.2t depending on the t
Շ 2
binding parametrization. These the upperet͑al.:alsoelectronic pro
where the plus sign applies to calculations*Theand the
Castro Neto
͒ include
effect of a third-nearest-neighbors hopping, which has a v
minus sign the lower ͑͒ band. It is clear from Eq. ͑6͒
of around 0.07 eV. A tight-binding fit to cyclotron reson
that the spectrum is symmetric around zero energy if tЈ
experiments ͑Deacon et al., 2007͒ finds tЈ Ϸ 0.1 eV.
= 0. For finite values of tЈ, the electron-hole symmetry is
broken and the and * bands become asymmetric. In
Fig. 3, we show the full band structure of graphene with
both t and tЈ. In the same figure, we also show a zoom in
of the band structure close to one of the Dirac points ͑at
the K or KЈ point in the BZ͒. This dispersion can be
5. anប = 1͒ ͚ e−ik·Rna͑k͒,
͑we use units such that = ͱN k
͑15͒
c
H=−t ͚is
by A = 3ͱ3a / 2.͗i,j͘,
2
It
†
͑a,ib,j + H.c.͒
where Nc is the number of unit cells.
c
tates for graphene is mation, we write the field an as a
. Dirac fermions
͚ † †
coming+ b,ib,j + H.c.͒, Fourier s
of carbon nanotubes ͑a,ia,j
− tЈ from expanding the
er shows 1 / ͱE singu- K. This produces an Јapproximation
͗͗i,j͘͘,
We consider the Hamiltonian ͑5͒ withas a sum of two ne
tion of the field an t = 0 and the
their electronic spec- the electron operators,
ourier transform of ͒ annihilates ͑creates͒ an electron
where the ͑ai, †
antization of ai, mo-
ular spin tube axis. ͒ on site Ӎ i −iK·RsublatticeЈ·Rna ͑an equ
to the ͑ = ↑ , ↓ an e
R on na + e−iK A ,
1,n 2,n
nanoribbons, whichis used for sublattice B͒, t͑Ϸ2.8 eV͒ i
lent definition
1
= ͚ e−ik·Rna͑k͒,
anearest-neighbor hopping energy ͑hopping between
ͱN c k
perpendicular to the
n ͑16͒
milar ferent sublattices͒, and t is the next −iKЈ·Rn
to carbon nano-
bn Ӎ e−iK·Rnb1,n + e nearest-neig
Ј b2,n ,
hopping energy1 ͑hopping in the same sublattice͒.
where Nc is the number of unit cells. Using this transfor-
energy bands derived from this Hamiltonian have
mation, we write the field an as a sum of two terms,
2009
form ͑Wallace, 1947͒
6. ͒/4 †
ͪ ͵ͩ
͑ai ,ץb†͒
+
xi
ͫͩ
0 − ͱ3͒/4
3a͑− i guage, the two-component
͑i = 1 , 2͒. It is clear that ץaround K ͱhas the fo
mentum y ⌿1͑r͒
ˆ
the effective Ham
ͪ
−ˆ3a͑i − ͱ3͒/4 3a͑1 − iͱclose to the K3a͑− i − 3͒/4 obeys
point, ˆ
ͩ
ͪͬ ͪͬ
ͩͪ ͬ ͪ
0 0 +ץ
3͒/4 0
oniant ͑18͒ is madeͱ3͒/4 two copies3a͑i − ͱthe1massless Di
of 0 of 3͒/4
ͬ
dxdy⌿†͑r͒
ͩ ͪ ͪͩ
HӍ− ץ⌿ ͑r͒
0 −ik/2
e
1 x y 1
− 3a͑1 + i −
ke Hamiltonian, 3a͑1− iͱ3͒/4 + ץforF 3a͑i −ͱ 3͒/4 = ץ⌿k/2 and
0
ˆ ͑r͒ †
ͫͩ
0 one holding−0iv ͑k͒ ·=ٌ͑r͒ iˆE͑r͒.
3a͑i + ͱ 3͒/4
ther fori −−ͱaround K0Ј. Note The wave function, in m
+⌿
− 3a͑− p 3a͑1 − i
2
3͒/4 ͱ3͒/4
0
ˆ ±,K p around K
y ⌿ ͑r͒
3 −ץa͑− i2− ͱ3͒/4
x
ͱ
2 ±e ͑r͒
that, in first quantized
0
y 2
= − i ͵ dxdy͓⌿ ͑r͒ · ٌ⌿ ͑r͒ + ⌿ ͑r͒ · ٌ⌿ for H =
uage,v the two-componentmentum vFwave where the
ˆ ˆ † ˆ
electron · k, function
ˆ ͑r͔͒,
†
K around K has the
F 1 * 2
1 2
r͔͒, ͑18͒
ͩ ͪ
lose to the K point, obeyseigenenergies E = ± vFk, that
the 2D Dirac equation,
respectively, and 1 k −i kgiven
e is /2
͑k͒ momentum/2arou
±,Kthe =
− iv · ٌ͑r͒ = E͑r͒. tion for
F
with Pauli matrices = ͑x , y͒, * = ͑x , −y͒, and ˆ
⌿† 2 ±e
ik
ˆ 1
͑
p ͱ
ͩ ͪ
i h= · .
= ͑a† , b†͒ ͑i = 1 , 2͒. It is clear that the effective Hamil-
i i 2 ͉p͉
The wave function, in momentum · k, wherethe m
onian ͑18͒ is made of two copies of the massless Dirac- space, for/2 the
1 e ik
for HK =͑k͒ = definition of h that the
ike Hamiltonian, one holding for p around K and the±,KЈ vF the
ͱ
It is clear from ˆ
mentum around K has theeigenenergies E =±evofk, tha
⌿†ˆ p form Ј͑r͒ are also eigenstates−i hk,/2
other for p around KЈ. Note that, in first quantized lan-
2 ± Fˆ
ˆ = 1 · 2D Dirac equation,
and
ͩ ͪ
guage, the two-component electron wave function ͑r͒,
i K
h . ͑22͒
lose to the K point, obeys the
mil- 2 ͉p͉−ik/2 respectively, ͑r͒, k is given
and
− iv · ٌ͑r͒ = E͑r͒. 1 e for
͑19͒ H KЈ
h= v= * · k. Note that t
ˆ ͑r͒ ±
F K
1
K
tion for the momentum aro
2
ac- ͑k͒ =
F
͑
ͱ2 the definitionTherefore,that the statesЈ a/2positive
mentum around K has the form ±e
he
It is clear from
K and related by time-rever
The wave function, in momentum space, /2 the mo-Ј arean equivalent equation for ͑r͒ with in
±,K ik for
ˆ electrons ͑holes͒ i ͑r͒
of hcoordinateshavekmom
K
an- −i k/2
origin of Equation ͑23͒ impliesein has its
helicity. 1 that
K
1 e
7. he hopping energies between different sites are m
͑5͒,
ed, leading to a new term to the original Hamilto
5͒, H = ͕␦t͑ab͒͑a†b + H.c.͒ + ␦t͑aa͒͑a†a + b†b ͖͒,
od ͚ ij i j
i,j
ij i j i j
Hod = ͚ ͑ab͒ †
͕␦tij ͑ai bj + H.c.͒ + ͑aa͒ †
␦tij ͑ai aj + †
bi bj͖͒,
͑144
i,j
or in Fourier space, ͑1
͚ ͚
† ជ
͑ab͒ i͑k−kЈ͒·Ri−i␦aa·kЈ
r Hod =
in Fourier space,
a kb kЈ ␦ti e + H.c.
k,kЈ ជ
i,␦ab
͚ ͚
† ជ
͑ab͒ i͑k−kЈ͒·Ri−i␦aa·kЈ ជ
Hod = a†kbkЈ † ␦ti e ͑aa͒ i͑k−kЈ͒·Ri−i␦ab·kЈ + H.c.
+ ͑akakЈ + ជ kbkЈ͒
k,kЈ
b
i,␦ab ជ
͚
␦ti e , ͑145
i,␦aa
͚
† ͑aa͒ † ជ
͑aa͒ i͑k−kЈ͒·Ri−i␦ab·kЈ
͑ab͒͑a a k + b b k ͒ , ͑
where ␦tij+ ͑␦tij Ј ͒ is k Ј changei ofethe hopping energ
k the ␦t
ជ
8. real space as
͵
A͑r͒ = Ax͑r͒ + iAy͑r͒.
d2r͕A͑r͒a†͑r͒b ͑r͒ + y
d can
= Dirac Hamiltonian1͑18͒, we isorder
In terms of D
Two
Eq. ͑146͒ as
1
͑149͒
Hodthe irac
cones
are
not
coupled
bH.c. rewrite
+ ͑r͓͒a†͑r͒a1͑r͒ + b†͑r͒b1͑r͔͖͒,
͵similar expression for cone 2 but with A replace
1 1 ͑14
Hod = ˆ ជ ˆ ˆ ˆ
d2r͓⌿†͑r͒ · A͑r͒⌿1͑r͒ + ͑r͒⌿†͑r͒⌿1͑r͔͒,
1 1
with a
by A*, where ͑150͒
ជ
where A = ͑Ax , Ay͒. This result shows that changes in the
͚ ͑ab͒ ជ
−i␦ab·K
A͑r͒ = ␦t ͑r͒e , ជ ͑14
hopping amplitude lead to the appearance of vector A
␦abជ
and scalar ⌽ potentials in the Dirac Hamiltonian. The
presence of a vector potential in the problem indicates
also be present, ជ
͚ ͑aa͒
͑r͒ = ␦t ͑r͒e −i ជ B =
ជ
.
ជ
that an effective magnetic field␦aa·K͑c / evF͒ ٌ ϫ A should
naively implying a broken time-reversal
͑14
␦aa
symmetry, although the original problem was time-
reversal invariant. This broken time-reversal symmetry
is not real since Eq. ͑150͒ ͑r͒ the *͑r͒, because of the inversio
Note that whereas is = Hamiltonian around
9. Defects
in
graphene
1. Grain
Boundary.
2. Liquid
environment
enhancement
on
mobility
in
graphene.
3. X-‐ray
irradiaIon
of
graphene.
10. Experimental
observaIon
of
defects
in
graphene
Vacancy
Extended
defect
=
Metallic
wire
Meyer,
Kisielowski,
Erni,
Rossell,
Crommie,
ZeTl,
Nano
Le..
(2008)
J.
Lahiri
et
al.,
Nature
Nanotech.
(2010)
11. Grain
Boundary
and
Point
Defects
What
is
Ime
scale
and
range
of
interacIon
between
defects
and
GB?
~1
nm
13. FormaIon
Energies
of
Defects
pris2ne
Cl-‐5577
GB-‐558
GB-‐575
All
energies
rim
inside
rim
inside
rim
inside
are
in
eV
C
6.1
3.8
4.2
3.1
SV
7.9
5.6
3.0
7.1
6.4
6.9
4.2
LocaIon
of
Vacancies
with
lower
formaIon
energies
15. Stability
of
585
and
555777
defects
Banhart,
Kotakoski,
Krasheninnikov,
ACS
Nano
2010
555777
is
1.2
eV
more
stable
Cretu,
Krasheninnikov
et
al.
PRL
2010
Lee
et
al.
PRL,
2005;
21. Vacancy
and
adatom
recombinaIon
near
GB
• Adatoms
are
very
mobile
–
low
diffusion
barrier
• Stretched
C-‐C
at
the
heptagon
accumulate
adatoms
T
=
2000
K
treconfiguraoon
=
0.5
ns
B. Wang, Y. Puzyrev, S. T. Pantelides, Carbon (2011)
22. Conclusion
• Vacancies
interact
and
recombine
t
~
10
ns
• Point
defects
interact
with
grain
boundaries
d
~
2
nm
• Grain
boundaries
act
as
sinks
for
vacancies
and
adatoms
Enhanced
defect
reacovity
at
grain
boundaries
23. Graphene
device
degradaIon
• Graphene
fabricated
by
mechanical
exfoliaIon
from
Kish
graphite
• Sweep
VG
with
VDS=5mV
24. MoIvaIon
and
Outline
Ø Experiment
[1]
o Graphene’s
resisIvity
response
to
x-‐ray
radiaIon,
ozone
exposure,
annealing.
o Defect
related
Raman
D-‐peak
appears
a…er
§ x-‐ray
irradiaIon
in
air
§ ozone
exposure,
decreases
a…er
annealing.
Ø Theory:
behavior
of
impuriIes
on
graphene
o Temperature
and
concentraIon
dependence.
o Need
to
remove
oxygen
without
vacancy
formaIon
(would
H
help?)
[1]
E.-‐X.
Zhang
et
al,
IEEE
Trans.
Nucl.
Sci.
58,
2961
(2011)
26. Graphene
device
degradaIon
Ozone
exposure
a)
80
8000
G -‐P e a k 60
Inte g ra te d
inte ns ity
A re a
6000
I D /I G
(1 0 0 % )
40 Defect
related
D-‐peak
4000
20 • increases
x-‐ray
exposure
2000
D -‐P e a k • decreases
a…er
temperature
anneal
0 0
P re 8
Mra d(S iO 2 ) 15
Mra d(S iO 2 ) A nne a l
1 0 -‐ke V
X -‐ra y
D os e
b)
27. TheoreIcal
Approach
O
O
desorpIon
Density
Func2onal
Theory
O
migraIon
DFT
• Defect
formaoon
energies
• Migraoon/desorpoon
barriers
O
dimer
Kine2c
Monte-‐Carlo
KMC
Defect
dynamics
• Temperature
• Inioal
concentraoon
28. Oxygen
Removal
and
Vacancy
GeneraIon
1.3
eV
Oxygen:
clustering
behavior
0.5
eV
0.8
eV
Removal
of
oxygen
Bridge 1.3
eV
• Pairs
O2
• Triplets
CO,
CO2,
VC
Top
Device
degradaoon
1.1
eV
CO,
CO2
1.1
eV
O2
29. High-‐temperature
Annealing
Vacancy
Concentraoon
of
vacancies
exceeds
Residual
oxygen
atom
concentraoon
of
residual
O
31. Temperature
Anneal
IniIal
Defect
ConcentraIon
Dependence
High
O
concentraoon
Lo
vacancy
surface
coverage
Low
O,
High
V
concentraoon
oxygen
T
iniIal
O
surface
coverage
High
T:
Removal
of
oxygen
>
0.05
iniIal
surface
coverage
leads
to
vacancy
formaIon
Low
T:
Oxygen
stays
on
the
surface
and
forms
clusters
Decrease
of
D-‐peak,
Increase
in
resisovity
Method
to
prevent
defect
forma2on
during
irradia2on/annealing?
32. Oxygen
and
Hydrogen
on
Graphene:
Binding
energies,
MigraIon
and
ReacIon
Barriers
O-‐H
is
most
likely
to
desorb
O
from
graphene
surface
H
Leaves
carbon
network
intact
33. Effect
of
Hydrogen
On
Oxygen
Annealing
Oxygen/ Low
High
Hydrogen
Concentra2ons
Low
2%
O,
10%
H
@
T
=
300
C
Final
defect
concentraIons?
High
15%
O,
1%
H
15%
O,
10%
H
34. Effect
of
Hydrogen
On
Oxygen
Annealing
Higher
Oxygen
concentraoon
Higher
Hydrogen
concentraoon
Hydrogen
is
removed
t
~
0.001
s
Oxygen
is
removed
t
~
0.0001
s
t
~
1
s
t
~
1
s
Removal
of
residual
Oxygen
Residual
Hydrogen
Causes
formaoon
of
large
Forms
clusters
L
~
0.5
nm
amount
of
Vacancies
No
Vacancies
are
formed
35. High
O,
High
H
concentraIons
Hydrogen
is
removed
first,
Removal
of
residual
Oxygen
Causes
formaoon
of
Vacancies
Effect
of
Hydrogen
On
Oxygen
Annealing
36. ScaTering
mechanisms
in
graphene
• Suspended
graphene
at
4K
μ
~200,000
cm2/V
[1]
• Suspended
graphene
at
300K
μ
~10,000
cm2/V
s
ü Out-‐of-‐plane
flexural
phonons
limit
[2]
• Suspended
graphene
in
non-‐polar
liquid
μ
~60,000
cm2/V
s
• Effect
of
liquids
on
the
flexural
phonons
Image
from
Meyer,
J.
C
.
ü Vacuum
ü Hexane
C6H14
ü Toluene
C6H5CH3
1. BoloIn,
K.
I.
et
al.
Solid
State
Comm.
2008
2. Castro,
E.
V.
et
al.
Phys
Rev
LeT.
2010
37. Electron
scaTering
due
to
flexural
ripples
𝐸↓𝑞 = 𝜅 𝑞↑4 ⟨|ℎ↓𝑞 |↑2 ⟩/2 = 𝑘↓𝐵 𝑇 /2
Harmonic
approximaIon
Fourier
components
of
2 T
hq
~
bending
correlaIon
funcIon
κ q4
h
at
300K
Deformaoon
tensor
𝑢 ↓𝑖𝑗 =1/2 ( 𝜕 𝑢↓𝑖 /𝜕 𝑥↓𝑗 + 𝜕 𝑢↓𝑗 /𝜕 𝑥↓𝑖 + 𝜕ℎ/𝜕 𝑥↓𝑖 𝜕ℎ/𝜕 𝑥↓𝑗 )
38. Electron
scaTering
due
to
flexural
phonons
Hopping
integrals
γ
are
modified
2
γ=
γ↓0 +( 𝜕γ/𝜕 𝑢↓𝑖𝑗 ) 𝑢↓𝑖𝑗
0
1
PotenIal
perturbaIon
due
to
ripples
-‐
random
sign-‐changing
‘magneIc
field’
3
1/𝜏 ≈2 𝜋/ℎ 𝑁( 𝐸↓𝐹 )〈 𝑉↓𝑞 𝑉↓− 𝑞 〉↓𝑞≈ 𝑘↓𝐹
~⟨|ℎ↓𝑞 |↑2 ⟩↑2
𝑉↑( 𝑥) =1/2 (2γ↓1 −γ↓2 −γ↓3 )
𝑉↑( 𝑦) =1/2 (γ↓2 −γ↓3 )
𝜌↓𝑟𝑖𝑝𝑝𝑙𝑒 ~1/𝜏 ~⟨|ℎ↓𝑞 |↑2 ⟩
↑2
Effect
of
liquids
ü Hexane
C6H14
Morozov
S.
V.
et.
al,
Phys.
Rev.
LeT
2006
ü Toluene
C6H5CH3
M.
I.
Katsnelson
and
A.
K.
Geim,
Phil.
Trans.
R.
Soc.
A,
2008
Castro,
E.
V.
et.
al
Phys
Rev
LeT
(2010)
39. Molecular
dynamics
with
classical
potenIals
• Large
system
10,000-‐50,000
atoms
L
~10nm
• Large
Ime
scale
~ns
• Bond-‐order
potenIals
for
C-‐H
• Boundary
condiIons
ü NPT
–
constant
pressure
ü NVT
–
constant
volume,
corresponding
to
P~0
41. Suspended
graphene
in
hexane
Hexane
molecules
envelopes
graphene
sheet
C
chain
aligned
parallel
to
the
plane
Mean
square
displacement
h2 = 0.39 Å2
hexane
42. Suspended
graphene
in
toluene
Toluene
molecules
envelopes
graphene
sheet
C
ring
aligned
parallel
to
the
plane
Mean
square
displacement
h2 = 0.42 Å2
toluene