LECTURE 7 : CALCULATING PROPERTIES Space correlation functions Radial distribution function Structure factor Coordination numbers, angles, etc.
|
|
- Daniella Leonard
- 7 years ago
- Views:
Transcription
1 We have generated sets of (x,y,z) positions for various times at various given thermodynamic conditions (N,V,T,P). Now, we use them. LECTURE 7 : CALCULATING PROPERTIES Space correlation functions Radial distribution function Structure factor Coordination numbers, angles, etc.
2 A) RADIAL DISTRIBUTION FUNCTION Structural caracterization: Probability densities ρ N (1) and ρ N (2) i.e. one can find N particles and N(N-1) pairs of particles in the total volume, respectively. Note thattheseare n=1 and n=2 cases of a generalcorrelation function g (n) givenby : Z N the partition function, V the volume, N the nb of particles
3 So thatone can write for e.g. n=2: which definesthe radial distribution (rdf) g N2 (r 1,r 2 )function, alsogivenby For an homogeneousisotropic system, one has ρ N (1) =ρ. Dependence of the rdfonly on relative distance between particles: So that ρg(r) is the conditional probability to find another particle ata distance r away fromthe origin.
4 g(r) is the pair correlation function In a simulation box with PBC, one cannot obtain the structure beyond r > L/2. Alternatively: Radial distribution function : ()= 1 (+ ) Pair correlation function: ()= ( ) Alternative definitions : Total distribution function: =4() Differential distribution function =4 1
5 Pair distribution function : examples Visual inspection allows to distinguishbetweena crystalline and an amorphousstructure CCP Ni lattice with EAM potential
6 Effect of thermodynamic variables : temperature Amorphous Se The integral of g(r) allows to determine the number of neighbors around a central atom. Remember The integral to the first minimum gives the coordination number. r m = 4 Caprion, Schober, PRB 2000 Running coordination number N(r) ()= 4
7 Effect of thermodynamic variables : pressure d-geo 2 Direct comparison with experiments can fail Simple force fields can not account for pressure-induced changes (metallization) Additional structural insight isprovided by partial correlation functions : Ge-Ge, Ge-O, O-O Expt. (neutron) Salmon, JPCM 2011 MD: 256 GeO 2 using Oeffner-Elliot FF Micoulaut, JPCM 2004
8 Effect of composition: extending to multicomponent systems This is case for most glasses and materials SiO 2, GeSe 2, SiO 2 -Na 2 O, Consider a system with n components having N 1, N 2, N n particles. Wecan write $$ ()= ( ) $ with α between [1,n] And for! #: % % $& ()= ( $ ) & Out of which can be computed the pair correlation function: % ' = 1 ( ( (),( (can be also neutron or XRD weighted)
9 Ge 1 O 2 Pair distribution function in multicomponent systems: GeO 2 Evidence for neighbour correlations Ge 3 Ge 1 Ge 2 O 3 O 1 O 3 O 3 O 1 O 3 D. Marrocchelli et al., 2010 O 1 O 2
10 Pair distribution function in multicomponent systems: GeSe 2 Evidence for homopolar bonds Ge-Ge and Se-Se Prepeaks in relevant pdfs
11 Thermodynamic quantities from the computed g(r): Energy First, one needs to remember that the energy is related to the partition function Q(N,V,β) as: where : -.,#, = / 0 1! = 1 0 1! 3 4&5(6 ) 7 λ comesfromthe integration of the momentump in the phase spacegivenby: so that:
12 and In order to compute the average energy, one needs to compute the average potential U. Assume the case of a pairwise potential, so that: i.e. U isa sumof termsdepending only between2 particles, and thuscontains N(N-1) terms. Then, wecan write: (i.e. all terms in the first line are the exact same integrals, just with different labels)
13 which containsa two-body probability distribution function ρ (2) (r 1,r 2 ) sothat<u> can berewritten as : where weremind (slide 2) that: One thus arrives to the result:
14 Example : Glass transition in a model A-B glass Flores-Ruiz et al. PRB 2010 Reproduction of the glass transition phenomenon
15 Thermodynamic quantities from the computed g(r): Pressure We use the Maxwell relation: The volume dependence can be made explicit by changing the variables: sothatwehave fromthe partition function Z N the desiredderivativefromv: And: which involvesthe force F i acting on a particle i
16 Again, for, pairwiseinteractions, F i can be written as : and since one has (interchanging i-j summations): Using Newton s third law, we furthermore have : and the Ensemble average is given by:
17 Wedo the same as for the energy: and for a pair potential U pair : And finally: The pressure canbecomputedfromthe derivative of the pair potentialand fromg(r).
18 Examples: equation of state of liquids GeO 2 SiO 2 Shell et al. PRE 2002 Micoulaut et al. PRE 2006
19 B) STATIC STRUCTURE FACTOR For a simple liquid, the static structure factor isgivenby : where ρ k is the Fourier transformof the microscopic density ρ(r). This readsas: and, remembering that ρ one has: If isotropic and uniform medium, remember that ρ(r,r )=ρ 2 g(r,r )
20 Also, g(r,r ) depends only on r-r, i.e.: Or (isotropic fluid, everything depends only on k= k ): The calculation of the structure factor S(k) isachieved via a Fourier transformof the pair distribution function g(r).
21 Calculating a structure factor S(k) from a MD simulation : 2 options 1. Calculate the pair correlation function g(r) from the MD trajectory, then use : 2. Calculate directly S(k) from the trajectory using: As 2 Se 3 Differences between both methodscan arise, and one islimited to r<l/2, i.e. k<π/l Effects of the components of the wavevector
22 Direct comparison with experiments : neutron or X-ray diffraction Intensityscatteredin the direction k f Equal to the computed structur efactor. Kob et al. 1999
23 Structure factor in multicomponent systems SiO 2, GeSe 2, SiO 2 -Na 2 O, Consider a system with n components havingn 1, N 2, N n particles. We can write Faber-Ziman partial structure factors: = $& (>)= (1+ $&) 2 % % exp [ E. ] out of which can becomputed a total structure factor: Neutron weighted: = H =,( J J ( K K ( = ( (H),( J J ( K K ( withb i the neutron scatteringcross section, c i the concentration of the species b=5.68 i fmfor Te (tabulated, depends on the isotope) X-ray weighted: = H =,( J J ( L (H)L ( (H)= ( (H),( J J ( L (H)L ( ( H) Withf i (k) the X-ray form factor (elastic or inelastic XRD)
24 v-sio 2 l-gese 2 Micoulaut et al., PRB 2009
25 Various levels of agreement between theory and experiments can be found 5 4 Ag25 3 Ag15 S (Q) 2 1 Ag Q (Å -1 ) Micoulaut et al Data Petri, Salmon, 1991
26 Detailed structural analysis from MD Neighbor distribution Remember = 4 First minimum of g(r) can beusedto define the coordination number. But this is an average. Details are provided from the statistical analysis of each atom. Allowsto characterize the nature of the neighborhood Can beextended to partial CN ( = ( 4
27 Examples-1 Amorphous Ge 1 Sb 2 Te 4 Raty et al. Solid State Sciences 2010 Straightforward 4 neighbours around Ge,Si Information on local geometry - short and long bond distance around Ge - CN Te >2
28 Examples-2: Statistics of neighbors with homopolar bonds Ga 11 Ge 11 Te 78 Voleska et al., PRB 2013
29 Detailed structural analysis from MD Bond angle distributions 1173 K SnSe 2 Depending on the system, provides information about the local geometry (tetrahedral, octahedral, ). Directional bonding vs non-directional 300 K SiO 2 -Na 2 O Micoulaut et al. PRB 2008 Cormack and Du, JNCS 2001
30 Detailed structural analysis from MD Ring statistics: serve to characterize the intermediate range order Remember the early work of Galeener (lecture 3) and the Raman characterization of rings Simulated positions can serve to define nodes and links. When connected sequentially without overlap, one has a path. A ring is therefore simply a closed path. Each of these rings is characterized by its size and can be classified. S. Le Roux, P. Jund, Comp. Mater. Sci. 2010
31 Conclusions MD trajectories, once properlygenerated canlead to variousstructural informations under various thermodynamic conditions pair distribution functions g(r) bond distances partial coordination numbers, coordination numbers neighborhood Structure factor S(k) information at intermediate lengthscales Many other quantities of interest Rings Bond angle distributions Topological constraints- > Rigidity transitions (next lectures) With imagination, one can find out much more or invent much more Next lecture : time correlations and linear response
32 Final recommendation regarding structural properties 1. Do the best you can. 2. Don t fool the reader. 3. Be honestwith the data 4. Do not attempt to dissimulate 5. Unique S(k)? Uncarefully simulated liquid GeTe 4 Atomic modeling of glass LECTURE7 MD CALCULATING
LECTURE 11 : GLASSY DYNAMICS - Intermediate scattering function - Mean square displacement and beyond - Dynamic heterogeneities - Isoconfigurational
LECTURE 11 : GLASSY DYNAMICS - Intermediate scattering function - Mean square displacement and beyond - Dynamic heterogeneities - Isoconfigurational Ensemble - Energy landscapes A) INTERMEDIATE SCATTERING
More informationSolidification, Crystallization & Glass Transition
Solidification, Crystallization & Glass Transition Cooling the Melt solidification Crystallization versus Formation of Glass Parameters related to the formaton of glass Effect of cooling rate Glass transition
More informationPARTIAL PAIR CORRELATION FUNCTIONS OF AMORPHOUS AND LIQUID Ge 15 Te 85
Journal of Optoelectronics and Advanced Materials Vol. 7, No. 4, August 2005, p. 1977-1981 PARTIAL PAIR CORRELATION FUNCTIONS OF AMORPHOUS AND LIQUID Ge 15 Te 85 I. Kaban, P. Jóvári a, W. Hoyer * Chemnitz
More informationObjectives: 1. Be able to list the assumptions and methods associated with the Virial Equation of state.
Lecture #19 1 Lecture 19 Objectives: 1. Be able to list the assumptions and methods associated with the Virial Equation of state. 2. Be able to compute the second virial coefficient from any given pair
More informationIonic Bonding Pauling s Rules and the Bond Valence Method
Ionic Bonding Pauling s Rules and the Bond Valence Method Chemistry 754 Solid State Chemistry Dr. Patrick Woodward Lecture #14 Pauling Rules for Ionic Structures Linus Pauling,, J. Amer. Chem. Soc. 51,,
More informationMatter, Materials, Crystal Structure and Bonding. Chris J. Pickard
Matter, Materials, Crystal Structure and Bonding Chris J. Pickard Why should a theorist care? Where the atoms are determines what they do Where the atoms can be determines what we can do Overview of Structure
More informationChapter 12 - Liquids and Solids
Chapter 12 - Liquids and Solids 12-1 Liquids I. Properties of Liquids and the Kinetic Molecular Theory A. Fluids 1. Substances that can flow and therefore take the shape of their container B. Relative
More informationPhotoinduced volume change in chalcogenide glasses
Photoinduced volume change in chalcogenide glasses (Ph.D. thesis points) Rozália Lukács Budapest University of Technology and Economics Department of Theoretical Physics Supervisor: Dr. Sándor Kugler 2010
More informationLesson 3. Chemical Bonding. Molecular Orbital Theory
Lesson 3 Chemical Bonding Molecular Orbital Theory 1 Why Do Bonds Form? An energy diagram shows that a bond forms between two atoms if the overall energy of the system is lowered when the two atoms approach
More information7. DYNAMIC LIGHT SCATTERING 7.1 First order temporal autocorrelation function.
7. DYNAMIC LIGHT SCATTERING 7. First order temporal autocorrelation function. Dynamic light scattering (DLS) studies the properties of inhomogeneous and dynamic media. A generic situation is illustrated
More informationSection 3: Crystal Binding
Physics 97 Interatomic forces Section 3: rystal Binding Solids are stable structures, and therefore there exist interactions holding atoms in a crystal together. For example a crystal of sodium chloride
More informationLecture 2 - Semiconductor Physics (I) September 13, 2005
6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-1 Lecture 2 - Semiconductor Physics (I) September 13, 2005 Contents: 1. Silicon bond model: electrons and holes 2. Generation and recombination
More informationAP Chemistry A. Allan Chapter 8 Notes - Bonding: General Concepts
AP Chemistry A. Allan Chapter 8 Notes - Bonding: General Concepts 8.1 Types of Chemical Bonds A. Ionic Bonding 1. Electrons are transferred 2. Metals react with nonmetals 3. Ions paired have lower energy
More informationLap Fillet Weld Calculations and FEA Techniques
Lap Fillet Weld Calculations and FEA Techniques By: MS.ME Ahmad A. Abbas Sr. Analysis Engineer Ahmad.Abbas@AdvancedCAE.com www.advancedcae.com Sunday, July 11, 2010 Advanced CAE All contents Copyright
More informationChapter Outline. How do atoms arrange themselves to form solids?
Chapter Outline How do atoms arrange themselves to form solids? Fundamental concepts and language Unit cells Crystal structures Simple cubic Face-centered cubic Body-centered cubic Hexagonal close-packed
More informationName Date Class STATES OF MATTER. SECTION 13.1 THE NATURE OF GASES (pages 385 389)
13 STATES OF MATTER SECTION 13.1 THE NATURE OF GASES (pages 385 389) This section introduces the kinetic theory and describes how it applies to gases. It defines gas pressure and explains how temperature
More informationWhich substance contains positive ions immersed in a sea of mobile electrons? A) O2(s) B) Cu(s) C) CuO(s) D) SiO2(s)
BONDING MIDTERM REVIEW 7546-1 - Page 1 1) Which substance contains positive ions immersed in a sea of mobile electrons? A) O2(s) B) Cu(s) C) CuO(s) D) SiO2(s) 2) The bond between hydrogen and oxygen in
More informationKINETIC MOLECULAR THEORY OF MATTER
KINETIC MOLECULAR THEORY OF MATTER The kinetic-molecular theory is based on the idea that particles of matter are always in motion. The theory can be used to explain the properties of solids, liquids,
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationWhat is molecular dynamics (MD) simulation and how does it work?
What is molecular dynamics (MD) simulation and how does it work? A lecture for CHM425/525 Fall 2011 The underlying physical laws necessary for the mathematical theory of a large part of physics and the
More information7.14 Linear triatomic: A-----B-----C. Bond angles = 180 degrees. Trigonal planar: Bond angles = 120 degrees. B < B A B = 120
APTER SEVEN Molecular Geometry 7.13 Molecular geometry may be defined as the three-dimensional arrangement of atoms in a molecule. The study of molecular geometry is important in that a molecule s geometry
More informationUntitled Document. 1. Which of the following best describes an atom? 4. Which statement best describes the density of an atom s nucleus?
Name: Date: 1. Which of the following best describes an atom? A. protons and electrons grouped together in a random pattern B. protons and electrons grouped together in an alternating pattern C. a core
More informationB) atomic number C) both the solid and the liquid phase D) Au C) Sn, Si, C A) metal C) O, S, Se C) In D) tin D) methane D) bismuth B) Group 2 metal
1. The elements on the Periodic Table are arranged in order of increasing A) atomic mass B) atomic number C) molar mass D) oxidation number 2. Which list of elements consists of a metal, a metalloid, and
More informationCHEMISTRY STANDARDS BASED RUBRIC ATOMIC STRUCTURE AND BONDING
CHEMISTRY STANDARDS BASED RUBRIC ATOMIC STRUCTURE AND BONDING Essential Standard: STUDENTS WILL UNDERSTAND THAT THE PROPERTIES OF MATTER AND THEIR INTERACTIONS ARE A CONSEQUENCE OF THE STRUCTURE OF MATTER,
More informationChapter Test B. Chapter: Measurements and Calculations
Assessment Chapter Test B Chapter: Measurements and Calculations PART I In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question. 1.
More informationStructure Factors 59-553 78
78 Structure Factors Until now, we have only typically considered reflections arising from planes in a hypothetical lattice containing one atom in the asymmetric unit. In practice we will generally deal
More information1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids
1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.
More information1. The Kinetic Theory of Matter states that all matter is composed of atoms and molecules that are in a constant state of constant random motion
Physical Science Period: Name: ANSWER KEY Date: Practice Test for Unit 3: Ch. 3, and some of 15 and 16: Kinetic Theory of Matter, States of matter, and and thermodynamics, and gas laws. 1. The Kinetic
More informationIntroduction to X-Ray Powder Diffraction Data Analysis
Introduction to X-Ray Powder Diffraction Data Analysis Center for Materials Science and Engineering at MIT http://prism.mit.edu/xray An X-ray diffraction pattern is a plot of the intensity of X-rays scattered
More informationVacuum Evaporation Recap
Sputtering Vacuum Evaporation Recap Use high temperatures at high vacuum to evaporate (eject) atoms or molecules off a material surface. Use ballistic flow to transport them to a substrate and deposit.
More informationChapter 5: Diffusion. 5.1 Steady-State Diffusion
: Diffusion Diffusion: the movement of particles in a solid from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance Diffusion is process
More informationModern Construction Materials Prof. Ravindra Gettu Department of Civil Engineering Indian Institute of Technology, Madras
Modern Construction Materials Prof. Ravindra Gettu Department of Civil Engineering Indian Institute of Technology, Madras Module - 2 Lecture - 2 Part 2 of 2 Review of Atomic Bonding II We will continue
More informationName period AP chemistry Unit 2 worksheet Practice problems
Name period AP chemistry Unit 2 worksheet Practice problems 1. What are the SI units for a. Wavelength of light b. frequency of light c. speed of light Meter hertz (s -1 ) m s -1 (m/s) 2. T/F (correct
More informationIntroduction to the Monte Carlo method
Some history Simple applications Radiation transport modelling Flux and Dose calculations Variance reduction Easy Monte Carlo Pioneers of the Monte Carlo Simulation Method: Stanisław Ulam (1909 1984) Stanislaw
More informationThe Quantum Harmonic Oscillator Stephen Webb
The Quantum Harmonic Oscillator Stephen Webb The Importance of the Harmonic Oscillator The quantum harmonic oscillator holds a unique importance in quantum mechanics, as it is both one of the few problems
More informationAl 2 O 3, Its Different Molecular Structures, Atomic Layer Deposition, and Dielectrics
Al 2 O 3, Its Different Molecular Structures, Atomic Layer Deposition, and Dielectrics Mark Imus Douglas Sisk, Ph.D., Mentor Marian High School RET Program University of Notre Dame Project Proposal Tunneling
More informationName Partners Date. Energy Diagrams I
Name Partners Date Visual Quantum Mechanics The Next Generation Energy Diagrams I Goal Changes in energy are a good way to describe an object s motion. Here you will construct energy diagrams for a toy
More information13.1 The Nature of Gases. What is Kinetic Theory? Kinetic Theory and a Model for Gases. Chapter 13: States of Matter. Principles of Kinetic Theory
Chapter 13: States of Matter The Nature of Gases The Nature of Gases kinetic molecular theory (KMT), gas pressure (pascal, atmosphere, mm Hg), kinetic energy The Nature of Liquids vaporization, evaporation,
More informationA pure covalent bond is an equal sharing of shared electron pair(s) in a bond. A polar covalent bond is an unequal sharing.
CHAPTER EIGHT BNDING: GENERAL CNCEPT or Review 1. Electronegativity is the ability of an atom in a molecule to attract electrons to itself. Electronegativity is a bonding term. Electron affinity is the
More informationLecture 3: Models of Solutions
Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP4, Thermodynamics and Phase Diagrams, H. K. D. H. Bhadeshia Lecture 3: Models of Solutions List of Symbols Symbol G M
More informationUsing light scattering method to find The surface tension of water
Experiment (8) Using light scattering method to find The surface tension of water The aim of work: The goals of this experiment are to confirm the relationship between angular frequency and wave vector
More informationIndiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance.
.1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations
More informationLecture 24 - Surface tension, viscous flow, thermodynamics
Lecture 24 - Surface tension, viscous flow, thermodynamics Surface tension, surface energy The atoms at the surface of a solid or liquid are not happy. Their bonding is less ideal than the bonding of atoms
More informationAtomic Structure Chapter 5 Assignment & Problem Set
Atomic Structure Name Warm-Ups (Show your work for credit) Date 1. Date 2. Date 3. Date 4. Date 5. Date 6. Date 7. Date 8. Atomic Structure 2 Study Guide: Things You Must Know Vocabulary (know the definition
More informationGibbs Free Energy and Chemical Potential. NC State University
Chemistry 433 Lecture 14 Gibbs Free Energy and Chemical Potential NC State University The internal energy expressed in terms of its natural variables We can use the combination of the first and second
More informationSymmetry and group theory
Symmetry and group theory or How to Describe the Shape of a Molecule with two or three letters Natural symmetry in plants Symmetry in animals 1 Symmetry in the human body The platonic solids Symmetry in
More informationNotes on Elastic and Inelastic Collisions
Notes on Elastic and Inelastic Collisions In any collision of 2 bodies, their net momentus conserved. That is, the net momentum vector of the bodies just after the collision is the same as it was just
More informationName Class Date. In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question.
Assessment Chapter Test A Chapter: States of Matter In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question. 1. The kinetic-molecular
More informationANSWER KEY : BUILD AN ATOM PART I: ATOM SCREEN Build an Atom simulation ( http://phet.colorado.edu/en/simulation/build an atom )
ANSWER KEY : PART I: ATOM SCREEN Build an Atom simulation ( http://phet.colorado.edu/en/simulation/build an atom ) 1. Explore the Build an Atom simulation with your group. As you explore, talk about what
More informationBonding & Molecular Shape Ron Robertson
Bonding & Molecular Shape Ron Robertson r2 n:\files\courses\1110-20\2010 possible slides for web\00bondingtrans.doc The Nature of Bonding Types 1. Ionic 2. Covalent 3. Metallic 4. Coordinate covalent Driving
More informationBoardworks AS Physics
Boardworks AS Physics Vectors 24 slides 11 Flash activities Prefixes, scalars and vectors Guide to the SI unit prefixes of orders of magnitude Matching powers of ten to their SI unit prefixes Guide to
More informationVocabulary: VSEPR. 3 domains on central atom. 2 domains on central atom. 3 domains on central atom NOTE: Valence Shell Electron Pair Repulsion Theory
Vocabulary: VSEPR Valence Shell Electron Pair Repulsion Theory domain = any electron pair, or any double or triple bond is considered one domain. lone pair = non-bonding pair = unshared pair = any electron
More informationIntroduction to Chemistry. Course Description
CHM 1025 & CHM 1025L Introduction to Chemistry Course Description CHM 1025 Introduction to Chemistry (3) P CHM 1025L Introduction to Chemistry Laboratory (1) P This introductory course is intended to introduce
More informationRotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn
More informationChapter Outline. Diffusion - how do atoms move through solids?
Chapter Outline iffusion - how do atoms move through solids? iffusion mechanisms Vacancy diffusion Interstitial diffusion Impurities The mathematics of diffusion Steady-state diffusion (Fick s first law)
More informationRapid structure determination of disordered materials: study of GeSe 2 glass
Solid State Communications 129 (2004) 239 243 www.elsevier.com/locate/ssc Rapid structure determination of disordered materials: study of GeSe 2 glass V. Petkov a, *, D. Qadir a, S.D. Shastri b a Department
More informationPreview of Period 2: Forms of Energy
Preview of Period 2: Forms of Energy 2.1 Forms of Energy How are forms of energy defined? 2.2 Energy Conversions What happens when energy is converted from one form into another form? 2.3 Efficiency of
More informationLesson 6: Earth and the Moon
Lesson 6: Earth and the Moon Reading Assignment Chapter 7.1: Overall Structure of Planet Earth Chapter 7.3: Earth s Interior More Precisely 7-2: Radioactive Dating Chapter 7.5: Earth s Magnetosphere Chapter
More informationPHYSICAL PROPERTIES: GLASS. Forensic Science CC 30.07 Spring 2007 Prof. Nehru
PHYSICAL PROPERTIES: GLASS Physical vs. Chemical Properties The forensic scientist must constantly determine those properties that impart distinguishing characteristics to matter, giving it a unique identity.
More informationWhen the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.
Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs
More informationSHAPES OF MOLECULES (VSEPR MODEL)
1 SAPES MLEULES (VSEPR MDEL) Valence Shell Electron-Pair Repulsion model - Electron pairs surrounding atom spread out as to minimize repulsion. - Electron pairs can be bonding pairs (including multiple
More informationElectron Microscopy 3. SEM. Image formation, detection, resolution, signal to noise ratio, interaction volume, contrasts
Electron Microscopy 3. SEM Image formation, detection, resolution, signal to noise ratio, interaction volume, contrasts 3-1 SEM is easy! Just focus and shoot "Photo"!!! Please comment this picture... Any
More informationPeriodic Table Questions
Periodic Table Questions 1. The elements characterized as nonmetals are located in the periodic table at the (1) far left; (2) bottom; (3) center; (4) top right. 2. An element that is a liquid at STP is
More informationThermodynamics: Lecture 8, Kinetic Theory
Thermodynamics: Lecture 8, Kinetic Theory Chris Glosser April 15, 1 1 OUTLINE I. Assumptions of Kinetic Theory (A) Molecular Flux (B) Pressure and the Ideal Gas Law II. The Maxwell-Boltzmann Distributuion
More informationES240 Solid Mechanics Fall 2007. Stress field and momentum balance. Imagine the three-dimensional body again. At time t, the material particle ( x, y,
S40 Solid Mechanics Fall 007 Stress field and momentum balance. Imagine the three-dimensional bod again. At time t, the material particle,, ) is under a state of stress ij,,, force per unit volume b b,,,.
More informationSputtering by Particle Bombardment I
Sputtering by Particle Bombardment I Physical Sputtering of Single-Element Solids Edited by R. Behrisch With Contributions by H. H. Andersen H. L. Bay R. Behrisch M. T. Robinson H. E. Roosendaal P. Sigmund
More informationChapter 3. 1. 3 types of materials- amorphous, crystalline, and polycrystalline. 5. Same as #3 for the ceramic and diamond crystal structures.
Chapter Highlights: Notes: 1. types of materials- amorphous, crystalline, and polycrystalline.. Understand the meaning of crystallinity, which refers to a regular lattice based on a repeating unit cell..
More informationAS Chemistry Revision Notes Unit 1 Atomic Structure, Bonding And Periodicity
AS Chemistry Revision Notes Unit Atomic Structure, Bonding And Periodicity Atomic Structure. All atoms have a mass number, A (the number of nucleons), and a proton number, Z (the number of protons). 2.
More informationX-ray diffraction techniques for thin films
X-ray diffraction techniques for thin films Rigaku Corporation Application Laboratory Takayuki Konya 1 Today s contents (PM) Introduction X-ray diffraction method Out-of-Plane In-Plane Pole figure Reciprocal
More informationThème Analytical Chemistry ECUE composant l UE
Thème Analytical Chemistry ECUE composant l UE UE 7.1 Performing analyses in the environment and complex systems UE 7.2 Heterogeneity and complexity UE 7.3 Processes in aquatic systems and at geo-interfaces
More informationCHEM 1301 SECOND TEST REVIEW. Covalent bonds are sharing of electrons (ALWAYS valence electrons). Use Lewis structures to show this sharing.
CEM 1301 SECOND TEST REVIEW Lewis Structures Covalent bonds are sharing of electrons (ALWAYS valence electrons). Use Lewis structures to show this sharing. Rules OCTET RULE an atom would like to have 8
More information100% ionic compounds do not exist but predominantly ionic compounds are formed when metals combine with non-metals.
2.21 Ionic Bonding 100% ionic compounds do not exist but predominantly ionic compounds are formed when metals combine with non-metals. Forming ions Metal atoms lose electrons to form +ve ions. Non-metal
More informationStatistical Mechanics, Kinetic Theory Ideal Gas. 8.01t Nov 22, 2004
Statistical Mechanics, Kinetic Theory Ideal Gas 8.01t Nov 22, 2004 Statistical Mechanics and Thermodynamics Thermodynamics Old & Fundamental Understanding of Heat (I.e. Steam) Engines Part of Physics Einstein
More informationPHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS
PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS 1. Photons 2. Photoelectric Effect 3. Experimental Set-up to study Photoelectric Effect 4. Effect of Intensity, Frequency, Potential on P.E.
More informationScience Standard Articulated by Grade Level Strand 5: Physical Science
Concept 1: Properties of Objects and Materials Classify objects and materials by their observable properties. Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 PO 1. Identify the following observable properties
More informationPERIODIC TABLE OF GROUPS OF ELEMENTS Elements can be classified using two different schemes.
1 PERIODIC TABLE OF GROUPS OF ELEMENTS Elements can be classified using two different schemes. Metal Nonmetal Scheme (based on physical properties) Metals - most elements are metals - elements on left
More informationChapter NP-5. Nuclear Physics. Nuclear Reactions TABLE OF CONTENTS INTRODUCTION OBJECTIVES 1.0 NUCLEAR REACTIONS 2.0 NEUTRON INTERACTIONS
Chapter NP-5 Nuclear Physics Nuclear Reactions TABLE OF CONTENTS INTRODUCTION OBJECTIVES 1.0 2.0 NEUTRON INTERACTIONS 2.1 ELASTIC SCATTERING 2.2 INELASTIC SCATTERING 2.3 RADIATIVE CAPTURE 2.4 PARTICLE
More informationMicroscopic and mesoscopic simulations of amorphous systems using LAMMPS and GPU-based algorithms
Microscopic and mesoscopic simulations of amorphous systems using LAMMPS and GPU-based algorithms E. Ferrero and F. Puosi Laboratoire Interdisciplinaire de Physique (LIPhy), UJF and CNRS 14/5/214 Journée
More informationChapter 22: The Electric Field. Read Chapter 22 Do Ch. 22 Questions 3, 5, 7, 9 Do Ch. 22 Problems 5, 19, 24
Chapter : The Electric Field Read Chapter Do Ch. Questions 3, 5, 7, 9 Do Ch. Problems 5, 19, 4 The Electric Field Replaces action-at-a-distance Instead of Q 1 exerting a force directly on Q at a distance,
More informationCollision of a small bubble with a large falling particle
EPJ Web of Conferences 67, 212 (214) DOI: 1.11/ epjconf/ 21467212 C Owned by the authors, published by EDP Sciences, 214 Collision of a small bubble with a large falling particle Jiri Vejrazka 1,a, Martin
More informationWhy? Intermolecular Forces. Intermolecular Forces. Chapter 12 IM Forces and Liquids. Covalent Bonding Forces for Comparison of Magnitude
1 Why? Chapter 1 Intermolecular Forces and Liquids Why is water usually a liquid and not a gas? Why does liquid water boil at such a high temperature for such a small molecule? Why does ice float on water?
More informationLimiting Reagent (using an analogy and a learning cycle approach)
Limiting Reagent (using an analogy and a learning cycle approach) Welcome: This is the fourth of a four- experiment sequence, covering four important aspects of chemistry, and utilizing a learning cycle
More informationMolecular Dynamics Simulations
Molecular Dynamics Simulations Yaoquan Tu Division of Theoretical Chemistry and Biology, Royal Institute of Technology (KTH) 2011-06 1 Outline I. Introduction II. Molecular Mechanics Force Field III. Molecular
More informationChemistry 105, Chapter 7 Exercises
hemistry 15, hapter 7 Exercises Types of Bonds 1. Using the periodic table classify the bonds in the following compounds as ionic or covalent. If covalent, classify the bond as polar or not. Mg2 4 i2 a(3)2
More informationHealth Science Chemistry I CHEM-1180 Experiment No. 15 Molecular Models (Revised 05/22/2015)
(Revised 05/22/2015) Introduction In the early 1900s, the chemist G. N. Lewis proposed that bonds between atoms consist of two electrons apiece and that most atoms are able to accommodate eight electrons
More informationSteady Heat Conduction
Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long
More informationMean Field Flory Huggins Lattice Theory
Mean Field Flory Huggins Lattice Theory Mean field: the interactions between molecules are assumed to be due to the interaction of a given molecule and an average field due to all the other molecules in
More informationEXPERIMENT 4 The Periodic Table - Atoms and Elements
EXPERIMENT 4 The Periodic Table - Atoms and Elements INTRODUCTION Primary substances, called elements, build all the materials around you. There are more than 109 different elements known today. The elements
More informationData Visualization for Atomistic/Molecular Simulations. Douglas E. Spearot University of Arkansas
Data Visualization for Atomistic/Molecular Simulations Douglas E. Spearot University of Arkansas What is Atomistic Simulation? Molecular dynamics (MD) involves the explicit simulation of atomic scale particles
More informationLecture 2 Linear functions and examples
EE263 Autumn 2007-08 Stephen Boyd Lecture 2 Linear functions and examples linear equations and functions engineering examples interpretations 2 1 Linear equations consider system of linear equations y
More informationGeometries and Valence Bond Theory Worksheet
Geometries and Valence Bond Theory Worksheet Also do Chapter 10 textbook problems: 33, 35, 47, 49, 51, 55, 57, 61, 63, 67, 83, 87. 1. Fill in the tables below for each of the species shown. a) CCl 2 2
More information2054-2. Structure and Dynamics of Hydrogen-Bonded Systems. 26-27 October 2009. Hydrogen Bonds and Liquid Water
2054-2 Structure and Dynamics of Hydrogen-Bonded Systems 26-27 October 2009 Hydrogen Bonds and Liquid Water Ruth LYNDEN-BELL University of Cambridge, Department of Chemistry Lensfield Road Cambridge CB2
More informationTitle: General Chemistry I. Department: Credits: 5 Lecture Hours:4 Lab/Studio Hours:3
Code: CHEM-101 Title: General Chemistry I Institute: STEM Department: Chemistry Course Description:The student will investigate the fundamental concepts of chemistry from a theoretical approach and participate
More informationFeature Commercial codes In-house codes
A simple finite element solver for thermo-mechanical problems Keywords: Scilab, Open source software, thermo-elasticity Introduction In this paper we would like to show how it is possible to develop a
More informationLecture 2 Macroscopic Interactions. 22.106 Neutron Interactions and Applications Spring 2010
Lecture 2 Macroscopic Interactions 22.106 Neutron Interactions and Applications Spring 2010 Objectives Macroscopic Interactions Atom Density Mean Free Path Moderation in Bulk Matter Neutron Shielding Effective
More informationHW 10. = 3.3 GPa (483,000 psi)
HW 10 Problem 15.1 Elastic modulus and tensile strength of poly(methyl methacrylate) at room temperature [20 C (68 F)]. Compare these with the corresponding values in Table 15.1. Figure 15.3 is accurate;
More informationPhysics Notes Class 11 CHAPTER 2 UNITS AND MEASUREMENTS
1 P a g e Physics Notes Class 11 CHAPTER 2 UNITS AND MEASUREMENTS The comparison of any physical quantity with its standard unit is called measurement. Physical Quantities All the quantities in terms of
More informationFigure 2.31. CPT Equipment
Soil tests (1) In-situ test In order to sound the strength of the soils in Las Colinas Mountain, portable cone penetration tests (Japan Geotechnical Society, 1995) were performed at three points C1-C3
More informationChemistry 13: States of Matter
Chemistry 13: States of Matter Name: Period: Date: Chemistry Content Standard: Gases and Their Properties The kinetic molecular theory describes the motion of atoms and molecules and explains the properties
More informationCBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology
CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,
More information