Primitive cells, Wigner-Seitz cells, and 2D lattices. 4P70, Solid State Physics Chris Wiebe
|
|
|
- Diana Hall
- 6 years ago
- Views:
Transcription
1 Primitive cells, Wigner-Seitz cells, and 2D lattices 4P70, Solid State Physics Chris Wiebe
2 Choice of primitive cells! Which unit cell is a good choice?! A, B, and C are primitive unit cells. Why?! D, E, and F are not. Why?! Notice: the volumes of A, B, and C are the same. Also, the choice of origin is different, but it doesn t matter! Also: There is only one lattice point in the primitive unit cells.
3 Wigner-Seitz cells! How can we choose primitive cells?! One algorithm is the Wigner- Seitz cell! Steps: (1) Draw lines to connect a given lattice point to all nearby lattice points! (2) At the midpoint and normal to these lines, draw new lines (or planes in 3D)! (3) The smallest volume enclosed in this way is the Wigner-Seitz primitive cell Wigner-Seitz cell
4 Finding Wigner-Seitz cells (M. C. Escher) Phopholipid bilayers (P. C. Mason et al, PRE, 63, (2001)) Homework: What are the Wigner-Seitz cells for these lattices?
5 Fundamental types of lattices! Crystal lattices can be mapped into themselves by the lattice translations T, and by other symmetry operations! Physicists use the symmetry of the unit cells to classify crystal structures and how they fill space.! In this course, you will not have to know how this is done (this involves the use of point operations and translation operators)! However, you do have to understand how we classify lattices! In 2D, there are only 5 distinct lattices. These are defined by how you can rotate the cell contents (and get the same cell back), and if there are any mirror planes within the cell.! From now on, we will call these distinct lattice types Bravais lattices.! Unit cells made of these 5 types in 2D can fill space. All other ones cannot. π We can fill space with a rectangular lattice by 180 o rotations (not 90 o why?) π/3 We can fill space with a hexagonal lattice by 60 o rotations Note: this is the primitive cell of a hexagonal lattice (why? See Kittel, fig 9b)
6 Fivefold rotations and quasicrystals! It turns out that mathematicians discovered that you can only fill space by using rotations of unit cells by 2π, 2π/2, 2π/3, 2π/4, and 2π/6 radians (or, by 360 o, 180 o, 120 o, 90 o, and 60 0 )! But, rotations of the kind 2π/5 or 2π/7 do not fill space!! A quasicrystal is a quasiperiodic nonrandom assembly of two types of figures (since we need two types, it is not a Bravais lattice you cannot fill space with just one repeating unit cell)! We will discuss these in Chapter Two Penrose tiling in 2D
7 The 2D Bravais lattices Note that this is the proper primitive cell for the centered rectangular lattice type (why? It contains only one lattice point) (this is called a rhombus)
8 The 3D Bravais Lattices! In 3D, there are 7 lattice systems, which give rise to 14 bravais lattices! The general lattice is triclinic, and all others are derived from putting restraints on the triclinic lattice! Know the conditions of each lattice (excellent test question )
9 The 14 Bravais lattices in 3D! Notice that we know have different lattice types:! P = primitive (1 lattice point)! I = Body-centred (2 lattice pts)! F = Face- centred (4 lattice pts)! C = Side-Centred (2 lattice pts)! In this course, we will concentrate upon only a few of these types
10 Cubic lattices: SC, BCC and FCC! For cubic systems, we have three bravais lattices: the simple cubic (SC), bodycentred cubic (BCC) and facecentred cubic (FCC).! The simple cubic has 1 lattice point per unit cell, with a total area of a 3! Number of nearest neighbours: 6! Nearest neighbour distance: a! Number of next-nearest neighbours: 12! Next-nearest neighbour distance: 2a (prove this!) Packing fraction = (atomic volume)/ (bravais unit cell volume) Simple cubic lattice (4/3)π(a/2) 3 (a 3 ) = π / 6
11 The Body-Centred Cubic Lattice (Li (at room temp.), Na, K, V, Cr, Fe, Rb, Nb, Mo, Cs, Ba, Eu, Ta) Body- Centred Cubic Lattice (BCC) Packing fraction = (atomic volume)/ ( bravais unit cell volume) (4/3)π( 3a/4) 3 (a 3 /2) = 3π / 8! The body-centred cubic lattice has 2 lattice points per unit cell, with a total primitive cell volume of a 3 /2! Number of nearest neighbours: 8! Nearest neighbour distance: 3 a/2 = a (prove this!)! Number of next-nearest neighbours: 6 (where are these?)! Next-nearest neighbour distance: a (prove this!)
12 The Body-Centred Cubic Lattice! The primitive cell of the BCC lattice is defined by the translation vectors: z a 1 = ½ a (x + y - z) a 2 = ½ a (-x+y + z) a 3 = ½ a (x - y + z) where x, y, and z are the Cartesian unit vectors. These translation vectors connect the lattice pt at the origin to the points at the body centres (and make a rhombohedron) The angle between adjacent edges is a a 3 x a 1 a 2 See figure 11 in Kittel for a picture of the primitive cell in more detail y
13 The Face-Centred Cubic Lattice (Al, Cu, Ni, Sr, Rh, Pd, Ag, Ce, Tb, Ir, Pt, Au, Pb, Th)! The face-centred cubic lattice has 4 lattice points per unit cell, with a total primitive cell volume of a 3 /4! Number of nearest neighbours: 12! Nearest neighbour distance: a/ 2 = a (prove this!)! Number of next-nearest neighbours: 6 (where are these?)! Next-nearest neighbour distance: a (prove this!) Packing fraction = (atomic volume)/ (bravais unit cell volume) = 2π / 6 (do this on your own)
14 The Face-Centred Cubic Lattice! The primitive cell of the FCC lattice is defined by the translation vectors: a 1 = ½ a (x + y) a 2 = ½ a (y + z) a 3 = ½ a (z + x) where x, y, and z are the Cartesian unit vectors. These translation vectors connect the lattice pt at the origin to the points at the face centres. The angles between the axes are 60
15 Wigner-Seitz cells for BCC, FCC lattices! Note: You can also construct Wigner-Seitz cells for the FCC and BCC lattices. These look a bit strange, but they will be useful when we look at reciprocal space in the next chapter.! These are made by taking the lines to the nearest and nextnearest neighbour points, and bisecting them with planes. The resulting figure is the Wigner-Seitz cell (which have the same volumes as the primitive cells we made above)
16 Wigner-Seitz cells BCC lattice Simple cubic lattice
17 Hexagonal unit cell! The primitive cell in a hexagonal system is a right prism based on a rhombus with an included angle of 120! Note here that a 1 = a 2 = a 3! Later, we will look at the hexagonal close-packed structure, which is this structure with a basis (and is related to the fcc structure). a 3 a 2 a (primitive cell is in bold)
Introduction to Solid State Physics
z y x Introduction to Solid State Physics Lecture 2 Prof. Igor Shvets ivchvets@tcd.ie Slide 1Lecture 2 Primitive Vectors of a Bravais Lattice By definition all Bravais lattices must be described by a set
CRYSTAL LATTICE. Defining lattice: Mathematical construct; ideally infinite arrangement of points in space.
CRYSTAL LATTICE How to form a crystal? 1. Define the structure of the lattice 2. Define the lattice constant 3. Define the basis Defining lattice: Mathematical construct; ideally infinite arrangement of
General Objective. To develop the knowledge of crystal structure and their properties.
CRYSTAL PHYSICS 1 General Objective To develop the knowledge of crystal structure and their properties. 2 Specific Objectives 1. Differentiate crystalline and amorphous solids. 2. To explain nine fundamental
Crystallography. Duration: three weeks (8 to 9 hours) One problem set. Outline: 1- Bravais Lattice and Primitive
Crystallography Duration: three weeks (8 to 9 hours) One problem set Outline: 1- Bravais Lattice and Primitive 2- Cubic lattices, Simple, Body-centered and Face-centered 3- Primitive Unit Cell, Wigner-Seitz
Chapter 1. Crystal Structure
Chapter 1. Crystal Structure Crystalline solids: The atoms, molecules or ions pack together in an ordered arrangement Amorphous solids: No ordered structure to the particles of the solid. No well defined
Two dimensional Bravais lattices
Two dimensional Bravais lattices Two dimensional Bravais lattices Square lattice Symmetries: reflection about both x and y rotations by 90 o,180 o Two dimensional Bravais lattices Rectangular lattice Square
بسم هللا الرحمن الرحیم. Materials Science. Chapter 3 Structures of Metals & Ceramics
بسم هللا الرحمن الرحیم Materials Science Chapter 3 Structures of Metals & Ceramics 1 ISSUES TO ADDRESS... How do atoms assemble into solid structures? How does the density of a material depend on its structure?
Analytical Methods for Materials
Analytical Methods for Materials Lesson 10 Crystallography and Crystal Structures, Part 2 Chapters 2 and 6 in Waseda Suggested Reading 258 Symmetry Operators All motions that allow a pattern to be transformed
Solid State Physics 460- Lecture 2a Structure of Crystals (Kittel Ch. 1)
Solid State Physics 460- Lecture 2a Structure of Crystals (Kittel Ch. 1) See many great sites like ob s rock shop with pictures and crystallography info: http://www.rockhounds.com/rockshop/xtal/index.html
Solid State Device Fundamentals
Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Office 4N101b 1 Solids Three types of solids classified according to atomic
Chapter One: The Structure of Metals
Fourth Edition SI Version Chapter One: The Structure of Metals 2010. Cengage Learning, Engineering. All Rights Reserved. 1.1 Importance of the structure: Structures Processing Properties Applications Classification
Fundamental concepts and language Unit cells Crystal structures! Face-centered cubic! Body-centered cubic! Hexagonal close-packed Close packed
Fundamental concepts and language Unit cells Crystal structures! Face-centered cubic! Body-centered cubic! Hexagonal close-packed Close packed crystal structures Density computations Crystal structure
3D 14 BRAVAIS LATTICES AND THE SEVEN CRYSTAL SYSTEM
االنظمة البلورية CRYSTAL SYSTEMS 3D 14 BRAVAIS LATTICES AND THE SEVEN CRYSTAL SYSTEM There are only seven different shapes of unit cell which can be stacked together to completely fill all space (in 3
Crystal structure of the material :- the manner in which atoms, ions, or molecules are spatially.
Crystal structure A crystalline material :- is one in which the atoms are situated in a repeating or periodic array over large atomic distances. Crystal structure of the material :- the manner in which
Schematic Interpretation of Anomalies in the Physical Properties of Eu and Yb Among the Lanthanides
International Journal of Materials Science and Applications 217; 6(4): 165-17 http://www.sciencepublishinggroup.com/j/ijmsa doi: 1.11648/j.ijmsa.21764.11 ISSN: 2327-2635 (Print); ISSN: 2327-2643 (Online)
(iii) Describe how you would use a powder diffraction pattern of this material to measure
Supplemental Problems for Chapter 5 100 45.29 Intensity, au 80 60 40 20 38.95 65.98 30 40 50 60 70 2!, 1) The figure above shows a schematic diffraction pattern for a cubic material, recorded with an X-ray
Physics of Materials: Symmetry and Bravais Lattice To understand Crystal Plane/Face. Dr. Anurag Srivastava
Physics of Materials: Symmetry and Bravais Lattice To understand Crystal Plane/Face Dr. Anurag Srivastava Atal Bihari Vajpayee Indian Institute of Information Technology and Manegement, Gwalior Physics
Chapter-3 MSE-201-R. Prof. Dr. Altan Türkeli
Chapter-3 MSE-201-R Prof. Dr. Altan Türkeli The Structure of Crystalline Solids FUNDAMENTAL CONCEPTS Solid materials may be classified according to the regularity with which atoms or ions are arranged
ECE440 Nanoelectronics. Lecture 08 Review of Solid State Physics
ECE440 Nanoelectronics Lecture 08 Review of Solid State Physics A Brief review of Solid State Physics Crystal lattice, reciprocal lattice, symmetry Crystal directions and planes Energy bands, bandgap Direct
Review key concepts from last lecture (lattice + basis = unit cell) Bravais lattices Important crystal structures Intro to miller indices
Outline: Review key concepts from last lecture (lattice + basis = unit cell) Bravais lattices Important crystal structures Intro to miller indices Review (example with square lattice) Lattice: square,
Chapter 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 Face-centered cubic Body-centered cubic Hexagonal close-packed Close packed
Packing of atoms in solids
MME131: Lecture 6 Packing of atoms in solids A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s topics Atomic arrangements in solids Points, directions and planes in unit cell References:
Topic 2-1: Lattice and Basis Kittel Pages: 2-9
Topic 2-1: Lattice and Basis Kittel Pages: 2-9 Summary: We begin our introduction of crystal structure by defining a few terms. The first is translational symmetry which explains the periodicity of a crystal.
Energy and Packing. typical neighbor bond energy. typical neighbor bond energy. Dense, regular-packed structures tend to have lower energy.
Energy and Packing Non dense, random packing Energy typical neighbor bond length typical neighbor bond energy r Dense, regular packing Energy typical neighbor bond length typical neighbor bond energy r
Structure of silica glasses (Chapter 12)
Questions and Problems 97 Glass Ceramics (Structure) heat-treated so as to become crystalline in nature. The following concept map notes this relationship: Structure of noncrystalline solids (Chapter 3)
UNIT V -CRYSTAL STRUCTURE
UNIT V -CRYSTAL STRUCTURE Solids are of two types: Amorphous and crystalline. In amorphous solids, there is no order in the arrangement of their constituent atoms (molecules). Hence no definite structure
Li Mass = 7 amu Melting point C Density 0.53 g/cm 3 Color: silvery
Blackline Master B02: Mendeleev s Element Cards H Mass = 1 amu Melting point -259 0 C Density 0.0909 g/cm 3 Color: colorless Li Mass = 7 amu Melting point 180.5 0 C Density 0.53 g/cm 3 Be Mass = 9 amu
Introduction to Engineering Materials ENGR2000 Chapter 3: The Structure of Crystalline Solids. Dr. Coates
Introduction to Engineering Materials ENGR2000 Chapter 3: The Structure of Crystalline Solids Dr. Coates Learning Objectives I 1. Describe difference in atomic/molecular structure between crystalline/noncrystalline
Ex: NaCl. Ironically Bonded Solid
Ex: NaCl. Ironically Bonded Solid Lecture 2 THE STRUCTURE OF CRYSTALLINE SOLIDS 3.2 FUNDAMENTAL CONCEPTS SOLIDS AMORPHOUS CRYSTALLINE Atoms in an amorphous Atoms in a crystalline solid solid are arranged
Chapter 8: Molecules and Materials
Chapter 8: Molecules and Materials Condensed Phases - Solids Bonding in Solids Metals Insulators Semiconductors Intermolecular Forces Condensed Phases - Liquids Carbon There are three forms of the element
Materials Science and Engineering
Introduction to Materials Science and Engineering Chap. 3. The Structures of Crystalline Solids How do atoms assemble into solid structures? How does the density of a material depend on its structure?
Chapter1: Crystal Structure 1
Chapter1: Crystal Structure 1 University of Technology Laser Engineering & Optoelectronic Department Glass: 3 rd year Optoelectronic Engineering Subject: Solid state physics & material science Ass. Prof.
9/16/ :30 PM. Chapter 3. The structure of crystalline solids. Mohammad Suliman Abuhaiba, Ph.D., PE
Chapter 3 The structure of crystalline solids 1 Mohammad Suliman Abuhaiba, Ph.D., PE 2 Home Work Assignments HW 1 2, 7, 12, 17, 22, 29, 34, 39, 44, 48, 53, 58, 63 Due Sunday 17/9/2015 3 Why study the structure
Symmetry in crystalline solids.
Symmetry in crystalline solids. Translation symmetry n 1,n 2,n 3 are integer numbers 1 Unitary or primitive cells 2D 3D Red, green and cyano depict all primitive (unitary) cells, whereas blue cell is not
Basic Solid State Chemistry, 2 nd ed. West, A. R.
Basic Solid State Chemistry, 2 nd ed. West, A. R. Chapter 1 Crystal Structures Many of the properties and applications of crystalline inorganic materials revolve around a small number of structure types
Chapter 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! Face-centered cubic! Body-centered cubic! Hexagonal close-packed Close packed
CHAPTER 3. Crystal Structures and Crystal Geometry 3-1
CHAPTER 3 Crystal Structures and Crystal Geometry 3-1 The Space Lattice and Unit Cells 3-2 Atoms, arranged in repetitive 3-Dimensional pattern, in long range order (LRO) give rise to crystal structure.
Materials Science ME 274. Dr Yehia M. Youssef. Materials Science. Copyright YM Youssef, 4-Oct-10
ME 274 Dr Yehia M. Youssef 1 The Structure of Crystalline Solids Solid materials may be classified according to the regularity with which atoms or ions are arranged with respect to one another. A crystalline
Crystal Structure. Insulin crystals. quartz. Gallium crystals. Atoms are arranged in a periodic pattern in a crystal.
Crystal Structure Atoms are arranged in a periodic pattern in a crystal. The atomic arrangement affects the macroscopic properties of a material. Many important materials (silicon, steel) are crystals
Single vs Polycrystals
WEEK FIVE This week, we will Learn theoretical strength of single crystals Learn metallic crystal structures Learn critical resolved shear stress Slip by dislocation movement Single vs Polycrystals Polycrystals
STATE OF SOLIDIFICATION & CRYSTAL STRUCTURE
STATE OF SOLIDIFICATION & CRYSTAL STRUCTURE Chapter Outline Determination of crystal properties or properties of crystalline materials. Crystal Geometry! Crystal Directions! Linear Density of atoms! Crystal
Fundamentals of Crystalline State and Crystal Lattice p. 1 Crystalline State p. 2 Crystal Lattice and Unit Cell p. 4 Shape of the Unit Cell p.
Fundamentals of Crystalline State and Crystal Lattice p. 1 Crystalline State p. 2 Crystal Lattice and Unit Cell p. 4 Shape of the Unit Cell p. 7 Crystallographic Planes, Directions, and Indices p. 8 Crystallographic
Figure.1. The conventional unit cells (thick black outline) of the 14 Bravais lattices. [crystallographic symmetry] 1
![Figure.1. The conventional unit cells (thick black outline) of the 14 Bravais lattices. [crystallographic symmetry] 1](/thumbs/95/125573205.jpg "Figure.1. The conventional unit cells (thick black outline) of the 14 Bravais lattices. [crystallographic symmetry] 1")
[crystallographic symmetry] The crystallographic space groups. Supplementary to { 9.6:324} In the 3-D space there are 7 crystal systems that satisfy the point (e.g., rotation, reflection and inversion)
CHAPTER 3: SYMMETRY AND GROUPS, AND CRYSTAL STRUCTURES. Sarah Lambart
CHAPTER 3: SYMMETRY AND GROUPS, AND CRYSTAL STRUCTURES Sarah Lambart RECAP CHAP. 2 2 different types of close packing: hcp: tetrahedral interstice (ABABA) ccp: octahedral interstice (ABCABC) Definitions:
EP 364 SOLID STATE PHYSICS. Prof. Dr. Beşire Gönül. Course Coordinator
EP 364 SOLID STATE PHYSICS Course Coordinator Prof. Dr. Beşire Gönül INTRODUCTION AIM OF SOLID STATE PHYSICS WHAT IS SOLID STATE PHYSICS AND WHY DO IT? CONTENT REFERENCES EP364 SOLID STATE PHYSICS INTRODUCTION
MME 2001 MATERIALS SCIENCE
MME 2001 MATERIALS SCIENCE 1 20.10.2015 crystal structures X tal structure Coord. # Atoms/ unit cell a=f(r) APF % SC 6 1 2R 52 BCC 8 2 4R/ 3 68 FCC 12 4 2R 2 74 HCP 12 6 2R 74 Theoretical Density, knowing
Solid State Device Fundamentals
Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Office 4N101b 1 Interatomic bonding Bonding Forces and Energies Equilibrium
9/29/2014 8:52 PM. Chapter 3. The structure of crystalline solids. Dr. Mohammad Abuhaiba, PE
1 Chapter 3 The structure of crystalline solids 2 Home Work Assignments HW 1 2, 7, 12, 17, 22, 29, 34, 39, 44, 48, 53, 58, 63 Due Sunday 12/10/2014 Quiz # 1 will be held on Monday 13/10/2014 at 11:00 am
9/28/2013 9:26 PM. Chapter 3. The structure of crystalline solids. Dr. Mohammad Abuhaiba, PE
Chapter 3 The structure of crystalline solids 1 2 Why study the structure of crystalline solids? Properties of some materials are directly related to their crystal structure. Significant property differences
CRYSTAL STRUCTURE TERMS
CRYSTAL STRUCTURE TERMS crystalline material - a material in which atoms, ions, or molecules are situated in a periodic 3-dimensional array over large atomic distances (all metals, many ceramic materials,
ENGINEERING MATERIALS LECTURE #4
ENGINEERING MATERIALS LECTURE #4 Chapter 3: The Structure of Crystalline Solids Topics to Cover What is the difference in atomic arrangement between crystalline and noncrystalline solids? What features
ASE324: Aerospace Materials Laboratory
ASE324: Aerospace Materials Laboratory Instructor: Rui Huang Dept of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin Fall 2003 Lecture 3 September 4, 2003 Iron and Steels
Lectures on: Introduction to and fundamentals of discrete dislocations and dislocation dynamics. Theoretical concepts and computational methods
Lectures on: Introduction to and fundamentals of discrete dislocations and dislocation dynamics. Theoretical concepts and computational methods Hussein M. Zbib School of Mechanical and Materials Engineering
The structures of pure metals are crystalline (crystal lattice) with regular arrangement of metal atoms that are identical perfect spheres.
HW#3 Louisiana Tech University, Chemistry 481. POGIL (Process Oriented Guided Inquiry Learning) Exercise on Chapter 3. Metals and Alloys. Why? Metals What is the structure of a metallic solid? What is
Example: Compute the wavelength of a 1 [kg] block moving at 1000 [m/s].
![Example: Compute the wavelength of a 1 [kg] block moving at 1000 [m/s].](/thumbs/95/123245062.jpg "Example: Compute the wavelength of a 1 [kg] block moving at 1000 [m/s].")
Example: Calculate the energy required to excite the hydrogen electron from level n = 1 to level n = 2. Also calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state
MSE420/514: Session 1. Crystallography & Crystal Structure. (Review) Amaneh Tasooji
MSE420/514: Session 1 Crystallography & Crystal Structure (Review) Crystal Classes & Lattice Types 4 Lattice Types 7 Crystal Classes SIMPLE CUBIC STRUCTURE (SC) Rare due to poor packing (only Po has this
Energy and Packing. Materials and Packing
Energy and Packing Non dense, random packing Energy typical neighbor bond length typical neighbor bond energy r Dense, regular packing Energy typical neighbor bond length typical neighbor bond energy r
Chem 253, UC, Berkeley. Chem 253, UC, Berkeley
1 2 Theorem: For any family of lattice planes separated by distance d, there are reciprocal lattice vectors perpendicular to the planes, the shortest being 2 /d. Orientation of plane is determined by a
Chapter 3: Atomic and Ionic Arrangements. Chapter 3: Atomic and Ionic Arrangements Cengage Learning Engineering. All Rights Reserved.
Chapter 3: Atomic and Ionic Arrangements 3-1 Learning Objectives 1. 2. 3. 4. 5. 6. 7. 8. Short-range order versus long-range order Amorphous materials Lattice, basis, unit cells, and crystal structures
Solid State-1 1) Ionic solids are characterised by 1) Good conductivity in solid state 2) High vapour pressure 3) Low melting point 4) Solubility in polar solvents 2) Three metals X, Y and Z are crystallised
How can we describe a crystal?
How can we describe a crystal? Examples of common structures: (1) The Sodium Chloride (NaCl) Structure (LiH, MgO, MnO, AgBr, PbS, KCl, KBr) The NaCl structure is FCC The basis consists of one Na atom and
Now, let s examine how atoms are affected as liquids transform into solids.
Now, let s examine how atoms are affected as liquids transform into solids. 1 Before we deal with PROPERTIES of materials, it s beneficial to remember where we have come from, and where we are going. Later,
Semiconductor Physics
10p PhD Course Semiconductor Physics 18 Lectures Nov-Dec 2011 and Jan Feb 2012 Literature Semiconductor Physics K. Seeger The Physics of Semiconductors Grundmann Basic Semiconductors Physics - Hamaguchi
Families on the Periodic Table
Families on the Periodic Table Elements on the periodic table can be grouped into families based on their chemical properties. Each family has a specific name to differentiate it from the other families
Solids. The difference between crystalline and non-crystalline materials is in the extent of ordering
Chapter 3 The Structure t of Crystalline Solids The difference between crystalline and non-crystalline materials is in the extent of ordering Both materials have the same composition but one is ordered
Lecture 2a - Structure of crystals - continued
Lecture 2a - tructure of crstals - continued olid tate Phsics 460- Lecture 2a tructure of rstals (Kittel h. 1) From Last Time rstals crstal is a repeated arra of atoms rstal Lattice + asis ee man great
Analytical Methods for Materials
Analytical Methods for Materials Lesson 12 Crystallography and Crystal Structures continued Suggested Reading Ch. 6 in Waseda Ch. 1 C. Kittel, Introduction to Solid State Physics, 3 rd Edition, Wiley (1956).
Crystal Structures of Interest
rystal Structures of Interest Elemental solids: Face-centered cubic (fcc) Hexagonal close-packed (hcp) ody-centered cubic (bcc) Diamond cubic (dc) inary compounds Fcc-based (u 3 u,nal, ß-ZnS) Hcp-based
New Materials from Mathematics Real and Imagined
New Materials from Mathematics Real and Imagined Richard James University of Minnesota Thanks: John Ball, Kaushik Bhattacharya, Jun Cui, Traian Dumitrica, Stefan Müller, Ichiro Takeuchi, Rob Tickle, Manfred
Condensed Matter in a Nutshell
PHYS 342/555 Condensed Matter in a Nutshell Instructor: Dr. Pengcheng Dai Professor of Physics The University of Tennessee (Room 407A, Nielsen, 974-1509) (Office hours: TR 1:10PM-2:00 PM) Lecture 2, room
Diffusion & Crystal Structure
Lecture 5 Diffusion & Crystal Structure Diffusion of an interstitial impurity atom in a crystal from one void to a neighboring void. The impurity atom at position A must posses an energy E to push the
416 Solid State Physics ; Introduction & Overview
416 Solid State Physics 8-29-2016; Introduction & Overview Assignment: Read chapter 1 of Kittel for next time on crystal symmetries. This course covers concepts in solid state physics. Note that physics-related
Chapter 3 Structure of Crystalline Solids
Chapter 3 Structure of Crystalline Solids Crystal Structures Points, Directions, and Planes Linear and Planar Densities X-ray Diffraction How do atoms assemble into solid structures? (for now, focus on
Condensed Matter Physics Prof. G.Rangarajan Department of Physics Indian Institute of Technology, Madras
Condensed Matter Physics Prof. G.Rangarajan Department of Physics Indian Institute of Technology, Madras Lecture - 3 Symmetry in Perfect Solids (Continued) (Refer Slide Time: 00:26) So, the last lecture,
MSE 170 Midterm review
MSE 170 Midterm review Exam date: 11/2/2008 Mon, lecture time Place: Here! Close book, notes and no collaborations A sheet of letter-sized paper with double-sided notes is allowed Material on the exam
Work hard. Be nice. Name: Period: Date: UNIT 2: Atomic Concepts Lesson 1: Give me an element, any element
1 Name: Period: Date: KIPP NYC College Prep General Chemistry UNIT 2: Atomic Concepts Lesson 1: Give me an element, any element Do Now: By the end of today, you will have an answer to: How do you know
Carbon nanostructures. (http://www.mf.mpg.de/de/abteilungen/schuetz/index.php?lang=en&content=researchtopics&type=specific&name=h2storage)
Carbon nanostructures (http://www.mf.mpg.de/de/abteilungen/schuetz/index.php?lang=en&content=researchtopics&type=specific&name=h2storage) 1 Crystal Structures Crystalline Material: atoms arrange into a
3.40 Sketch within a cubic unit cell the following planes: (a) (01 1 ) (b) (112 ) (c) (102 ) (d) (13 1) Solution
3.40 Sketch within a cubic unit cell the following planes: (a) (01 1 ) (b) (11 ) (c) (10 ) (d) (13 1) The planes called for are plotted in the cubic unit cells shown below. 3.41 Determine the Miller indices
CH445/545 Winter 2008
CH445/545 Winter 2008 Assignment # 1 - due 01/18/08 60 total points SHOW ALL WORKING FOR FULL CREDIT, ANSWERS WITHOUT WORKING WILL BE PENALIZED! 1. Text Ch. 1 # 2 "Calculate the size of the largest sphere
CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS ev /atom = exp. kt ( =
CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS Vacancies and Self-Interstitials 5.1 Calculate the fraction of atom sites that are vacant for copper at its melting temperature of 1084 C (1357 K). Assume
Chemistry*120* * Name:! Rio*Hondo*College* * * EXAMPLE*EXAM*1*!
Chemistry*120* * Name: EXAMPLE*EXAM*1* Exam)#1 100)points) Directions:)Answereachquestionbelowtothebestofyourability.Showallworkwherecalculations arerequired.aninformationsheetwithaperiodictableisattachedtothebackoftheexam;youmay
Chapter 10. Liquids and Solids
Chapter 10. Liquids and Solids Three States of Matter H 2 O Volume constant constant no Shape constant no no Why in three different states? 1 Intermolecular Force dipole-dipole attraction V dip-dip : 1.
These metal centres interact through metallic bonding
The structures of simple solids The majority of inorganic compounds exist as solids and comprise ordered arrays of atoms, ions, or molecules. Some of the simplest solids are the metals, the structures
Chem 241. Lecture 19. UMass Amherst Biochemistry... Teaching Initiative
Chem 241 Lecture 19 UMass Amherst Biochemistry... Teaching Initiative Announcement March 26 Second Exam Recap Water Redox Comp/Disproportionation Latimer Diagram Frost Diagram Pourbaix Diagram... 2 Ellingham
Twins & Dislocations in HCP Textbook & Paper Reviews. Cindy Smith
Twins & Dislocations in HCP Textbook & Paper Reviews Cindy Smith Motivation Review: Outline Crystal lattices (fcc, bcc, hcp) Fcc vs. hcp stacking sequences Cubic {hkl} naming Hcp {hkil} naming Twinning
SCOPE OF ACCREDITATION TO ISO/IEC 17025:2005
SCOPE OF ACCREDITATION TO ISO/IEC 17025:2005 WESTMORELAND MECHANICAL TESTING & RESEARCH, INC. 221 Westmoreland Drive Youngstown, PA 15696 Michael Self Phone: 724 537 3131 E-mail: mself@wmtr.com CHEMICAL
CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS
CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS Vacancies and Self-Interstitials 5.1 Calculate the fraction of atom sites that are vacant for copper at its melting temperature of 1084 C (1357 K). Assume
Problems. 104 CHAPTER 3 Atomic and Ionic Arrangements
104 CHAPTER 3 Atomic and Ionic Arrangements Repeat distance The distance from one lattice point to the adjacent lattice point along a direction. Short-range order The regular and predictable arrangement
Structure factors and crystal stacking
Structure factors and crystal stacking Duncan Alexander EPFL-CIME 1 Contents Atomic scattering theory Crystal structure factors Close packed structures Systematic absences Twinning and stacking faults
CLASS TEST GRADE 11. PHYSICAL SCIENCES: CHEMISTRY Test 7: Chemical systems
CLASS TEST GRADE PHYSICAL SCIENCES: CHEMISTRY Test 7: Chemical systems MARKS: 45 TIME: hour INSTRUCTIONS AND INFORMATION. Answer ALL the questions. 2. You may use non-programmable calculators. 3. You may
Point Defects in Metals
CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS Point Defects in Metals 5.1 Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 327 C (600 K). Assume an energy
Metallic crystal structures The atomic bonding is metallic and thus non-directional in nature
Chapter 3 The structure of crystalline solids Hw: 4, 6, 10, 14, 18, 21, 26, 31, 35, 39, 42, 43, 46, 48, 49, 51, 56, 61 Due Wensday 14/10/2009 Quiz1 on Wensday 14/10/2009 Why study the structure of crystalline
Point coordinates. Point coordinates for unit cell center are. Point coordinates for unit cell corner are 111
Point coordinates c z 111 Point coordinates for unit cell center are a/2, b/2, c/2 ½ ½ ½ Point coordinates for unit cell corner are 111 x a z 000 b 2c y Translation: integer multiple of lattice constants
Where do we start? ocreate the Universe oform the Earth and elements omove the elements into their correct positions obuild the atmosphere and oceans
Where do we start? ocreate the Universe oform the Earth and elements omove the elements into their correct positions obuild the atmosphere and oceans 1 The BIG BANG The Universe was created 13.8 billion
Evidence of Performance regarding the requirements for float glass according to EN 572
Evidence of Performance regarding the requirements for float glass according to EN 572 Test Report 605 32401 Client Noval Glass Industrial Group (China) Co., Ltd. Noval Glass Industiral Zone Qingdao, 523965
New Materials from Mathematics Real and Imagined
New Materials from Mathematics Real and Imagined on the occasion of the 10 th anniversary of the Max Planck Institute for Mathematics in the Sciences Richard D. James MIS-MPI and the University of Minnesota
VI. THE STRUCTURE OF SOLIDS
VI. THE STRUCTURE OF SOLIDS 6-1 MOTIVATION We have come a great distance in the last several weeks. If everything is going according to plan, you are beginning to picture engineering as the design of energy
E3 Redox: Transferring electrons. Session one of two First hour: Discussion (E1) 2nd and 3rd hour: Lab (E3, Parts 1 and 2A)
E3 Redox: Transferring electrons Session one of two First hour: Discussion (E) 2nd and 3rd hour: Lab (E3, Parts and 2A) Oxidation-Reduction (Redox) Reactions involve electron transfer. Change in charge
Two marks questions and answers. 1. what is a Crystal? (or) What are crystalline materials? Give examples
UNIT V CRYSTAL PHYSICS PART-A Two marks questions and answers 1. what is a Crystal? (or) What are crystalline materials? Give examples Crystalline solids (or) Crystals are those in which the constituent
LAB II CRYSTAL STRUCTURE AND CRYSTAL GROWTH PART 1: CRYSTAL GROWTH. I. Introduction
LAB II CRYSTAL STRUCTURE AND CRYSTAL GROWTH This lab will be divided into two parts. In the first part, you will be growing crystals from a seed crystal in a very visual demonstration of heterogeneous