9/16/ :30 PM. Chapter 3. The structure of crystalline solids. Mohammad Suliman Abuhaiba, Ph.D., PE
|
|
- Karin McCormick
- 6 years ago
- Views:
Transcription
1 Chapter 3 The structure of crystalline solids 1 Mohammad Suliman Abuhaiba, Ph.D., PE
2 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 3 Why study the structure of crystalline solids? Properties of some materials are directly related to their crystal structure. Significant property differences exist between crystalline and noncrystalline materials having the same composition.
4 4 Crystal structures Fundamental concepts Crystalline materials: Atoms or ions form a regular repetitive, grid-like pattern, in 3D A lattice: collection of points called lattice points, arranged in a periodic pattern so that the surroundings of each point in the lattice are identical
5 5 Crystal structures Unit Cells Atoms arrange themselves into an ordered, 3d pattern called a crystal Unit cell (UC): smallest repeating volume within a crystal Each cell has all geometric features found in the total crystal
6 6 Metallic crystal structures Lattice Parameter: size & shape of UC, includes: 1. dimensions of sides of UC 2. angles between sides
7 7 Metallic crystal structures Face Centered Cubic (FCC) FCC: AL. Cu, Pb, Ag, Ni 4 atoms per unit cell Lattice parameter, a FCC Coordination Number (CN): # of atoms touching a particular atom, or # of nearest neighbors for that particular atom
8 8 Metallic crystal structures Face Centered Cubic (FCC) CN =12 APF = 0.74 Metals typically have relatively large APF to max shielding provided by the free electron cloud
9 9 Metallic crystal structures Face Centered Cubic (FCC)
10 10 Metallic crystal structures Example problem 3.1 Calculate 1. lattice parameter in terms of atomic radius R 2. volume of FCC UC in terms of R 3. atomic packing factor
11 11 Metallic crystal structures Body Centered Cubic (BCC) 2 atoms/uc Lattice parameter, a BCC CN = 8 APF = 0.68
12 12 Metallic Crystal Structures Hexagonal Closed-Packed Structure (HCP) c/a = No of atoms = 6 APF = 0.74
13 13 Density computation Density (No. of atoms/cell)(atomic mass) (volume of unit cell)(n ) (atoms)(g/mole) (cm )(atoms/mole) g cm 3 3 A
14 14 Density computation Example problem 3.2 Copper has an atomic radius of nm, an FCC crystal structure, and an atomic weight of 63.5 g/mol. Compute its theoretical density and compare the answer with its measured density.
15 15 Polymorphism and Allotropy Polymorphism: Materials that can have more than one crystal structure When found in pure elements condition is termed Allotropy A volume change may accompany transformation during heating or cooling. This volume change may cause brittle ceramic materials to crack and fail. Ex: Fe has BCC at RT which changes to FCC at 912 C
16 16 Crystal systems 7 possible systems (T3.2) and (F3.4).
17 17 Crystallographic Point Coordinates Point
18 18 Crystallographic Point Coordinates Example Problem 3.3 For the unit cell shown, locate the point having coordinates
19 19 Crystallographic Point Coordinates Example Problem 3.4 Specify point coordinates for all atom positions for a BCC UC.
20 20 Crystallographic Directions Metals deform in directions along which atoms are in closest contact. Many properties are directional. Miller indices are used to define directions.
21 21 Crystallographic Directions Procedure of finding Miller indices: RH coordinate system Find coordinates of 2 points along direction Subtract tail from head Clear fractions Enclose No s in [634] A direction and its ve are not identical A direction and its multiple are identical
22 22 Example Problem 3.5 Determine the indices for the direction shown in the figure.
23 23 Example Problem 3.6 Draw a direction within a cubic UC
24 24 Crystallographic Directions Families of directions Identical directions: any directional property will be identical in these directions Directions in cubic crystals having same indices without regard to order or sign are equivalent
25 25 Crystallographic Directions Miller-Bravais indices for hexagonal unit cells Directions in HCP: 3-axis or 4-axis system Move in each direction to get from tail to head of direction, while for consistency still making sure that u + v = -t
26 26 Crystallographic Directions Miller-Bravais indices for hexagonal unit cells Conversion from 3 axis to 4 axis: u = 1/3(2u` - v`) v = 1/3(2v` - u`) t = -(u + v) w = w` u`, v`, w`: indices in 3 axis system Clear fraction or reduce to lowest integer for values of u, v, t, and w.
27 27 Crystallographic Directions Example Problem 3.8 a) Convert [111] direction into four-index system for hexagonal crystals. b) Draw [111] direction within a HCP cell that utilizes a three-axis (a 1, a 2, z) coordinate system.
28 28 Example Problem 3.9 Determine the directional indices (fourindex system) for the direction shown.
29 29 Crystallographic planes Crystal contains planes of atoms that influence properties and behavior of a material. Metals deform along planes of atoms that are most tightly packed together. The surface energy of different faces of a crystal depends upon the particular crystallographic planes.
30 30 Crystallographic planes Calculation of planes Identify points at which plane intercepts x,y,z coordinates. If plane passes in origin of coordinates; system must be shifted. Take reciprocals of intercepts Clear fractions but do not reduce to lowest integer.
31 31 Crystallographic planes Calculation of planes Notes: Planes and their ve are identical Planes and their multiple are not identical For cubic crystals, planes and directions having the same indices are perpendicular to one another
32 32 Crystallographic planes Example Problem 3.10 Determine Miller indices for the plane shown in the figure.
33 33 Crystallographic planes Example Problem 3.11
34 34 Crystallographic planes Example Problem 3.12 Determine Miller Bravais indices for the plane shown in the hexagonal unit cell.
35 35 Crystallographic planes Atomic arrangements and Families of planes {} 2 or more planes may belong to same family of planes (same planner density) In cubic system only, planes having same indices irrespective of order & sign are equivalent. Ex: {111} is a family of planes that has 8 planes.
36 36 Linear and Planar Densities Repeat distance: distance between lattice points along the direction Repeating distance between equivalent sites differs from direction to direction. Ex: in the [111] of a BCC metal, lattice site is repeated every 2R. Ex: repeating distance in [110] for a BCC is, but for FCC.
37 37 Linear and Planar Densities Linear density: No of atoms per unit length along the direction. Equivalent directions have identical LDs In general, LD = 1 / repeat distance Example: find linear density along [110] for FCC. LD = number of atoms centered on direction vector length of direction vector
38 38 Linear and Planar Densities Planar packing fraction: fraction of area of the area of a plane actually covered by atoms In cubic systems, a direction that has the same indices as a plane is perpendicular to that plane. PD = number of atoms centered on a plane area of plane
39 39 Linear and Planar Densities PD = number of atoms centered on a plane area of plane
40 40 Linear and Planar Densities Ex: How many atoms per mm 2 are there on the (100) and (111) planes of lead (FCC) LD & PD are important considerations relative to the process of slip. Slip is the mechanism by which metals plastically deform Slip occurs on the most closely packed planes along directions having greatest LD
41 41 Crystallographic planes Closed Packed Planes and directions Close packed planes are (0001) & (0002) named basal planes. An HCP unit cell is built up by stacking together CPPs in a ABABAB stacking sequence.
42 42 Crystallographic planes Closed Packed Planes and directions Atoms in plane B (0002) fit into valleys between atoms on plane A (0001) Center atom in a basal plane is touched by: 6 atoms in same plane 3 atoms in a lower plane 3 atoms in upper plane CN =12
43 43 Crystallographic planes Closed Packed Planes and directions In FCC, CPPs are of the form {111} When parallel (111) planes are stacked: atoms in plane B fit over valleys in plane A atoms in plane C fit over valleys in both A & B 4 th plane fits directly over atoms in A A stacking sequence ABCABCABC is produced using (111) plane CN = 12
44 44 Crystallographic planes Closed Packed Planes and directions
45 45 Single Crystals Properties of single crystal materials depend upon chemical composition & specific directions within crystal Mohammad Suliman Abuhaiba, Ph.D., PE
46 46 Polycrystalline Materials Many properties of polycrystalline materials depend upon the physical and chemical char of both grains and grain boundaries.
47 47 Polycrystalline Materials Figure 3.18: stages in solidification of a polycrystalline material; square grids depict unit cells a) Small crystallite nuclei b) Growth of crystallites c) Upon completion of solidification, grains having irregular shapes have formed d) Grain structure as it would appear under the microscope; dark lines are grain boundaries
48 48 Polycrystalline Materials Figure 3.18
49 49 Anisotropy Anisotropic material: properties depend on the crystallographic direction along which the property is measured Isotropic material: properties are identical in all directions Most polycrystalline materials will exhibit isotropic properties. Table 3.3
50 50 Anisotropy
51 51 X-Ray Diffraction: Determination of Crystal Structures X-rays Electromagnetic radiation Wavelengths between 0.1Å & 100Å Similar to inter-atomic distances in a crystal
52 52 X-Ray Diffraction: Determination of Crystal Structures X-ray diffraction is a tool used to: 1. Identify phases by comparison with data from known structures 2. Quantify changes in cell parameters, orientation, crystallite size and other structural parameters 3. Determine crystallographic structure of novel or unknown crystalline materials.
53 53 X-Rray diffraction: Determination of Crystal Structures - Bragg s law An X-ray incident upon a sample will either: 1. Be transmitted: ray will continue along its original direction 2. Be scattered by electrons of the atoms in the material Interested in peaks formed when scattered X-rays constructively interfere.
54 54 X-Rray diffraction: Determination of Crystal Structures - Bragg s law Constructive Interference
55 55 X-Rray diffraction: Determination of Crystal Structures - Bragg s law Destructive Interference
56 56 X-Rray diffraction: Determination of Crystal Structures - Bragg s law Angle between transmitted & Bragg diffracted beams is always equal to 2θ This angle is readily obtainable in experimental situations Results of X-ray diffraction are frequently given in terms of 2θ
57 57 X-Rray diffraction: Determination of Crystal Structures - Bragg s law
58 58 X-RAY Diffraction: Determination of Crystal Structures - Inter-planar spacing Distance between adjacent parallel planes of atoms with the same Miller indices, d hkl In cubic cells, it s given by d hkl a o h k l
59 59 Example Calculate distance between adjacent (111) planes in gold which has a lattice constant of A.
60 60 X-RAY Diffraction: Determination of Crystal Structures - Powder diffraction A powder is a polycrystalline material There are all possible orientations of the crystals Similar planes in different crystals will scatter in different directions
61 61 X-RAY Diffraction: Determination of Crystal Structures - Powder diffraction In single crystal X-ray diffraction there is only one orientation. For a given wavelength & sample setting relatively few reflections can be measured: possibly zero, one or two As other crystals are added with slightly different orientations, several diffraction spots appear at the same 2θ value and spots start to appear at other values of 2θ.
62 62 X-RAY Diffraction: Determination of Crystal Structures - Powder diffraction Schematic diagram of an x-ray diffracto - meter T = x-ray source S = specimen C = detector O = axis of rotation of specimen & detector
63 63 X-RAY Diffraction: Determination of Crystal Structures - X-ray Diffractometer As the counter moves at constant angular velocity, a recorder automatically plots diffracted beam intensity as a function of 2q.
64 64 X-RAY Diffraction: Determination of Crystal Structures - X-ray Diffractometer Fig 3.22: a diffraction pattern for a powdered specimen High-intensity peaks result when Bragg diffraction condition is satisfied by some set of crystallographic planes. These peaks are plane-indexed in the figure
65 65 X-RAY Diffraction: Determination of Crystal Structures - X-ray Diffractometer Unit cell size & geometry may be resolved from angular positions of diffraction peaks Arrangement of atoms within unit cell is associated with relative intensities of these peaks.
66 66 X-RAY Diffraction: Determination of Crystal Structures Indexing Diffraction Pattern λ = 2 d sin θ d hkl a o h k l
67 67 Example Problem 3.13 For BCC iron, compute a. inter-planar spacing b. diffraction angle for (220) set of planes The lattice parameter for Fe is nm. Also, assume that monochromatic radiation having a wavelength of nm is used, and the order of reflection is 1.
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
More information9/28/2013 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
More informationMetallic 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
More informationEx: 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
More informationAtomic Densities. Linear Density Number of atoms per length whose centers lie on the direction vector for a specific crystallographic direction.
Atomic Densities Linear Density Number of atoms per length whose centers lie on the direction vector for a specific crystallographic direction. Planar Density Number of atoms per unit area that are centered
More informationIntroduction 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
More informationAtomic Densities. Linear Density. Planar Density. Linear Density. Outline: Planar Density
Atomic Densities Outline: Atomic Densities - Linear Density - Planar Density Single- vs poly- crystalline materials X-ray Diffraction Example Polymorphism and Allotropy Linear Density Number of atoms per
More informationStructure 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)
More informationChapter-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
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! Face-centered cubic! Body-centered cubic! Hexagonal close-packed Close packed
More informationChapter 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
More informationFundamental 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
More informationMME 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
More informationPacking 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:
More informationMaterials 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?
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 Face-centered cubic Body-centered cubic Hexagonal close-packed Close packed
More informationبسم 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?
More informationCarbon 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
More informationCHAPTER 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.
More informationExample: 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
More informationSTATE 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
More informationChapter 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
More informationEnergy 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
More informationSingle 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
More informationCrystal 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
More informationCRYSTAL 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,
More informationDiffraction Basics. The qualitative basics:
The qualitative basics: Diffraction Basics Coherent scattering around atomic scattering centers occurs when x-rays interact with material In materials with a crystalline structure, x-rays scattered in
More informationChapter 3 Basic Crystallography and Electron Diffraction from Crystals. Lecture 9. Chapter 3 CHEM Fall, L. Ma
Chapter 3 Basic Crystallography and Electron Diffraction from Crystals Lecture 9 Outline The geometry of electron diffraction Crystallography Kinetic Theory of Electron diffraction Diffraction from crystals
More informationThe Science and Engineering of Materials, 4 th ed Donald R. Askeland Pradeep P. Phulé. Chapter 3 Atomic and Ionic Arrangements
The Science and Engineering of Materials, 4 th ed Donald R. Askeland Pradeep P. Phulé Chapter 3 Atomic and Ionic Arrangements 1 Objectives of Chapter 3 To learn classification of materials based on atomic/ionic
More informationIdentification of Crystal Structure and Lattice Parameter. for Metal Powders Using X-ray Diffraction. Eman Mousa Alhajji
Identification of Crystal Structure and Lattice Parameter for Metal Powders Using X-ray Diffraction Eman Mousa Alhajji North Carolina State University Department of Materials Science and Engineering MSE
More informationSingle crystal X-ray diffraction. Zsolt Kovács
Single crystal X-ray diffraction Zsolt Kovács based on the Hungarian version of the Laue lab description which was written by Levente Balogh, Jenő Gubicza and Lehel Zsoldos INTRODUCTION X-ray diffraction
More informationProblems. 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
More informationEnergy 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
More informationCHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES
CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES ISSUES TO ADDRESS... How do atoms assemble into solid structures? (for now, focus on metals) How does the density of a material depend on its structure? When
More informationHow do atoms assemble into solid structures? How does the density of a material depend on its structure?
제 3 장 : 결정질고체의구조 ISSUES TO ADDRESS... How do atoms assemble into solid structures? How does the density of a material depend on its structure? When do material properties vary with the sample (i.e., part)
More informationChapter 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
More informationGeneral 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
More informationDensity Computations
CHAPTER 3 THE STRUCTURE OF CRYSTALLINE SOLIDS Fundamental Concepts 3.1 What is the difference between atomic structure and crystal structure? Unit Cells Metallic Crystal Structures 3.2 If the atomic radius
More informationUNIT 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
More informationTwo 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
More informationMaterials Lab 1(MT344) X-ray Diffractometer Operation and Data Analysis. Instructor: Dr. Xueyan Wu ( 吴雪艳 )
Materials Lab 1(MT344) X-ray Diffractometer Operation and Data Analysis Instructor: Dr. Xueyan Wu ( 吴雪艳 ) Goals To give students a practical introduction into the use of X-ray diffractometer and data collection.
More informationPoint 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
More informationENGINEERING 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
More informationMaterials and their structures
Materials and their structures 2.1 Introduction: The ability of materials to undergo forming by different techniques is dependent on their structure and properties. Behavior of materials depends on their
More informationExperiment 2b X-Ray Diffraction* Optical Diffraction Experiments
* Experiment 2b X-Ray Diffraction* Adapted from Teaching General Chemistry: A Materials Science Companion by A. B. Ellis et al.: ACS, Washington, DC (1993). Introduction Inorganic chemists, physicists,
More informationLecture C4b Microscopic to Macroscopic, Part 4: X-Ray Diffraction and Crystal Packing
Lecture C4b Microscopic to Macroscopic, Part 4: X-Ray Diffraction and Crystal Packing X-ray Diffraction Max von Laue won the 1914 Nobel Prize for his discovery of the diffraction of x-rays by crystals.
More informationPoint coordinates. x z
Point coordinates c z 111 a 000 b y x z 2c b y Point coordinates z y Algorithm 1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a,
More informationE45 Midterm 01 Fall 2007! By the 0.2% offset method (shown on plot), YS = 500 MPa
1.!Mechanical Properties (20 points) Refer to the following stress-strain plot derived from a standard uniaxial tensile test of a high performance titanium alloy to answer the following questions. Show
More information11.3 The analysis of electron diffraction patterns
11.3 The analysis of electron diffraction patterns 277 diameter) Ewald reflecting sphere, the extension of the reciprocal lattice nodes and the slight buckling of the thin foil specimens all of which serve
More informationThe object of this experiment is to test the de Broglie relationship for matter waves,
Experiment #58 Electron Diffraction References Most first year texts discuss optical diffraction from gratings, Bragg s law for x-rays and electrons and the de Broglie relation. There are many appropriate
More informationChapter 12 The Solid State The Structure of Metals and Alloys
Chapter 12 The Solid State The Structure of Metals and Alloys The Solid State Crystalline solid a solid made of an ordered array of atoms, ion, or molecules Amorphous solids a solid that lacks long-range
More informationASE324: 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
More informationReview of Metallic Structure
Phase Diagrams Understanding the Basics F.C. Campbell, editor Copyright 2012 ASM International All rights reserved www.asminternational.org Appendix A Review of Metallic Structure The word metal, derived
More informationMSE420/514: 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
More informationSolid 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
More informationChapter 7: Dislocations and strengthening mechanisms
Chapter 7: Dislocations and strengthening mechanisms Introduction Basic concepts Characteristics of dislocations Slip systems Slip in single crystals Plastic deformation of polycrystalline materials Plastically
More informationCHAPTER. The Structure of Crystalline Solids
CHAPTER 4 The Structure of Crystalline Solids 1 Chapter 4: The Structure of Crystalline Solids ISSUES TO ADDRESS... What are common crystal structures for metals and ceramics? What features of a metal
More informationBackground Statement for SEMI Draft Document 5945 New Standard: Test Method for Determining Orientation of A Sapphire Single Crystal
Background Statement for SEMI Draft Document 5945 New Standard: Test Method for Determining Orientation of A Sapphire Single Crystal Notice: This background statement is not part of the balloted item.
More informationCRYSTAL 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
More informationStrain. Two types of stresses: Usually:
Stress and Texture Strain Two types of stresses: microstresses vary from one grain to another on a microscopic scale. macrostresses stress is uniform over large distances. Usually: macrostrain is uniform
More informationChapter1: 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.
More informationTEM and Electron Diffraction Keith Leonard, PhD (1999) U. Cincinnati
TEM and Electron Diffraction Keith Leonard, PhD (1999) U. Cincinnati Electron Microscopes: Electron microscopes, such as the scanning electron microscope (SEM) and transmission electron microscope (TEM)
More informationMaterials Science. Imperfections in Solids CHAPTER 5: IMPERFECTIONS IN SOLIDS. Types of Imperfections
In the Name of God Materials Science CHAPTER 5: IMPERFECTIONS IN SOLIDS ISSUES TO ADDRESS... What are the solidification mechanisms? What types of defects arise in solids? Can the number and type of defects
More informationTwins & 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
More informationStudent Name: ID Number:
Student Name: ID Number: DEPARTMENT OF MECHANICAL ENGINEERING CONCORDIA UNIVERSITY MATERIALS SCIENCE - MECH 1/ - Sections T & X MIDTERM 003 Instructors: Dr. M.Pugh & Dr. M.Medraj Time Allowed: one (1)
More informationLECTURE 7. Dr. Teresa D. Golden University of North Texas Department of Chemistry
LECTURE 7 Dr. Teresa D. Golden University of North Texas Department of Chemistry Diffraction Methods Powder Method For powders, the crystal is reduced to a very fine powder or microscopic grains. The sample,
More informationMaterials 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
More informationX-RAY DIFFRACTION. X- Ray Sources Diffraction: Bragg s Law Crystal Structure Determination
X-RAY DIFFRACTION X- Ray Sources Diffraction: Bragg s Law Crystal Structure Determination Part of MATERIALS SCIENCE & ENGINEERING A Learner s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani
More informationCHAPTER 2. Structural Issues of Semiconductors
CHAPTER 2 Structural Issues of Semiconductors OUTLINE 1.0 Energy & Packing 2.0 Materials & Packing 3.0 Crystal Structures 4.0 Theoretical Density, r 5.0.Polymorphism and Allotropy 6.0 Close - Packed Crystal
More informationDiffraction: Powder Method
Diffraction: Powder Method Diffraction Methods Diffraction can occur whenever Bragg s law λ = d sin θ is satisfied. With monochromatic x-rays and arbitrary setting of a single crystal in a beam generally
More informationLecture C4a Microscopic to Macroscopic, Part 4: X-Ray Diffraction and Crystal Packing
Lecture C4a Microscopic to Macroscopic, Part 4: X-Ray Diffraction and Crystal Packing X-ray Diffraction Max von Laue won the 1914 Nobel Prize for his discovery of the diffraction of x-rays by crystals.
More informationPhysics 6180: Graduate Physics Laboratory. Experiment CM5: X-ray diffraction and crystal structures
Physics 6180: Graduate Physics Laboratory Experiment CM5: X-ray diffraction and crystal structures References: Preston and Dietz, Expt. 10 pp. 180-197 Eisberg and Resnick, Quantum Physics, Sec. 9 Kittel,
More informationReview 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,
More information3.40 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
More informationThis lecture is part of the Basic XRD Course.
This lecture is part of the Basic XRD Course. Basic XRD Course 1 A perfect polycrystalline sample should contain a large number of crystallites. Ideally, we should always be able to find a set of crystallites
More information(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
More informationIt is instructive however for you to do a simple structure by hand. Rocksalt Structure. Quite common in nature. KCl, NaCl, MgO
Today the structure determinations etc are all computer -assisted It is instructive however for you to do a simple structure by hand Rocksalt Structure Quite common in nature KCl, NaCl, MgO 9-1 Typical
More informationMETALLIC CRYSTALS. tend to be densely packed. have several reasons for dense packing: have the simplest crystal structures.
METALLIC CRYSTALS tend to be densely packed. have several reasons for dense packing: -Typically, only one element is present, so all atomic radii are the same. -Metallic bonding is not directional. -Nearest
More informationFundamentals of X-ray diffraction and scattering
Fundamentals of X-ray diffraction and scattering Don Savage dsavage@wisc.edu 1231 Engineering Research Building (608) 263-0831 X-ray diffraction and X-ray scattering Involves the elastic scattering of
More informationIntroduction to Engineering Materials ENGR2000 Chapter 4: Imperfections in Solids. Dr. Coates
Introduction to Engineering Materials ENGR000 Chapter 4: Imperfections in Solids Dr. Coates Learning Objectives 1. Describe both vacancy and self interstitial defects. Calculate the equilibrium number
More informationChapter 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
More informationEngineering Materials Department of Physics K L University
Engineering Materials Department of Physics K L University 1 Crystallography Bonding in solids Many of the physical properties of materials are predicated on a knowledge of the inter-atomic forces that
More informationINGE Engineering Materials. Chapter 3 (cont.)
Some techniques used: Chapter 3 (cont.) This section will address the question how do we determine the crystal structure of a solid sample? Electron microscopy (by direct and indirect observations) Scanning
More informationSolid 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
More informationActivation of deformation mechanism
Activation of deformation mechanism The deformation mechanism activates when a critical amount of mechanical stress imposed to the crystal The dislocation glide through the slip systems when the required
More informationChapter 3: Structures of Metals & Ceramics
Chapter 3: Structures of Metals & Ceramics School of Mechanical Engineering Professor Choi, Hae-Jin Chapter 3-1 Chapter 3: Structures of Metals & Ceramics ISSUES TO ADDRESS... How do atoms assemble into
More informationStructure-Property Correlation [1] Structure-processing-properties-performance relation
MME 297: Lecture 04 Structure-Property Correlation [1] Structure-processing-properties-performance relation Dr. A. K. M. Bazlur Rashid Professor, Department of MME BUET, Dhaka Topics to discuss today...
More informationX-RAY DIFFRACTION in POWDERS
X-RAY DIFFRACTION in POWDERS PURPOSE: To learn x-ray powder-pattern diffraction techniques, to verify Vegard's law for copper-nickel alloys, to determine the nickel content in some American and Canadian
More information4-Crystal Defects & Strengthening
4-Crystal Defects & Strengthening A perfect crystal, with every atom of the same type in the correct position, does not exist. The crystalline defects are not always bad! Adding alloying elements to a
More informationSpreadsheet Applications for Materials Science
Spreadsheet Applications for Materials Science Introduction to X-ray Powder Diffraction Introduction X-ray powder diffraction is a powerful analytical technique that is widely used in many fields of science
More informationImpurities in Solids. Crystal Electro- Element R% Structure negativity Valence
4-4 Impurities in Solids 4.4 In this problem we are asked to cite which of the elements listed form with Ni the three possible solid solution types. For complete substitutional solubility the following
More informationIntroduction to Engineering Materials ENGR2000 Chapter 7: Dislocations and Strengthening Mechanisms. Dr. Coates
Introduction to Engineering Materials ENGR2000 Chapter 7: Dislocations and Strengthening Mechanisms Dr. Coates An edge dislocation moves in response to an applied shear stress dislocation motion 7.1 Introduction
More informationX-Ray Diffraction. Nicola Pinna
X-Ray Diffraction Nicola Pinna Department of Chemistry, CICECO, University of Aveiro, 3810-193 Aveiro, Portugal. School of Chemical and Biological Engineering, College of Engineering, Seoul National University
More informationMovement of edge and screw dislocations
Movement of edge and screw dislocations Formation of a step on the surface of a crystal by motion of (a) n edge dislocation: the dislocation line moves in the direction of the applied shear stress τ. (b)
More informationPowder X-ray Diffraction
Powder X-ray Diffraction The construction of a simple powder diffractometer was first described by Hull in 1917 1 which was shortly after the discovery of X-rays by Wilhelm Conrad Röntgen in1895 2. Diffractometer
More informationENERGY AND PACKING. Chapter 3 CRYSTAL STRUCTURE & PROPERTIES MATERIALS AND PACKING METALLIC CRYSTALS ISSUES TO ADDRESS...
Chapter 3 CRYSTAL STRUCTURE & PROPERTIES ISSUES TO ADDRESS... 1. How do s assemble into solid structures? (For now, focus on metals) ENERGY AND PACKING non dense, random packing bond energy Energy bond
More informationChapter 8 Strain Hardening and Annealing
Chapter 8 Strain Hardening and Annealing This is a further application of our knowledge of plastic deformation and is an introduction to heat treatment. Part of this lecture is covered by Chapter 4 of
More informationUNIVERSITY OF OSLO. Faculty of Mathematics and Natural Sciences
Page 1 UNIVERSITY OF OSLO Faculty of Mathematics and Natural Sciences Exam in MENA3100 Characterization of materials Day of exam: 12th. June 2015 Exam hours: 14:30 This examination paper consists of 5
More information