Chapter 3: Structures via Diffraction

Slides:



Advertisements
Similar presentations
TOPIC 3 STRUCTURE OF SOLIDS
Advertisements

Single Crystal A garnet single crystal found in Tongbei, Fujian Province, China. If the extremities of a single crystal are permitted to grow without any.
Fundamental Concepts Crystalline: Repeating/periodic array of atoms; each atom bonds to nearest neighbor atoms. Crystalline structure: Results in a lattice.
Why Study Solid State Physics?
Crystal diffraction Laue Nobel prize Max von Laue
Chapter 3: The Structure of Crystalline Solids
CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES
CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES
TOPIC 3: STRUCTURE OF SOLIDS
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.
SUMMARY: BONDING Type Bond Energy Comments Ionic Large!
Wigner-Seitz Cell The Wigner–Seitz cell around a lattice point is defined as the locus of points in space that are closer to that lattice point than to.
Lec. (4,5) Miller Indices Z X Y (100).
Solid Crystallography
Solid State Physics 2. X-ray Diffraction 4/15/2017.
Chapter 3 -1 ISSUES TO ADDRESS... How do atoms assemble into solid structures? How does the density of a material depend on its structure? When do material.
Chapter 3: Structure of Metals and Ceramics Goals – Define basic terms and give examples of each: Lattice Basis Atoms (Decorations or Motifs) Crystal Structure.
Chapter 3: The Structure of Crystalline Solids
King Abdulaziz University Chemical and Materials Engineering Department Chapter 3 The Structure of Crystalline Solids Session II.
Why do we care about crystal structures, directions, planes ?
Recall Engineering properties are a direct result of the structure of that material. Microstructure: –size, shape and arrangement of multiple crystals.
Why do we care about crystal structures, directions, planes ?
Chapter 3- CRYSTAL SYSTEMS General lattice that is in the shape of a parallelepiped or prism. a, b, and c are called lattice parameters. x, y, and z here.
X-Ray Diffraction ME 215 Exp#1. X-Ray Diffraction X-rays is a form of electromagnetic radiation having a range of wavelength from nm (0.01x10 -9.
Crystallography and Structure ENGR 2110 R. R. Lindeke.
Chapter 3: The Structure of Crystalline Solids
CHE (Structural Inorganic Chemistry) X-ray Diffraction & Crystallography lecture 2 Dr Rob Jackson LJ1.16,
Miller Indices And X-ray diffraction
Chapter 3: The Structure of Crystalline Solids
Remember Miller Indices?
BRAVAIS LATTICE Infinite array of discrete points arranged (and oriented) in such a way that it looks exactly the same from whichever point the array.
Chapter 3: The Structure of Crystalline Solids
SUMMARY: BONDING Type Bond Energy Comments Ionic Large!
W.D. Callister, Materials science and engineering an introduction, 5 th Edition, Chapter 3 MM409: Advanced engineering materials Crystallography.
Crystallographic Points, Directions, and Planes. ISSUES TO ADDRESS... How to define points, directions, planes, as well as linear, planar, and volume densities.
Chapter 3: Structures via Diffraction Goals – Define basic ideas of diffraction (using x-ray, electrons, or neutrons, which, although they are particles,
ENGR-45_Lec-04_Crystallography.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Licensed Electrical.
Linear and Planar Atomic Densities
Properties of engineering materials
IPCMS-GEMME, BP 43, 23 rue du Loess, Strasbourg Cedex 2
Fourier transform from r to k: Ã(k) =  A(r) e  i k r d 3 r Inverse FT from k to r: A(k) = (2  )  3  Ã(k) e +i k r d 3 k X-rays scatter off the charge.
ME 330 Engineering Materials
The Structure of Crystalline Solids
CHARACTERIZATION OF THE STRUCTURE OF SOLIDS
Chapter 3: The Structure of Crystalline Solids
Materials Engineering
Diffraction in TEM Janez Košir
Ch.4 Atomic Structure of Solid Surfaces.
OM INSTITUTE OF TECHNOLOGY,VANTVACHHODA
Remember Miller Indices?
Chapter 3: Structure of Metals and Ceramics
Chap 3 Scattering and structures
Crystallographic Points, Directions, and Planes.
THE SPACE LATTICE AND UNIT CELLS CRYSTAL SYSTEMS AND BRAVAIS LATTICES.
CHAPTER 3: STRUCTURE OF CRYSTALLINE SOLIDS
SUMMARY: BONDING Type Bond Energy Comments Ionic Large!
Lecture 2.1 Crystalline Solids.
Crystallographic Points, Directions, and Planes.
Lecture 2.1 Crystalline Solids.
Chapter 1 Crystallography
UNIT-1 CRYSTAL PHYSICS.
CRYSTAL SYSTEMS General lattice that is in the shape of a parallelepiped or prism. a, b, and c are called lattice parameters. x, y, and z here are called.
(1) Atomic Structure and Interatomic Bonding
PHY 752 Solid State Physics
Electron diffraction Øystein Prytz.
CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES
Why Study Solid State Physics?
MILLER PLANES Atoms form periodically arranged planes Any set of planes is characterized by: (1) their orientation in the crystal (hkl) – Miller indices.
PHY 752 Solid State Physics
Crystalline Solids (고체의 결정구조)
Presentation transcript:

Chapter 3: Structures via Diffraction Goals – Define basic ideas of diffraction (using x-ray, electrons, or neutrons, which, although they are particles, they can behave as waves) and show how to determine: Crystal Structure Miller Index Planes and Determine the Structure Identify cell symmetry.

Chapter 3: Diffraction Learning Objective Know and utilize the results of diffraction pattern to get: – lattice constant. – allow computation of densities for close-packed structures. – Identify Symmetry of Cells. – Specify directions and planes for crystals and be able to relate to characterization experiments.

CRYSTALS AS BUILDING BLOCKS • Some engineering applications require single crystals: --diamond single crystals for abrasives --turbine blades Fig. 8.30(c), Callister 6e. (Fig. 8.30(c) courtesy of Pratt and Whitney). (Courtesy Martin Deakins, GE Superabrasives, Worthington, OH. Used with permission.) • Crystal properties reveal features of atomic structure. --Ex: Certain crystal planes in quartz fracture more easily than others. (Courtesy P.M. Anderson)

POLYCRYSTALS • Most engineering materials are polycrystals. 1 mm Adapted from Fig. K, color inset pages of Callister 6e. (Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany) 1 mm Nb-Hf-W plate with an electron beam weld. • Each "grain" is a single crystal. • If crystals are randomly oriented, overall component properties are not directional. • Crystal sizes range from 1 nm to 2 cm (i.e., from a few to millions of atomic layers).

SIMPLE Diffraction in Crystals and Polycrystals Diffraction Pattern Transmission Electron Microscopy (TEM) Tantalum with ordered structure containing Oxygen. kx ky Ta diffraction Ta2O5 oxygen diffraction Two ordered patterns appear, one w/ Ta and the other w/ O.

Diffraction by Planes of Atoms Light gets scattered off atoms…But since d (atomic spacing) is on the order of angstroms, you need x-ray diffraction (wavelength ~ d). To have constructive interference (I.e., waves ADD).

Diffraction Experiment and Signal Scan versus 2x Angle: Polycrystalline Cu Measure 2θ Diffraction collects data in “reciprocal space” since it is the equivalent of a Fourier transform of “real space”, i.e., eikr, as k ~ 1/r. How can 2θ scans help us determine crystal structure type and distances between Miller Indexed planes (I.e. structural parameters)?

Crystal Structure and Planar Distances Bravais Lattice Constructive Interference Destructive Interference Reflections present Reflections absent BCC (h + k + l) = Even (h + k + l) = Odd FCC (h,k,l) All Odd or All Even (h,k,l) Not All Odd or All Even HCP Any other (h,k,l) h+2k=3n, l = Odd n= integer h, k, l are the Miller Indices of the planes of atoms that scatter! So they determine the important planes of atoms, or symmetry. Distances between Miller Indexed planes For cubic crystals: For hexagonal crystals:

Allowed (hkl) in FCC and BCC for principal scattering (n=1) h,k,l all even or odd? 100 1 No 110 2 111 3 Yes 200 4 210 5 211 6 220 8 221 9 300 310 10 311 11 222 12 320 13 321 14 Self-Assessment: From what crystal structure is this? h + k + l was even and gave the labels on graph above, so crystal is BCC.

Diffraction of Single 2D Crystal Grain Lattice of Atoms: Crystal Grain Diffraction Pattern in (h,k) plane Powder diffraction figures taken from Th. Proffe and R.B. Neder (2001) http://www.uni-wuerzburg.de/mineralogie/crystal/teaching/pow_a.html

Diffraction of Multiple Single 2D Crystal Grains (powders) Multiple Crystal Grains: 4 Polycrystals Diffraction Pattern in (h,k) plane (4 grains) Diffraction Pattern in (h,k) plane (40 grains) Powder diffraction figures taken from Th. Proffe and R.B. Neder (2001) http://www.uni-wuerzburg.de/mineralogie/crystal/teaching/pow_a.html

Example from Graphite Diffraction from Single Crystal Grain Mutlple Grains: Polycrystal Powder diffraction figures taken from Th. Proffe and R.B. Neder (2001) http://www.uni-wuerzburg.de/mineralogie/crystal/teaching/pow_a.html

Example from Aluminum Diffraction from Mutlple Grains of Polycrystalline Aluminum Powder diffraction figures taken from Th. Proffe and R.B. Neder (2001) http://www.uni-wuerzburg.de/mineralogie/crystal/teaching/pow_a.html

Example from QuasiCrystals Remember there is no 5-fold symmetry alone that can fill all 3-D Space!

SUMMARY Materials come in Crystalline and Non-crystalline Solids, as well as Liquids/Amoprhous. Polycrystals are important. Crystal Structure can be defined by space lattice and basis atoms (lattice decorations or motifs), which can be found by diffraction. Only 14 Bravais Lattices are possible (e.g. FCC, HCP, and BCC). Crystal types themselves can be described by their atomic positions, planes and their atomic packing (linear, planar, and volumetric). We now know how to determine structure mathematically and experimentally by diffraction.