Determination of Crystal Structure (Chapt. 10)

Slides:

Advertisements

Similar presentations

Fundamental Concepts Crystalline: Repeating/periodic array of atoms; each atom bonds to nearest neighbor atoms. Crystalline structure: Results in a lattice.

Advertisements

t1 t2 6 t1 t2 7 8 t1 t2 9 t1 t2.

Chap 8 Analytical Instruments. XRD Measure X-Rays “Diffracted” by the specimen and obtain a diffraction pattern Interaction of X-rays with sample creates.

Experimentally, the Bragg law can be applied in two different ways:

What is diffraction? Diffraction – the spreading out of waves as they encounter a barrier.

CHAPTER 3: CRYSTAL STRUCTURES X-Ray Diffraction (XRD)

Solids Image:Wikimedia Commons User Alchemistry-hp.

CHAPTER 2 : CRYSTAL DIFFRACTION AND PG Govt College for Girls

Announcements 1)Revised Lab timings: 1-3 PM (all groups) 2) Quiz 1, 28 th Jan 2014, Tuesday 7:30 PM, WS 209, WS 213.

Lecture 8b X-Ray Diffraction. Introduction I History 1895 Wilhelm Conrad R ӧ ntgen discovered X-rays 1905 Albert Einstein introduces the concept of photons.

Lec. (4,5) Miller Indices Z X Y (100).

Solid State Physics 2. X-ray Diffraction 4/15/2017.

Yat Li Department of Chemistry & Biochemistry University of California, Santa Cruz CHEM 146C_Experiment #3 Identification of Crystal Structures by Powder.

CHE (Structural Inorganic Chemistry) X-ray Diffraction & Crystallography lecture 3 Dr Rob Jackson LJ1.16,

What do X-ray powder diffraction patterns look like? What do X-ray powder diffraction patterns look like?

Sections 12.1 – 12.2 Types of Solids Metallic Solids Bill Vining SUNY Oneonta.

Indexing cubic powder patterns

Homework Answers – Constant T so P vap is constant at 28.0 mm Hg – a) melting, b) no change, still liquid – boils when P atm gets down.

Order in crystals Symmetry, X-ray diffraction. 2-dimensional square lattice.

Shared by 8 unit cells Shared by 2 unit cells.

Anandh Subramaniam & Kantesh Balani

Chapter 12: Solids. Types of Solids: Ionic Molecular Network: crystalline amorphous Metallic.

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 TRIVIA ROUND 2!

CENG151 Introduction to Materials Science and Selection

Crystallographic Axes are imaginary reference lines which often coincide with symmetry axes or normals to symmetry planes as in symmetry axes these aid.

VIII. Kinematical Theory of Diffraction 8-1. Total Scattering Amplitude The path difference between beams scattered from the volume element apart is The.

Analysis of XRD Test.

CHE (Structural Inorganic Chemistry) X-ray Diffraction & Crystallography lecture 2 Dr Rob Jackson LJ1.16,

Miller Indices And X-ray diffraction

Introduction to Crystallography

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.

Determination of Crystal Structure (From Chapter 10 of Textbook 2) Unit cell  line positions Atom position  line intensity (known chemistry) Three steps.

PHYS 430/603 material Laszlo Takacs UMBC Department of Physics

Diffraction Basics Coherent scattering around atomic scattering centers occurs when x-rays interact with material In materials with a crystalline structure,

Logarithm Review ab = c, (a > 0, a ≠ 1) logac = b log c = log10c

Chapter 3: Structures via Diffraction Goals – Define basic ideas of diffraction (using x-ray, electrons, or neutrons, which, although they are particles,

Review of Chapter 10 (condensed states of matter) A.P. Chem Pressure→ Temperature→ SOLID Defined: Structural units held together by attractive forces enough.

Electron Microcopy 180/ Useful info – many websites. Images here from

Crystallography ll.

Crystal Structures & X-ray Diffraction Chemistry 123 Spring 2008 Dr. Woodward.

PHY1039 Properties of Matter Crystallography, Lattice Planes, Miller Indices, and X-ray Diffraction (See on-line resource: )

Suggestion on note taking No lab tomorrow CHEM 1211 Lab manual.

Chapter 2.2 The Multiplication Principle of Equality.

Chapter 6 Solid-State Chemistry. Problems n n 6.9, 6.13, 6.14.

X-Ray Diffraction Spring 2011.

Diffraction: Intensity (From Chapter 4 of Textbook 2 and Chapter 9 of Textbook 1) Electron  atoms  group of atoms or structure  Crystal (poly or single)

Created By: Dave Burgess Earth Science Mineral Profile Bornite Human Uses The primary use of bornite is as an ore for copper. The copper within the bornite.

Sections 12.1 – 12.2 Types of Solids Metallic Solids.

Point Groups (Crystal Classes)

11.7 Structures of Solids Zek Zhang Kevin Nash, *Matt Coleman¯\_( ツ )_/¯ *yeah were not racist, the non-white is not last.

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.

Solids Image:Wikimedia Commons User Alchemistry-hp.

Basic Crystallography for X-ray Diffraction Earle Ryba.

Elements of Materials Science and Engineering

King Abdulaziz University Chemical and Materials Engineering Department Chapter 3 The Structure of Crystalline Solids Session III.

EBB245 Material Characterisations Lecture 2. X-ray Diffraction Methods Dr Zainovia Lockman Lecture 2. X-ray Diffraction Methods Dr Zainovia Lockman 1.

Crystal Structure and Crystallography of Materials Chapter 14: Diffraction Lecture No. 2.

CHARACTERIZATION OF THE STRUCTURE OF SOLIDS

Expanding the Kinetic Theory

The Electromagnetic Spectrum

Solid state chemistry Chapter 3

Theory and Practice of X-ray Crystal Structure Determination

Chapter 1 Crystallography

Main Types of Industrial Material

Thermal Energy & Heat Capacity:

XRD Applications.

X-ray Diffraction Main Reference

Counting Atoms in Unit Cells:

Counting Atoms in Unit Cells:

Presentation transcript:

Determination of Crystal Structure (Chapt. 10) 1. Use the angular positions of the diffraction lines to determine the shape and size of the unit cell.  Assume either cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, or triclinic.  Assign Miller indices to each reflection (“index the pattern”).  If a match is not obtained, the assumption of  should be changed and the pattern indexed again.  Calculate the size of the unit cell based on the positions and Miller indices of the diffraction lines. 2. With the measured density of the material, the chemical composition, and the size of the unit cell, calculate the number of atoms per unit cell. 3. Find the positions of the atoms in the unit cell by using the relative intensities of the diffraction lines. Guess Guess Correct? No Yes Done

Preliminary Treatment of Data We want the values of sin2q for each diffraction line (in order to find the cell size and shape), however, there can be errors to what we measure, including extraneous lines in the diffraction pattern, and systematic errors (misalignment, film shrinkage, absorption, etc.) Extraneous Lines 1. X-ray beam with multiple wavelengths: 2. Contaminants or impurities in the sample, or the specimen mount! Systematic Errors 1. Film shrinkage (see Fig. 6-5 Cullity) 2. Specimen is off-centered in Debye-Scherrer camera (see Fig. 11-3 Cullity) 3. Absorption in the sample Answer mix in a reference material and calibrate. (see Fig. 10-1 Cullity)

Cubic Crystals (Indexing the Patterns) Simple cubic: 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, etc. Body-centered cubic: 2, 4, 6, 8, 10, 12, 14, 16, . . . Face-centered cubic: 3, 4, 8, 11, 12, 16, 19, 20, . . . Diamond cubic: 3, 8, 11, 16, 19, 24, 27, 32, . . .

Corrections for Systematic Errors Absorption error can be lumped into this error.

Correction for Systematic Error Differentiation of Bragg’s Law: For a cubic crystal: Fractional error in a (goes to zero as q  90)

Correction for Systematic Error At small f (large q), this could be approximated as:

Correction for Systematic Error

Nelson-Riley

Indexing Patterns for Non-Cubic Crystals Tetragonal Depends on (c/a), but not on a. Requires two ranges to cover what is covered by one range of d Negative scaling

Dull-Harvey Chart

Indexing Patterns for Non-Cubic Crystals Tetragonal Depends on (c/a), but not on a.

Scales for Left Side of Above Equations d scale sin2q scale

Hexagonal Hull-Davey Chart

Zinc Example (Cu Ka) From table 10-2 (sin2q)

10-5 10-7 10-8

Chapter 10 Example

Extended Hull-Davey Chart

Hull-Davey for Cubic

Sin2q Scale of Table 10-5

Chapter 10 Example