# Diffraction Basics. The qualitative basics:

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 certain directions will be in-phase or amplified Measurement of the geometry of diffracted x-rays can be used to discern the crystal structure and unit cell dimensions of the target material The intensities of the amplified x-rays can be used to work out the arrangement of atoms in the unit cell

2 The chief result of the interaction of X-rays with atoms in the specimen is scattering Scattering is the emission of X-rays of the same frequency (energy) as the incident X-rays in all directions (but with much lower intensity)

3

4 The Generalized 2D Laue Equation: p (cosν cos µ ) = ± hλ (h is the order of the diffraction, here 0 or 1)

5

6 In the specialized case where the angle of incidence µ is 90 the equation becomes: p cosν = ± hλ

7 For a two-dimensional lattice array of atoms, the Laue equations are: a (cosν cos µ ) = ± hλ 1 1 b (cosν cos µ ) = ± kλ 2 2

8 The Laue diffraction cones for the A and B directions are shown below:

9 Diffraction will only occur when the diffraction angles define the same direction. In the case below this is when the cones intersect to form the lines OX and OY

10 In a three-dimensional lattice array, there will be multiple Laue diffraction cones. Below a simple diagram shows three first order cones in ABC space

11 There are now three Laue equations requiring a simultaneous solution (i.e., there must be a diffraction direction common to all three cones): a (cosν1 cos µ 1) = ± hλ b (cosν 2 cos µ 2) = ± kλ c (cosν 3 cos µ 3) = ± lλ A unique solution is difficult to obtain In Laue diffraction, the crystal is fixed and oriented with a lattice axis parallel to the beam λ is varied by using white radiation With monochromatic radiation, movement of the crystal is required for diffraction to occur

12

13 White Radiation Monochromatic Method Laue: stationary single crystal Powder: specimen is polycrystalline, and therefore all orientations are simultaneously presented to the beam Rotation, Weissenberg: oscillation, De Jong-Bouman: single crystal rotates or oscillates about chosen axis in path of beam Precession: chosen axis of single crystal precesses about beam direction

14 The Bragg Law X-ray beam encounters a 3-d lattice array at left. Assume the following: A third-order cone about OA A second-order cone about OB A first-order cone about OC We assume these cones intersect at a common line satisfying the diffraction condition.

15 The rays scattered by adjacent atoms on OA atoms have a path difference of three wavelengths Those about OB have a path difference of two wavelengths About OC, one wavelength difference These points of coherent scatter define a plane with intercepts 2a, 3b, 6c (A, B, C ) and a Miller index of (321)

16 The Bragg Law bottom line : A diffraction direction defined by the intersection of the h th order cone about the a axis, the k th order cone about the b axis and the l th order cone about the c axis is geometrically equivalent to a reflection of the incident beam from the (hkl) plane referred to these axes. in other words: Diffraction from a lattice array of points may be functionally treated as reflection from a stack of planes defined by those lattice points

17

18 On the previous diagram, the reflected rays combine to form a diffracted beam if they differ in phase by a whole number of wavelengths, that is, if the path difference AB- AD = nλ where n is an integer. Therefore AB = d sinθ and AD = AB cos 2θ = d (cos 2θ ) sinθ nλ = = d d (cos 2θ ) sinθ sinθ d (1 cos 2θ ) sinθ d = (2sin sinθ 2 θ ) n λ = 2d sinθ

19 In the Bragg Law, n λ = 2d sinθ, n is the order of diffraction Above are 1 st, 2 nd, 3 rd and 4 th order reflections from the (111) face of NaCl. By convention, orders of reflections are given as 111, 222, 333, 444, etc. (without the parentheses)

20 The Reciprocal Lattice Problems addressed by this unusual mental exercise: How do we predict when diffraction will occur in a given crystalline material? How do we orient the X-ray source and detector? How do we orient the crystal to produce diffraction? How do we represent diffraction geometrically in a way that is simple and understandable?

21 The first part of the problem Consider the diffraction from the (200) planes of a (cubic) LiF crystal that has an identifiable (100) cleavage face. To use the Bragg equation to determine the orientation required for diffraction, one must determine the value of d 200. Using a reference source (like the ICDD database or other tables of x-ray data) for LiF, a = Å, thus d 200 will be ½ of a or Å. From Bragg s law, the diffraction angle for Cu Kα 1 (λ = ) will be θ. Thus the (100) face should be placed to make an angle of with the incident x-ray beam and detector. If we had no more complicated orientation problems, then we would have no need for the reciprocal space concept. Try doing this for the (246) planes and the complications become immediately evident.

22 The second part of the problem Part of the problem is the three dimensional nature of the diffracting planes. They may be represented as vectors where d hkl is the perpendicular from the origin to the first hkl plane: While this is an improvement, the graphical representation is still a mess a bunch of vectors emanating from a single point radiating into space as shown on the next slide ----

23

24 Ewald proposed that instead of plotting the d hkl vectors, that the reciprocal vector be plotted, defined as: d * hkl d 1 hkl The units are in reciprocal angstroms and defines a reciprocal space. The points in the space repeat at perfectly periodic intervals, defining a space lattice called a reciprocal lattice Figure 3.3 can now be reconstructed plotting the reciprocal vectors instead of the d hkl vectors The comparison is shown in the following slides

25

26

27 Any lattice vector in the reciprocal lattice represents a set of Bragg plans and can be resolved into its components: * d = ha + kb + hkl * * lc * In orthogonal crystal systems, the d and d* are simple reciprocals. In non-orthogonal systems, the reciprocals (since they are vectors) are complicated by angular calculations Because the angle β is not 90, the calculation of d* and a* involve the sin of the interaxial angle.

28 The table below shows the relationships between axes in direct and reciprocal space. At the bottom is a very complex trigonometric function that defines the parameter V used in the triclinic system. V 1 V * = = a* b* c*(1 cos α * cos β * cos γ * + 2cosα *cos β *cosγ *) 1/ 2

29

30

31 Figure 3.7 shows the arrangement where the (230) point is brought into contact with the Ewald sphere. By definition CO = 1 λ and OA = d *(230) 2 hence sinθ = OA = CO d* (230) 1/ λ / 2 λ = 2sinθ d * (230) from the definition of the reciprocal vector d (230) d 1 * (230) substitution yields: λ = sinθ 2 d (230 ) The Bragg Relationship!

32

33 The Powder Diffraction Pattern Powders (a.k.a. polycrystalline aggregates) are billions of tiny crystallites in all possible orientations When placed in an x-ray beam, all possible interatomic planes will be seen By systematically changing the experimental angle, we will produce all possible diffraction peaks from the powder

34 There is a d* hkl vector associated with each point in the reciprocal lattice with its origin on the Ewald sphere at the point where the direct X-ray beam exists. Each crystallite located in the center of the Ewald sphere has its own reciprocal lattice with its orientation determined by the orientation of the crystallite with respect to the X-ray beam

35 The Powder Camera The Debye- Scherrer powder camera

36 Debye diffraction rings from the d* 100 reflection. Note the 1 st and 2 nd order cones, and back reflections

37

38 Some Debye-Scherrer Powder Films

39 The Powder Diffractometer Think of the diffractometer as a device for measuring diffractions occurring along the Ewald sphere it s function is to move all of the crystallites in the powder and their associated reciprocal lattices, measuring diffractions as they intersect the sphere Because of the operational geometry of diffractometers, there must be a very large number of small crystallites (a.k.a., statistically infinite amount of randomly oriented crystallites ) for the diffractometer to see all of the possible diffractions By convention (but not by accident note Fig 3.7) diffraction angles are recorded as 2θ. Data are commonly recorded as 2θ and intensity

40

41

42

43 Conclusions The geometry of powder diffraction is best understood through the use of the reciprocal lattice and the Ewald sphere The powder diffractometer is a device for directly applying these constructions to measure d-spacings in crystalline materials X-ray diffraction allows direct measurement of the lattice Much information about the crystal structure can be obtained from variations in intensity (and the complete some reflections in the pattern)

44 Next week: Diffraction Intensity: The rest of the fingerprint Origin, Variations, Extinctions and Error Sources in diffraction experiments

### 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

### 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

### Single 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

### LECTURE 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,

### 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

### Atomic 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

### 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

### Identification 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

### An Introduction to X-Ray Powder Diffraction. credits to: Scott A Speakman, Patrick McArdle Edited by Di Cicco 2014

An Introduction to X-Ray Powder Diffraction credits to: Scott A Speakman, Patrick McArdle Edited by Di Cicco 2014 LATTICE ARRAYS AND BRAVAIS LATTICES Crystalline materials differ from amorphous materials

### Workshop RIETVELD REFINEMENT OF DIFFRACTION PATTERNS Program Monday June 1st, Introduction to Rietveld refinement S.

Workshop RIETVELD REFINEMENT OF DIFFRACTION PATTERNS Program Monday June 1st, 2009 9.00 13.00 Introduction to Rietveld refinement S.Enzo Università di Sassari X-ray diffraction for bulk samples and thin

### X-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

### Materials 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.

### Experiment 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,

### Key crystallographic concepts: Theory of diffraction. (Crystallography y without tears, Part 1)

Protein Crystallography (3) Key crystallographic concepts: Theory of diffraction. (Crystallography y without tears, Part 1) Cele Abad-Zapatero University of Illinois at Chicago Center for Pharmaceutical

### 11.3 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

### Lecture 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.

### 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

### Basic X-ray Powder Diffraction (XRPD)

Basic X-ray Powder Diffraction (XRPD) Solid-State, Material Science Crystalline (Scattering : diffraction) Non-crystalline (Scattering) Analytical Tool Qualitative and Quantitative Analysis Quantitative

### The 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

### X-ray Diffraction (XRD)

هب انم خدا X-ray Diffraction (XRD) 1.0 What is X-ray Diffraction 2.0 Basics of Crystallography 3.0 Production of X-rays 4.0 Applications of XRD 5.0 Instrumental Sources of Error 6.0 Conclusions Bragg s

### Chapter 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

### Atomic 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

### X-ray diffraction. Talián Csaba Gábor University of Pécs, Medical School Department of Biophysics

X-ray diffraction Talián Csaba Gábor University of Pécs, Medical School Department of Biophysics 2012.10.11. Outline of the lecture X-ray radiation Interference, diffraction Crystal structure X-ray diffraction

### Thin Film Scattering: Epitaxial Layers

Thin Film Scattering: Epitaxial Layers 6th Annual SSRL Workshop on Synchrotron X-ray Scattering Techniques in Materials and Environmental Sciences: Theory and Application May 29-31, 2012 Thin films. Epitaxial

### Travaux Pratiques de Matériaux de Construction

Travaux Pratiques de Matériaux de Construction Section Matériaux 6 ème semestre 2009 Etude de Matériaux Cimentaire Par Diffraction des Rayons X Responsable: Silke Ruffing E-Mail: silke.ruffing@epfl.ch

### Fundamentals of Crystalline State p. 1 Introduction p. 1 Crystalline state p. 2 Crystal lattice and crystal structure p. 4 Shape of the unit cell p.

Preface p. xvii Fundamentals of Crystalline State p. 1 Introduction p. 1 Crystalline state p. 2 Crystal lattice and crystal structure p. 4 Shape of the unit cell p. 6 Content of the unit cell p. 7 Asymmetric

### X-ray diffraction

2.2.3.- X-ray diffraction 2.2.3.1.- Origins and fundamentals of the technique The first experimental evidence concerning x-ray diffraction was given by Max von Laue who in 1912 demonstrated that x-rays

### Fundamentals 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

### This 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

### INGE 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

### Physics 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,

### Physics 4780: Atomic and Nuclear Physics Laboratory. Experiment CM5: X-ray diffraction and crystal structures Lab Location: MH 3010

Physics 4780: Atomic and Nuclear Physics Laboratory Experiment CM5: X-ray diffraction and crystal structures Lab Location: MH 3010 References: Preston and Dietz, Expt. 10 pp. 180-197 Eisberg and Resnick,

### LECTURE 8. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 8 Dr. Teresa D. Golden University of North Texas Department of Chemistry Practical applications for lattice parameter measurements: -determine composition (stoichiometry) of the sample -determine

### Background 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.

### AP 5301/8301 Instrumental Methods of Analysis and Laboratory Lecture 5 X ray diffraction

1 AP 5301/8301 Instrumental Methods of Analysis and Laboratory Lecture 5 X ray diffraction Prof YU Kin Man E-mail: kinmanyu@cityu.edu.hk Tel: 3442-7813 Office: P6422 Lecture 5: Outline Review on crystallography

### TEM 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)

### Answer All Questions. All Questions Carry Equal Marks. Time: 20 Min. Marks: 10.

Code No: 09A1BS02 Set No. 1 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD I B.Tech. I Mid Examinations, November 2009 ENGINEERING PHYSICS Objective Exam Name: Hall Ticket No. A Answer All Questions.

### X-Ray Diffraction by Macromolecules

N. Kasai M. Kakudo X-Ray Diffraction by Macromolecules With 351 Figures and 56 Tables Kodansha ~Springer ... Contents Preface v Part I Fundamental 1. Essential Properties of X-Rays................. 3 1.1

### Thin Film Scattering: Epitaxial Layers

Thin Film Scattering: Epitaxial Layers Arturas Vailionis First Annual SSRL Workshop on Synchrotron X-ray Scattering Techniques in Materials and Environmental Sciences: Theory and Application Tuesday, May

### 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

### Earth & Planetary Science Applications of X-Ray Diffraction: Advances Available for Research with our New Systems

Earth & Planetary Science Applications of X-Ray Diffraction: Advances Available for Research with our New Systems James R. Connolly Dept. of Earth & Planetary Sciences University of New Mexico 401/501

### Engineering 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

### Advanced Methods for Materials Research. Materials Structure Investigations Materials Properties Investigations

Advanced Methods for Materials Research Materials Structure Investigations Materials Properties Investigations Advanced Methods for Materials Research 1. The structure and property of sample and methods

### X-RAY DIFFRACTIO N B. E. WARREN

X-RAY DIFFRACTIO N B. E. WARREN Chapter 1 X-Ray Scattering by Atom s 1.1 Classical scattering by a free electron 1 1.2 Polarization by scattering 4 1.3 Scattering from several centers, complex representation

### High Resolution X-ray Diffraction

High Resolution X-ray Diffraction Nina Heinig with data from Dr. Zhihao Donovan Chen, Panalytical and slides from Colorado State University Outline Watlab s new tool: Panalytical MRD system Techniques:

### Travaux Pratiques de Matériaux de Construction. Etude de Matériaux Cimentaires par Diffraction des Rayons X sur Poudre

Travaux Pratiques de Matériaux de Construction Section Matériaux 6 ème semestre 2015 Etude de Matériaux Cimentaires par Diffraction des Rayons X sur Poudre Study Cementitious Materials by X-ray diffraction

### X-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

### Characterization of Materials Using X-Ray Diffraction Powder Diffraction

Praktikum III, Fall Term 09 Experiment P1/P2; 23.10.2009 Characterization of Materials Using X-Ray Diffraction Powder Diffraction Authors: Michael Schwarzenberger (michschw@student.ethz.ch) Philippe Knüsel

### 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

### It 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

### Strain. 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

### Bio5325 Fall Crystal Vocabulary

Crystals and Crystallization Bio5325 Fall 2007 Crystal Vocabulary Mosaicity (mosaic spread) Protein crystals are imperfect, consisting of a mosaic of domains that are slightly misaligned. As a result,

### Diffraction: 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

### Uses of Powder Diffraction. Diffraction

Powder X-ray X Diffraction Brendan J. Kennedy School of Chemistry The University of Sydney Uses of Powder Diffraction Qualitative Analysis Identification of single-phase materials Identification of multiple

### Lecture 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.

### DIFFRACTION METHODS IN MATERIAL SCIENCE. PD Dr. Nikolay Zotov Tel Room 3N16.

DIFFRACTION METHODS IN MATERIAL SCIENCE PD Dr. Nikolay Zotov Tel. 0711 689 3325 Email: zotov@imw.uni-stuttgart.de Room 3N16 Lecture 5 OUTLINE OF THE COURSE 0. Introduction 1. Classification of Materials

### Powder 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

### Lesson 1 X-rays & Diffraction

Lesson 1 X-rays & Diffraction Nicola Döbelin RMS Foundation, Bettlach, Switzerland February 11 14, 2013, Riga, Latvia Electromagnetic Spectrum X rays: Wavelength λ: 0.01 10 nm Energy: 100 ev 100 kev Interatomic

### CHARACTERISATION OF CRYSTALLINE AND PARTIALLY CRYSTALLINE SOLIDS BY X-RAY POWDER DIFFRACTION (XRPD)

2.9.33. Characterisation of crystalline solids by XRPD EUROPEAN PHARMACOPOEIA 6.0 with its standard deviation. The mean values for x 10 and x 90 must not deviate by more than 5 per cent from the certified

### 3.091 Introduction to Solid State Chemistry. Lecture Notes No. 5 X-RAYS AND X-RAY DIFFRACTION

3.091 Introduction to Solid State Chemistry Lecture Notes No. 5 X-RAYS AND X-RAY DIFFRACTION * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Sources

### X-ray diffraction and structure analysis Introduction

Teknillisen fysiikan ohjelmatyö X-ray diffraction and structure analysis Introduction Oleg Heczko 120 100 80 118 12-5 125 Ni-Mn-Ga (298K) SQRT(Intensity) 60 40 20 015 200 123 12-7 20-10 20,10 20-8 040

### X-Rays and X-ray Mineralogy

GLY 4200 X-Rays and X-ray Mineralogy X-radiation is a type of electromagnetic radiation, like visible light, UV, IR, etc. The range in wavelength from approximately 10-6 to 10-1 nm. They were first discovered

### X-Rays and X-ray Mineralogy

GLY 4200 X-Rays and X-ray Mineralogy X-radiation is a type of electromagnetic radiation, like visible light, UV, IR, etc. The range in wavelength from approximately 10-6 to 10-1 nm. They were first discovered

### Chapter 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

### Review 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

### DIFFRACTION METHODS IN MATERIAL SCIENCE. PD Dr. Nikolay Zotov Tel Room 3N16.

DIFFRACTION METHODS IN MATERIAL SCIENCE PD Dr. Nikolay Zotov Tel. 0711 689 3325 Email: zotov@imw.uni-stuttgart.de Room 3N16 Lecture 5 OUTLINE OF THE COURSE 0. Introduction 1. Classification of Materials

### A Brief History of XRD 1895: Röntgen discovers X-Rays received the first Nobel prize in physics in 1901

X-ray Diffraction A Brief History of XRD 1895: Röntgen discovers X-Rays received the first Nobel prize in physics in 1901 1912: Laue diffracts X-Rays from single crystal 1914 Nobel prize in Physics 1912:

### BRUKER ADVANCED X-RAY SOLUTIONS

BRUKER ADVANCED X-RAY SOLUTIONS Configuration Measuring circle diameter Angle range 360 (Theta and 2 Theta, without additional equipment) Horizontal or vertical, Theta/2 Theta or Theta/Theta geometry (can

### X-Ray Diffraction Analysis

162402 Instrumental Methods of Analysis Unit III X-Ray Diffraction Analysis Dr. M. Subramanian Associate Professor Department of Chemical Engineering Sri Sivasubramaniya Nadar College of Engineering Kalavakkam

### Microstructural Characterization of Materials

Microstructural Characterization of Materials 2nd Edition DAVID BRANDON AND WAYNE D. KAPLAN Technion, Israel Institute of Technology, Israel John Wiley & Sons, Ltd Contents Preface to the Second Edition

### Introduction to Powder Diffraction/Practical Data Collection

Durham University Chemistry Department Introduction to Powder Diffraction/Practical Data Collection Dr Ivana Evans Durham, January 2007 Durham Outline Information in a powder pattern What is diffraction

### 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?

### 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

### 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

### (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

### 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

### Basics of XRD part I. 1 KIT 10/31/17. Name of Institute, Faculty, Department. The Research University in the Helmholtz Association

Basics of XRD part I Dr. Peter G. Weidler Institute of Functional Interfaces IFG 1 KIT 10/31/17 The Research University in the Helmholtz Association Name of Institute, Faculty, Department www.kit.edu Overview

### GEOL.3070 EARTH MATERIALS I FORENSIC APPLICATIONS OF X-RAY DIFFRACTION

GEOL.3070 EARTH MATERIALS I FORENSIC APPLICATIONS OF X-RAY DIFFRACTION NAME I. Introduction Our knowledge of the crystalline state is gained by studies utilizing x-rays (the field of x- ray crystallography).

### 1 Safety First. Updated MD February 10, 2014

Experiment 13. X-ray Diffraction Updated MD February 10, 2014 1 Safety First During this experiment we are using a strong x-ray source. It is well shielded. Before switching it on, check if all unused

### Crystallographic Textures Measurement

Crystallographic Textures Measurement D. V. Subramanya Sarma Department of Metallurgical and Materials Engineering Indian Institute of Technology Madras E-mail: vsarma@iitm.ac.in Macrotexture through pole

### Rietveld refinement of ZrSiO 4 : application of a phenomenological model of anisotropic peak width

Rietveld refinement of ZrSiO 4 : application of a phenomenological model of anisotropic peak width A. Sarkar, P. Mukherjee, P. Barat Variable Energy Cyclotron Centre 1/A Bidhan Nagar, Kolkata 700064, India

### A Brief History of XRD 1895: Röntgen discovers X-Rays received the first Nobel prize in physics in 1901

X-ray Diffraction A Brief History of XRD 1895: Röntgen discovers X-Rays received the first Nobel prize in physics in 1901 1912: Laue diffracts X-Rays from single crystal 1914 Nobel prize in Physics 1912:

### A Brief Introduction to Structural Biology and Protein Crystallography

A Brief Introduction to Structural Biology and Protein Crystallography structural biology of H2O http://courses.cm.utexas.edu/jrobertus/ch339k/overheads-1/water-structure.jpg Protein polymers fold up into

### Instrument Configuration for Powder Diffraction

Instrument Configuration for Powder Diffraction Advanced X-ray Workshop S.N. Bose National Centre for Basic Sciences, 14-15/12/2011 Innovation with Integrity Overview What is the application? What are

### Orientation / Texture Polyethylene films

Application Note PT-002 Orientation / Texture Polyethylene films Polyethylene (PE) film is one of the most commonly used polymeric products and orientation measurements of this material are of great interest.

### Lecture course on solid state physics for Nano, 2019

Prof. U. Pietsch Department of Physics, University of Siegen Lecture course on solid state physics for Nano, 2019 Lecture 1 Introduction in crystallography Objectives of the course To provide the basic

### GEOLOGY Vol. III - Modern XRD Methods in Mineralogy - Robert E. Dinnebier and Karen Friese

MODERN XRD METHODS IN MINERALOGY Robert E. Dinnebier and Karen Friese Max-Planck-Institute for Solid State Research, Stuttgart, Germany Keywords: powder diffraction, single crystal diffraction, synchrotron

### Multiple film plane diagnostic for shocked lattice measurements invited

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 74, NUMBER 3 MARCH 2003 Multiple film plane diagnostic for shocked lattice measurements invited Daniel H. Kalantar, a) E. Bringa, M. Caturla, J. Colvin, K. T. Lorenz,

### Signals from a thin sample

Signals from a thin sample Auger electrons Backscattered electrons BSE Incident beam secondary electrons SE Characteristic X-rays visible light 1-100 nm absorbed electrons Specimen electron-hole pairs

### Steps in solving a structure. Diffraction experiment. Obtaining well-diffracting crystals. Three dimensional crystals

Protein structure from X-ray diffraction Diffraction images: ciprocal space Protein, chemical structure: IALEFGPSLKMNE Conformation, 3D-structure: CRYST1 221.200 73.600 80.900 90.00 90.00 90.00 P 21 21

### 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

### Characterisation of materials using x-ray diffraction and X-ray powder diffraction. Cristina Mercandetti Nicole Schai

P1 and P2 Characterisation of materials using x-ray diffraction and X-ray powder diffraction Cristina Mercandetti Nicole Schai Supervised by Taylan Oers and Pawel Kuczera Report ETH Zurich 2012 TABLE OF

### 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

### Residual Stress and Springback Prediction

Residual Stress and Springback Prediction Presenter: Jyhwen Wang, TAMU PIs: Bruce Tai and Jyhwen Wang, TAMU Yannis Korkolis, UNH Jian Cao, Northwestern Executive Summary: Objective/Industrial Need: accurate

### Condensed Matter II: Particle Size Broadening

Condensed Matter II: Particle Size Broadening Benjamen P. Reed & Liam S. Howard IMAPS, Aberystwyth University March 19, 2014 Abstract Particles of 355µm silicon oxide(quartz)were subjected to a ball milling