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

Size: px
Start display at page:

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

Transcription

1 DIFFRACTION METHODS IN MATERIAL SCIENCE PD Dr. Nikolay Zotov Tel Room 3N16 Lecture 5

2 OUTLINE OF THE COURSE 0. Introduction 1. Classification of Materials 2. Defects in Solids 3. Basics of X-ray and neutron scattering 4. Diffraction studies of Polycrystalline Materials 5. Microstructural Analysis by Diffraction 6. Diffraction studies of Thin Films 7. Diffraction studies of Nanomaterials 8. Diffraction studies of Amorphous and Composite Materials 2

3 OUTLINE OF TODAY S LECTURE Scattering from Single Crystals (Short Repetition) Scattering from Polycrystalline Materials Powder Diffraction Intensities Selection Rules Types of Detectors Powder Diffractometers Diffraction Pattern measured What to do now? 3

4 SCATTERING EXPERIMENT Source Detector Sample Sources Types; How to select them Sample Polycrystalline Sample Detectors Types; How to select them 4

5 Conditions for Scattering from Single Crystal Q = ng hkl The diffraction from a single crystal is located only at the reciprocal lattice points k' Q k 0 Ewald construction Every spot is a given reflection hkl with intensity (darkness) ~ F hkl 2. Some reciprocal lattice points are missing because of the presence of selection rules. 5

6 Scattering Amplitude/ Scattering Intensity A(Q) = = {Σ f j (Q)exp(-½u j Q 2 )exp(iq.x j )} {Σ exp (i.q.t mnp )} = F hkl {Σ Σ Σ exp (i.q.t mnp )} I(Q) ~ A(Q) 2 = F hkl 2 L(Q) ; L(Q) is the so-called Laue function 6

7 Laue Function L(Q) = {Σ Σ Σ exp (i.q.t mnp )} {Σ Σ Σ exp (i.q.t mnp )}* = T mnp = ma+nb+pc = [sin 2 (MQ.a/2)/sin 2 (Q.a/2)] [sin 2 (NQ.b/2)/sin 2 (Q.b/2)] [sin 2 (PQ.c/2)/sin 2 (Q.c/2)] M,N,P number of unit cells along x,y,z directions Sinc function Maximum of the Sinc Function Q.a = 2hp Q.b = 2kp Q.c = 2lp Another derivation of the Laue conditions 7

8 Scattering from a Polycrystalline Sample Polycrystalline sample = Aggregate of crystallites (small single crystals) with different shape, size and orientation. k i Q k f For random orientation of the crystallites, the scattered X-rays (neutrons or electrons) lay on cone(s) with opening angle = 4Q; r = (2p/l) sin(q) k=2 p/l Q r The reciprocal space of a polycrystal represents a system of concentric spheres with radii d hkl * = 1/d hkl 8

9 Effect of Preffered Orientation Random Orientations Preffered Orientations Debey-Scherrer rings r Ring For random orientation, the intensities depend only on the diffraction angle 2Q! For a sample with a preffered orientation individual diffraction spots on the DS rings with inhomogeneous intensity distribution. 9

10 Powder Diffraction Intensities I hkl = ( I o /R SD2 ) m hkl F hkl 2 Pol Lor Abs Primary beam Intensity Distance Sample- Detector Polarization Factor Absorption Factor Multiplicity Factor Lorentz factor Structure Factor 10

11 Multiplicity Factors The multiplicity of the reflections reflects the point symmetry of the crystal (100) Tetragonal Crystal {100} = (100); (010); (-100); (0-1 0) {001} = (001); (00-1) c (001) 11

12 Multiplicity Factors for general reflections (hkl) 12

13 Multiplicity Factors for general reflections (hkl) Point group 2/m generates 4-symmetry equivalent objects m = 4 13

14 Multiplicity Factors for general reflections (hkl) m = 8 14

15 Multiplicity Factors for general reflections (hkl) m = 8 15

16 Polarization Factor Z Electromagnetic wave is a transverse wave I= E sc 2 = E o 2 Pol(Q) k i k f 2Q I = E 2 Y X Vertical plane Z ~ 1 Incident wave polarized in the vertical scattering plane Pol(Q) = cos(2q) Incident wave polarized in the horisontal scattering plane ½[1 + cos 2 (2Q)] Unpolarized incident wave Laboratoty X-ray tubes give unpolarized X-rays 16

17 Lorentz Factor I Geometric factor, relating the scattered intensity to the density of scattered X-ray (neutrons). Diffraction Cone 2p/l 4Q Peremeter of the circular base of the cone: C = 2pr = (4p 2 /l)sin(2q) Density of diffraction spots along the cone (homogeneous distribution) : ~ 1/ sin(2q) 17

18 Lorentz Factor II Radius of Reciprocal Sphere (RS) Q = G hkl r RS = d hkl * = 1/d hkl = (2/l)sin(Q) Density of diffraction spots on the RS ~ 1/sin(Q) Bragg equation Polycrystalline materials Lor(Q) = 1/sin(Q)sin(2Q) 18

19 19

20 Beers Law I = I o exp(-µx) The thickness x varies with 2Q! Absorption Factor Reflection Geometry A(Q) = 1 exp(-2µd/sin(q)) Transmission Geometry (Cylindrical samples) Numerical Methods 20

21 A = (1/pR 2 ) 0 R rdr 0 2p df exp[-µl(r,f,2q)] µr Collaso et al. (1998) 21

22 Structure Factor/ General Selection Rules F Q =Σ f j (Q) exp(iq.x j ) F hkl = fexp[i2p(h.0+k.0+l.0)] + Q = G hkl BCC metals fexp[i2p(h.1/2+k.1/2 + l.1/2)] = f {1 + exp[ip(h+k+l)]} h+k+l = 2n (even) F hkl = f h+k+l = 2n+1 (odd) F hkl = 0 absent!!! 1 2 Atom 1 (0,0,0) Atom 2 (1/2,1/2,1/2) 22

23 Structure Factor/ General Selection Rules F Q =Σ f j (Q) exp(i.q.x j ) Hexagonal-closed packed (HCP) Metals Atoms at (0,0,0) and (1/3, 2/3,1/2) F hkl = f{1 + exp[2pi(h/3+2k/3+l/2)]} F hkl2 = 4f 2 cos 2 [p(h/3+2k/3+l/2]] 0 h+2k = 3n and l = odd absent f 2 h+2k = 3n±1 and l = even I hkl ~ 3f 2 h+2k = 3n±1 and l = odd present 4f 2 h+2k = 3n and l = even 23

24 Structure Factor/ General Selection Rules 4 Atome in the unit cell: (0,0,0) (1/2,1/2,0); (1/2,0,1/2); (0,1/2,1/2) Fcc metals F hkl = f Cu {exp[i2p(h0+k0+l0)] + exp[i2p(h1/2+k1/2 + l0)] + exp[i2p(h1/2+k0 + l1/2)] + exp[i2p(h0+k1/2 + l1/2)]} = f Cu {1 + (-1) (h+k) + (-1) (h+l) + (-1) (k+l) } F hkl = 4f Cu F hkl = 0 if all h,k,l are even or all are odd if mixed parity

25 General Selection Rules 25

26 Systematic Absences for Screw Axes 26

27 Systematic Absences for Glide Planes 27

28 Selection of Detectors 2D detector 1D detector Dimensionality 0D Detector ( Point detector) 1D Detector (PSD detector) 2D Detector High-resolution, lower cost Quick measurement of large 2Q ranges Quick measurement of large portions of rec. space Quick investigation of preffered orientation Expensive 28

29 Point Detectors Gas-proportional Detectors X-ray photon e - Ar/Xe + Scintilator Detectors photon NaI(Tl) X-ray photon Solid State Detectors Si(Li) High Energy resolution!!! (Cooling necessary) 29

30 POSITION SENSITIVE DETECTORS 2Q range ~ 2-4 deg 2Q range ~ deg 30

31 2D Detectors Debey-Scherrer Cameras Gas Detectors CCD Cameras 31

32 Debey Scherrer Cameras Debey-Scherrer (DS) rings The DS rings are cross-section of the diffraction cones with the cylindrical surface of the film. Wet photographic processes, Densitometer (scanner) for reading of intensities 32

33 2D Gaseous Dtectors Vantec 500 (Bruker) e - X-ray photon 2D network of wires The parts of the Debey-Sherrer rings are cross-sections of the diffraction cones with the flat 2D surface of the detector o 2Q range measured simultaneously 33

34 Sn Thin Film Large crystallites 34

35 Diffraction Patterns from 2D images Strong preffered orientation of some reflections 35

36 CCD DETECTORS Gd 2 O 2 S:(Eu,Tb) 36

37 CCD DETECTORS 37

38 Powder Diffractometers Historically, first were used Point-Detectors. In order to measure many diffraction lines, movement of tube/sample/detector are necessary: Q - Q diffractometers (scans) (sample fixed) Q - 2Q diffractometers (scans) (tube fixed) Scattering condition: angle between k i and k f = 2Q 38

39 Q - Q Diffractometers Liquid Samples Molten Samples Low-Temperature/High-Temperature Furnaces Deformation Rigs Detector Tube Sample Holder Counter weights 39

40 Q 2Q Diffractometers X-ray tubes Divergent Beam Divergent Slit(s)/ Colimator(s) Smaller Colimator: Smaller Illuminated Sample Area less Divergence Receiving Slit(s) Smaller Slit: Higher Resolution Lower Intensity Diffractometer Circle Larger Radius: Less Intensity (1/R 2 ) Higher resolution 40

41 Integral Intensity Geometrical Divergence of X-ray (neutrons) Dispersion of wavelengths Distribution of I(2Q) around the ideal Brag positions 2Q B. Misorientation of crystallites Integral Intensity ~ I o m F 2 LPA L(Q B)dQ B 2Q B L(Q B)dQ B ~ MNP = V/V uc I(2Q B ) ~ Vm F 2 LPA Given phase (structure) gives a unique set of diffraction lines at specific 2Q positions and with specific integral intensities proportional to the volume of the sample (untextured samples) 41

42 Diffraction Pattern - So now what? 5000 Intensity (counts) / Peak Fitting List of d-spacings and Intensities l = nm 2Q (degrees) 42

43 Unknown (new) phase Diffraction Pattern Known (exsisting) phase Indexing as a triclinic crystal Indexing Search Match Lattice Parameters Determination Lattice Parameters Refinement Phase Indentification (using the ICDD Data Base) Space Group Determination (selection rules) Structure Determination (Patterson methods and/or Direct methods) Structure Refinement (Rietveld method) 43

44 Chemical Constraints: Ni,Ti,O 44

45 Ag(200) Ag F m-3m (fcc) Sn (200) Ag (111) Sn I 4 1 /amd Ag 3 Sn P mna Ag Sn (101) Ag3Sn (201) Ag3Sn (020) Ag3Sn (012) (211) X Sn (211) Ag 3 Sn Sn 45

46 Simple Example of Profile Fitting Intensity (counts) Peak Position Peak Intensity Integral Intensity FWHM Q (degrees) 46

47 Lattice Parameter Calculations - Example Ag 3 Sn Orthorhombic [PDF Card (a=5.968, b = , c= Å)] 1/d hkl2 = h 2 /a 2 + k 2 /b 2 + l 2 /c 2 2Q (hkl) d hkl (201) (020) b = 2d 020 = Å (211) Accurate Determination of Lattice Parameters = Multiple Reflexions + Least-Squares Rietveld 47

48 Rietveld refinement Shape memory alloy NiTi, RT Martensite 89 wt% P 2 1 /m a = 4.639(2) Å b = 4.119(2) Å c = 2.898(1) Å ß = (2)o Austenite 11 wt% P m -3 m a = 11.31(1) Å Pseudo-Voigt R wp ~ 6 % 48

DIFFRACTION METHODS IN MATERIAL SCIENCE. PD Dr. Nikolay Zotov Lecture 6

DIFFRACTION METHODS IN MATERIAL SCIENCE. PD Dr. Nikolay Zotov   Lecture 6 DIFFRACTION METHODS IN MATERIAL SCIENCE PD Dr. Nikolay Zotov Email: zotov@imw.uni-stuttgart.de Lecture 6 OUTLINE OF THE COURSE 0. Introduction 1. Classification of Materials 2. Defects in Solids 3+4. Basics

More information

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

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 7 OUTLINE OF THE COURSE 0. Introduction 1. Classification of Materials

More information

Single crystal X-ray diffraction. Zsolt Kovács

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

More information

Fundamentals of X-ray diffraction and scattering

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

More information

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 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

More information

DIFFRACTION METHODS IN MATERIAL SCIENCE. PD Dr. Nikolay Zotov Lecture 7

DIFFRACTION METHODS IN MATERIAL SCIENCE. PD Dr. Nikolay Zotov   Lecture 7 DIFFRACTION METHODS IN MATERIAL SCIENCE PD Dr. Nikolay Zotov Email: zotov@imw.uni-stuttgart.de Lecture 7 OUTLINE OF THE COURSE 0. Introduction 1. Classification of Materials 2. Defects in Solids 3+4. Basics

More information

Diffraction Basics. The qualitative basics:

Diffraction 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 information

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. 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

More information

DIFFRACTION METHODS IN MATERIAL SCIENCE. Lecture 7

DIFFRACTION METHODS IN MATERIAL SCIENCE. Lecture 7 DIFFRACTION METHODS IN MATERIAL SCIENCE PD Dr. Nikolay Zotov Tel. 0711 689 3325 Email: zotov@imw.uni-stuttgart.de Room 3N16 Lecture 7 Practicum 15.12.2016 15:15 Room 3P2! Lectures 16.12.2016 11:00 Room

More information

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 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 information

9/29/2014 8:52 PM. Chapter 3. The structure of crystalline solids. Dr. Mohammad Abuhaiba, PE

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 information

9/28/2013 9:26 PM. Chapter 3. The structure of crystalline solids. Dr. Mohammad Abuhaiba, PE

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

More information

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.

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

More information

9/16/ :30 PM. Chapter 3. The structure of crystalline solids. Mohammad Suliman Abuhaiba, Ph.D., PE

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

More information

Diffraction: Powder Method

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

More information

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, 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

More information

DIFFRACTION METHODS IN MATERIAL SCIENCE. PD Dr. Nikolay Zotov Room 2Q15. Lecture 9

DIFFRACTION METHODS IN MATERIAL SCIENCE. PD Dr. Nikolay Zotov   Room 2Q15. Lecture 9 DIFFRACTION METHODS IN MATERIAL SCIENCE PD Dr. Nikolay Zotov Email: zotov@imw.uni-stuttgart.de Room 2Q15 Lecture 9 OUTLINE OF THE COURSE 0. Introduction 1. Classification of Materials 2. Defects in Solids

More information

Atomic Densities. Linear Density. Planar Density. Linear Density. Outline: Planar Density

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

More information

Strain. Two types of stresses: Usually:

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

More information

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. 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 information

X-Ray Diffraction by Macromolecules

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

More information

X-RAY DIFFRACTIO N B. E. WARREN

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

More information

The object of this experiment is to test the de Broglie relationship for matter waves,

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

More information

TEM and Electron Diffraction Keith Leonard, PhD (1999) U. Cincinnati

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)

More information

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 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 information

X-ray Diffraction (XRD)

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

More information

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

More information

Microstructural Characterization of Materials

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

More information

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 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 information

It is instructive however for you to do a simple structure by hand. Rocksalt Structure. Quite common in nature. KCl, NaCl, MgO

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

More information

Thin Film Scattering: Epitaxial Layers

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

More information

Powder X-ray Diffraction. Brendan J. Kennedy School of Chemistry The University of Sydney

Powder X-ray Diffraction. Brendan J. Kennedy School of Chemistry The University of Sydney Powder X-ray Diffraction Brendan J. Kennedy School of Chemistry The University of Sydney State of the Art on Earth1912 Bragg s X-ray tube Laue X-ray Diffractometer State of the Art on Mars 2012 Prototype

More information

Electron Microscopy. Dynamical scattering

Electron Microscopy. Dynamical scattering Electron Microscopy 4. TEM Basics: interactions, basic modes, sample preparation, Diffraction: elastic scattering theory, reciprocal space, diffraction pattern, Laue zones Diffraction phenomena Image formation:

More information

Chapter 12 The Solid State The Structure of Metals and Alloys

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

More information

Lesson 1 Good Diffraction Data

Lesson 1 Good Diffraction Data Lesson 1 Good Diffraction Data Nicola Döbelin RMS Foundation, Bettlach, Switzerland Digital Diffractometers Transmission Geometry Debye-Scherrer Geometry Reflective Geometry Bragg-Brentano Geometry Glass

More information

Spreadsheet Applications for Materials Science

Spreadsheet 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 information

Lesson 3 Sample Preparation

Lesson 3 Sample Preparation Lesson 3 Sample Preparation Nicola Döbelin RMS Foundation, Bettlach, Switzerland January 14 16, 2015, Bern, Switzerland Repetition: Bragg-Brentano Diffractometer Typical Configuration (with Kβ filter)

More information

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

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

More information

This lecture is part of the Basic XRD Course.

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

More information

Basic X-ray Powder Diffraction (XRPD)

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

More information

Introduction to Powder Diffraction/Practical Data Collection

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

More information

Metallic crystal structures The atomic bonding is metallic and thus non-directional in nature

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

More information

X-ray diffraction

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

More information

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 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

More information

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 ) 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 information

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. 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 information

Grazing Incidence X-Ray Diffraction of Longitudinal and Perpendicular Magnetic Recording Media for HDD

Grazing Incidence X-Ray Diffraction of Longitudinal and Perpendicular Magnetic Recording Media for HDD Grazing Incidence X-Ray Diffraction of Longitudinal and Perpendicular Magnetic Recording Media for HDD Michio OHSAWA, Fuji Electric Corporate Research and Development, Ltd. ohsawa-michio@fujielectric.co.jp

More information

11.3 The analysis of electron diffraction patterns

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

More information

What if your diffractometer aligned itself?

What if your diffractometer aligned itself? Ultima IV Perhaps the greatest challenge facing X-ray diffractometer users today is how to minimize time and effort spent on reconfiguring of the system for different applications. Wade Adams, Ph.D., Director,

More information

INGE Engineering Materials. Chapter 3 (cont.)

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

More information

Diffraction: Real Samples Powder Method

Diffraction: Real Samples Powder Method Diffraction: Real Samples Powder Method Diffraction: Real Samples Up to this point we have been considering diffraction arising from infinitely large crystals that are strain free and behave like ideally

More information

Characterization of Materials Using X-Ray Diffraction Powder Diffraction

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

More information

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.   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

More information

Uses of Powder Diffraction. Diffraction

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

More information

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 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 information

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

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

More information

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

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:

More information

X-Ray Diffraction. Nicola Pinna

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

More information

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

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:

More information

Travaux Pratiques de Matériaux de Construction

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

More information

High Resolution X-ray Diffraction

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:

More information

EVOLUTION OF TEXTURE AND DISLOCATION DISTRIBUTIONS IN HIGH-DUCTILE AUSTENITIC STEEL DURING DEFORMATION

EVOLUTION OF TEXTURE AND DISLOCATION DISTRIBUTIONS IN HIGH-DUCTILE AUSTENITIC STEEL DURING DEFORMATION 36 37 EVOLUTION OF TEXTURE AND DISLOCATION DISTRIBUTIONS IN HIGH-DUCTILE AUSTENITIC STEEL DURING DEFORMATION Shigeo Sato 1), Toshiki Yoshimura 2), Nao Yamada 3) Kazuaki Wagatsuma 1), and Shigeru Suzuki

More information

X-RAY DIFFRACTION IN SEMICONDUCTOR INDUSTRY AND RESEARCH

X-RAY DIFFRACTION IN SEMICONDUCTOR INDUSTRY AND RESEARCH X-RAY DIFFRACTION IN SEMICONDUCTOR INDUSTRY AND RESEARCH M. Leszczyński High Pressure Research Center UNIPRESS, Sokolowska 29/37, 01 142 Warsaw, Poland, e-mail: mike@unipress.waw.pl ABSTRACT The paper

More information

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

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

More information

Thin Film Scattering: Epitaxial Layers

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

More information

Lesson 1 X-rays & Diffraction

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

More information

Structure of silica glasses (Chapter 12)

Structure of silica glasses (Chapter 12) Questions and Problems 97 Glass Ceramics (Structure) heat-treated so as to become crystalline in nature. The following concept map notes this relationship: Structure of noncrystalline solids (Chapter 3)

More information

Signals from a thin sample

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

More information

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 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 information

A - Transformation of anatase into rutile

A - Transformation of anatase into rutile Exercise-Course-XRD.doc 1/12 04/06/2012 A - Transformation of anatase into rutile Anatase and rutile are two distinct phases of titanium dioxide TiO 2. The stable phase is rutile. 1. Structural study Anatase:

More information

Powder X-ray Diffraction

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

More information

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) 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 information

UNIT V -CRYSTAL STRUCTURE

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

More information

Instrument Configuration for Powder Diffraction

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

More information

X-ray Powder Diffraction in Catalysis

X-ray Powder Diffraction in Catalysis X-ray Powder Diffraction in Catalysis 0/63 Introduction Introduction: scope of this lecture This lecture is designed as a practically oriented guide to powder XRD in catalysis, not as an introduction into

More information

TEM imaging and diffraction examples

TEM imaging and diffraction examples TEM imaging and diffraction examples Duncan Alexander EPFL-CIME 1 Diffraction examples Kikuchi diffraction Epitaxial relationships Polycrystalline samples Amorphous materials Contents Convergent beam electron

More information

Example: Compute the wavelength of a 1 [kg] block moving at 1000 [m/s].

Example: Compute the wavelength of a 1 [kg] block moving at 1000 [m/s]. 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 information

OPTIMIZING XRD DATA. By: Matthew Rayner

OPTIMIZING XRD DATA. By: Matthew Rayner OPTIMIZING XRD DATA By: Matthew Rayner 1 XRD Applications PANalytical classifies XRD applications in 4 groups 1. Powders 2. Nanomaterials 3. Solid objects 4. Thin films Many day-to-day samples cross these

More information

More Thin Film X-ray Scattering and X-ray Reflectivity

More Thin Film X-ray Scattering and X-ray Reflectivity Stanford Synchrotron Radiation Laboratory More Thin Film X-ray Scattering and X-ray Reflectivity Mike Toney, SSRL 1. Introduction (real space reciprocal space) 2. Polycrystalline film (no texture) RuPt

More information

Materials Science and Engineering

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?

More information

RAPID QUANTITATIVE MEASUREMENT SYSTEM FOR RETAINED AUSTENITE (Multi-PSPC System)

RAPID QUANTITATIVE MEASUREMENT SYSTEM FOR RETAINED AUSTENITE (Multi-PSPC System) The Rigaku Journal Vol. 3/ No. 2/1986 Product Information RAPID QUANTITATIVE MEASUREMENT SYSTEM FOR RETAINED AUSTENITE (Multi-PSPC System) Fig. 1. Rigaku/Rapid Quantitative Measurement System for Retained

More information

Basic Crystallography

Basic Crystallography Basic Crystallography Data collection and processing Louise N. Dawe, PhD Wilfrid Laurier University Department of Chemistry and Biochemistry References and Additional Resources Faculty of Science, Bijvoet

More information

Chapter1: Crystal Structure 1

Chapter1: Crystal Structure 1 Chapter1: Crystal Structure 1 University of Technology Laser Engineering & Optoelectronic Department Glass: 3 rd year Optoelectronic Engineering Subject: Solid state physics & material science Ass. Prof.

More information

Problems. 104 CHAPTER 3 Atomic and Ionic Arrangements

Problems. 104 CHAPTER 3 Atomic and Ionic Arrangements 104 CHAPTER 3 Atomic and Ionic Arrangements Repeat distance The distance from one lattice point to the adjacent lattice point along a direction. Short-range order The regular and predictable arrangement

More information

Practical X-Ray Diffraction

Practical X-Ray Diffraction Typical Example Practical X-Ray Diffraction White powder sample of NaCl,KCl,KNO 3 (trace of H 2 O) Département de chimie Université Laval Prof. Josée BRISSON Dr. Wenhua BI 2014-03-20 Powder X-Ray Diffraction

More information

Rietveld combined analysis: examples. Luca Lutterotti Dipartimento di Ingegneria dei Materiali e delle Tecnologie Industriali Università di Trento

Rietveld combined analysis: examples. Luca Lutterotti Dipartimento di Ingegneria dei Materiali e delle Tecnologie Industriali Università di Trento Rietveld combined analysis: examples Luca Lutterotti Dipartimento di Ingegneria dei Materiali e delle Tecnologie Industriali Università di Trento Maud program: Methodology implementation Rietveld based

More information

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 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

More information

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 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 information

Basics of X-Ray Diffraction

Basics of X-Ray Diffraction Basics of X-Ray Diffraction Crystalline materials are characterized by the orderly periodic arrangements of atoms. The (200) planes of atoms in NaCl The (220) planes of atoms in NaCl The unit cell is the

More information

Basics of XRD part IV

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

More information

MICROSTRUCTURAL CHARACTERIZATION OF NANOCRYSTALLINE POWDERS AND THIN FILMS BY X-RAY POWDER DIFFRACTION

MICROSTRUCTURAL CHARACTERIZATION OF NANOCRYSTALLINE POWDERS AND THIN FILMS BY X-RAY POWDER DIFFRACTION MICROSTRUCTURAL CHARACTERIZATION OF NANOCRYSTALLINE POWDERS AND THIN FILMS BY X-RAY POWDER DIFFRACTION Zdeněk MATĚJ a, Lea NICHTOVÁ a, Radomír KUŽEL a a Faculty of Mathematics and Physics, Charles University

More information

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 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 information

Structure factors and crystal stacking

Structure factors and crystal stacking Structure factors and crystal stacking Duncan Alexander EPFL-CIME 1 Contents Atomic scattering theory Crystal structure factors Close packed structures Systematic absences Twinning and stacking faults

More information

Microstructural parameters from Multiple Whole Profile (MWP) or Convolutional Multiple Whole Profile (CMWP) computer programs

Microstructural parameters from Multiple Whole Profile (MWP) or Convolutional Multiple Whole Profile (CMWP) computer programs Microstructural parameters from Multiple Whole Profile (MWP) or Convolutional Multiple Whole Profile (CMWP) computer programs Iuliana Dragomir-Cernatescu School of Materials Science and Engineering, Georgia

More information

TEM imaging and diffraction examples

TEM imaging and diffraction examples TEM imaging and diffraction examples Duncan Alexander EPFL-CIME 1 Diffraction examples Kikuchi diffraction Epitaxial relationships Polycrystalline samples Amorphous materials Contents Convergent beam electron

More information

Basics of X-Ray Powder Diffraction

Basics of X-Ray Powder Diffraction Basics of X-Ray Powder Diffraction Scott A. Speakman, Ph.D. For assistance in the X-ray lab, please contact Charles Settens settens@mit.edu Scott A. Speakman, Ph.D. http://prism.mit.edu/xray Training Required

More information

X-Ray Analytical Methods

X-Ray Analytical Methods X-Ray Analytical Methods X-rays were discovered by W.C. Röentgen in 1895, and led to three major uses: X-ray radiography is used for creating images of light-opaque materials relies on the relationship

More information

Lecture course on solid state physics for Nano, 2019

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

More information