DIFFRACTION METHODS IN MATERIAL SCIENCE. Lecture 7

Transcription

1 DIFFRACTION METHODS IN MATERIAL SCIENCE PD Dr. Nikolay Zotov Tel Room 3N16 Lecture 7 Practicum :15 Room 3P2! Lectures :00 Room 3P2!

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 Texture Analysis Pole Figures Measurement of Pole Figures Characteristics of Textures Examples Diffraction Studies of Thin Films Grazing Incidence X-ray Diffraction (GIXRD) X-ray/Neutron Reflectivity 3

4 TEXTURE ANALYSIS Texture is the distribution of the orientations of grains in a polycrystalline sample Every colour different crystallite orientation Orientaionn Distribution Function (ODF) ODF(g) = 1/V V(g)/ g; g =f,y,q - Euler angles describing the orientaion of the sample 4

5 Representation of Texture Pole Figures Measuring grid North Pole Reference Sphere Bunge South Pole Pole figure = variation in the diffracted intensity with respect to the orientation of the crystallites. 5

6 Representation of Texture Pole Figures 6

7 Measurements of Texture X-rays, neutrons (Monochromatic Beam) # Eulerian Cradle # Point Detector or 2D detector (Image Plate, CCD) Neutrons Time-of-Flight X-ray Neutrons Surface texture Bulk Texture 7

8 Texture Measurements with Eulerian Cradle and Point Detector Modes w - f y(c) - f Reflection geometry (Horisontal Scattering Plane) Full Eulerian Cradle 8

9 Texture Measurements with Image Plate (CCD) Reconstruction of Pole figures from Intensities along the partial Debye rings 9

10 g-tial alloy Determination of Texture from 2D Measurements (111) Pole Figures Bob He, Bruker (2011) 10

11 Texture Measurements with Neutrons (TOF) Simultaneous measurement of different scattering angles Measurement of Bulk Texture 11

12 Limestone, LANSCE (USA) Wenk (2001) 12

13 Reconstruction of Pole Figures from Neutron Diffraction Experiments Limestone 13

14 Characteristics of Textures Types Random Texture (no prefered orientation) Fiber Texture Single-Crystal-like Texture Deformation Textures in cold(hot)-rolled metals/alloys (Distribution of grains with a given hkl) Strength of Texture (Number of grains with a given orientation) Shrapness of Texture (Variations of the individual grains around the average orientation) 14

15 Types of Texture Single-Crystal-like Textures Typical for epitaxial thin films 15

16 Types of Texture Ag 200 Fiber Texture (crystallites tilted ~ 55 o with respect to surface with random orientation in the plane of film) Single-Crystal Texture (crystallites oriented mostly with (100) planes paralell to the surface) 16

17 TYPES OF TEXTURES Deformation Textures in Mecanically-cycled NiTi Shape Memory Alloy Individual Pole Figures Zotov (2014) 17

18 f = f 1 y = F 18

19 Orientation Distribution Functions Brass Deformation Texture ODF(f 1,F,f 2 ) 19

20 20

21 TYPES OF TEXTURES Deformation Textures in Mecanically-cycled NiTi Shape Memory Alloy (BCC) ODF 21

22 Cold-Rolled Austenitic Steel Morikawa et al., Mater. Trans. (2010) 22

23 Examples of Strength and Sharpness Ag 200 Stronger/sharper Weaker/more diffuse 23

24 Single-Crystal Texture NiW (111) Textures Bachmann et al. (2012) Sharpness of Texture increases with annealing time 24

25 Classification according to Dimentionallity Bulk Materials (single crystals) Polycrystalline/Microcrystalline Materials Thin Films (polycrystalline; single-crystal or amorphous) Single-Layer Multilayer Nanostructures 25

26 Specific Diffraction Methods for Thin Films Small thickness of the TF Small Diffraction Volume Weak signal/noise ratios Strong Effect of Substrate Grazing Incidence X-ray/Neutron Reflectivity Reciprocal Space Mapping Rocking curves Penetration Depth (63% absorption) sin(a)sin(2q-a) t 63 = µ[sin(a) + sin(2q-a)] Gold, CuK a, m 4000 cm -1 Penetration depth (mm) 10 0 a=2q/2 a=20 o a=10 o a=5 o a=2 o a=1 o Diffraction angle ( o 2Q) 26

27 Grazing Incidence Method Principle Conventional Geometry/Scan Q/2Q Relatively large wavelength (small absorption) 2Q Stationary Primary Beam making very small angle with the sample (0.1 5 o ) Only Detector (2Q) Scan 27

28 Parallel Beam 28

29 Conventional X-ray Diffraction only grains with hkl parallel to the surface (blue) Grazing Incidence X-ray Diffraction all grains 29

30 Examples of Grazing Incidence Diffraction Ti coated with Hydroxyapatite (HA) Large a Small a 30

31 CdSSe on Graphite Substrates Only Graphite Peaks! Q-2Q scan Grazing Incidence 31

32 Ti Anodization Kosanovic (2012) 32

33 In-situ Growth of Ag and Sn Thin Layers Grazing Incidnce Ag 3 Sn(100) Ag 3 (020) Ag 3 Sn (012) Ag 3 Sn(221) ANKA Synchrotron Source l = 1.0 Å a = 4 o Time (s) Depostion first of Sn Deposition of Ag on top Sn is textured I 200 < I 101 No Ag peaks! Diret formation of Ag 3 Sn T (degrees) Sn(200) Sn (101) Sn(220) Sn(211) 33

34 Grazing Incidence of aged In-Ag Bilayers AgIn 2 Ag 2 In Ag Rossi, Zotov (2016) 34

35 Applications of Grazing Incidence Diffraction Thin film Phase Analysis Oxidation products Corrosion Products Monitoring In-situ TF Deposition Near-Surface Depth Profiling Orientation of TF with respect to substrate 35

36 X-ray/Neutron Reflectivity from TF and Multilayers Q/2Q scans, but both Q and 2Q are small r 1 r 2 Dr = r 1 - r 2 Constructive interference of X-rays/Neutrons scattered from the differen (layers/interfaces). 36

37 Effect of Surface/Interface Roughness J. Daillant, A. Gibaud, X-ray and neutron reflectivity- Principlesand Applications, p

38 Effect of Surface/Interface Roughness Roughness chemical gradients geometrical roughness 38

39 Reflectivity Examples Sardela (IUC) 39

40 Kiessig fringes m=1 m=2 Kiessig fringes: Q 2 a c2 = m 2 (l/2d) 2 m is the number of the corrsponding maximum 40

41 Rafailovic et al. (2009) 41

42 Fiting of Reflectivity Data Intensity (a.u.) Edge of TER Kiessig oscillations (fringes) ,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 Diffraction angle ( o 2 ) Mo Mo Mo W Si r t [Å] s [Å]

43 X-ray Reflectivity Applications Determination of Thicknesses Determination of Interface Roughnesses Density Fluctuations Roughness Correlations Determination of Refractive Indeces 43

44 Sources O. Engler, V. Randle, Introduction to texture analysis, 2000 H.J. Bunge, Texture analysis in material science, 1982 J. Daillant, A. Gibaud, X-ray and Neutron Reflectivity, Springer Practicum :15 Room 3P2 Lectures :00 Room 3P2 44