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 7

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 Orientation Distribution Function (ODF) ODF(g) = 1/V V(g)/ g; g =f, Q,y - Euler angles describing the orientaion of the sample Relative volume fraction of crystallites with orientation g, g + dg 4

5 Representation of Texture Stereographic Projections North Pole Z P y Reference Sphere Z P f Y X y/2 South Pole [001] Z 5

6 Representation of Texture Pole Figures 6

7 Representation of Texture Pole Figures Measuring grid Bunge Pole figure = variation in the diffracted intensity as a function of the orientation of the crystallites given as points on a stereographic projection. 7

8 Measurements of Texture Source (hkl) Q Q Detector A B Tilt of Sample y Bragg equation: 2d hkl sin(q) = l 8

9 Measurements of Texture measured Intensities: I hkl (f,y) Intensity of powder specimens I hkl ~ V I hkl (f,y) ~ V(f,y) Reflection geometry The intensity at every point (f,y) is proportional to the Volume of the crystallites with this orientation 9

10 X-rays, neutrons (Monochromatic Beam) # Eulerian Cradle Measurements of Texture # Point Detector or 2D detector (Image Plate, CCD) Neutrons Time-of-Flight X-ray Electrons Neutrons Surface texture Bulk Texture 10

11 Texture Measurements with Eulerian Cradle and Point Detector Reflection geometry (Vertical Scattering Plane) Modes w - f y(c) - f Full Eulerian Cradle 11

12 Texture Measurements with Eulerian Cradle and Point Detector 1/4 Eulerian Cradle X-ray Tube X-Y-Z Table f Colimator for parallel beam Scinti Detector Graphite Monocromator Colimator 12

13 Texture Measurements with Image Plate (CCD) Reconstruction of standard pole figures from Intensities along the Debye rings measured at different w; Mapping (h,w) (f,y) 13

14 Determination of Texture from 2D Measurements g-tial alloy (111) Pole Figures Bob He, Bruker (2011) 14

15 Texture Measurements with Neutrons (TOF) w Only w rotations necessary Simultaneous measurement of different scattering angles at different banks (panels) of detectors simultaneous measurement of different pole figures Measurement of Bulk Texture 15

16 Limestone, LANSCE (USA) Wenk (2001) 16

17 Reconstruction of Pole Figures from Neutron Diffraction Experiments Limestone 17

18 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) 18

19 Types of Texture Single-Crystal-like Textures Y Typical for epitaxial thin films {100} <100>Textur X 19

20 Types of Texture Ag 200 Fiber Texture (crystallites tilted ~ 55 o with respect to the surface with random orientation in the plane of film) Single-Crystal Texture (crystallites oriented mostly with (100) planes paralell to the surface) 20

21 TYPES OF TEXTURES Deformation Textures in Mecanically-cycled NiTi Shape Memory Alloy Individual Pole Figures Zotov (2014) 21

22 Types of Textures Cold-rolled textures (111) (200) Typical fcc Texture Components Leffers & Ray (2009) (111) (200) Leffers & Ray (2009) 22

23 Cold-Rolled Austenitic Steel Morikawa et al., Mater. Trans. (2010) 23

24 Examples of Strength and Sharpness Ag 200 Stronger/sharper Weaker/more diffuse 24

25 Single-Crystal Texture NiW (111) Textures Bachmann et al. (2012) Sharpness of Texture increases with annealing time 25

26 f = f 1 y = F 26

27 Orientation Distribution Functions Brass Deformation Texture ODF(f 1,F,f 2 ) 27

28 28

29 TYPES OF TEXTURES Deformation Textures in Mecanically-cycled NiTi Shape Memory Alloy (BCC) ODF Calculation of ODF requires at least 3 different pole figures 29

30 Classification according to Dimentionallity Bulk Materials (single crystals) Polycrystalline/Microcrystalline Materials Thin Films (polycrystalline; single-crystal or amorphous) Single-Layer Multilayer Nanostructures 30

31 Specific Diffraction Methods for Thin Films Small thickness of the TF Small Diffraction Volume Weak signal/noise ratios Strong Effect of the Substrate Grazing Incidence X-ray/Neutron Reflectivity 31

32 Reflection geometry a f = a i = Q Specific Diffraction Methods for Thin Films Penetration Depth I = I o A(Q) = I o [1-exp(-2µt/sin(Q)] a i a f = 2Q -a i 0.63 = I/I o = 1-exp(-2µt 63 /sin(q)] t 63 ~ sin(q)/2µ Penetration Depth (63% absorption) Reflection geometry; a f a i sin(a i )sin(2q-a i ) t 63 ~ µ[sin(a i ) + sin(2q-a i )] Gold, CuK a, m 4000 cm -1 Penetration depth (mm) 10 0 a=2q/ a=20 o a=10 o a=5 o a=2 o a=1 o Diffraction angle ( o 2Q) 32

33 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 33

34 Grazing Incidence Method Principle Parallel Beam 34

35 Grazing Incidence Method Principle 35

36 Examples of Grazing Incidence Diffraction Ti coated with Hydroxyapatite (HA) Large a Small a 36

37 CdSSe on Graphite Substrates Only Graphite Peaks! Q-2Q scan Grazing Incidence 37

38 Ti Anodization Kosanovic (2012) 38

39 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) 39

40 Grazing Incidence of aged In-Ag Bilayers AgIn 2 Ag 2 In Ag Rossi, Zotov (2016) 40

41 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 41

42 X-ray/Neutron Reflectivity from TF and Multilayers Q = 4psin(Q)/l Q << G hkl Reflection Transmission Absorption Vacuum/Air Q (hkl) 0 a i TF Substrate a f = 2Q -a i 42

43 X-ray/Neutron Reflectivity from TF and Multilayers Z r = E r /E o Snell Law cos(a i ) = ncos(a t ) n - Refractive index d - Dispersion term ß - Absorption term d = (l 2 /2p) r e r ; ß = (l/4p) µ; r Density of the material r e = 2.81 x m Transmited wave possible only if cos(a t ) 1; a i a c Critical angle a c = (2d) ½ ; a i a c Total external reflection Scattering vector: Q Z = (2p/l)[sin(a i ) + sin(a f )] Q c = (16pr e r) ½ I ref = rr* = r 2 43

44 X-ray/Neutron Reflectivity from TF and Multilayers Constructive interference of waves reflected from the different layers (j) Amplitude of total reflected wave r = S r j,j+1 exp(iq Z z j ) For large number of sharp layers r ~ 4pr e /Q Z2 [ r(z) z] exp (izq z ) dz = = 4pr e /Q Z2 FT [ r(z) z] R = r 2 ~ Q Z 4 Salamon et al. (2013) 44

45 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 45

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

47 Effect of Surface/Interface Roughness Roughness chemical gradients geometrical roughness 47

48 Reflectivity Examples Sardela (IUC) 48

49 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 49

50 Rafailovic et al. (2009) 50

51 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]

52 X-ray Reflectivity Applications Determination of Thicknesses Determination of Interface Roughnesses Density Fluctuations Roughness Correlations Determination of Refractive Indeces 52

53 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 53