diffraction methods in material science ... of the course 0. introduction 1. classification of...
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OUTLINE OF THE COURSE0. 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
9. Practical Aspects
OUTLINE OF TODAY‘S LECTURE
Phase Identification
Texture measurements
Point Groups
Preparation for the Examination
Phase Identification
Chemical Composition
Unknown Known
Automatic Search-Match Select Elements
Search-Match with Restrictions
Expected Phases
Find PDF Numbers
Compare with Experiment
Phase Identification
Phase Identification
Search-Match with Elements (La, Fe, Co, O)
Sample prepared by
Thermal Spraying
Phase Identification
Crystal System Rhombohedral
Space Group R -3c
Point Group 3m
Diffrences to the cubic phase
# shifts of some stong peaks
# presence of additional very weak peaks
Comparison with PDF File (1-082-1964)
a
b
Point Group -3m = -3 2/m
Indexing
Bragg Law sin2(Q) = l2/4d2
For cubic materials 1/d2 = (h2 + k2 + l2)/a2
sin2(Q) = l2/4d2 = const((h2 + k2 + l2)
sin2(Q)/sin2(Q)min = (h2 + k2 + l2)/N
Nsin2(Q)/sin2(Q)min = (h2 + k2 + l2) integer
sin2(Q) sin2(Q)/sin2(Q)min (h2 + k2 + l2) h k l
0.04 1 1 1 0 0
0.08 2 2 1 1 0
0.12 3 3 1 1 1
0.158 ~4 4 2 0 0
0.198 ~5 5 2 1 0
0.236 ~6 6 2 1 1
LaFe0.6Co0.4O3 Cubic PDF 40-0224
sin2(Q) sin2(Q)/sin2(Q)min (h2 + k2 + l2) h k l
0.04 1 1 1 0 0
0.08 2 2 1 1 0
0.12 3 3 1 1 1
0.158 ~4 4 2 0 0
0.198 ~5 5 2 1 0
0.236 ~6 6 2 1 1
La0.5Sr0.5Fe0.6Co0.4O3(Rhom) → La(Fe,Co)O3 + SrLaFeO4+ Fe0.6Co0.4 + La2O3
Phase IdentificationExpected Phases
FeOFe2O3
Co3O4
CoOSrO2
Processes during deposition – Decomposition and reduction to metals
La0.4Sr0.6Fe1-yCoyO3
Cubic; a = 3.911(1) Å
+
Sr0.9La1.1FeO4
Tetragonal; a = 3.8796(3) Å
c = 12.788(3) Å
Quantitative Phase Analysis
Rietveld
X-ray tube
Sample holderEulerian cradle
Ge monochromatorin the scattered beam
Detector
Slit (5 x 5 mm)2Q axis
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TEXTURES
TEXTURES
# Align Sample (Height determination)
# Q/2Q Scan; Select (hkl)
# Additional scan(s) of this reflection
Fit of peak position
# Set Q/2Q at the position of the selected
reflection
# Define the steps Df (5o) and Dy (1o)
# Select Time per step (s)
# Measure pole figure
f in the range 0 – 360
Y in the range 0 – 85
Low-Q reflections stronger
Ag Thin Film
(111)
(200)
Time = 30 s/step
Background/Peak Ratio large due to
small volume of sample
Select (111) peak
Fiber Texture with 2 components:
# Crystallites with (111) planes paralell to the surface
# Crystallites with (111) planes at 55o to the surface
Ag Thin Film
Fcc Lattice
Multgiplicity
m(hhh) = 8
m(h00) = 6
General Condition
Why are the (hhh) reflections stronger?# Structure factor# Multiplicity
TexturesCu Foil
(200)
In this Cu foil:
(111) very very weak
(200) very strong
In this Cu foil:
(111) very weak
(200) very strong
Clear indication for texture
General condition
The (200) was very strong → time 5 s/step
Cu Foil
Profile Fitting
! WinPLOTR profile fitting results:
! data file: Zotov_T2T_1cu200.ASC
!
!
! 2theta(deg.) sig_2theta d(A) Intensity sig_int
!--------------------------------------------------------------------------------
59.338 0.001 1.55619 3423 16
h = 0.354
Pseudo-Voigt Function
pV = hL + (1-h)G
Ka1 + Ka2
D = l/ßcos(Q)
ß = 0.442o 2Q; ß = 0.0077 rad
D = 1.79/(0.0077*cos(29.669)) =
= 26.8 nm
Scherrer Calculator
D = kl/ßcos(Q)
k – Shape Factor
k = 4pArea/Perimeter2 ;
k = 1 spherical nanoparticles
(grains)
TexturesCu Foil
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Rolling (Deformation) Textures
Typical fcc texture-components
(111) (200)
(111) (200)
Leffers & Ray (2009)
Leffers & Ray (2009)
Point Groups
Crystal System 32 Point Groups (Crystal Classes)Orientation rules!!!
Triclinic 1, -1
Monoclinic 2; m, 2/m;
b || 2
Orthorhombic 222, mm2, 2/m 2/m 2/m
(|| a || b || c)
Tetragonal 4, -4, 4/m, 422, 4mm, -42m, 4/m 2/m 2/m
(|| c || b || [110] )
Hexagonal 3, -3, 32, 3m, -32/m, 6, -6, 6/m, 622, 6mm, -6m2,
6/m 2/m 2/m
(|| c || a || [1-10] )
Cubic 23, 2/m 3, 432, -43m, 4/m -3 2/m
(|| a || [111] || [1-10] )
The symmetry elements are oriented in different direction in the unit cell!!!
Symmetry Elements
Point Groups
How we know there is a an inversion centre?
# N-fold rotational axis ┴ Mirror plane
always generates inversion centre
# -3 generates an inversion centrem
n
11 centro-symmetric point groups
−1 2/m mmm 4/m 4/mmm −3 −3m 6/m 6/mmm m−3 m−3m
Point Groups
m ┴ m → 2-fold axis2 ┴ m → Inversion centre
mmm
Point Groups
Number of independent symmetry elements?
Point Group symbol: a b c
Symmetry elemnt a paralell (perpendicular) to 1st direction
Symmetry elemnt b paralell (perpendicular) to 2st direction
Symmetry elemnt c paralell (perpendicular) to 3rd direction
422
4 || Z
2 || [010]
2‘ || [110]
The point groups contain (usually) more symmetry operations than given in the
Point group symbol.
SingleCrystals
Amourphous Materials
Polycrystalline Materials
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Diffraction
Basic Recommended Literature
● Modern Diffraction Methods
Eds. E.J. Mittemeijer, U. Welzel, Wiley VCH 2013
● Fundamentals of Materials Science
E.J. Mittemeijer, Springer-Verlag, 2010
● X-ray Diffraction by Polycrystalline Materials
R. Guinebretiere; Wiley, Online Library, 2010
http://onlinelibrary.wiley.com/book/10.1002/9780470612408
● Diffraction Methods in Material Science
Ed. J. Hasek; Nova Science Publishers, 1993
● Elements of Modern X-ray Physics
J. Als-Nielsen & Des McMorrow; John Wiley and Sons, 2001
● Physics of Amorphous Materials
Stephen Elliot; Longman Scientific
● Diffraction Physics
J. Cowley; Elsevier 1995
# Consultations: 27.02 11:00 – 12:00, Room 2P4
# 01.03.2018 2P4 10:00
Written Exam, 90 min
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EXAM