Wednesdays at One
Transcript of Wednesdays at One
X RAY DIFFRACTION 101X-RAY DIFFRACTION 101
Wednesdays at OneUNL REU in Nanomaterials andUNL REU in Nanomaterials and
Nanoscience
Jeff ShieldDepartment of Mechanical EngineeringDepartment of Mechanical Engineering
University of Nebraska
What we can discoverWhat we can discover . . .
C t l t t i•Crystal structures: size and shape of unit cells•Atomic positions •Determine phases present p
and their relative amounts•Crystal orientation (“texture”)
•Grain/crystal sizes•Grain/crystal sizes•Residual stress/strain
But first some crystallographyBut first, some crystallography. . .
“Peroidicity”:Peroidicity :equal, predictable spacing between atoms
“C t l” P idi 3D f t“Crystal”: Peroidic 3D array of atoms
More definitionsMore definitions
“Unit Cell”:Unit Cell :Smallest, most symmetric part of crystal
• Requirements: Shape of unit cell must completely fill spacecompletely fill space
Bravais LatticeBravais LatticeDescribes how to “decorate” the
seven crystal systemsy ySimple (Primitive)—P Body-centered—I Face centered FFace-centered—F
Cubic: P, I, F
T t l P ITetragonal: P, I
Hexagonal: P
Rhombohedral: R
Orthorhombic: P, I, F, C
Monoclinic: P, C
Triclinic: P
Back to X-raysBack to X raysX-radiation: Part of electromagnetic spectrum
Why can x-rays be used to analyze crystals via diffraction?Answer: Their wavelength is of the same order as the distance between atoms
X-ray GenerationX ray GenerationLaboratory-scale:
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X-ray “Tube”0 V
e-
e-
X
Target
X-rays
-40 kV Target
Characteristic X-raysCharacteristic X raysIncoming electrons ionize atomsRelaxation leads to emission of x-ray e- e-
ΔECharacteristic of atome
e-
eΔE
e-
e-
e-
e-
X-ray
Need to isolate one wavelength:Need to isolate one wavelength:“Monochromation”
Bragg’s LawggSo, conditions for constructive interference (“DIFFRACTION”)
Path difference = λ
•Ray A’C’ travels farther than AC by the distance shown in red•Each red segment is dsin θ in length
•So, diffraction occurs when
λ= 2dsin θλ= 2dsin θ
Diffraction Experimentsp“Bragg-Brentano” geometry
Diffraction angle is changed systematically-either sample and detector rotate, or source and point
detector rotate
Source Detector
Diffraction PatternsDiffraction Patterns700080009000
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y100020003000400050006000
Inte
nsity
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Two Theta
P k t d h diff ti diti ti fi dPeaks are generated when diffraction conditions satisfiedEach peak is from a different set of planes in the crystalIn a powder or polycrystalline material, there will be peaks from all possible planesp p
Alternatively, detection by an “AREA DETECTOR” captures all diffraction peaks at once
Quick but detectors are expensiveQuick, but detectors are expensive
Diffraction Experimentsp“Debye-Scherrer” geometry
Powder sample is hit with x-rays
Sample
AreaD t tDetector
Diffraction PatternsDiffraction Patterns
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•Crystals with different
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Bravais lattices will have different diffraction patterns•Two crystals can have
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Two Theta
Two crystals can have the same Bravais lattice, but they will always have different lattice
t
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Thus, diffraction patterns are UNIQUE to
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pa given crystal (aka,
phase)
“PHASE ANALYSIS”0
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PHASE ANALYSIS
Diffraction Peak PositionsDiffraction Peak Positions
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Peak positions
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p
•λ=2dsin θ
•For cubic materials:0
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20 40 60 80 100 120
Two Theta
•For cubic materials:
d=a/(h2+k2+l2)½
•So, knowing {hkl}, you can find a!
Diffraction Peak IntensitiesDiffraction Peak IntensitiesThe peak intensities tell us two primary things:p p y g
1. Atom positions
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2. Crystal orientation
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Diffraction Peak Intensities: Atom Positions
The intensity of a given diffraction peak {hkl}:
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y g p { }
I = KןF 2p ן
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nsityK is a constant for a peak
F is the structure factor
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Two Theta
p is the multiplicity
Two Theta
d t itixi, yi and zi are atom positionsf is the atomic scattering factor—depends on atom type and diffraction angle
Diffraction Peak Intensities: Orientations
I = KןF 2p ן
i th lti li it Random orientationp is the multiplicity
“p” is usually assumed
Random orientation
p yfor random orientation. If non-random, p depends on the degree of crystal
Non-random orientation
on the degree of crystal orientation
Diffraction Peak WidthsDiffraction Peak Widths
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Peak widths tell
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Inte
nsityus:
1 Crystallite size0
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Two Theta
1. Crystallite size
2. Strain
•Smaller grains/crystals → broader peaks•More strain → broader peaks
X-ray DiffractionX ray DiffractionTells us a lot about our material
Crystal/atomic structureOrientationGrain sizeGrain size
Stress/strain
Lots more possible!!!Lots more possible!!!• In situ experiments (temperature, stress, etc.)• High-intensity sources (Synchrotron sources)