luca lutterotti department of materials engineering and ...chateign/formation/course/... · •...
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Line broadening analysis
Luca Lutterotti
Department of Materials Engineering and Industrial Technologies
University of Trento - Italy
Informations: microstructure• Crystallite sizes, anisotropic, distribution• Microstrain (III kind), distribution, dislocation or point defects density• Antiphase domains (intermetallics…)• Stacking and deformation faults probability, intrinsic, extrinsic
Crystallites distribution
Line broadening methodsAre based on profile analysis:
• Crystallites and microstrain have a different broadening behavior in 2theta
Several methods available:• Scherrer equation (1918):
• Williamson-Hall plot• Warren-Averbach or Fourier analysis• ......
Instrumental broadening must be subtractedTwo reflections are needed to separate crystallite and microstrain broadeningMore reflections for anisotropic broadening
Planar defects analysis was developed by Warren (see book)
The Warren-Averbach analysisWarren treatment for a 00l peak:
(Stokes treatment: A=ASA
I)
Fourier coefficients:
Get the profiles for Fourier transformWe need two peaks of different order, same hkl direction
W-A continue.....
Planar faults
No faults assumed
Stacking and deformation faults
Order-disorder transition in intermetallicApplications:
• High temperature structural material• Oxidation resistance• Blade material for Gas turbine
Main problem:• Ductility (forming and shaping)• Brittle at low temperature
Disordered phase is more ductile
Materials:• FeAl, Ni3Al, NiAl, TiAl...
Disordering FeAl by ball-milling
0
50
100
150
200
30 40 50 60 70 80 90 100
Inte
nsity
-1/2
[cou
nts-1
/2]
2θ [degrees]
0.5 h
1.5 h
3 h
6 h
12 h
0 h
Faults effect
0
100
200
300
400
500
70 75 80 85 90 95 100
Inte
nsity
(cou
nts)
2θ (degrees)
a)
70 75 80 85 90 95 1002θ (degrees)
b)
Anisotropic size model Faulting model (Warren)
Defect analysis on ball-milled FeAl
FeAl annealing (neutron-XRD meas.)
0.000
0.200
0.400
0.600
0.800
1.000
0.00
0.01
0.02
0.03
0.04
0.05
0 100 200 300 400 500 600 700 800
LRO XRD (RT measurments)LRO neutron
Deformation faultsMicrostrainAntiphase
LRO
Defects
Temperature [ÞC]