Transcript SANS investigation of materials for high

Scattering contrast dependence on
thermal-expansion-coefficient difference
of phases in two-phase system
P. Strunz1,2, R. Gilles3, D. Mukherji4, M. Hofmann5, D. del Genovese4,
J. Roesler4, M. Hoelzel3 and V. Davydov1
Physics Institute, CZ-25068 Řež near Prague ([email protected])
2Research Centre Řež, CZ-25068 Řež near Prague, Czech Republic
1Nuclear
3TU
München, ZWE FRM-II, Lichtenbergstr. 1, D-85747 Garching, Germany
4TU
Braunschweig, IfW, Langer Kamp 8, D-38106 Braunschweig, Germany
5TU
Darmstadt c/o FRM II, Lichtenbergstr. 1, D-85747 Garching, Germany
Outline
 Observation of SANS
intensity increase
 Theory
 Simulation
 Experiment
• diffraction
• SANS
 Prospective application
Project supported by the European Commission under the 6th Framework Programme through the Key Action:
Strengthening the European Research Area, Research Infrastructures. Contract n°: RII3-CT-2003-505925 '
May 1, 2020
1
SANS – tool for microstructural characterization
 Microstructural characterization: essential part in any alloy development
 Neutron scattering: increasingly complementing XRD, SEM, TEM
10000
DA
ST
MST
MST-1
-1
-1
d/d (cm sr )
1000
scattering caused by
 γ’ precipitates (ordered fcc L12 crystal structure)
 coherently embedded in γ
matrix (crystal structure fcc A1)
100
10
1
0.1
azimuthal average
0.01
1E-3
0.01
0.1
-1
Q (Å )

DT706 superalloy (wt.%: Fe=22,
Cr=18, Nb=2.9, Ti=1.9, Al=0.55,
C=0.03, Ni = balance)
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2
SANS data intensity in “low”-temperature region
 Increase of the integral SANS intensity from γ' precipitates at low
1061K = 788°C
1107K = 834°C
and intermediate temperatures during the temperature decrease
 DT706 (SINQ, SANS-II)
 17% increase, nearly linear
PSI (SANS-II), DT706
0.014
Integral intensity (rel. units)
0.012
coolin
g
0.010
0.008
formation of
' precipitates
Integral intensity
0.006
0.004
heating
Possible cause
 volume fraction change of γ’
 change in the size
distribution of γ’ precipitates
 γ’ scattering contrast
change
0.002
400
600
800
1000
1200
1400
temperature (K)
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3
scattering contrast change
 scattering length densities (SLD) m,p=[bm,p]/am,p3 (matrix, precip.)
 [bm], [bp] not changed but am, ap change with temperature
 Can it significantly change the scattering contrast?
 T    p T    m T 
2
2
 bp bm 
 3
 3 
 a T  a T  
m
 p

2
 Answer: yes, under certain circumstances
 Circumstances (fulfilled in superalloys)
 low Δ with respect to 
 high volume fraction (to make SANS visible)
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Theory – scattering contrast
 Scattering contrast of a two-phase system
 T 
2
  p T    m T 
2
 bp bm 

 3
 3
 a T  a T  
m
 p

2
 [bm], [bp] usually unknown, but temperature independent
 known [b]alloy
 c … volume fraction of γ’ precipitates
 T 2
 1
 bp balloy 
 3





1  c(T )  a p T  vc T , c  
2
vc T , c  
1
1 c
c

am3 T  a3p T 
(
 the average unit cell volume
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Theory - integral SANS intensity
when a part of the assymptotic (Porod) region is used:
 the shape of the scattering curve cannot change (Porod law)
 only the dependence of the specific interface and sample
thickness on the temperature has to be taken into account =>
 a p T  
  T 2
I T   C2 
 3 v T , c  
 c

2
 where all T-independent parameters are in the constant C2
 the ratio (ap/νc1/3)2 is only marginally temperature dependent
=> temperature dependence of intensity driven by numerator
in the scattering contrast form:
 bp balloy 
 3


 a T  v T , c  
c
 p

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Scattering contrast simulation
 using lattice parameters of γ and γ’ determined in DT706
 the temperature dependence for various [Σb]p (fixed [Σb]alloy)
 volume fraction fixed (c=0.1)
2
 (T) simulation
c=0.1
balloy=3.34076E-12 cm
1E20
bp [cm]
 increasing / decreasing
3.8E-12
3.0E-12
3.55E-12
1E19
3.25E-12
3.42E-12
3.33E-12
3.38E-12
3.372E-12
3.366E-12
3.35E-12
-4
 (T) (cm )
1E18
2
1E17
1E16
3.36E-12
1E15
temperature
dependence determines
which SLD (precipitate
or matrix) is smaller
 strong correlation “curve
shape” – “magnitude of
the scattering contrast”
1E14
0
100
200
300
400
500
600
700
800
900
1000
temperature (°C)
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Scattering contrast simulation
 volume-fraction change simulation:
 change of the curve due to [Σb]p change can be nearly
equivalently achieved by changing c
2
 (T) simulation
bp [cm]
balloy=3.34076E-12 cm
1E20
c=0.10 3.0E-12
-4
 (T) (cm )
c=0.75 3.25E-12
=>
 [Σb]p and volume
fraction of precipitates
are correlated
parameters
c=0.5 3.25E-12
c=0.25 3.25E-12
c=0.10 3.25E-12
2
1E19
c=0.01 3.25E-12
3.33E-12
1E18
0
100
200
300
400
500
600
700
800
900
1000
temperature (°C)
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Experimental and results - Diffraction experiment
 DT706 samples
 in-situ at elevated temperatures at FRM-II (SPODI and
StressSpec)
 Initial heat treatment:
 solution treatment step at 1080°C for 2 h (dissolve γ’)
 stabilization step at 835°C for 10 h (new population of γ’
precipitates)
 In situ measurement:
 temporary stops (≤2 h) during the temperature decrease
(700, 600, 500, 400, 300, 200, 100°C, RT)
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Measured and fitted data (n/100s)
Experimental and results - Diffraction peaks
10000
Measured intensity
Fit
Deconvoluted profile
DT706
StressSpec
311
100°C
8000
6000
2000
and 331 (SPODI)
0
103.0
103.5
104.0
104.5
105.0
105.5
106.0
106.5
107.0
Measured and fitted data (n/100s)
2 (°)
300
DT706
SPODI
331
400°C
Measured intensity
Fit
Deconvoluted profile
 instrumental profile
deconvoluted using
ProfEdgeReal program
250
200
150
 γ’ peaks: 10% of γ peaks
100
50
0
135
 Figs.: γ and γ’ double peaks
recorded at StressSpec and
SPODI
450
350
range (separation of the γ and
γ’ peaks)
 reflection 311 (StressSpec)
4000
400
 Largest accessible anglular
136
137
138
139
2 (°)
140
141
142
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Experimental and results – lattice parameters
3.67
0.006
 Combination of the
DT706, SPODI and StressSpec results
3.66
0.005

3.64


fit
fit
0.004
3.63
0.003
3.62
3.61
0.002
misfit
3.60
0.001
misfit (dimensionless)
lattice parameter (Å)
3.65
data obtained form
both SPODI and
StressSpec
=> the evolution of the
lattice parameters
and misfit (RT-835°C)
3.59
3.58
0
200
400
600
800
1000
0.000
1200
Temperatutre (°C)
 Approximation of lattice parameter by quadratic polynomial
 am(T) = 3.585155 + 4.5891E-5×T + 2.1355E-8×T2
 ap(T) = 3.598196 + 4.1247E-5×T + 1.7052E-8×T2
[matrix]
[γ']
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Integral intensity (neutrons / monitor count)
Experimental and results – SANS integral intensity
0.0125
PSI (SANS-II), DT706
0.0120
 SANS II, SINQ
 Porod region of the
scattering curve:
 sample-to-detector
distance 5m
 λ = 4.55 Å
-1
(11
) Q = 0.01-0.08 Å
 I(T) corrected for
background and
transmission
Data: Data1_SumoverMonCorr
Model: ScatteringIntensity
Weighting:
I
w = 1/(data1_errcorr)^2
0.0115
Chi^2/DoF
= 1.54271
R^2
= 0.96364
0.0110
 a p T  
  T 2
I T   C2 
 3 v T , c  
 c

0.0105
measured integral intensity
fit
confidence bands
0.0100
0
100 200 300 400 500 600 700 800 900
2
const
cR
Sbp
Agp
Bgp
Cgp
2.649E-22
0.14372
3.09932E-12
3.598196
4.1247E-5
1.7052E-8
±2.133E-20
±2163.1
±6.15067E-10
±0
±0
±0
temperature (°C)
 The weighted fit using the derived theory and the analytical
approximation of am(T) and ap(T) from neutron diffraction
 The fitted parameters are C2, cR and [Σb]p.
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Integral SANS data evaluation and discussion
Tab. 1. The results of the fit for various cR
C2
(10-22
cm4 pR
cR, vol. [b]p
fraction
at RT
(10-12
cm)
neutrons/
count)
0.05
0.10
0.14372
0.15
0.20
3.0744
3.0877
3.09932
3.1010
3.1144
2.674
2.661
2.649
2.648
2.635
monitor
(109
cm-2)
[b]m
(10-12
cm)
mR (109
cm-2)
R (109
cm-2)
(R)2
(1019
cm-4)
65.942
66.227
66.476
66.512
66.800
3.35463
3.36858
3.38085
3.38262
3.39674
72.733
73.036
73.302
73.340
73.646
-6.792
-6.809
-6.826
-6.828
-6.846
4.613
4.636
4.659
4.662
4.687
 [Σb]p and cR parameters are correlated
 Nevertheless, the resulting ΔρR is very insensitive to the input
value of cR
 => scattering contrast (ΔρR)2 can be determined without a nontrivial measurement of composition of the individual phases
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Temperature dependence of the scattering contrast
19
 scattering
5.0x10
temperature evolution
of the scattering contrast
19
-4
scattering contrast (R) (cm )
4.8x10
contrast of γ’ in γ
matrix, DT706
19
2
4.6x10
19
4.4x10
 most probable
19
4.2x10
and extreme
values of cR
scattering contrast when
cR=0.14327
19
4.0x10
19
3.8x10
cR=0.05
cR=0.20
19
3.6x10
0
100
200
300
400
500
600
700
800
900
temperature (°C)
May 1, 2020
14
Summary
 The expressions for SANS scattering contrast dependence on
temperature (no phase-composition changes) <= difference in
thermal expansions of γ and γ’ in Ni superalloys.
 Simulation: this difference is the determining factor for the (Δρ)2
temperature dependence
 The hypothesis proven by experiment on a Ni-Fe-base alloy
DT706. The evolution of lattice parameters of both phases
obtained from the in-situ wide angle neutron diffraction. The
theoretical scattering contrast dependence was then
successfully fitted to the measured SANS integral intensity.
 The magnitude of (ΔρR)2 is firmly connected with the particular
shape of the SANS integral intensity temperature dependence
=> used for the determination of the scattering contrast without
the knowledge of the compositions of the individual phases
 Investigation of superalloys with no scattering contrast at RT
May 1, 2020
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Acknowledgments
 The authors are indebted to SINQ (PSI Villigen, Switzerland)
and FRM II (TU Muenchen, Germany) for providing the beam
time at the SANS-II facility and diffractometers StressSpec
and SPODI
 NMI3 support is acknowledged as well (6th Framework
Programme ‘Strengthening the European Research Area,
Research Infrastructures’ - contract no. RII3-CT-2003505925
 We thank the sample environment group of FRM II (A.
Schmidt and A. Pscheidt) for support during the hightemperature experiment
May 1, 2020
16
May 1, 2020
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volume fraction temperature dependence
cT  
1
3
a
1
 a T  pR
  1
1
3
 cR
 a T  amR
3
m
3
p
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