1. November 29, 2015 1 Scattering contrast dependence on thermal-expansion-coefficient difference of phases in two-phase system P. Strunz 1,2, R. Gilles 3, D. Mukherji 4, M. Hofmann 5, D. del Genovese 4, J. Roesler 4, M. Hoelzel 3 and V. Davydov 1 1 Nuclear Physics Institute, CZ-25068 Řež near Prague (strunz@ujf.cas.cz)strunz@ujf.cas.cz 2 Research Centre Řež, CZ-25068 Řež near Prague, Czech Republic 3 TU München, ZWE FRM-II, Lichtenbergstr. 1, D-85747 Garching, Germany 4 TU Braunschweig, IfW, Langer Kamp 8, D-38106 Braunschweig, Germany 5 TU Darmstadt c/o FRM II, Lichtenbergstr. 1, D-85747 Garching, Germany 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 ' Outline  Observation of SANS intensity increase  Theory  Simulation  Experiment diffraction SANS  Prospective application

2. November 29, 2015 2 SANS – tool for microstructural characterization  Microstructural characterization: essential part in any alloy development  Neutron scattering: increasingly complementing XRD, SEM, TEM  Microstructural characterization: essential part in any alloy development  Neutron scattering: increasingly complementing XRD, SEM, TEM scattering caused by  γ’ precipitates (ordered fcc - L12 crystal structure)  coherently embedded in γ matrix (crystal structure fcc - A1) scattering caused by  γ’ precipitates (ordered fcc - L12 crystal structure)  coherently embedded in γ matrix (crystal structure fcc - A1)  DT706 superalloy (wt.%: Fe=22, Cr=18, Nb=2.9, Ti=1.9, Al=0.55, C=0.03, Ni = balance)

3. November 29, 2015 3 SANS data intensity in “low”-temperature region  Increase of the integral SANS intensity from γ' precipitates at low and intermediate temperatures during the temperature decrease  DT706 (SINQ, SANS-II)  17% increase, nearly linear  Increase of the integral SANS intensity from γ' precipitates at low and intermediate temperatures during the temperature decrease  DT706 (SINQ, SANS-II)  17% increase, nearly linear Possible cause  volume fraction change of γ’  change in the size distribution of γ’ precipitates  γ’ scattering contrast change Possible cause  volume fraction change of γ’  change in the size distribution of γ’ precipitates  γ’ scattering contrast change

4. November 29, 2015 4 scattering contrast change  scattering length densities (SLD)  m,p =[  b m,p ]/a m,p 3 (matrix, precip.)  [  b m ], [  b p ] not changed but a m, a p change with temperature  Can it significantly change the scattering contrast?  scattering length densities (SLD)  m,p =[  b m,p ]/a m,p 3 (matrix, precip.)  [  b m ], [  b p ] not changed but a m, a p change with temperature  Can it significantly change the scattering contrast?  Answer: yes, under certain circumstances  Circumstances (fulfilled in superalloys)  low Δ  with respect to   high volume fraction (to make SANS visible)  Answer: yes, under certain circumstances  Circumstances (fulfilled in superalloys)  low Δ  with respect to   high volume fraction (to make SANS visible)

5. November 29, 2015 5 Theory – scattering contrast  Scattering contrast of a two-phase system  [  b m ], [  b p ] usually unknown, but temperature independent  known [  b] alloy  c … volume fraction of γ’ precipitates  [  b m ], [  b p ] usually unknown, but temperature independent  known [  b] alloy  c … volume fraction of γ’ precipitates  the average unit cell volume

6. November 29, 2015 6 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 => 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 =>  where all T-independent parameters are in the constant C 2  the ratio (a p /ν c 1/3 ) 2 is only marginally temperature dependent => temperature dependence of intensity driven by numerator in the scattering contrast form:  where all T-independent parameters are in the constant C 2  the ratio (a p /ν c 1/3 ) 2 is only marginally temperature dependent => temperature dependence of intensity driven by numerator in the scattering contrast form:

7. November 29, 2015 7 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)  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)  increasing / decreasing temperature dependence determines which SLD (precipitate or matrix) is smaller  strong correlation “curve shape” – “magnitude of the scattering contrast”  increasing / decreasing temperature dependence determines which SLD (precipitate or matrix) is smaller  strong correlation “curve shape” – “magnitude of the scattering contrast”

8. November 29, 2015 8 Scattering contrast simulation  volume-fraction change simulation:  change of the curve due to [Σb] p change can be nearly equivalently achieved by changing c  volume-fraction change simulation:  change of the curve due to [Σb] p change can be nearly equivalently achieved by changing c =>  [Σb] p and volume fraction of precipitates are correlated parameters =>  [Σb] p and volume fraction of precipitates are correlated parameters

9. November 29, 2015 9 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)  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)

10. November 29, 2015 10 Experimental and results - Diffraction peaks  Largest accessible anglular range (separation of the γ and γ’ peaks)  reflection 311 (StressSpec) and 331 (SPODI)  Figs.: γ and γ’ double peaks recorded at StressSpec and SPODI  instrumental profile deconvoluted using ProfEdgeReal program  γ’ peaks: 10% of γ peaks  Largest accessible anglular range (separation of the γ and γ’ peaks)  reflection 311 (StressSpec) and 331 (SPODI)  Figs.: γ and γ’ double peaks recorded at StressSpec and SPODI  instrumental profile deconvoluted using ProfEdgeReal program  γ’ peaks: 10% of γ peaks

11. November 29, 2015 11 Experimental and results – lattice parameters  Approximation of lattice parameter by quadratic polynomial  a m (T) = 3.585155 + 4.5891E-5×T + 2.1355E-8×T2 [matrix]  a p (T) = 3.598196 + 4.1247E-5×T + 1.7052E-8×T2 [γ']  Approximation of lattice parameter by quadratic polynomial  a m (T) = 3.585155 + 4.5891E-5×T + 2.1355E-8×T2 [matrix]  a p (T) = 3.598196 + 4.1247E-5×T + 1.7052E-8×T2 [γ']  Combination of the data obtained form both SPODI and StressSpec => the evolution of the lattice parameters and misfit (RT-835°C)  Combination of the data obtained form both SPODI and StressSpec => the evolution of the lattice parameters and misfit (RT-835°C)

12. November 29, 2015 12 Experimental and results – SANS integral intensity  SANS II, SINQ  Porod region of the scattering curve:  sample-to-detector distance 5m  λ = 4.55 Å  Q = 0.01-0.08 Å -1  I(T) corrected for background and transmission  SANS II, SINQ  Porod region of the scattering curve:  sample-to-detector distance 5m  λ = 4.55 Å  Q = 0.01-0.08 Å -1  I(T) corrected for background and transmission  The weighted fit using the derived theory and the analytical approximation of a m (T) and a p (T) from neutron diffraction  The fitted parameters are C 2, c R and [Σb] p.  The weighted fit using the derived theory and the analytical approximation of a m (T) and a p (T) from neutron diffraction  The fitted parameters are C 2, c R and [Σb] p.

13. November 29, 2015 13 Integral SANS data evaluation and discussion  [Σb] p and c R parameters are correlated  Nevertheless, the resulting Δ ρ R is very insensitive to the input value of c R  [Σb] p and c R parameters are correlated  Nevertheless, the resulting Δ ρ R is very insensitive to the input value of c R  => scattering contrast (Δ ρ R ) 2 can be determined without a non- trivial measurement of composition of the individual phases

14. November 29, 2015 14 Temperature dependence of the scattering contrast  most probable and extreme values of c R  scattering contrast of γ’ in γ matrix, DT706

15. November 29, 2015 15  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 (Δ ρ ) 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 (Δρ R ) 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  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 (Δ ρ ) 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 (Δρ R ) 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 Summary

16. November 29, 2015 16  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 (6 th Framework Programme ‘Strengthening the European Research Area, Research Infrastructures’ - contract no. RII3-CT-2003- 505925  We thank the sample environment group of FRM II (A. Schmidt and A. Pscheidt) for support during the high- temperature experiment  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 (6 th Framework Programme ‘Strengthening the European Research Area, Research Infrastructures’ - contract no. RII3-CT-2003- 505925  We thank the sample environment group of FRM II (A. Schmidt and A. Pscheidt) for support during the high- temperature experiment Acknowledgments

17. November 29, 2015 17

18. November 29, 2015 18 volume fraction temperature dependence