1. High temperature thermal diffusivity of combustion synthesized samples Dominique Vrel CNRS-LIMHP, UPR 1311, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois, Marie-France Beaufort, Benoît Cochepin CNRS-LMP, UMR 6630, Bât. SP2MI, Bd M. & P. Curie, BP 30179 86962 Futuroscope-Chasseneuil du Poitou Cedex, France

2. vrel@limhp.univ-paris13.fr2 Modeling studies Equation in 1D with the following approximation : Importance  in modeling before scaling-up;  in determination of kinetic parameters such as use of Boddington model (thermal profile analysis, TPA)

3. vrel@limhp.univ-paris13.fr3 Measuring thermal diffusivity  Impossible at high temperature on reactants  Easy at low temperature on reactants and products  Not possible during reaction (coupled equations with kinetics)  … Not practically possible on products at high temperature: re-crystallization, sintering, stress relaxation, homogenization of structure and composition (long time at high temperature) We need to find a way to determine thermal diffusivity as fast as possible, just after reaction

4. vrel@limhp.univ-paris13.fr4 A weird sample

5. vrel@limhp.univ-paris13.fr5 IR streak image - principle

6. vrel@limhp.univ-paris13.fr6 IR streak image - result Reference frame Igniter is on Reaction propagates Reaction pauses Reaction re-starts – Hot spot

7. vrel@limhp.univ-paris13.fr7 TRXRD – no second reaction  XRD, 25 pps  Left shift = temperature increase 2d sin  =  if  d   1 reaction only  1 re-heating can be used to estimate thermal diffusivity

8. vrel@limhp.univ-paris13.fr8 Hot spot diffusion  i for the space step; n for the time step  77 space steps (77 pixels on the IR image)  25 time steps per second  2 unknowns:  and 

9. vrel@limhp.univ-paris13.fr9 Golden section search To determine the unknowns, starting from an experimental temperature profile, we model the evolution of temperature with arbitrary values of  and , and then minimize the sum of differences between the final calculated profile and the final experimental profile

10. vrel@limhp.univ-paris13.fr10 Flow chart

11. vrel@limhp.univ-paris13.fr11 Modeling results

12. vrel@limhp.univ-paris13.fr12 Thermal diffusivity – results

13. vrel@limhp.univ-paris13.fr13 Weaker hot spots with nickel with finer C

14. vrel@limhp.univ-paris13.fr14 Finer C particles

15. vrel@limhp.univ-paris13.fr15 Calculated thermal diffusivity

16. vrel@limhp.univ-paris13.fr16 And before reaction ?  Noisy data  Calculated value of thermal diffusivity sets the lower limit for the real value : method measures only the part of the heat flowing through the sample that contributes to the temperature increase and neglects the part that contributes to the heat losses.  System might reach equilibrium, where the heat flowing through the sample only compensate the heat losses

17. vrel@limhp.univ-paris13.fr17 Results before reaction

18. vrel@limhp.univ-paris13.fr18 Summary

19. vrel@limhp.univ-paris13.fr19 Conclusions  Method is easy and seems trustworthy References  Dominique Vrel, Nikhil Karnatak, Marie-France Beaufort, Sylvain Dubois, In-situ measurement of high-temperature thermal diffusivity in a combustion-synthesized ceramic, European Physical Journal B 33 (2003), 31-39.  Dominique Vrel, Nikhil Karnatak, Ellen M. Heian, Sylvain Dubois and Marie-France Beaufort, Measurement of thermal diffusivities during self-propagating high temperature synthesis, submitted, International Journal of Self-Propagating High- Temperature Synthesis.  Should be applied with care  Cannot be used on any sample; needs instability  Could be improved by a « controlled hot spot ».