High temperature thermal diffusivity of combustion synthesized samples Dominique Vrel CNRS-LIMHP, UPR 1311, 99 avenue Jean-Baptiste Clément, 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 Futuroscope-Chasseneuil du Poitou Cedex, France

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)

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

A weird sample

IR streak image - principle

IR streak image - result Reference frame Igniter is on Reaction propagates Reaction pauses Reaction re-starts – Hot spot

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

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 

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

Flow chart

Modeling results

Thermal diffusivity – results

Weaker hot spots with nickel with finer C

Finer C particles

Calculated thermal diffusivity

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

Results before reaction

Summary

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),  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 ».