Transcript diffusivité thermique

Measurement of thermal diffusivities during
self-propagating high temperature synthesis
1,3
Vrel ,
2,3
Karnatak ,
2,3
Heian ,
Dominique
Nikhil
Ellen M.
2,3
2,3
Sylvain Dubois , Marie-France Beaufort
1- Laboratoire d’Ingénierie des Matériaux et des Hautes Pressions, UPR1311-CNRS, 99 avenue J.-B. Clément, 93430 Villetaneuse –France
2- Laboratoire de Métallurgie Physique, UMR6630 CNRS/Université de Poitiers, Bat SP2MI, BP 30179, Bd Marie et Pierre Curie, 86962 Futuroscope cedex, France
3- Groupe Français d’Autocombustion, GDR2391SC CNRS, J.-C. Niepce, LRRS, BP 47870, 21078 Dijon cedex, France
Introduction
First experimental observation
thermal diffusivity (or thermal conductivity) is very difficult to calculate in porous samples
(percolation phenomena, nature of the grain interfaces, heat transfer through the pores,...)
two exothermic peaks
thermal diffusivity is difficult to measure at high temperature, especially on metastable samples:
measurement procedure is time consuming, and recrystallization, sintering, relaxation of internal
stresses, ... might occur, invalidating the result
apparently two consecutives reactions, the second propagating from the end of the sample
...but no observed phenomenon could explain what triggered the second reaction
but thermal diffusivity plays a key role during the reaction...
measurement of thermal diffusivity implies the generation of a hot spot either before the reaction
onset or after the reaction completion (decoupling heat transfer and heat generation during
reaction is an almost impossible task; one has to make assumption on one parameter to estimate
the other)
one of our sample displaying a "natural", very intense hot spot at the end of the reaction, gave us
the opportunity to validate a new method to estimate thern1al diffusivity
this method is based on the lateral observation of the hot spot back in the sample; for a greater
accuracy, it is therefore important that the position of the temperature maximum to shift with time
(next figure).
(the results presented here have already been published in the European Physical Journal B 33,1, pp. 31-39;
the proceedings will present additiona1 results with less intense instabilities and before the reaction onset)
Is there a second reaction ?
infrared analysis (left)
the propagation was not fully stable:
pause after the reaction propagated
about 80% of the sample length
This thermal wave can be used to measure the thermal diffusivity !
discretization of the heat transfer equation in 1D
hot spot when the reaction re-started
(reaction from a preheated sample)
time-resolved X RD (right)
when the reaction front crossed the
beam spot, Ti peaks abruptly disappears and TiC peaks appears
when the second wave crossed the
beam spot, a left shift is observed:
same lines, left shifted due to the
temperature (increased lattice
parameter)
conclusion
no second reaction
propagation of a thermal wave
(modified Boddington model for radiative heat losses)
2 parameters
→ thermal diffusivity
→ heat losses
optimization of these parameters by
a double golden section search
least square methods between
- a profile calculated from an initial profile using these
parameters for one second
- the experimental profile one second after the first one
Algorithm for the gold number dichotomy method (or the
optimization of thermal diffusivity. Note that for each value of
this parameter, heat losses are optimized using the same process
Results
first points have to be discarded (very high value for the sum of the squares)
stable value for about 30 consecutive points
a = 2.0x10-6m2s-1 (± 10%)
evolution afterwards is too weak for thermal diffusivity to be estimated:
strong discrepancy between successive points.
Conclusions
a new method for thermal diffusivity measurements, based on the lateral observation
of a sample during cooling, has been validated.
it requires a hot spot at the end of the propagation of the reaction; if this hot spot
is intense enough the results are trustworthy.
this method has been expanded to less intense hot spots (smaller instabilities or no instability);
results will be presented in the proceedings
a value of 2.0x10-6m2s-1 has been measured on a TiC sample with 40% porosity
Acknowledgments
The authors would like to express their gratitude to Mo Gailhanou and D. Thiaudière, from the LURE
facility for their help during the TRXRD experiments.
Ellen M. Heian and Nikhil Karnatak wish to thank, respectively, the French Ministry of Research
(Direction de la Recherche) and the Région Poitou-Charentes for financial support.