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MEASUREMENT OF THERMAL DIFFUSIVITY OF REACTION BONDED SILICON NITRIDE
J.-J. Serra, M. Jaymes, M. Cantarel
To cite this version:
J.-J. Serra, M. Jaymes, M. Cantarel. MEASUREMENT OF THERMAL DIFFUSIVITY OF REAC-
TION BONDED SILICON NITRIDE. Journal de Physique Colloques, 1986, 47 (C1), pp.C1-635-C1-
639. �10.1051/jphyscol:1986197�. �jpa-00225628�
MEASUREMENT OF THERMAL D I F F U S I V I T Y OF REACTION BONDED S I L I C O N NITRIDE
J.-J. SERRA, M. JAYMES
and
M. CANTARELE.T.C.A., 16 bis Avenue Prieur d e la CGte d'Or, F-94114 Arcueil Cedex, France
RBsumS
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La d i f f u s i v i t d thermique d l Z c h a n t i l l o n s d e n i t r u r e d e s i l i c i u m l i b p a r r k c t i o n , p r o v e n a n t d e d i f f 6 r e n t s f o u r n i s s e u r s , a d t d d d t e r m i n b e 1 l ' a i d e du f o u r s o l a i r e d e 1'ETCA. Deux mdthodes d e mesure, a d a p t b e s 1 ce t y p e d e ma- t b r i e l , o n t permis d e d i f f d r e n c i e r l e s o r i g i n e s d e s m a t d r i a u x . C e t t e i n s t a l l a - t i o n permet d ' d t u d i e r d e s d p r o u v e t t e s r e l a t i v e m e n t i m p o r t a n t e s , e t donc r e p r b - s e n t a t i v e s du m a t d r i a u o p d r a t i o n n e l .Abstract-The t h e r m a l d i f f u s i v i t y of samples o f r e a c t i o n bonded s i l i c o n n i t r i d e from d i f f e r e n t s o u r c e s , was measured u s i n g t h e ETCA s o l a r f u r n a c e . Two mea- surement methods, s u i t a b l e f o r u s e w i t h t h i s t y p e of equipment, allowed t h e d i f f e r e n t m a t e r i a l o r i g i n s t o b e d e t e r m i n e d . T h i s i n s t a l l a t i o n a c c e p t s r e l a - t i v e l y l a r g e samples which a r e t h e r e f o r e r e p r e s e n t a t i v e of t h e b u l k m a t e r i a l .
I
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INTRODUCTIONThe t h e r m a l d i f f u s i v i t y of s t r u c t u r a l m a t e r i a l s i s a n e s s e n t i a l p a r a m e t e r i n t h e d e f i n i t i o n of t h e i r thermomechanical p r o p e r t i e s . T h i s p a r a m e t e r c a n b e d e t e r m i n e d , a t h i g h t e m p e r a t u r e u s i n g v a r i o u s dynamic methods on g e n e r a l l y t h i n samples.
The u t i l i z a t i o n of a 45 kW s o l a r f u r n a c e , s u c h a s t h e ETCA f u r n a c e , a l l o w s r e l a t i v e l y t h i c k samples t o b e u s e d which a r e more r e p r e s e n t a t i v e o f t h e b u l k m a s e r i a l . I n measurements a t h i g h t e m p e r a t u r e t h e modulated i n c i d e n t f l u x method i s u s e d and, around ambient t e m p e r a t u r e , a method i s used b a s e d upon m a t e r i a l r e s p o n s e t o a f l u x window. These methods were a p p l i e d t o t h e c a l c u l a t i o n of t h e t h e r m a l d i f f i i s i v i t y of d i s c s of r e a c t i o n bonded s i l i c o n n i t r i d e .
2
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EXPERIMBTAL EQUIPMENT 2.1 G e n e r a t i o n of t h e r m a l f l u xThe f r o n t of t h e samples i s s u b j e c t t o a l i g h t f l u x from a compound s o l a r f u r n a c e , a d e s c r i p t i o n of which h a s a l r e a d y been p u b l i s h e d / I / .
The f u r n a c e c o m p r i s e s t h r e e main e l e m e n t s :
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a h e l i o s t a t : a p l a n e r e f l e c t o r 17.4 x 13.2 m, t h e p u r p o s e of which i s t o r e f l e c t t h e s u n ' s r a y s i n t h e d i r e c t i o n of t h e o p t i c a l a x i s of a concave m i r r o r .Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986197
JOURNAL
DE PHYSIQUE
- a concentrating mirror, focal length 10.75 m, the projection of which covers an area of 10 m x 10 m.
- an attenuator which acts as a servo-controlled flux modulator and varies the flux density reaching the concentrator focus between 0 and 500 w/cm2. This attenuator comprises a system of vertical flaps placed on the parallel rays, between the heliostat and the concentrator. This configuration conserves the same distribution of energy in space, in the focal plane.
2.2 Mounting of samples
The samples, in the form of discs, are held at three points by a concentric grip clip with ceramic pads. The assembly is placed behind a water-cooled diaphragm of the same diameter as the sample, which protects surrounding experimental equipment.
2.3 Temperature measurement
The high temperatures on both sides of the samples are measured by optical pyrometry (Barnes 12.550) in the infra-red area, above 4 pm. This avoids errors due to random reflections of the sun's rays, as the radiation spectrum leaving the overall optical system is limited to wavelengths less than 2.8 pm. Around ambient temperature, only the temperature on the rear face of the samples needs to be measured. It is measured by a thermocouple. Signals from the temperature sensors are recorded by an automatic data collection system (HP 30528) and transferred to a computer (HP 98268) for processing.
3 - PROCESSING OF RESULTS 3.1 Principle of methods used
The methods used to interpret the thermograms for the calculation of the diffusivity are based upon the model of the plane wall of finite thickness (cf. Fig. 1). The sample of thickness e receives, on one side (x
=e), a thermal flux, the time
variation of which is known. Consideration is then given to the temperature variation in relation to the temperature existing at the beginning of the flux pulse:
0(x,
t)=
T (x,
t)- T (x, 0). This flux law may be either applied to a wall which was not penetrated by any flux, or superimposed on a wall already penetrated by a constant flux. The heat exchange of the two sides will be defined by local Biot numbers P o and /3e (px
=ehx/A, where A i s the thermal conductivity and hx the heat loss parame- ter at x
=0 and x
=e).
thE%lx
Heat loss Heat loss
Figure 1: Schematic drawing of the sample arrangement
At high temperature, the wall is subjected to a sinusoidal wave variation in flux, pulsing
w .This then results in a stabilized temperature cycle situation on each side. The sinusoidal wave signal on the unexposed side (x
=0) is out of phase in relation to that of the exposed side (x
=e) by an amount A and its amplitude is attenuated in a ratio P (figure 2). These two values are function of the two inter- mediate variables po and b, where b
=e G / 2 a , and a is the thermal diffusivity / 3 / . Thus, by measuring A and P, it is possible to calculate b and a (as
wand e are known) 141.
3.3 Flux window 151
In the medium temperature range, a thermal pulse will be used, in a flux window, duration
t, such that the term at/e2 will be greater than 0.5. At the end of the window, during cooling, loss coefficients will be assumed to be the same on both sides. Under these conditions, material temperature during cooling tends towards a negative exponential function in time. The semi-logarithmic representation of func- tion N
=9 (0, t)/9 (0,
t)accepts an asymptote (figure 3). In this case, measuring the parameters of this straight line will give the Biot number and diffusivity values.
Figure 2: Measurement principle for sinusoidal wave flux method
Figure 3: Measurement principle for flux window method
4 - EXPERIMENTAL RESULTS
Samples of reaction bonded silicon nitride from three different sources were studied.
The samples were in the form of discs, 50
mm diameter and5 mm thick. Their physical and mechanical characteristics are shown in Table 1.
Results concerning variations of thermal diffusivity with temperature are shown in figure 4. It will be seen that the values obtained by the two methods agree quite well (the critical point between the two methods occurring around 300° C).
The results show a considerable difference between the diffusivities of the three
materials, especially at low temperatures. Values obtained for A and B become the
JOURNAL DE PHYSIQUE
Table 1: Main characteristics of samples tested.
* Manufacturer's data
** Parameters measured by ourselves (method described in 1 6 1 ) .
same at high temperatures. The physical and mechanical properties shown in Table 1 give no explanation for this difference in behaviour. Conversely, there are
considerable differences in sample composition, determined using the method described in 171. Depending upon the sample concerned, this method showed two or three phases band
,5Si N and Si ON
).Materials A contained 21% Psi N , the remainder
2 2
c o m p r i ~ i n g ~ d ~ i ~ ~ ~ and a small quantity of Si ON sampleZ 4 contained 91% Psi N 3 4' with the remaining 9% formed by
n!Si N and S$ 06' in equal proportions. Concerning the C samples, these contained 33% p 3 ~ i 3 ~ 4 and2672'uSi3N,,, without any apparent silicon oxynitride. The differences observed in thermal d~ffusivity would therefore appear to be the result of differences in composition.
I
A B C
0
WINDOW F L U X O A o
M O D U L A T I O N
Apparent density g/cm3
2.45 2.35 2.55
6..
5
..
4
..
S I N U S O I D A L WAVE M O D U L A T I O N
I
- 5
o A e e m p l e eJ
A B e e m p l e e.
-
v c e e m p l e ew P
:)=
V) a 0
.A- .A-
s
A v 10
,
Temperature ('c)200 400 600 800 1000
Open porosity
(2) (*)25 17 - 20
15 - 25
Figure 4: Comparison between diffusivity results obtained for the three types of material.
Poisson's coefficient
(**)
0.235 0.225 0.235
Young's modulus GPa
(**)
155
135
170
Due to its thermal flux modulation system, the ETCA solar furnace is well suited for the determinateion of diffusivity. Two measuring methods were developed to study variations of this parameter, from ambient temperature up to high temperatures.
Installation dimensions allow relatively large samples to be tested (up to more than 10
mmthick). Results obtained for reaction bonded silicon nitride clearly showed the difference between three materials from different sources. These results thus demon- strate the installation's capabilities in the investigation of material characteris- tics at high temperature.
REFERENCES
/I/ JAYMES M. - Rev. Int. Htes Temp. RQfract. 12 (1975), 301-306 /2/ SERRA J.J., JAYMES M, Rpt. ETCA (1983) 83-R-037
/3/ COWAN R.J. - J. Appl. Phys. 32 (1961), 1363-1370
/ 4 /
SERRA J.J., MASCLET P., JAYMES M., CANTAREL M.
Rev. Int. Htes Temp. RQfract. 20 (1983), 69-79 /5/ SERRA J.J., JAYMES M, Rpt. ETCA (1985) 85-R-008 /6/ GLANDUS J.C. - Thesis (1981) Limoges 15-81
/ 7 /
