FR2745636A1 - High temperature thermal conductivity measuring appts. for ceramic materials - Google Patents

Abstract

The appts. includes a sealed enclosure (16) housing a horizontal base (2) covered by a bell shaped envelope (3). Both the base and the envelope have a double wall cooled by a water circuit. An inlet (5) and an outlet (6) are provided for evacuating the enclosure and filling it with a neutral gas. A sample of the material to be tested (10) is placed inside the enclosure. The sample is placed on a graphite resistor (26) resting on two conducting vertical bars fixed in the base. A graphite cap (24) covers the top surface of the sample. A thermocouple (34) is inserted into the cap to measure its temperature. A second thermocouple (14) measures the temperature at the top surface of the sample while a third one determines the temperature of the sample lower surface.

Description

METHOD FOR DETERMINING THE THERMAL CONDUCTIVITY OF A
HIGH TEMPERATURE MATERIAL AND CONDUCTIMETER FOR
IMPLEMENTING THIS METHOD.

DESCRIPTION
Technical area
The invention relates to a method for determining the thermal conductivity of materials, under a controlled atmosphere and at high temperature, that is to say up to temperatures of about 2500 C at least.

 This method is particularly applicable to the obtaining of safe thermal data concerning new insulating or superinsulating materials, at high temperature. As such, it can be used in particular for the characterization of materials for use in aerospace systems.

 The invention also relates to a conductivity meter designed to allow the acquisition of the necessary measures to implement the aforementioned method.

State of the art
According to the known methods, the thermal conductivity K of a material is determined at a temperature T by bringing a sample of this material of thickness e and of section S to the average temperature T and establishing between the two aces of the sample a predetermined temperature difference AT. The thermal conductivity K 2 the temperature T is deduced from the measurement of the thermal flux # necessary to maintain this temperature difference #T, from the relationship
# .e
S. # T
To implement this method, an apparatus, called a conductivity meter, is used which comprises a measurement chamber receiving the sample, delimited by a confinement enclosure. The conductivity meter further comprises means for establishing the average temperature T in the sample. , means for establishing the temperature difference AT, and means for measuring the heat flow as well as the temperatures at different points.

 This measurement method and the conductivity meter which ensures its implementation have two notable disadvantages.

 The first disadvantage relates to the fact that the measured heat flux is influenced by the unavoidable existence of thermal losses in the apparatus.

 The second disadvantage relates to the inability of existing conductivity meters to perform measurements at high temperatures, for example about 2500 C.

 To eliminate the first of these disadvantages, different solutions have been proposed.

 One of these solutions, illustrated by the document EP-A-0 325 430, consists in determining the heat losses by measuring the temperature at different points of the apparatus, in order to correct the results of the measurements made.

 Another solution is to reduce heat losses by coating the test piece with a sheet of aluminum or polished copper.

 A third solution, illustrated by document FR-A-2 683 908, proposes to determine the thermal losses during a preliminary test, without temperature difference between the two faces of the sample.

 The first two solutions only partially eliminate the influence of heat losses. In addition, they make the device complex and expensive, especially in the first case.

 The third solution eliminates these disadvantages and provides a precise measurement of the thermal conductivity. The implementation remains however long and the problem of high temperatures is not solved.

Presentation of the invention
The main subject of the invention is a method for determining the thermal conductivity of a material in a single measurement, with great precision and at temperatures which can reach high values, without any thermal losses having to be taken into account. account during measurements or their subsequent processing.

et de la fonc
tion linéaire précédemment établie pour l'intervalle
de températures immédiatement inférieur.According to the invention, this result is obtained by means of a method for determining the thermal conductivity of a material, over a high temperature range, characterized in that it comprises the following steps - measurement, on a sample of thickness e of the material,
of the heat flux O passing through this sample and
the temperature Tf of a cold face of the sample,
in steady state, when a hot face of this
sample is heated to different temperatures
fixed Tc distributed over said range, these temperatures
Tc being chosen so that the conductivity varies sen
as linearly with the temperature between
successive fixed temperatures Tc and at least between
corresponding temperature pairs Tf and Tc
at the two lowest Tc values - determination, for corresponding Tm temperatures
to the average arithmetic of each of the pairs of
temperatures Tf and Tc, with thermal conductivity
average measured Km.mes of the material, from the # .e
relation Km.mes = ;;
S (Tc - Tf) - establishment of a first linear function K1 (T),
which represents the variations of a conductivity
calculated heat K.cal of the material, depending on
the temperature T, in the temperature range
Tf-Tc corresponding to the lowest value of Tc,
from the two lowest temperatures Tm and
measured average thermal conductivities Km.mes
previously determined for these two temperatures
Tm; and establishment of a series of linear functions
K2 (T) ... Kn (T), in each temperature range
which separates two successive values of Tc from the Km.mes relation

and the function
Linearity previously established for the interval
immediately lower temperatures.

an advantage, gold. measures the tnermic flow # and the temperature Tf ~ by placing the sample in a conductivity meter,
so that his hot face and his cold face
are respectively in contact with an emitting means
able to emit heat at fixed temperatures
Tc and a heat flow measurement means, and
so that all the other aces of the exchange
are thermally insulated by heating the hot face of the sample
average transmitter at different fixed temperatures
Tc; and - by measuring, in steady state, the heat flux
O and the temperature Tf of the cold face, for each
one of the fixed temperatures Tc.

 The successive fixed temperatures Tc are chosen, preferably, so as to be regularly spaced by a difference substantially less than the minimum difference between the temperatures Tf and Tc, over the temperature range considered. This difference between the successive fixed temperatures Tc can be, for example, about 100 C.

 The value of the lowest fixed temperature Tc may especially be set at about 500 ° C. The highest value of this fixed temperature Tc is limited only by the nature of the means used to heat the hot face of the sample. In the case where this means is a graphite resistor, this value is about 2500 C.

 Advantageously, the first linear function K1 (T) is established by calculating the coefficients a1 and b1 of the equation K1 (T) = a1 + b1, for the values of T and K1 which respectively correspond to the two lowest temperatures Tm. and the two thermal conductivities measured Km.mes at these temperatures.

 Moreover, we establish, by increasing iteration, the sequence of linear functions K2 (T). .

Kn (T), by calculating the coefficients a2 and b2, ... an and bn of the equations K2 (T) = a2T + b2,. .. Kn (T) = anT + bn, from the systems

dans lesquels Tc(1), Tc(2), ... Tc(n-1), Tc(n) désignent les températures fixes Tc pour les première à énième mesures, K1(Tc(1)) ...Kn-1 (Tc(n-1)) représentent les valeurs de K1 à Kn-1 respectivement aux températures Tc(1) à Tc(n-1) et C2 à Cn représentant des constantes définies par

où Km.mes(2), ... Xm.mes(n) représentent les valeurs de
Km.mes pour les deuxième à énième mesures et ou Tf(2) à
Tf(n) désignent les températures Tf pour les deuxième à énième mesures.

in which Tc (1), Tc (2), ... Tc (n-1), Tc (n) designate the fixed temperatures Tc for the first to nth measures, K1 (Tc (1)) ... Kn- 1 (Tc (n-1)) represent the values of K1 to Kn-1 respectively at temperatures Tc (1) to Tc (n-1) and C2 to Cn representing constants defined by

where Km.mes (2), ... Xm.mes (n) represent the values of
Km.mes for the second to nth measures and or Tf (2) to
Tf (n) denote the temperatures Tf for the second to nth measures.

 The invention also relates to a conductivity meter designed to allow the acquisition of the necessary measures for the implementation of the method defined above.

This conductivity meter, which can be used over a high temperature range, is characterized by the fact that it comprises - a confinement enclosure, delimiting a chamber
measure able to receive a sample of one
material whose conductivity it is desired to measure
mique; a means for heating a hot face of
the sample, placed in the measuring chamber and
able to provide heating on said beach of
temperatures - a radiative fluxmeter consisting of a cap in
contact with the cold side of the sample; and means for measuring the temperatures Tc and Tf of the
hot and cold faces of the sample, respectively
is lying.

 In a preferred embodiment, the heating means comprise a resistor.

 In this embodiment, the radiative flowmeter comprises a means for measuring a temperature Tr of the cap, integrated in the latter.

 Furthermore, the means for measuring the temperature Tc of the hot face comprise a removable thermocouple capable of measuring the temperature Tc up to about 14000C and a pyrometer capable of measuring the temperature Tc up to about 2500 ° C.

Brief description of the drawings
A preferred embodiment of the invention will now be described, by way of nonlimiting example, with reference to the accompanying drawings, in which:
FIG. 1 is a vertical sectional view schematically illustrating a conductivity meter according to the invention
FIG. 2 is a sectional view on a larger scale of the active parts of the conductivity meter of FIG. 1
3 represents the variations of the thermal conductivity: N (er.W / cm.C) of a fictitious sample, as a function of the temperature T (in), the curves I, II and III respectively corresponding to the conductivity theoretical temperature of the material and the thermal conductivity calculated by the method according to the invention, at fixed temperatures Tc of the hot face and at average temperatures Tm
FIG. 4 shows the variations of the thermal conductivity K (in W / cm · 0C) of a first real sample, as a function of the temperature
T (in C), curves IV and V respectively corresponding to the reference thermal conductivity and to the thermal conductivity calculated by the method according to the invention, at fixed temperatures Tc of the hot face; and
- Figures 5 and o are curves similar to those of Figure 3, respectively in the case of a second and a third real samples.

Detailed statement of a preferred embodiment
From the measurements made on a sample of material placed in a conductivity meter as schematically illustrated in FIG. 1, the method according to the invention makes it possible to determine with a great accuracy the thermal conductivity of this material, in a range of high temperatures. In practice, this temperature range can in particular range from about 500 ° C. to about 25 ° C.

The tested material may in particular be a new insulating or superinsulating material whose safety behavior is desired to be known in a safe manner when one of its faces is subjected to a very high temperature. It is understood that the results will be decisive as to the possible use of this material in the aerospace industry.
A sample of the material to be tested is cut to have two opposite parallel faces, separated by a thickness e (in cm), and a section S (in cl2). This section S is, for example, square.

 The sample is designated by the reference 10 and its opposite parallel faces by the references 12 and 14 in Figures 1 and 2. When the sample 10 is placed in the conductivity meter and when it is in operation, the faces 12 and 14 constitute respectively the hot face and the cold face of this sample.

 As shown schematically in Figure 1, the conductivity meter comprises a containment chamber 16 composed mainly of a horizontal bottom 2 and a bell-shaped envelope 3, sealingly resting on the bottom 2. The envelope 3 and the bottom 2 are double-walled, cooled by a circulation of water. They internally delimit a measuring chamber 4, in which the sample 10 is received, as well as the active parts of the conductivity meter, illustrated in more detail in FIG. 2. Pipes 5 and 6 connect the measurement chamber 4 to external circuits. allowing respectively to evacuate and introduce a neutral gas such as argon in this chamber.

 As seen in Figure 2, the periphery of the sample 10 is surrounded by a guard piece 11 made of the same material as the sample.

 More precisely, the guard piece 11 is a piece that surrounds the sample 10 and has the same thickness e as the latter. An annular space 13 of small thickness is provided between the sample 10 and the guard piece 11. This arrangement makes it possible to reduce the lateral thermal losses to a very small value.

 The assembly formed by the sample 10 and the guard piece 11 rests on the side of the hot lower face 12 of the sample, on a graphite resistor 26, which constitutes a heating means, by which the hot face of the sample can be heated to a temperature Tc of, for example, between 5000C and 2500C. For this purpose, the resistor 26 is in intimate contact with the hot lower face 12 of the sample 10.

 The resistor 26 rests on the bottom 2 of the containment enclosure 1 via two vertical bars 7 through which is also fed the supply current of the resistor.

 In order that the majority of the heat generated by the resistor 26 serves to heat the sample 10, a thermal insulation plate 20 is placed below the resistor and a thermally insulating frame 18 tightly surrounds the peripheral surface of the room. guard 11.

 On the other hand, the cold upper face 14 of the sample 10 is not thermally insulated.

This characteristic makes it possible to measure under the conditions of use of the tested material. In addition, it facilitates the implementation of the device.

 To enable the measurement of the heat flux passing through the sample, a radiative flowmeter constituted by a cap 24 made of a thermally conductive material such as graphite is placed on its cold upper face 14. A thermocouple 34, integrated in the cap 24, measures the radiation temperature Tr of the latter.

 To measure the temperature Tf of the cold upper face 14 of the sample, a second thermocouple 38 is used, placed at this face 14.

 Finally, the measurement of the temperature Tc of the hot inner face 12 of the sample is carried out, up to 1400 C, by means of a third thermocouple 30 removably placed at this face 12. of this temperature, using a pyrometer 28, after taking care to disassemble the thermocouple 36, so that it is not damaged.

 Preferably, the thermocouples 34, 36 and 38 are thermocouples of very small diameter, chosen to be operational under the test conditions.

 The pyrometer 28 is placed under the thermal insulation plate 20 and oriented upwards along the vertical axis of the enclosure. An axial passage 30 is formed in the plate 20, in front of the pyrometer 28, to allow the latter to directly measure the temperature of the hot lower face 12 of the sample. A support 8 makes it possible to mount the pyrometer on the bottom 2.

 Pyrometer 28, which may be of any type capable of measuring temperatures between about 900 ° C. and about 2500 ° C., is cooled by a water circuit 32.

The principle of the conductivity meter illustrated in FIG. 1 is based on the measurement of the thermal flow # passing through the sample, in steady state, when its hot face is heated to a fixed temperature Tc, in the temperature range that the resistor can reach. 26. By measuring, in addition, the temperatures Tc and Tf, respectively of the hot faces 12 and cold 14 of the sample 10, a corresponding value of the thermal conductivity can be obtained.
K (in W / cm.0C), from the relation # .e
K = (1).

S (Tc - Tf)
The value of the thermal flux # (in W) is given by the relation
Q, = k (Tr4 - To4) (2), in which - k is a characteristic coefficient of the transmitted cap
sif 24 - Tr is the radiation temperature of the emitted cap
sif (in "C") and - To is the temperature of the containment enclosure 16 (in C)
The temperature To of the containment enclosure 16 is the temperature of the water used to cool the latter. Moreover, the temperature
Tr is measured by the thermocouple 34. The heat flux # can therefore be determined from the relation (2).

 Furthermore, the thermal flux thus determined and the Tc and Tf measurements made on the thermocouples 36 and 38, or on the pyrometer 28 for measuring the temperature Tc beyond 1400 C, to calculate the thermal conductivizé K from the relation (1).

 The measurements made with the aid of the conduc-timétre are carried out under a controlled atmosphere, and preferably under argon. Indeed, the flow transfer problems caused by the contact resistances between the resistor 26, the sample 10 and the cap 24 do not make it possible to perform precise measurements under vacuum.

hat 24 do not allow to perform precise measurements under vacuum.

The conductivity meter illustrated in FIG. 1 is used, during a first step, to determine the values of the thermal conductivity K given by relation (1), for successive fixed values of the temperature Tc of the hot face 12 of the sample 10. More precisely, the temperature Tc is given successive fixed values, separated by a constant difference, so as to scan the entire range of temperatures considered. Thus, for the above-mentioned temperature range from about 500.degree. C. to about 25.degree. C., and fixing the difference between the fixed temperatures Tc and 1000.degree. C., the values Tc (1) = 5000.degree. 2) = 6000C,
Tc (3) = 700 ° C, .... Tc (n) = 25000C (with n = 21 in this example).

For each successive fixed value
Tc (1) to Tc (n), it is expected to establish a steady state and the heat flow # is measured as well as the temperatures Tc and Tf using the thermocouples 34, 36 and 38. The values of the temperatures Tf corresponding to each of the temperatures Tc (1) to Tc (n) are denoted by Tf (1) to Tf (n)
The measurements made make it possible to determine, using the relation (1), the values of the thermal conductivity K which correspond to each of the temperature pairs Tc and Tf.

Given the insulating or superinsulating nature of the material constituting the sample 10 tested, there is a very high thermal gradient between the two faces 12 and 14 of this sample. Consequently, the thermal conductivity obtained by the relation (1) corresponds to an average conductivity, which will be called "measured mean conductivity" and which will be referred to as "Km.mes". The values of the measured average conductivity corresponding to each of the pairs Tc (1), Tf (1); Tc (2), Tf (2) .... Tc (n),
Tf (n) are therefore designated by Km.mes (1), Km.mes (2) .... Km.mes (n), respectively.

dans laquelle K(T) est la fonction qui relie la conductivité vraie du matériau à la température T, dans l'intervalle de températures Tf-Tc.In general, the mathematical expression of the calculated average thermal conductivity
Km.cal is given by the relation

where K (T) is the function which relates the true conductivity of the material to the temperature T, in the temperature range Tf-Tc.

It follows from this relation (3) that it is not possible to assign each measured average conductivity Km.mes to a temperature, except in the case where the function K (T) is a straight line in the temperature range. Tf-Tc considered. In the latter case, the measured average conductivity KL.mes, corresponding to a temperature pair Tc,
Tf given, can be attributed to the average temperature
Tm given by the relationship
Tc + Tf
Tm = (4)
2
By convention, we will designate by Tm (l),
Tm (2) .... Tm (n) the average temperatures Tm corresponding respectively to the temperature pairs Tc (1), Tf (1); Tc (2), Tf (2). . Tc (n), Tf (n).

 In practice, the function K (T) is never a straight line. However, when the temperatures between which this function is integrated according to the relation (3) are separated by a sufficiently small difference, the function K (T) is comparable to a line segment on the interval considered.

 The method according to the invention exploits this observation, starting the measurements at sufficiently low temperatures Tc so that the difference between the values of Tc and Tf corresponding to at least the two lowest Tc values is small enough to allow the Tc assimilation of the function K (T) to a line segment on each of the intervals Tf-Tc concerns.

 The method according to the invention also exploits this observation by considering that the difference between the first two average temperatures Tm (1) and Tm (2) is sufficiently small for the function K (T) to be comparable to a straight line over this interval. .

 Concretely, these results are obtained by giving respectively Tc (1) and Tc (2) the values already mentioned of 500 C and 6000C.

The first two values sm.mes (1) and
Km.mes (2) of the average measured thermal conductivity can therefore be attributed to the first two average temperatures Tm (1) and Tm (2), respectively.

 On the other hand, when the temperature Tc rises above 6000C, the difference between the temperatures Tc and Tf is too great for the function N (T) to be assimilated to a straight line.

 Moreover, the continuation of this assimilation up to the measurements corresponding to the highest temperature Tc (n) would lead to attribute the measured average thermal conductivity Km.mes (n) to the average temperature Tm (n), that is, that is, a maximum temperature value substantially less than the value Tc (n) up to which it is desired to know the thermal conductivity.

successive fixed temperatures Tc (1), Tc (2), .... Tc (n) a sufficiently low value for the function K (T) to be assimilated to a line segment, on each interval between two values of Tc successive.

 Concretely, this result is obtained, in the embodiment described, giving this difference a value of 100 C.

 Thanks to the judicious choice of the first temperatures Tc (1) and Tc (2) and the difference between the different values given at fixed temperatures Tc, the method according to the invention makes it possible to solve the relation (3) by assimilating the function K (T) to a succession of line segments on the temperature ranges taken into account during measurements on the conductivity meter of FIGS. 1 and 2.

 On this basis, the measurements made on the conductivity meter make it possible to determine the thermal conductivity of the tested material, in the temperature range considered, by implementing the steps that will now be described.

 As a result of the measurement step, the heat flux values # and the temperature Tf corresponding to each of the values given at the temperature Tc c in the temperature range under consideration are acquired on the conductimetric that is, 500 C, 600 C, 700 C, 2300 C, 2400 C and 2500 C in the preferred embodiment), the corresponding values of the conductivity are determined using the relation (1). average thermal measured Km.mes.

The choice of the first two values Tc (l) and Tc (2) (500 C and o00 C) given at the temperature c making it possible to assign the corresponding values
Km.mes (1) and Km.mes (2) of the average conductivity measured at the average temperatures Tm (1) and Tm (2) and to assimilate the forron: S (T) to a straight line between these Km.mes ( 1) and Km.mes (2) of the average conductivity measured at the average temperatures Tm (1) and Tm (2) and to assimilate the function K (T) to a straight line between these two mean temperatures, we then determine, by the calculation, the values of the coefficients a1 and bl in the equation of this line K1 (T) = a1 T + b1.

km.mes(l) = a1Tm(l) + b1 km. mes(2) = a1Tm(2) + bl
Les valeurs choisies pour les premières températures Tc(1) et Tc(2) permettent d'extrapoler la fonction linéaire K1 (T) ainsi déterminée vers le bas jusqu'à la température Tf(1) et vers le haut jusqu'à la température Tc(1). More precisely, the values of these coefficients a1 and b1 are obtained by solving the system

km.mes (l) = a1Tm (l) + b1 km. my (2) = a1Tm (2) + bl
The values chosen for the first temperatures Tc (1) and Tc (2) make it possible to extrapolate the linear function K1 (T) thus determined down to the temperature Tf (1) and upwards to the temperature Tc (1).

 The accuracy of the linear function K1 (T) can be verified by comparing the value of the average measured thermal conductivity Km.mes (1) with the value of the calculated average conductivity Km.cal (1) obtained with the aid of the relation (3) and the function K1 (T) between the temperatures Tf (1) and Tc (1). This comparison will be made in the examples that will be given later.

When the equation of the first linear function K1 (T) has been determined in the manner just described, it is established by increasing iteration a series of linear functions K? (T), K3 (T) Kn (T) each of which is defined respectively on the temperature range Tc (1) -Tc (2); Tc (2)
TC (3); .... Tc (n-1) -Tc (n).

 The technique used to establish each of these linear functions K2 (T) to Kn (T) is identical. Only the determination of the linear function K2 (T) will therefore be described in detail.

ou encore

The relation (3), applied to the temperature interval Tf (2) -Tc (2), is written

or

In this equation (4), the first term is known. Indeed, Km.cal (2) corresponds, as we have already noted, to the average conductivity measured km.mes
(2). Furthermore, the values Tc (2) and Tf (2) were measured on the conductivity meter and the function K1 (T) was determined during the previous step of the process. The first term of equation (4) can therefore be likened to a known constant C2.

soit, puisque la fonction K2(T) est, par hypothèse, une fonction linéaire d'équation K2(T) = a2 T + b2 sur l'intervalle de températures Tc(1)-Tc(2)

Equation (4) then becomes

either, since the function K2 (T) is, by hypothesis, a linear function of equation K2 (T) = a2 T + b2 over the temperature range Tc (1) -Tc (2)

<tb> a2 / 2 <SEP> [(Tc (2)) <SEP> - <SEP> (Tc (1))] <SEP> + <SEP> b2 <SEP> [Tc (2) <SEP> - <SEP> Tc (1)] <SEP> = <SEP> C2 <SEP> (5)
<Tb>
Moreover, since the function K1 (T) is defined up to the temperature Tc (1), the value of the thermal conductivity K (Tc (1)) is already known at this temperature. The equation of the linear function K2 (T) is therefore written for this temperature Tc (1)
K (Tc (1)) = a2 TC (1) + b2 (6)
The resolution of the system formed by equations (5) and (6) makes it possible to determine the coefficients a2 and b2. The equation of the linear function K2 (T), defined over the temperature interval Tc (1), is thus obtained. - Tc (2).

 The repetition of these operations makes it possible to determine, step by step, the equations of the functions K3 (T) to Xn (T), in a similar manner.

The accuracy of linear functions K2 (T) to
Kn (T) can also be verified by comparing the mean measured thermal conductivity values
Km.mes (n) to mean calculated thermal conductivity values Sm.cal (2) to Km.cal (n) obtained from relation (3) and K2 (T) functions to K (T).

 In practice, the calculations which have just been explained are advantageously carried out by a computer which thus determines, for the material under test, the evolution of its thermal conductivity calculated with the temperature, in the temperature range considered, from the measurements performed in the conductivity meter of Figures 1 and 2.

 The calculations used in the process according to the invention were validated by modeling, under conditions identical to those of the real tests, from a fictitious sample of a known thermal conductivity material, having a thickness e of 1 cm, a section S of 25 cm 2, the emissivity of the cold face being 0.8. The temperature To of the environment was assumed to be 20 ° C.

 By fictitiously varying the temperature Tc of the hot face from 500 ° C. to 2000 ° C., in steps of 100 ° C., the temperature Tf of the cold face was calculated for each value of Tc. This calculation was done by finite differences, in steps of 0.1 mm. By hypothesis, the radiation temperature Tr is assumed equal to the temperature Tf.

We then calculated, for each value of
Tc, the temperature Tm determined by the relation (4), the thermal flux, determined by the relation (2), the measured average thermal conductivity Km.mes (Tm), determined by the relation (1), the calculated thermal conductivity K .cal (Tc) at the temperature Tc, obtained by the method according to the invention and, in order to validate the results, the calculated average thermal conductivity Km.cal (Tm), given by the relation (3).

 The results of this modeling are given in Table A.

TABLE A
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tc (C) Tm (C) # (W) Km.mes (Tm) Km.cal (Tm) K.cal (Tc)
310 310 500 405 12.26 2.58D-03 2.60D-03 2.98D-03
360 360 600 460 17.37 2.90D-03 2.91D-03 3.41D-03
405 405 700 553 23.13 3.14D-03 3.14D-03 3.37D-03
444 444 800 622 29.13 3.27D-03 3.29D-03 3.61D-03
479 479 900 690 35.43 3.37D-03 3.38D-03 3.41D-03
511 511 1000 755 42.01 3.44D-03 3.43D-03 3.55D-03
538 538 1100 819 48.22 3.43D-03 3.45D-03 3.33D-03
564 564 1200 882 54.82 3.45D-03 3.45D-03 3.49D-03
588 588 1300 944 61.48 3.45D-03 3.46D-03 3.40D-03
611 611 1400 1006 66.41 3.47D-03 3.47D-03 3.75D-03
634 634 1500 1067 75.91 3.51D-03 3.51D-03 3.88D-03
658 658 1600 1129 84.36 3.58D-03 3.59D-03 4.53D-03
684 684 1700 1192 94.28 3.71D-03 3.71D-03 4.96D-03
711 711 1600 1256 105.46 3.67D-03 3.37D-03 5.78D-03
738 738 1900 1319 117.64 4.05D-03 4.06D-03 6.14D-03
766 766 2000 1388 131.32 4.26D-03 4.26D-03 6.50D-03
The results of the modeling carried out on a fictitious sample are also shown in FIG.

More precisely, curve I of FIG. 3 represents the evolution of the known theoretical thermal conductivity K (in W / cm C) of the modeled material as a function of the temperature T (in C). Curve II illustrates the evolution of the calculated thermal conductivity, K.cal (Tc) for the different temperatures
Tc, according to the method of the invention, as a function of the temperature T. Finally, the curve III represents the variation of the calculated average thermal conductivity Dm.cal (Tm) for the different temperatures Tm, according to the relation (3).

The results shown in Table A and in Figure 3 show that the only use of the relation (1) does not make it possible to determine the conductivity of the sample (compare curves I and III in FIG. 3, knowing that Km. my (Tm) and
Km.cal (Tm) are substantially equal, as shown in Table A).

On the other hand, these results show that the calculated thermal conductivities K.cal (Tc) at the temperatures Tc, according to the process of the invention, are practically identical to the theoretical thermal conductivities (compare the curves I and II)
These results also show that the average thermal conductivities calculated .Nm.cal (Tm) at the temperatures Tm, obtained by the relation (3), are practically identical to the average thermal conductivities measured m (Tm) at the same temperatures m.

 The calculation steps of the method according to the invention thus make it possible to determine, with great precision, the thermal concuctibilities of a material at very high temperatures, the upper limit of which depends only on the heating means used in the conductivity meter. .

In order to validate the accuracy of the measurements made by the conductivity meter of FIGS. 1 and 2, a complete characterization of three real materials has also been performed, to compare the calculated thermal conductivity K.cal (Tc) with the temperatures Tc, obtained by the method according to the invention, to the thermal conductivity K.ref (Tc) of the same materials, at temperatures Tc, obtained by the relation
K.ref (Tc) = a (Tc) .p.Cp (Tc) (7) in which - a represents the thermal diffusivity of the material (in cm2 / s) - p represents the density of the material (in
g / cm2); and - Cp represents the specific heat of the material (in J / g.0C)
Thus, for each of the three materials tested, the thermal diffusivity was measured under argon, between 500 C and 2000 C, with an accuracy of 5 E. The density p 2 was measured at 20 C with an accuracy of 1%. Finally, the specific heat Cp was measured between 5000C and 600 C, with an accuracy limited to 7 i, given the very low mass of the specimen. These measurements were carried out under nitrogen, with a kinetics of 5 C / mm. Beyond 600 C, the values of Cp were taken from the tables.

 Thus, for each of the three test materials, the values of the reference thermal conductivity K.ref (Tc), given by the relation (7), were determined at temperatures Tc of between 500 and 2000 C.

 In addition, tests were carried out on the same materials to determine the calculated thermal conductivities K.cal. (Tc), at temperatures Tc, obtained by the process according to the invention. The measurements, carried out under argon, were carried out using the conductimetre of FIGS. 1 and 2, by varying the temperature Tc from 500 ° C. to 2500 ° C., in steps of 100 ° C.

 To verify the reproducibility of the measurements, each of the two series of tests was carried out on three samples of each material, 1.20 cm thick.

 The uncertainty in the conductivity measurement performed by the process according to the invention is estimated at 15%. This uncertainty is due to inaccuracy in the measurements of the temperatures Tc, Tf and Tr, leading to an error estimated between 5 + and 12% depending on the configurations and the test temperature, and the lateral thermal losses, leading to an error. estimated at about 5 i.

 The results of the various measurements are given in Tables B to F for the first material, consisting of "CALCHRB" (standard name), in Tables G to L for the second material, consisting of "CALCARB" (registered name). ), and on Tables M to Q, for the third material, consisting of "CALCBRB" (registered name) high density.

Tables 3, C and D; G, H and I; and M,
N and O are tables similar to Table A which give the results of the measurements and calculations for each of the three samples, successively in the case of the first material, in the case of the second material and in the case of the third material.

 For each of the materials tested, only one of the samples was characterized up to 2500 C, these are the samples for which the results are shown in Tables D, I and O. On the other samples, the measurements were not performed only up to 2000 C, to avoid a large consumption of resistors.

 Tables E, J and P respectively summarize for each of the three materials the calculated thermal conductivities K.cal (Tc) at temperatures Tc, using the method according to the invention, for the three samples, indicating the average conductivities obtained. as well as the inserts.

 Finally, the tables F, L and Q give, respectively for each of the three materials, the values of Cp and a at the temperatures considered, the reference thermal conductivities K.ref obtained from the relation (7), the thermal conductivities calculated K.cal obtained by the process according to the invention, and the differences between these two conductivities.

TABLE B
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tm (C) # (W) Km.mes (Tm) Km.cal (Tm) K.cal (Tc)
242 250 500 375 8 86 1.70D-03 1.72D-03 2.05D-03
282 291 600 445 12.31 1.91D-03 1.91D-03 2.31D-03
318 330 700 515 16.12 2.09D-03 2.09D-03 2.61D-03
353 367 800 583 20.56 2.28D-03 2.28D-03 2.85D-03
386 403 900 651 25.48 2.46D-03 2.47D-03 3.22D-03
418 439 1000 719 31.02 2.65D-03 2.67D-03 3.50D-03
450 474 1100 787 37.39 2.87D-03 2.88D-03 3.95D-03
482 510 1200 855 44.65 3.11D-03 3.11D-03 4.27D-03
512 545 1300 922 52.36 3.33D-03 3.34D-03 4.79D-03
544 581 1400 990 61.61 3.61D-03 3.60D-03 5.27D-03
573 622 1500 1061 70.91 3.88D-03 3.89D-03 5.96D-03
604 660 1600 1130 82.15 4.19D-03 4.20D-03 6.48D-03
634 698 1700 1199 94.13 4.51D-03 4.53D-03 7.38D-03
666 739 1800 1269 108.28 4.90D-03 4.91D-03 8.06D-03
698 780 1900 1340 123.96 5.310-03 5.32D-03 9.30D-03
731 820 2000 1410 141.84 5.77D-03 5.77D-03 1.00D-02
TABLE C
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tc (C) # (W) Km.mes (Tm) Km.cal (Tc) K.cal (Tc)
242 271 500 385 8.86 1.86D-03 1.87D-03 2.17D-03
281 317 600 458 12.21 2.07D-03 2.07D-03 2.43D-03
318 362 700 531 16.12 2.29D-03 2.29D-03 2.90D-03
353 405 800 602 20.56 2.50D-03 2.52D-03 3. llD-03
388 447 900 673 25.81 2.73D-03 2.75D-03 3.58D-03
421 490 1000 745 31.58 2.970-03 2.99D-03 3.77D-03
453 530 1100 815 38.03 3.20D-03 3.22D-03 4.18D-03
484 571 1200 885 45.14 3.44D-03 3.45D-03 4.36D-03
515 610 1300 955 53.18 3.70D-03 3.67D-03 4.87D-03
546 651 1400 1025 62.23 3.99D-03 3.91D-03 5.10D-03
575 627 1500 1063 71.68 3.94D-03 4.04D-03 5.67D-03
607 664 1600 1132 83.29 4.27D-03 4.30D-03 6.24D-03
537 701 1700 1200 95.39 4.58D-03 4.59D-03 7.000-03
668 740 1800 1270 109.22 4.95D-03 4.94D-03 8.16D-03
700 780 1900 1340 125.00 5.36D-03 5.35D-03 9.33D-03
733 822 2000 1411 142.98 5.83D-03 5.84D-03 1.13 D-02
TABLE D
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tc (C) # (W) Km.mes (Tm) Km.cal (Tm) K.cal (Tc)
239 259 500 379 8.63 1.72D-03 1.74D-03 2.02D-03
278 302 600 451 11 92 1.92D-03 1.91D-03 2.26D-03
314 342 700 521 15.66 2.10D-03 2.09D-03 2.61D-03
348 381 800 590 19 88 2.28D-03 2.29D-03 2.86D-03
382 419 900 659 24 85 2.48D-03 2.49D-03 3.26D-03
415 457 1000 728 30.47 2.69D-03 2.70D-03 3.53D-03
447 493 1100 796 36.75 2.91D-03 2.91D-03 3.95D-03
478 529 1200 864 43 69 3.13D-03 3.14D-03 4.26D-03
509 565 1300 932 51.55 3.37D-03 3.37D-03 4.75D-03
540 601 1400 1000 60.40 3.63D-03 3.62D-03 5.14D-03
567 636 1500 1068 68.97 3.83D-03 3.89D-03 5.77D-03
599 680 1600 1140 80.27 4.19D-03 4.19D-03 6.32D-03
629 720 1700 1210 92.04 4.51D-03 4.51D-03 7.10D-03
660 761 1800 1280 105.52 4.87D-03 4.87D-03 7.83D-03
692 803 1900 1351 120.90 5.29D-03 5.27D-03 9.00D-03
724 847 2000 1423 137.90 5.74D-03 5.73D-03 1 O1D-02
757 893 2100 1496 157.23 6.25D-03 6.26D-03 6.26D-03 1.18D-02
792 942 2200 1571 179 86 6.86D-03 6.890-03 1.35D-02
829 1000 2300 1650 206.34 7.62D-03 7.65D-03 1.59D-02
868 1067 2400 1733 237.29 8.54D-03 8.58D-03 1.87D-02
911 1135 2500 1817 275.30 9.68D-03 9.67D-03 2.21D-02
TABLE E

<tb> Temp. <SEP> Conductivity <SEP> calculated <SEP> in <SEP> W / Cm C <SEP> Difference <SEP> max
<tb> in <SEP> C <SEP> Ech. <SEP> n <SEP> 1 <SEP> Ech. <SEP> n <SEP> 2 <SEP> Runtime <SEP> n <SEP> 3 <SEP> Average <SEP> by <SEP>%
<tb><SEP> 500 <SEP> 2.20E-03 <SEP> 2.17E-03 <SEP> 2.02E-03 <SEP> 2.13E-03 <SEP> 3
<tb><SEP> 600 <SEP> 2.31E-03 <SEP> 2.43E-03 <SEP> 2.26E-03 <SEP> 2.33E-03 <SEP> 4
<tb><SEP> 700 <SEP> 2.61E-03 <SEP> 2.90E-03 <SEP> 2.61E-03 <SEP> 2.71E-03 <SEP> 7
<tb><SEP> 800 <SEP> 2.85E-03 <SEP> 3.11E-03 <SEP> 2.86E-03 <SEP> 2.94E-03 <SEP> 6
<tb><SEP> 900 <SEP> 3.22E-03 <SEP> 3.58E-03 <SEP> 3.26E-03 <SEP> 3.35E-03 <SEP> 7
<tb><SEP> 1000 <SEP> 3.50E-03 <SEP> 3.77E-03 <SEP> 3.53E-03 <SEP> 3.60E-03 <SEP> 5
<tb><SEP> 1100 <SEP> 3.95E-03 <SEP> 4.18E-03 <SEP> 3.95E-03 <SEP> 4.03E-03 <SEP> 4
<tb><SEP> 1200 <SEP> 4.27E-03 <SEP> 4.37E-03 <SEP> 4.26E-03 <SEP> 4.30E-03 <SEP> 1
<tb><SEP> 1300 <SEQ> 4.79E-03 <SEP> 4.87E-03 <SEP> 4.75E-03 <SEP> 4.80E-03 <SEP> 1
<tb><SEP> 1400 <SEP> 5.27E-03 <SEP> 5.10E-03 <SEP> 5.14E-03 <SEP> 5.17E-03 <SEP> 2
<tb><SEP> 1500 <SEP> 5.96E-03 <SEP> 5.67E-03 <SEP> 5.77E-03 <SEP> 5.80E-03 <SEP> 3
<tb><SEP> 1600 <SEP> 6.48E-03 <SEP> 6.24E-03 <SEP> 6.32E-03 <SEP> 6.35E-03 <SEP> 2
<tb><SEP> 1700 <SEP> 7.38E-03 <SEP> 7.00E-03 <SEP> 7.10E-03 <SEP> 7.16E-03 <SEP> 3
<tb><SEP> 1800 <SEP> 8.06E-03 <SEP> 8.16E-03 <SEP> 7.83E-03 <SEP> 8.02E-03 <SEP> 2
<tb><SEP> 1900 <SEP> 9.30E-03 <SEP> 9.33E-03 <SEP> 9.00E-03 <SEP> 9.21E-03 <SEP> 1
<tb><SEP> 2000 <SEP> 1.00E-02 <SEP> 1.13E-02 <SEP> 1.01E-02 <SEP> 1.05E-02 <SEP> 8
<tb><SEP> 2100 <SEP> 1.18E-02
<tb><SEP> 2200 <SEP> 1.35E-02
<tb><SEP> 2300 <SEP> 1.59E-02
<tb><SEP> 2400 <SEP> 1.87E-02
<tb><SEP> 2500 <SEP> 2.21E-02
<Tb>
TABLE F

<SEP> Heat <SEP> specific <SEP> in <SEP>"a"<SEP> in <SEP> Cm / s <SEP> Conductivity <SEP> in <SEP> Difference
<tb> Temp.
<Tb>

<SEP> J / g. <SEP> C <SEP> W / Cm C
<tb><SEP> in <SEP> C <SEP> Cp <SEP> measured <SEP> Cp <SEP> library <SEP>"to"<SEP> measured <SEP> K.ref. <SEP> K.cal <SEP> in <SEP>%
<tb><SEP> 500 <SEP> 1.6 <SEP> 1.56 <SEP> 9.70E-03 <SEP> 2.42E-03 <SEP> 2.13E-03 <SEP> -12
<tb><SEP> 600 <SEP> 1.7 <SE> 1.65 <SEP> 1.04E-02 <SEP> 2.75E-03 <SEP> 2.33E-03 <SEP> -15
<tb><SEP> 700 <SEP> 1.70 <SEP> 1.11E-02 <SEP> 3.02E-03 <SEP> 2.71E-03 <SEP> -10
<tb><SEP> 800 <SEP> 1.76 <SEP> 1.20E-02 <SEP> 3.38E-03 <SEP> 2.94E-03 <SEP> -13
<tb><SEP> 900 <SE> 1.81 <SEP> 1.30E-02 <SEP> 3.76E-03 <SEP> 3.35E-03 <SEP> -11
<tb><SEP> 1000 <SEP> 1.84 <SEP> 1.40E-02 <SEP> 4.12E-03 <SEP> 3.60E-03 <SEP> -13
<tb><SEP> 1100 <SEP> 1.87 <SEP> 1.52E-02 <SEP> 4.55E-03 <SEP> 4.03E-03 <SEP> -11
<tb><SEP> 1200 <SEP> 1.90 <SEP> 1.65E-02 <SEP> 5.02E-02 <SEP> 4.30E-03 <SEP> -14
<tb><SEP> 1300 <SEP> 1.92 <SEP> 1.77E-02 <SEP> 5.44E-03 <SEP> 4.80E-03 <SEP> -12
<tb><SEP> 1400 <SEP> 1.94 <SEP> 1.93E-02 <SEP> 5.99E-03 <SEP> 5.17E-03 <SEP> -14
<tb><SEP> 1500 <SE> 1.96 <SEP> 2.10E-02 <SEP> 6.59E-03 <SEP> 5.08E-03 <SEP> -12
<tb><SEP> 1600 <SEP> 1.98 <SEP> 2.23E-02 <SEP> 7.06E-03 <SEP> 6.35E-03 <SEP> -10
<tb><SEP> 1700 <SEP> 2.02 <SEP> 2.46E-02 <SEP> 7.95E-03 <SEP> 7.16E-03 <SEP> -10
<tb><SEP> 1800 <SEP> 2.04 <SEP> 2.67E-02 <SEP> 8.71E-03 <SEP> 8.02E-03 <SEP> -8
<tb><SEP> 1900 <SEP> 2.06 <SEP> 3.10E-02 <SEP> 1.02E-02 <SEP> 9.21E-03 <SEP> -10
<tb><SEP> 2000 <SEP> 2.08 <SEP> 3.35E-02 <SEP> 1.11E-02 <SEP> 1.05E-02 <SEP> -6
<Tb>
TABLE G
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tc (C) Tm (C) # (W) Km.mes (Tm) Km.cal (Tm) K.cal (Tc)
285 306 500 403 12.60 3.12D-03 3.13D-03 3.48D-03
328 355 600 477 17.31 3.39D-03 3.41D-03 3.84D-03
367 401 700 550 22.56 3.62D-03 3.65D-03 4.10D-03
405 446 800 623 28 58 3.89D-03 3.89D-03 4.46D-03
440 488 900 694 35 30 4.11D-03 4.11D-03 4.72D-03
473 529 1000 764 42.51 4.33D-03 4.34D-03 5.12D-03
505 569 1100 834 50.48 4.56D-03 4.57D-03 5.48D-03
536 607 1200 903 59 20 4.79D-03 4.82D-03 5.95D-03
567 646 1300 973 68.97 5.06D-03 5.08D-03 6.42D-03
597 685 1400 1042 79.52 5.34D-03 5.36D-03 6.92D-03
625 744 1500 1122 90.40 5.74D-03 5.72D-03 7.76D-03
654 785 1600 1192 102.80 6.05D-03 6.06D-03 8.09D-03
684 827 1700 1263 116.91 6.43D-03 6.44D-03 9.23D-03
714 869 1800 1334 132.41 6.83D-03 6.84D-03 9.61D-03
744 912 1900 1406 149 39 7.26D-03 7.28D-03 1.09D-02
775 956 2000 1478 168.58 7.75D-03 7.75D-03 1.13D-02
TABLE H
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tm (C) # (W) Km.mes (Tm) Km.cal (Tm) K.cal (Tc)
282 302 500 401 12.31 2.98D-03 3.00D-03 3.34D-03
325 350 600 475 16.95 3.25D-03 3.26D-03 3.69D-03
364 395 700 547 22 12 3.48D-03 3.51D-03 3.98D-03
402 438 800 619 28.15 3.73D-03 3.74D-03 4.34D-03
437 479 900 689 34.70 3.96D-03 3.97D-03 4.56D-03
470 518 1000 759 41.82 4.16D-03 4.18D-03 4.95D-03
502 555 1100 827 49 69 4.38D-03 4.39D-03 5.13D-03
533 591 1200 895 58.31 4.600-03 4.60D-03 5.61D-03
563 627 1300 963 67.65 4.82D-03 4.81D-03 5.86D-03
593 663 1400 1031 78 05 5.08D-03 5.040-03 6.46D-03
622 670 1500 1085 89.19 5.16D-03 5.24D-03 6.78D-03
653 708 1600 1154 102.35 5.51D-03 5.53D-03 7.81D-03
683 745 1700 1222 116.42 5.85D-03 5.85D-03 8.35D-03
714 784 1800 1292 132.41 6.26D-03 6.25D-03 1 OOD-02
746 824 1900 1362 150.57 6.77D-03 6.71D-03 1.09D-02
779 866 2000 1433 171 15 7.25D-03 7.270-03 1.33D-02
TABLE I
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tc (C) Tm (C) # (W) Km.mes (Tm) Km.cal (Tm) K.cal (Tc)
287 299 500 399 12.79 3.05D-03 3.07D-03 3.14D-03
330 345 600 472 17.55 3.30D-03 3.33D-03 3.76D-03
370 389 700 544 23.00 3.55D-03 3.57D-03 4.05D-03
408 430 800 615 29 21 3.79D-03 3.80D-03 4.37D-03
443 470 900 685 35 92 4.01D-03 4.010-03 4.63D-03
476 507 1000 753 43 22 4.21D-03 4.22D-03 4.96D-03
508 544 1100 822 51.28 4.43D-03 4.43D-03 5.28D-03
539 579 1200 889 60.09 4.64D-03 4.64D-03 5.59D-03
568 613 1300 956 69.31 4.84D-03 4.85D-03 6.03D-03
597 648 1400 1024 79.52 5.08D-03 5.09D-03 6.45D-03
625 679 1500 1089 90 40 5.29D-03 5.33D-03 6.93D-03
654 714 1600 1157 102.80 5.57D-03 5.60D-03 7.68D-03
683 751 1701 1226 116 42 5.88D-03 5.91D-03 8.310-03
713 789 1800 1294 131.87 6.26 6.26D-03 9.31D-03
744 827 1900 1363 149.39 6.68D-03 6.66D-03 1.03D-02
775 867 2000 1433 168 58 7.14D-03 7.12D-03 1.17D-02
807 909 2100 1504 190 27 7.67D-03 7.66D-03 1.32D-02
840 953 2200 1576 214 75 8.27D-03 8.29D-03 1.52D-02
875 1000 2300 1650 243.20 8.98D-03 9.03D-03 1.75D-02
913 1050 2400 1725 277.17 8.96D-03 9.91D-03 2.00D-02
955 1104 2500 1802 318.73 1.10D-02 1.09D-02 2.35D-02
TABLE J

<tb> Temp. <SEP> Calculated <SEP> Concitivity <SEP> in <SEP> W / Cm C <SEP> Max SEP> Max
<tb> in <SEP> C <SEP> Ech. <SEP> n <SEP> 1 <SEP> Ech. <SEP> n <SEP> 2 <SEP> Ech. <SEP> n <SEP> 3 <SEP> Average <SEP> in <SEP>%
<tb><SEP> 500 <SE> 3.48E-03 <SEP> 3.34E-03 <SEP> 3.41E-03 <SEP> 3.41E-03 <SEP> 2
<tb><SEP> 600 <SEP> 3.84E-03 <SEP> 3.69E-03 <SEP> 3.76E-03 <SEP> 3.76E-03 <SEP> 2
<tb><SEP> 700 <SEP> 4.10E-03 <SEP> 3.96E-03 <SEP> 4.05E-03 <SEP> 4.04E-03 <SEP> 1
<tb><SEP> 800 <SEQ> 4.46E-03 <SEP> 4.34E-03 <SEP> 4.37E-03 <SEP> 4.39E-03 <SEP> 2
<tb><SEP> 900 <SEQ> 4.72E-03 <SEP> 4.56E-03 <SEP> 4.63E-03 <SEP> 4.64E-03 <SEP> 2
<tb><SEP> 1000 <SEP> 5.12E-03 <SEP> 4.95E-03 <SEP> 4.96E-03 <SEP> 5.01E-03 <SEP> 2
<tb><SEP> 1100 <SEP> 5.48E-03 <SEP> 5.13E-03 <SEP> 5.28E-03 <SEP> 5.30E-03 <SEP> 3
<tb><SEP> 1200 <SEP> 5.95E-03 <SEP> 5.61E-03 <SEP> 5.59E-03 <SEP> 5.72E-03 <SEP> 4
<tb><SEP> 1300 <SEP> 6.42E-03 <SEP> 5.86E-03 <SEP> 6.03E-03 <SEP> 6.10E-03 <SEP> 5
<tb><SEP> 1400 <SEP> 6.92E-03 <SEP> 6.46E-03 <SEP> 6.45E-03 <SEP> 6.61E-03 <SEP> 5
<tb><SEP> 1500 <SEP> 7.76E-03 <SEP> 6.78E-03 <SEP> 6.93E-03 <SEP> 7.16E-03 <SEP> 8
<tb><SEP> 1600 <SEP> 8.09E-03 <SEP> 7.81E-03 <SEP> 7.68E-03 <SEP> 7.68E-03 <SEP> 3
<tb><SEP> 1700 <SEP> 9.23E-03 <SEP> 8.35E-03 <SEP> 8.31E-03 <SEP> 8.63E-03 <SEP> 7
<tb><SEP> 1800 <SEP> 9.61E-03 <SEP> 1.00E-02 <SEP> 9.31E-03 <SEP> 9.64E-03 <SEP> 4
<tb><SEP> 1900 <SEP> 1.09E-02 <SEP> 1.09E-02 <SEP> 1.03E-02 <SEP> 1.07E-03 <SEP> 2
<tb><SEP> 2000 <SEP> 1.13E-02 <SEP> 1.33E-02 <SEP> 1.17E-02 <SEP> 1.21E-02 <SEP> 10
<tb><SEP> 2100 <SEP> 1.32E-02
<tb><SEP> 2200 <SEP> 1.52E-02
<tb><SEP> 2300 <SEP>! <SEP><SEP> 1.75E-02 <SEP>
<tb><SEP> 2400 <SEP> 2.00E-02
<tb><SEP> 2500 <SEP> 2.35E-02
<Tb>
TABLE L

<tb> Temp. <SEP> Heat <SEP> specific <SEP> in <SEP>"a"<SEP> in <SEP> Cm / s <SEP> Conductivity <SEP> in <SEP> Difference
<tb> J / g. C <SEP> W / Cm C
<tb> in <SEP> C <SEP> Cp <SEP> measured <SEP> Cp <SEP> hiblic <SEP>"to"<SEP> measured <SEP> K.ref. <SEP> K.cal. <SEP> in <SEP>%
<tb><SEP> 500 <SEP> 1.6 <SEP> 1.56 <SEP> 9.60E-03 <SEP> 3.74E-03 <SEP> 3.41E-03 <SEP> -9
<tb><SEP> 600 <SEP> 1.7 <SE> 1.65 <SEP> 9.70E-03 <SEP> 4.00E-03 <SEP> 3.76E-03 <SEP> -6
<tb><SEP> 700 <SEP> 1.70 <SEP> 1.00E-02 <SEP> 4.25E-03 <SEP> 4.04E-03 <SEP> -5
<tb><SEP> 800 <SEP> 1.76 <SEP> 1.05E-03 <SEP> 4.62E-03 <SEP> 4.39E-03 <SEP> -5
<tb><SEP> 900 <SEP> 1.81 <SEP> 1.11E-02 <SEP> 5.02E-03 <SEP> 4.64E-03 <SEP> -8
<tb><SEP> 1000 <SEP> 1.84 <SEP> 1.17E-02 <SEP> 5.38E-03 <SEP> 5.01E-03 <SEP> -7
<tb><SEP> 1100 <SEP> 1.87 <SEP> 1.25E-02 <SEP> 5.84E-03 <SEP> 5.30E-03 <SEP> -9
<tb><SEP> 1200 <SEP> 1.90 <SE> 1.33E-02 <SEP> 6.32E-03 <SEP> 5.72E-03 <SEP> -9
<tb><SEP> 1300 <SEP> 1.92 <SE> 1.41E-02 <SEP> 6.77E-03 <SEP> 6.61E-03 <SEP> -10
<tb><SEP> 1400 <SEP> 1.94 <SEP> 1.50E-02 <SEP> 7.28E-03 <SEP> 6.61E-03 <SEP> -9
<tb><SEP> 1500 <SE> 1.96 <SE> 1.60E-02 <SEP> 7.84E-03 <SEP> 7.16E-03 <SEP> -9
<tb><SEP> 1600 <SEP> 1.98 <SEP> 1.69E-02 <SEP> 8.37E-03 <SEP> 7.86E-03 <SEP> -6
<tb><SEP> 1700 <SEP> 2.02 <SEP> 1.80E-02 <SEP> 9.09E-03 <SEP> 8.63E-03 <SEP> -5
<tb><SEP> 1800 <SEP> 2.04 <SEP> 1.93E-02 <SEP> 9.84E-03 <SEP> 9.64E-03 <SEP> -2
<tb><SEP> 1900 <SEP> 2.06 <SEP> 2.05E-02 <SEP> 1.06E-02 <SEP> 1.07E-02 <SEP> 1
<tb><SEP> 2000 <SEP> 2.08 <SEP> 2.16E-02 <SEP> 1.12E-02 <SEP> 1.21E-02 <SEP> 8
<Tb>
TABLE M
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tc (C) Tm (C) # (W) Km.mes (Tm) Km.cal (Tm) K.cal (Tc)
370 388 500 444 23.00 9.68D-03 1.00D-02 1.02D-02
425 451 600 525 32.53 1.05D-02 1.04D-02 1.08D-02
477 508 700 604 43.46 1.09D-02 1.09D-02 1.13D-02
523 563 800 681 55.42 1.12D-02 1.12D-02 1.17D-02
566 613 900 756 68.54 1.15D-02 1.16D-02 1.22D-02
605 660 1000 830 82.53 1.17D-02 i.19D-02 1.25D-02
644 708 1100 904 98.39 1.20D-02 1.22D-02 1.28D-02
681 754 1200 977 115.44 1.24D-02 1.24D-02 1.30D-02
716 799 1300 10 ;; 9 133.49 1.28D-02 1.26D-02 1.33D-02
750 843 1400 1121 152.97 1.32 1.28D-02 1.37D-02
779 855 1500 1177 171.19 1.27D-02 1.30D-02 1.42D-02
811 895 1600 1247 193.12 1.31D-02 1.33D-02 1.51D-02
844 936 1700 1319 217.86 1.37D-02 1.37D-02 1.64D-02
876 976 1800 1388 244.05 1.42D-02 1.42D-02 1.81D-02
909 1020 1900 1460 273.44 1.49D-02 1.49D-02 2.08D-02
944 1064 2000 1532 30.42 1.58D-02 1.58D-02 2.40D-02
TABLE N
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tc (C) Tm (C) # (W) Km.mes (Tm) Km.cal (Tm) K.cal (Tc)
373 384 500 442 23.45 9.70D-03 9.78D-03 1.02D-02
430 445 600 522 33.31 1.03D-02 1.04D-02 1.09D-02
482 502 700 601 44.65 1.08D-02 1.09D-02 1.13D-02
530 555 800 677 57.43 1.13D-02 1.13D-02 1.19D-02
573 605 900 752 70.99 1.16D-02 1.15D-02 1.21D-02
614 652 1000 826 86.01 1.19D-02 1.19D-02 1.25D-02
652 697 1100 898 101.91 1.21D-02 1.22D-02 1.27D-02
688 741 1200 970 118.89 1.24D-02 1.24D-02 1.34D-02
722 782 1300 1041 136.79 1.27D-02 1.27D-02 1.38D-02
755 823 1400 1111 156.00 1.30D-02 1.30D-02 1.46D-02
788 862 1500 1181 177.16 1.33D-02 1.34D-02 1.54D-02
822 903 1600 1251 201.12 1.39D-02 1.39D-02 1.65D-02
855 943 1700 132 '226.62 1.44D-02 1.44D-02 1.79D-02
889 984 1800 1392 255.33 1.SOD-02 1.50D-02 1.96D-02
923 1025 1900 1463 286.68 1.57D-02 1.58D-02 2.14D-02
957 1075 2000 1537 320.81 1.66D-02 1.67D-02 2.39D-02
TABLE O
K = Conductivity (W / Cm C)
Tr (C) Tf (C) Tc (C) Tm (C) # (W) Km.mes (Tm) Km.cal (Tm) K.cal (Tc)
367 381 500 440 22.56 9.10D-03 9.23D-03 9.68D-03
425 443 600 521 32.34 9.S9D-03 9.93D-03 1.05D-02
477 501 700 600 43.46 1.05D-02 1.05D-02 1.10D-02
525 555 800 677 55.99 1.10D-02 1.10D-02 1.17D-02
569 606 900 753 69.64 1.14D-02 1.14D-02 1.21D-02
610 654 1000 827 84.45 1.17D-02 1.18D-02 1.26D-02
649 699 1100 899 100.58 1.20D-02 1.21D-02 1.28D-02
685 744 1200 972 117.40 1.24D-02 1.24D-02 1.35D-02
719 785 1300 1042 135.13 1.26D-02 1.27D-02 1.39D-02
752 826 1400 1113 154.18 1.29D-02 1.31D-02 1.47D-02
782 896 1500 1198 173.16 1.38D-02 1.35D-02 1.52D-02
812 938 1600 1259 193.84 1.41D-02 1.40D-02 1.61D-02
842 979 1700 1339 216.30 1.44D-02 1.44D-02 1.69D-02
871 1022 1800 1411 239.81 1.48D-02 1.49D-02 1.93D-02
902 1074 1900 1487 267.00 1.55D-02 1.55D-02 1.92D-02
933 1119 2000 1559 296.42 1.62D-02 1.62D-02 2.05D-02
965 1163 2100 1631 329.27 1.69D-02 1.69D-02 2.21D-02
996 1205 2200 1702 363.62 1.75D-02 1.76D-02 2.35D-02 1027 1247 2300 1773 400.58 1.83D-02 1.84D-02 2.53D-02 1062 1298 2400 1849 445.51 1.94D-02 1.93D-02 2.73D- 02
TABLE P

<tb> Temp. <SEP> Conductivity <SEP> calculated <SEP> in <SEP> W / Cm C <SEP> Difference <SEP> max
<tb> in <SEP> C <SEP> Ech. <SEP> n <SEP> 1 <SEP> Ech. <SEP> n 2 <SEP> Runtime <SEP> n <SEP> 3 <SEP> Average <SEP> by <SEP>%
<tb><SEP> 500 <SEP> 1.02E-02 <SEP> 1.02E-02 <SEP>) .68D-03 <SEP> 1.00E-02 <SEP> 2
<tb><SEP> 600 <SEP> 1.08E-02 <SEP> 1.09E-02 <SEP> 1.05E-02 <SEP> 1.07E-02 <SEP> 2
<tb><SEP> 700 <SEP> 1.13E-02 <SEP> 1.13E-02 <SEP> 1.10E-02 <SEP> 1.12E-02 <SEP> 1
<tb><SEP> 800 <SEP> 1.17E-02 <SEP> 1.19E-02 <SEP> 1.17E-02 <SEP> 1.18E-02 <SEP> 1
<tb><SEP> 900 <SEQ> 1.22E-02 <SEP> 1.21E-02 <SEP> 1.21E-02 <SEP> 1.21E-02 <SEP> 1
<tb><SEP> 1000 <SEP> 1.25E-02 <SEP> 1.25E-02 <SEP> 1.26E-02 <SEP> 1.25E-02 <SEP> 1
<tb><SEP> 1100 <SEP> 1.28E-02 <SEP> 1.27E-02 <SEP> 1.28E-02 <SEP> 1.28E-02 <SEP> 0
<tb><SEP> 1200 <SEP> 1.30E-02 <SEP> 1.34E-02 <SEP> 1.35E-02 <SEP> 1.33E-02 <SEP> 2
<tb><SEP> 1300 <SE> 1.33E-02 <SEP> 1.38E-02 <SEP> 1.39E-02 <SEP> 1.37E-02 <SEP> 2
<tb><SEP> 1400 <SEP> 1.37E-02 <SEP> 1.46E-02 <SEP> 1.47E-02 <SEP> 1.43E-02 <SEP> 3
<tb><SEP> 1500 <SEP> 1.42E-02 <SEP> 1.54E-02 <SEP> 1.52E-02 <SEP> 1.49E-02 <SEP> 3
<tb><SEP> 1600 <SEP> 1.51E-02 <SEP> 1.65E-02 <SEP> 1.61E-02 <SEP> 1.59E-02 <SEP> 4
<tb><SEP> 1700 <SE> 1.64E-02 <SEP> 1.79E-02 <SEP> 1.69E-02 <SEP> 1.71E-02 <SEP> 5
<tb><SEP> 1800 <SEQ> 1.81E-02 <SEP> 1.96E-02 <SEP> 1.83E-02 <SEP> 1.87E-02 <SEP> 5
<tb><SEP> 1900 <SEP> 2.08E-02 <SEP> 2.14E-02 <SEP> 1.92E-02 <SEP> 2.05E-02 <SEP> 5
<tb><SEP> 2000 <SE> 2.40E-02 <SEP> 2.39E-02 <SEP> 2.05E-02 <SEP> 2.28E-02 <SEP> 5
<tb><SEP> 2100 <SEP> 2.21E-02
<tb><SEP> 2200 <SEP> 2.35E-02
<tb><SEP> 2300 <SEP> 2.53E-02
<tb><SEP> 2400 <SEP> 2.73E-02
<tb><SEP> 2500
<Tb>
TABLE Q

<SEP> Heat <SEP> specific <SEP> in <SEP>"a"<SEP> in <SEP> Cm / s <SEP> Conductivity <SEP> in <SEP> Difference
<tb> Temp.
<Tb>

<SEP> J / g. C <SEP> W / Cm C
<tb><SEP> in <SEP> C <SEP> Cp <SEP> measured <SEP> Cp <SEP> library <SEP>"to"<SEP> measured <SEP> K.ref. <SEP> K. <SEP> cal <SEP> in <SEP>%
<tb><SEP> 500 <SEP> 1.6 <SEP> 1.56 <SEP> 1.70E-02 <SEP> 9.95E-03 <SEP> 1.00E-02 <SEP> 1
<tb><SEP> 600 <SEP> 1.7 <SE> 1.65 <SE> 1.70E-02 <SEP> 1.05E-02 <SEP> 1.07E-02 <SEP> 2
<tb><SEP> 700 <SEP> 1.70 <SEP> 1.70E-02 <SEP> 1.08E-02 <SEP> 1.12E-02 <SEP> 3
<tb><SEP> 800 <SEQ> 1.76 <SEP> 1.70E-02 <SEP> 1.12E-02 <SEP> 1.18E-02 <SEP> 5
<tb><SEP> 900 <SE> 1.81 <SEP> 1.70E-02 <SEP> 1.15E-02 <SEP> 1.21E-02 <SEP> 5
<tb><SEP> 1000 <SEP> 1.84 <SEP> 1.70E-02 <SEP> 1.17E-02 <SEP> 1.25E-02 <SEP> 7
<tb><SEP> 1100 <SEP> 1.87 <SEP> 1.75E-02 <SEP> 1.23E-02 <SEP> 1.28E-02 <SEP> 4
<tb><SEP> 1200 <SEP> 1.90 <SEP> 1.80E-02 <SEP> 1.28E-02 <SEP> 1.33E-02 <SEP> 4
<tb><SEP> 1300 <SEP> 1.92 <SEP> 1.85E-02 <SEP> 1.33E-02 <SEP> 1.37E-02 <SEP> 3
<tb><SEP> 1400 <SEP> 1.94 <SEP> 1.93E-02 <SEP> 1.40E-02 <SEP> 1.43E-02 <SEP> 2
<tb><SEP> 1500 <SEP> 1.96 <SEP> 2.01E-02 <SEP> 1.48E-02 <SEP> 1.49E-02 <SEP> 1
<tb><SEP> 1600 <SEP> 1.98 <SEP> 2.10E-02 <SEP> 1.56E-02 <SEP> 1.59E-02 <SEP> 2
<tb><SEP> 1700 <SEP> 2.02 <SEP> 2.19E-02 <SEP> 1.66E-02 <SEP> 1.71E-02 <SEP> 3
<tb><SEP> 1800 <SEP> 2.04 <SEP> 2.30E-02 <SEP> 1.76E-02 <SEP> 1.87E-02 <SEP> 6
<tb><SEP> 1900 <SEP> 2.06 <SEP> 2.41E-02 <SEP> 1.86E-02 <SEP> 2.05E-02 <SEP> 10
<tb><SEP> 2000 <SEP> 2.08 <SEP> 2.52E-02 <SEP> 1.97E-02 <SEP> 2.28E-02 <SEP> 16
<Tb>
The results detailed in these tables are illustrated in FIGS. 4 to 6, which respectively correspond to the first, second and third materials. In each of these figures, the curve IV represents the variations of the reference thermal conductivity K.ref obtained from of the relation (7), as a function of the temperature T, while the curve V represents the variations of the calculated thermal conductivity K. cal obtained by the method according to the invention, also as a function of the temperature T.

 The results illustrated in particular in Tables F, L and Q and in FIGS. 4 to 6 show that there is a great deal of agreement between the calculated thermal conductivities obtained by the process according to the invention and the reference thermal conductivities obtained from the relation (7). Thus, whatever the material tested and the test conditions, the dispersion of the measurements is at most 10 i.

 The results of the modeling and real tests make it possible to conclude that the method according to the invention makes it possible to determine the thermal conductivity of a material up to very high temperatures (for example, 25,000 C in the case of the conductivity meter used), with an uncertainty of not more than 15%.

Claims (10)

 immediately lower temperatures.  Linearity previously established for the interval  and the function

 K2 (T) ... Kn (T), in each range of temperatures that separates two successive values of Tc from the relation  Tm; and - establishment of a series of linear functions  previously determined for these two renewals  measured average thermal conductivities Km.mes  from the two lowest temperatures Tm and  Tf-Tc corresponding to the lowest value of c,  the temperature T, in the temperature range  calculated heat K.cal of the material, depending on  which represents the variations of a conductivity  S (Tc - Tf) - establishment of a first linear function K1 (T),  relation Km.mes =;  average measured Km.mes of the material, from the # .e  temperatures Tf and Tc, with thermal conductivity  to the arithmetic mean of each of the pairs of  at the two lowest Tc values - determination, for corresponding Tm temperatures  corresponding temperature pairs Tf and Tc  successive fixed temperatures Tc and at least between  as linearly with the temperature between  Tc being chosen so that the conductivity varies sen  fixed Tc distributed over said range, these temperatures  sample is heated to different temperatures  in steady state, when a hot face of this  the temperature Tf of a cold face of the sample,  heat flow through this sample and  1. A method for determining the thermal conductivity of a material, over a high temperature range, characterized in that it comprises the following steps - measurement, on a sample of thickness e of the material,  2. Method according to claim 1, characterized in that measuring the heat flow <t> and the temperature Tf - by placing the sample (10) in a conductivity meter,  so that his hot face and his cold face  are respectively in contact with an emitting means  (26) capable of emitting heat at temperatures  Tc and thermic flow measurement means (24)  that, and so that all the other faces of  the sample are thermally isolated - by heating the hot face of the sample (10) by  the transmitter means (26) at different temperatures  fixed Tc; and - by measuring, in steady state, the heat flux  # and the temperature Tf of the cold side, for each  one of the fixed temperatures Tc.  3. Method according to any one of claims 1 and 2, characterized in that the successive fixed temperatures Tc are regularly spaced by a difference less than the minimum difference between the temperatures Tf and Tc, over the temperature range considered. .  4. Method according to any one of the preceding claims, characterized in that the lowest value of Tc is about 500 C.  5. Method according to any one of the preceding claims, characterized in that the first linear function Kl (T) is established by calculating the coefficients a1 and 21 of the equation K1.  (T) = a1T + b1, for the values of T and K1 which respectively correspond to the two lowest temperatures Tm and to the two measured thermal conductivities Km.mes determined at these two temperatures.  6. Method according to claim 5, characterized in that it establishes, by increasing iteration, the sequence of linear functions K2 (T) ... Kn (T), by calculating the coefficients a2 and b2, ... an and bn equations K2 (T) = a2T + b2, ... Kn (T) = anT + bn, from the systems

 in which Tc (1), Tc (2),. .. Tc (n-1), Tc (n) denote fixed temperatures Tc for the first to nth measures, K1 (Tc (l)) ... Kn-1 (Tc (nl)) represent the values of K1 to Kn-1 respectively at temperatures Tc (1) to Tc (nl) and C2 to Cn representing constants defined by

 where Km.mes (2), ... tQm.mes (n) represent the values of Km.mes for the second to nth measures and where Tf (2) to Tf (n) denote the temperatures Tf for the second to nth measures.  7. Conductivity meter adapted to be used over a high temperature range, characterized in that it comprises - an enclosure (1) for confinement, delimiting a chamber  measuring range (4) suitable for receiving a sample (10)  of a material whose conductivity is to be measured  thermal - heating means (26) of a hot face (12) of  the sample, placed in the measuring chamber (4),  able to provide heating on said beach of  temperatures; a radiative fluxmeter (24) consisting of a hat  in contact with a cold face (14) of the sample  tillon; and measuring means (36, 38) for the temperatures Tc and  Tf hot and cold faces of the sample, res  tively.  8. Conductivity meter according to claim 7, characterized in that the heating means comprise a resistor (26).  9. Conductivity meter according to any one of claims 7 and 8, characterized in that the radiation fluxmeter (24) comprises measuring means  (34) a temperature Tr of the cap, integrated in the latter.  10. Conductivity meter according to any one of claims 7 to 9, characterized in that the means for measuring the temperature Tc of the hot face (12) comprise a removable thermocouple (36) capable of measuring the temperature Tc jus' to about 14000C and a pyrometer (28) capable of measuring the temperature Tc to about 2500 "C.