Thermal Conductivity using the Multiproperty Apparatus

After the electrical resistivity and total emissivity have been determined as functions of temperature (long sample data), the effective length of the sample is shortened. The upper portion of the sample slides through the upper electrode clamp and the lower portion of the sample slides through the lower electrode clamp.

The test cell is evacuated, and the sample heated so that the maximum temperature (near the sample center) reaches the desired test temperature. A temperature profile, consisting of about twenty temperatures measured as a function of the z coordinate, is obtained by moving the pyrometer from an arbitrary zero reference point near the lower end of the sample, to a roughly corresponding position near the upper electrode. The current flow is reversed and second temperature profile obtained. Computer program PROFIL is used to collect the temperature versus position data. Two extra data points are taken on the second profile. For these two points, the current is varied but the position is maintained constant. Thus the temperature change caused by a slight change in current is determined. With each temperature versus position point, the current flow is also measured. At the conclusion of the profile determinations, the average current is calculated and the individual temperature data are corrected to what the temperature would be if the average current had been flowing when the temperature measurement was taken.

The thermal conductivity and Thomson coefficient are calculated using Eq. (9) with the right-hand side set equal to zero (steady-state), i.e.,

The temperature profiles are analyzed using advanced mathematical techniques involving SPLINE functions to yield values of T, dT/dZ, and d^2T/dZ^2 at any location Z. These values of T are used to calculate the values of resistivity and hemispherical emissivity at various values of Z. Thus an array of about twenty equations is set up and solved for the three unknowns, lambda, d lamba/dT and u. Since lambda and d lambda/dT are related, the actual solution involves lambda_0 + lambda_1 , and lambda_2 where lambda = lambda_0 + lambda_1 T^2 . Because the temperature range over which the profile is limited to several hundred degrees, lambda = lambda_0 + lambda_1 T is usually and adequate representation. The computer program SPLINE uses the temperature versus position data collected by program PROFIL along with coefficients for resistivity and hemispherical emittance file generated by program LSAMPL to calculate the spline fits for T(Z), dT/dZ(Z), d^2T/dZ^2 , resistivity(Z), hemispherical emissivity(Z) and to set up the array and calculate lambda_0, lambda_1, lambda_2 and u.

After the conductivity values have been determined over one temperature interval, profile data at higher temperatures are obtained and the process repeated. Additional long sample data are taken in between some profile determinations to determine any changes in the emissivity and resistivity. To obtain optimum thermal conductivity data, the short sample length should be decreased as one goes to higher temperatures so that the profile data T(Z), approximates a reasonably "sharp" parabola and not a "shallow" one. Typical thermal conductivity results are given in Figure 15.

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