## Thermal Property Measurements

Coefficient of Thermal Expansion. The coefficient of thermal expansion (CTE) of the TBC in the in-plane direction should match as closely as possible the CTE of the bond coat. The expansion in the through-thickness direction is not of great interest, which is fortunate because this measurement is relatively difficult to perform. The in-plane expansion on a freestanding sample can be determined using a conventional pushrod dilatometer (ASTM C 228). In the case of a differential pushrod dilatometer, the differential expansion between the sample and a known standard reference material is measured as a function of temperature. The expansion of the sample is computed from this differential expansion and the expansion of the standard. The measurements are made under computer control, and linear expansion is calculated at preselected temperature intervals. The expansion can be monitored with the visual display during the measurement process. Seven standard reference materials for expansion are available from the National Institute of Standards (NIST, formerly the National Bureau of Standards), including materials with low, moderate, and large expansion. For purposes of calibration and checkout, one NIST standard is measured against another NIST standard.

Specific Heat. Measurements of the specific heat of TBCs can be easily performed using differential scanning calorimetry (ASTM E 1269). Reference and sample holders are equipped with heaters and temperature sensors that detect temperature fluctuations of the sample holder with respect to the reference holder as both are heated. A high-gain, closed-loop electronic system provides differential electrical power rate that can be read out directly in millicalories per second and that is equivalent to the rate of energy absorption or evolution of the sample. The specific heat is calculated by comparing this rate with the rate measured during the heating of a known mass of sapphire. The experiments are performed under computer control, and specific heat is automatically calculated at equal temperature intervals.

The procedure is to measure the differential power required to heat the empty pan at the same rate as the reference empty pan (blank amplitude). The data are collected and stored in the computer. The sapphire standard (whose mass and specific heat are known) is then placed in the empty pan, and the differential power required to heat this pan at the same rate as the reference empty pan is measured to obtain the standard amplitude. Next, the sample is substituted for the sapphire standard and the sample amplitude is determined. The computer then calculates the specific heat. The results for ZrO2-8wt%Y2O3 coatings are very close to those predicted from the rule of mixtures, as calculated using values for the pure oxides (Ref 10).

Thermal Transport Properties. Thermal conductivity can be calculated from:

where 1 is the thermal conductivity, q is the heat flux, A is the cross-sectional area conducting the flux q, and dT/dx is the temperature gradient. Alternatively, conductivity can be determined from:

where a is the thermal diffusivity, Cp is the specific heat, and p is the density. It should be noted that thermal conductivity cannot be measured directly. Equation 4 involves steady-state determinations, and Eq 5 involves transient determinations. Relatively large errors have been documented for steady-state determinations, even under good conditions (Ref 11). Because specific heat and density (expansion) measurements are straightforward, and because diffusivity measurements involve only length and time, transient techniques are more attractive, especially for the small samples associated with coatings in the through-thickness direction. In addition, the diffusivity technique is much faster and costs less.

A particularly useful diffusivity technique (Ref 12) is the laser flash method, ASTM E 1461-92. It is shown schematically in Fig. 8. The sample, normally the size of a nickel, is held at the desired measurement (e.g., room temperature, 100 °C, 200 °C, etc.). The front surface receives a pulse of energy from the laser, which soon raises the back face temperature a degree or two. The rear face temperature response is normalized and compared with the theoretical model based on Carslaw and Jaeger's solution to one-dimensional heat flow (Ref 13). Using that model, diffusivity values can be obtained at any percent rise of the curve. For example, at 50% rise, the diffusivity is calculated from:

1=aCpp

where l is the sample thickness and t0.5 is the elapsed time needed for the rear-face temperature to reach one-half of its maximum rise (Fig. 8).

maximum

It is possible to measure freestanding coatings, but it is also possible to measure the coatings on the substrate. In the latter case, the effects of any interfacial resistance are included in the calculated diffusivity/conductivity of the coating. Because TBCs may be translucent, part of the laser beam could penetrate significantly into the sample, violating an assumed boundary condition. Thus, for freestanding coatings, it is necessary to put a very thin opaque layer on at least one surface. In the case of TBCs on substrates, this is not a problem because the substrate side faces the laser.

Thermal conductivity values in the literature have rarely been corrected for thermal expansion, because the expansion correction has been within the accuracies of steady-state determinations of conductivity. This general practice is usually followed when computing thermal conductivity from transient measurements: density and diffusivity values are not corrected for expansion. If one does correct density for expansion by dividing by (L0 + AL)3, one must also correct the diffusivity values by multiplying by (L0 + AL)2, where L0 is the length at the reference (room) temperature and AL is the length change at any temperature from that at the reference temperature. Thus the total correction is a factor of (L0 + AL)-1 For TBCs at operating temperature, this correction is less than 2%.

Thermal diffusivity and conductivity values may increase after thermal cycling (Ref 10, 14) or upon heat treatment to progressively higher temperatures (Fig. 9). These effects may be due to closing of horizontal microcracks. In addition, the conductivity/diffusivity of the TBCs can be thickness dependent due to the somewhat cone-shape structure. It should also be noted that the in-plane conductivity values of TBCs are different from the through-thickness values because of the lamellar nature of thermally sprayed coatings and the columnar structure of zirconia deposited by physical vapor deposition. In general, the in-plane values are relatively unimportant for TBC applications.

References cited in this section

10. T.A. Taylor, Thermal Properties and Microstructure of Two Thermal Barrier Coatings, Surf. Coat. Technol., Vol 54/55, 1992, p 53-57

11. R.E. Taylor, Things Mother Never Taught Me (About Thermophysical Properties of Solids), Therm. Conduct., Vol 21, C.J. Creamers and H.A. Fine, Ed., Plenum Publishing Corp., 1991, p 41-49

12. R.E. Taylor and K.D. Maglic, Pulse Method for Thermal Diffusivity Measurements, Compendium of Thermophysical Property Measurement Methods, Vol 1, K.D. Maglic, Ed., Plenum Publishing Corp., 1984, p 305-336

13. H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Oxford University Press, 1959

14. R.E. Taylor, On Material Changes and Heating Rate Dependent Properties, Therm. Conduct., Vol 20, D.P.H. Hasselman and J R. Thomas, Jr., Ed., Plenum Publishing Corp., 1989, p 93-101

Microstructural Characterization of Coatings and Thin Films

S.J. Bull, AEA Technology

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