#### Installation — business terrible - 1 part

September 8th, 2015

Thermal conductivity (k with units W m-1 K-1) describes the ability of a material to transport thermal energy because of temperature gradient. Steady-state thermal conductivity is a constant of proportionality between the heat flux (time rate of heat flow per unit area) through a solid and the imposed temperature gradient as described by (4) [52]:

(4)

where Q is the heat flow (J s-1 or W), A is cross sectional area (m2), к is thermal conductivity (W m-1 K-1), AT is temperature gradient (K), and x is distance (m).

In electrically insulating solids, heat is transferred in the form of elastic waves or phonons [1]. Anything that affects the propagation of the phonons through the solid affects the thermal conductivity of the solid. In a pure crystalline ceramic, the intrinsic thermal conductivity is limited by the energy dissipated during phonon-phonon collisions or so-called Umklapp processes [15]. Commonly, the intrinsic thermal conductivity of solids is described by (5).

к = 1 Cvl, (5)

3

where C isthe heat capacity per unit volume (J m-3 K-1), v is the phonon velocity (m s-1), and l is phonon mean free path (m).

Phonon velocity and mean free path are difficult to measure accurately in polycrystalline materials, so (5) is normally restricted to theoretical predictions. The values of thermal conductivity observed in polycrystalline ceramics are often significantly less than the intrinsic values predicted or those measured for single crystals. Specimen characteristics such as temperature, impurities, grain size, porosity, and preferred orientation affect the phonon mean free path thereby changing thermal conductivity [1]. Though not an oxide, this effect is pronounced in aluminum nitride. The intrinsic thermal conductivity of AlN is 280 W m-1 K-1 [16], but thermal conductivities in the range of 50-150 W m-1 K-1 are often observed in sintered materials because of the presence of grain boundaries and second phases [53].

The thermal conductivity of large grained (100 pm or more) ceramics can be determined by direct measurement techniques described in ASTM standards C 201-93 (Standard Test Method for Thermal Conductivity of Refractories), C 1113-99 (Standard Test Method for Thermal Conductivity of Refractories by Hot Wire), and E 1225-99 (Standard Test Method for Thermal Conductivity of Solids by Means of the Guarded-Comparative-Longitudinal Heat Flow Technique). These methods lend themselves to quality control-type assessment of the thermal conductivity of macroscopic parts in standard shapes (e. g., 9 in. straight brick or monolithic materials cast to specific dimensions). The sizes prescribed by these standards insure that the specimen thickness is sufficient to reflect the effects of grain boundaries, pores, and other specimen characteristics. The relative error of the techniques ranges from ~10 to ~30% depending on the material and technique. This degree of precision is normally sufficient for material selection and design calculations. Some common design considerations influenced by thermal conductivity include cold-face temperature, interface temperatures between working lining and insulating lining materials, heat loss, and estimating

the required thickness for each component in a system. For example, the heat flux through a refractory material can be calculated using (4). Assuming a characteristic thermal conductivity for an insulating firebrick of 0.25 W m-1 K-1 at the mean temperature of the wall, a heat flow of 5000 J s-1 would be predicted per square meter of area for a hot face temperature of 1200°C (1473 K), a cold face temperature of 200°C (473 K), and a wall thickness of 5 cm (0.05 m).

For dense specimens of fine-grained (less than 100 pm) technical ceramics, the thermal conductivity can be determined with greater precision using an indirect method by which thermal diffusivity (a with units of m2 s-1) is measured and then converted to thermal conductivity. For small specimens, precise control of heat flow and accurate determination of small temperature gradients can be difficult, leading to unacceptably large error in the direct measurement of thermal conductivity of small specimens. As a consequence, determination of thermal diffusivity by impulse heating of thin specimens followed by conversion to thermal conductivity has evolved as the preferred measurement technique [54, 55]. The technique is described in ASTM standard E1461-01 (Standard Test Method of Thermal Diffusivity by the Flash Method). Measured thermal diffusivity is used to calculate thermal conductivity using (6):

where a is thermal diffusivity (m2 s-1), к is thermal conductivity (W (m-1 K)-1), CP is heat capacity (J kg-1 K-1), p is density (kg m-3).