Polycrystalline ceramics often contain a pore volume fraction which can vary from < 1% to > 95%. This paper discusses how pores and interfaces modulate the thermal properties of a porous solid with a particular focus on relations between microstructure and the thermal conductivity of ceramics.
First, the effect of grain size on the effective thermal conductivity of the solid phase in a porous polycrystalline ceramic is examined. Two contributions can be identified. Finite grain size at the nanoscale, with interfaces essentially parallel and perpendicular to heat flow, inhibits grain thermal conductivity by removal of low frequency phonons. Then each grain-grain interface crossing the heat flow path acts as a site of Kapitza resistance. These localized thermal resistances, due to grain boundary disorder, are typically in the range of 0.5 x 10-8 m2KW-1 to 1.0 x 10-8 m2KW-1. Data is presented for porous alumina ceramics showing how, due to these two effects, the thermal conductivity of the polycrystalline alumina solid phase is reduced from 33 Wm-1K-1 for an average grain size of 2 mm to 8 Wm-1K-1 for an average grain size of 0.25 mm.
Second, at the macroscopic scale, a tool box of analytical relations is proposed to describe the effective thermal conductivity of the porous ceramic as a function of solid phase thermal conductivity, pore thermal conductivity and pore volume fraction (vp). For vp < 0.65, the Maxwell-Eucken relation for closed porosity and Landauer relation for open porosity give good agreement to measurements on tin oxide, alumina and zirconia. For vp > 0.65, Landauer’s effective medium expression becomes of restricted use. In fact a natural limit to achieving low thermal conductivity in a porous solid seems to be approached. This is explained by the condition of continuity in the solid skeleton for maintaining a minimum of mechanical strength. Useful predictions for highly porous cellular materials can then be made with models described by the Hashin-Shtrikman upper bound, Russell’s relation or the Glicksman-Schuetz relation.
Finally, the approach is illustrated with examples of porous materials with low values of thermal conductivity. These include kaolin based foams, ceramic green bodies, sunflower pith aggregates and silica aerogels.