Field‐Property Bounds for Porous Sintered Ceramics

Three sets of equations provide upper and lower values bound ing the experimentally obtained electrical and thermal conduc tivities as well as the magnetic permeabilities (=“field properties”) of porous ceramics. These equations are as I‐order upper bound: φ p =φ M (1 ‐P ) (φ=effective field property of the porous material, φ M =field property of the nonporous material, P =porosity), and as I‐order lower bound: φ r =φ M (1‐ P ) 7 . Closer bounds corresponding to isotropic porous materials are the II‐order upper bound: φ P II ,= φ M ,[2(1‐ P)/ (2+P)], and the II‐order lower bound: φ PIII =φ M (1‐ P) 3 . Even closer bounds, referring to isotropic porous materials containing closed, unconnected pores are the III‐order upper bound: φ P III = φ M (1‐ P) 3/2 , and the III‐order lower bound: φ PIII = φ M (1‐ p)3 .