  Thermal conductivity of nanocrystalline and ultra-nanocrystalline films is
analyzed with effective medium theory (EMT) models. The existing EMT models use
the spherical inclusion approximation. Although this approximation works quite
well it is inconsistent, mostly with respect to the maximal packing of 74{\%},
which may be unrealistic for polycrystalline films. To check the consistency of
these models we devise an EMT model with arbitrarily shaped inclusions. We pick
the EMT model with cubic inclusions and we compare its results with the results
of the EMT model with spherical inclusions. It is found a very good agreement
between both calculations. This agreement is explained by general geometrical
arguments. We further employ these models to analyze thermal conductivity of
nanocrystalline and ultra-nanocrystalline diamond films. It is noticed that the
effective conductivity is strongly affected not only by the boundary Kapitza
resistance but also by intra-grain scattering for grain sizes below 100 nm.
Generally, both intra-grain conductivity and Kapitza resistance increase with
grain size. However, the effect of Kapitza resistance increase is negligible
due to the geometrical factor accompanying Kapitza resistance contribution to
the effective conductivity.
