  Despite the fast development of computational materials modelling,
theoretical description of macroscopic elastic properties of textured
polycrystalline aggregates starting from basic principles remains a challenging
task. In this communication we use a supercell-based approach to obtain the
elastic properties of random solid solution cubic ZrAlN system as a function of
the metallic sublattice composition and texture descriptors. The employed
special quasi-random structures are optimised not only with respect to short
range order parameters, but also to make the three cubic directions
$[1\,0\,0]$, $[0\,1\,0]$, and $[0\,0\,1]$ as similar as possible. In this way,
only a small spread of elastic constants tensor components is achieved and an
optimum trade-off between modelling of chemical disorder and computational
limits regarding the supercell size is achieved. The single crystal elastic
constants are shown to vary smoothly with composition, yielding
$x\approx0.4$-0.5 an alloy constitution with an almost isotropic response.
Consequently, polycrystals with this composition are suggested to have Young's
modulus independent on the actual microstructure. This is indeed confirmed by
explicit calculations of polycrystal elastic properties, both within the
isotropic aggregate limit, as well as with fibre textures with various
orientations and sharpness. It turns out, that for low AlN mole fractions, the
spread of the possible Young's moduli data caused by the texture variation can
be larger than 100 GPa. Consequently, our discussion of Young's modulus data of
cubic ZrAlN contains also the evaluation of the texture typical for thin films.
