Is there any reference for the coefficients of thermal expansion of hexagonal single crystals? Especially, I need to know the probable differences between the coefficients at different directions (e.g. "a" and "c" directions)?
IMHO hcp describe a hexagonally closed packed crystal structure, so it would typically be a metal. Probably you mean some hexagonal ceramic material with anisotropic thermal expansion. Look specifically for literature for your material, either macroscopically measured thermal exansion coefficients (typically dilatometry on single crystals) or on temperature dependent diffraction data.
There are some books for your reading:
Properties of Materials : Anisotropy, Symmetry, Structure: Anisotropy ...
By Robert E. Newnham (Oxford)
Heat Capacity and Thermal Expansion at Low Temperatures (1999)
de T.H.K. Barron , G.K. White (Kluwer)
If it is single crystal, the thermal expansion in each crystallographic direction will be given by a second rank tensor, see the Newnham reference in Tapan's answer above, or see Tensor Properties of Solids by Richard Tinder. The attached image gives the relationship between change in strain (effect) due to a change in temperature (cause), given by Tinder, where alphaij is the thermal expansion tensor. Note that Neumann's principle states that "the symmetry elements of any physical property of a crystal must include the symmetry elements of the point group of the crystal (DoITPoMS)", see http://www.doitpoms.ac.uk/tlplib/tensors/symmetry.php which also gives the form of the tensor for Hexagonal crystal systems.
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