In the present contribution monophase hexagonal polycrystals showing anisotropic thermal expansion are considered. If the polycrystal is stress-free at T₀, temperature change to T₁ will lead to thermal misfit between differently oriented grains causing the above-mentioned thermal microstresses and microstrains. The corresponding multivariate Gaussian microstrain distribution can be calculated (neglecting plastic deformation and surface effects; assuming randomly oriented grains) on the basis of statistical and internal-energy considerations [1,3]:

(i) The average strain leads to average lattice parameters somewhat different from the equilibrium lattice parameters at T₁. The average strain can be used to define a strain scale with <Δε_ij> = 0.

(ii) The joint second central moments <Δε_ijΔε_mn> of the microstrain distribution around the average <Δε_ij> = 0 are proportional (constant K) to the corresponding components of the elastic compliance tensor in the crystal’s frame of reference, <Δε_ijΔε_mn> = Ks_ijmn. On the basis of these second moments the expected hkl-dependent microstrain broadening can be calculated [4].

The following experimental model cases were considered:

(a) Neutron-diffraction experiments on polycrystalline hexagonal zinc at ambient temperature (T₀, microstrain-free state) and after cooling to T₁ = 10 K.

(b) Synchrotron X-ray diffraction applied to polycrystalline hexagonal ε-iron nitride after cooling from 673 K (production temperature, T₀) to ambient temperature, T₁.

Both materials exhibit hkl-dependent microstrain broadening at T₁. For zinc this broadening is especially pronounced for 00l reflections, which is compatible with zinc’s high elastic compliance along [001] directions. In both cases, comparison of the experimental data with theory [1,3] indicates that local plastic deformation had occurred. This conclusion is also supported by the observed characteristic reflection asymmetries, where the skewnesses of the hk0 and 00l reflections have inverse signs.

[1] W. Kreher, W. Pompe, Internal Stresses in Heterogeneous Solids, Akademie-Verlag Berlin (1989).

[2] A. J. C. Wilson, Nuovo Cimento 1 (1955) 277.

[3] W. S. Kreher, Comp. Mater. Sci. 7 (1996) 147.

[4] A. Leineweber, J. Appl. Cryst. 39 (2006) 509.

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