Stress gradients in the direction of the surface normal influence the shape of the interplanar spacing “d” vs. sin2ψ (where ψ is the specimen tilt) plot obtained from the surface layers of a specimen.(1-3) If the gradients are caused by the shear stresses σ13, σ23, the “d” vs. sin2ψ plot exhibits “psi-splitting”, that is the “d” values measured at positive ψ tilts are different from the values measured at negative if tilts. (2) If the shear stresses σ13, σ23, are zero, but the normal stress σ33 exists in the layets penetrated by the x-ray beam, “d” vs. sin2ψ, plot exhibits curvature. (3) Various methods have been proposed to obtain the complete stress tensor from split or curved “d” vs. sin2ψ data, and all of these methods require the “unstressed” lattice spacing “d0” for their calculations.
Determination of constant lattice spacing trajectories in lattice QCD