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1For instance, the ODF f(g) of a considered phase describes only the probability that 100f(g)dg (%) of all crystal lattice cells of this phase are oriented close to the orientation g, independently of the grain positions, grain structure and any potential special orientation correlations of the neighboring grains.
2In order to avoid misunderstandings we have to underline that in the definition of Walpole (1960), who dealt with ellipsoids too, true self-consistency is only achieved by including the inversion relation. He used an elegant mathematical technique to obey the inversion relation, but the price was the introduction of an artificial matrix that remains physically undefined. Only for very special cases with known exact solutions can this matrix be fixed. Therefore this approach, despite its ability to describe several mixed phases, did not undergo any further development in the direction of our interest.