The quartet revisited

Using an unbiased and very general joint density of the atomic position vectors we are able to calculate different probabilities for the sign of the quartet given its second neighborhood. One already knows that additional chemical information alters the joint probability distribution (j.p.d.) of structure factors. That is, they can and will give different j.p.d.'s for the quartet invariant given its second neighborhood. In this paper we show that even without additional chemical information the j.p.d.'s of structure factors can be strongly different from the classical ones if we impose a general j.p.d. for the atomic vectors based on the fact that the real distribution of the atomic position vectors is a sum of delta functions.