Triplet phase invariants: Formula for centric case from fourth-order determinantal joint probability distributions.

A formula is derived for centrosymmetric crystals from fourth-order determinantal joint probability distributions that provides, for the triplet invariants, values of P(+)/P(-), the ratio of the probability that an invariant has a plus sign associated with it to the probability that it has a minus sign. The formula makes use of the entire data set in the computations for each invariant. Test calculations indicate that many hundreds of invariants can be selected by use of the formula with essential certainty that their value is equal to zero. Several invariants whose value is equal to pi can also be selected on occasion with very high reliability.