Estimate of Structure Invariants

Strueture invariants are produets of strueture factors that remain invariant whatever the origin. They may be written as 

The first structure invariant containing phase information is the triplet invariant, which is the most important one (together with the quartet invariants). Since the moduli are known from the experiment, it is usual to refer to structure invariants as to a combination of phases, e.g., the sum  

A probabilistic formula for estimating structure invariants has been given by Cochran  

The Cochran formula, Equation (9), estimates the triplet phase only exploiting the information contained in the three moduli hl, kU h+kl- The representation theory proposed by Giacovazzo indicates how the information contained in all reciprocal space could be used to improve the Cochran s estimate of The conclusive conditional probability distribution has again a von Mises expression  

We will denote such a probability by Pio(3 hi,h2) emphasize the fact that the formula explores the reciprocal space by means of a ten-node figure. 

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