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In a series consisting of +1 and -1, a pair of the i -th and j -th elements, a( i ) and a( j ), is characterized by two integers; one is the separation m = j - i ( j > i ) and the other is the sum d of m - 1 numerals between the two elements. If the pair is denoted by [ a ( i ), a ( j ); m , d ], all pairs in a series belong to one of the following four types for given parameters m and d : [1, 1; m , d ],[1, \bar1; m , d ], [\bar1, 1; m , d ] and [\bar1, \bar1; m , d ], where 1 and \bar1 are used instead of +1 and -1. Out of these four types, it has been verified that two types of pairs [1, \bar1; m , d ] and [\bar1, 1; m , d ] appear alternately in any series and therefore the total numbers of pairs are equal to each other for these two types or are different at most by unity. This correlation is applied to a layer structure such as Laves phase, and specific relations are derived.

Diffuse scattering due to short range order (SRO) of the hexagonal ζ phase, Ag–Al, has been studied by X-ray and electron diffraction methods. Intensity distribution was measured in the reciprocal space at room temperature. Peculiar distribution was found such as a thin plate and a hinge shape on h 3 =0 and 1 planes in the c * direction, respectively. The maxima on these planes are shifted from 1/3, 1/3, h 3 and 2/3, 2/3, h 3 positions. SRO parameters α l m n of a single crystal of Ag–34 at.%Al alloy have been determined by the Fourier transformation of X-ray diffuse intensity. It has been found from the electron diffraction patterns that the shift of the diffuse maxima from 1/3, 1/3, h 3 decreases almost linearly with increasing Al concentration. The Fermi-surface-imaging theory seems to be appropriate to interpret the observations.

Disordered hexagonal close packed ζ phase. Ag-Al, was studied by X-ray and electron diffraction methods. Diffuse scattering due to short range order was observed. The diffuse intensity distribution is characterized by its peculiar shape and the shift of the maximum position with the change of the Al concentration. The features resemble those of fcc disordered alloys such as Cu 3 Au and αCu-Al where the Fermi surfaces are reflected in the diffuse scattering of X-rays.