Three-dimensional modulation

A characteristic feature of these partially oxidized bis(oxalato)platinate salts of divalent cations is the coexistence of two modulations of the lattice over a wide temperature range (a) a one-dimensional modulation, as detected by the appearance of diffuse lines on X-ray films, perpendicular to the [Pt(C204)2] anion stacking direction and surrounding the even Bragg reflection layer lines of non-zero order (b) a three-dimensional modulation which gives rise to a complicated pattern of fine satellite spots in the neighbourhood of every reciprocal layer line. 

Szydlowska J, Mieczkowski J, Matraszek J, Bmce DW, Gorecka E, Pociecha D, Guillon D (2003) Bent-core liquid crystals forming two- and three-dimensional modulated structures. Phys Rev E 67 031702-1-031702-5... 

Fig. 3 An intrinsically three dimensional module formed from two different submodules...

In addition to one-dimensional modulations considered above, both two-and three-dimensional modulations are possible. Furthermore, atomic parameters affected by modulations may be one or several of the following positional (as shown in Figure 1.52 and Figure 1.53), occupancy, thermal displacement, and orientation of magnetic moments. The latter, i.e. commensurately or incommensurately modulated orientations of magnetic moments are quite common in various magnetically ordered structures (e.g. pure lanthanide metals such as Er and Ho), and both the value of the modulation vector and the amplitude of the modulation function often vary with temperature. 

Conventional lattices may be perturbed by functions with different periodicity, e.g. by sinusoidal or saw-tooth-like modulations, see section 1.21 in Chapter 1. In the simplest case (one-dimensional modulation), Eq. 5.1 becomes d / = h + kb + k + wq assuming that the perturbation function is periodic and has the modulation vector q. In a case of three-dimensional modulation, a total of six indices (k, k, I, m, n, and p) are required to identify every point observed in reciprocal space = ha + kb + /c +... 

Salmio R.P., Saarikoski H., Saarinen J., Westerholm J., Turunen J., Three-dimensionally modulated graded-index diffractive elements by thermal ion exchange in glass. Opt. Lett. 22... 

Memory cube, a three-dimensional module consisting of stacked memory devices such as DRAMs or SRAMs. 

Three-dimensional modulation in fluids corresponds to a so-called isotropic Lifshitz-point, which can describe three-phase equilibrium with a middle microemulsion (sponge) phase and which can thus be treated as a special tri-critical point. Both the interfadal tensions between the water-rich and microemulsion phase and between oil-rich and microemulsion phases will vanish at the tricritical Lifshitz point much faster than at a tricritical point in ordinary multicomponent fluid mixtures, since the gradient-term coefficient cq also vanishes. ... 

Yamamoto, A. (1982). Modulated Structure of Wustite (Fej. O) (Three-Dimensional Modulation) . Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry 38 1451-1456. 

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