Phase changes commensurate-incommensurate

Ar and evidently much larger for Ne. Therefore, we would expect Kr and Xe to undergo the commensurate-incommensurate phase changes more easily than Ar or Ne. 

Previously, sudden changes of amplitudes of magnetic satellites observable below 2 K [7] were interpreted in terms of lock-in transitions into phases with commensurate propagation vectors. Within the framework of the thermodynamic potential (5) it is impossible to describe a low-temperature transition from an incommensurate phase into a commensurate phase at zero external magnetic field. 

A main field of activities is focused on structure and reactivity in two-dimensional adlayers at electrode surfaces. Significant new insights were obtained into the specific adsorption and phase formation of anions and organic monolayers as well as into the underpotential deposition of metal ions on foreign substrates. The in situ application of structure-sensitive methods with an atomic-scale spatial resolution, and a time resolution up to a few microseconds revealed rich, potential-dependent phase behavior. Randomly disordered phases, lattice gas adsorption, commensurate and incommensurate (compressible and/or rotated) stmctures were observed. Attempts have been developed, often on the basis of concepts of 2D surface physics, to rationalize the observed phase changes and transitions by competing lateral adsorbate-adsorbate and adsorbate-substrate interactions. 

The above examples clearly proved that the surface heterogeneity can change the character of the gas-liquid transitions in adsorbed monolayers and mechanism of the adsorbate condensation. In surface layers, one can also observe the commensurate-incommensurate-type transitions. Unfortunately, our knowledge of the behavior of incommensurate phases on nonuniform surfaces is still very limited. Only theoretical articles relevant to this problem are available [12]. 

Following the pioneer work of Beebe et al. [168], the adsorption of krypton at 77 K has also been used for the determination of relatively small siuface areas, because its saturation vapor pressure is quite low (Pq near 267 Pa). Unfortunately, however, there are some complications in the interpretation of the adsorption isotherm. Thus, the working temperature is well below the triple point of bulk Kr (116 K approximately), but if the solid is taken as the reference state, the isotherm shows an xmusually sharp upward turn at the high-pressure end. Moreover, the BET plot is frequently not linear due to the kink produced by the phase change from a commensurate to an incommensurate structure. 

Modulations are normally described as waves. The modulation wave can fit exactly with the underlying unmodulated component, or more precisely with the unit cell of the underlying component, in which case the structure is described as a commensurately modulated structure. In cases where the dimensions of the modulation are incommensurate (i.e., do not fit) with the unit cell of the underlying structure, the phase is an incommensurately modulated phase. Modulation changes are normally continuous and reversible. 

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