Commensurate-incommensurate transition phase diagram

Fig. 20. Phase diagram of the triangular lattice gas model with nearest-neighbor repulsion and next-nearest neighbor attraction, for JmJJ = — 1, in the coverage-temperature plane. For fl=0.5 a Kost tz-Thouless transition occurs at Ti and a commensurate-incommensurate transition at Tj. Two commensurate. 3 x 3 phases (with ideal coverages of 1/3 and 2/3, respectively) occur, as well as several two-phase regions, as indicated in the figure. Here l.g. stands for lattice gas and LI for lattice liquid . (From Landau. )...

Figure 11. Phase diagram for akermanite solid solutions (Ca2MgSi207 - Ca2FeSi207). Transition temperatures between commensurate and incommensurate phases increase with Fe content. Modified from Figure 12 in Seifert et al. (1987).

Figure 47. Phase diagram of N2 on boron nitride based on adsorption isotherms coverage is repotted in units of the complete Vs mono-layer obtained from the top of the fluid to commensurate solid isotherm substep at low temperatures less than 51 K. Commensurate solid phase (C), fluid phase (F), reentrant fluid phase (RF). The solid lines correspond to phase boundaries based on measured features, the dotted line is an expected phase boundary, and the triangle marks the tricritical point. Second-layer growth instead of a transition to an incommensurate solid phase is expected beyond the reentrant fluid phase in the temperature range studied. (Adapted from Fig. 4 of Ref. 1.)...

Figure 51. Experimental phase diagram of CO physisorbed on graphite with the phases fluid (F), commensurate (CD) and incommensurate (ID) orientationaliy disordered solids, reentrant fluid (RF), second-layer fluid (2F), vapor (2V), liquid (2L), and orientationaliy disordered solid (2SD) phases. Filled circles and triangles represent phase boundary locations from heat capacity and vapor pressure measurements, respectively. Solid and dashed lines indieate phase boundaries believed to be associated with first-order and continuous transitions, respectively dash-dotted lines correspond to speculated boundaries. The large filled triangle and the large filled circle mark the two-dimensional Potts tricritical and critical points, respectively the tricritical point marked with an open triangle is tentative. Lines I-VII with arrows are experimental paths of the heat capacity scans shown in Fig. 52. Coverage unity corresponds to a coverage of CO forming a complete (Vs x VS) monolayer. (Adapted from Fig. 1 of Ref. 112.)...

The introduction of Xe in a layer of Kr stabilizes the V3xV3 commensurate structure [84]. The analysis of the corresponding binary phase diagram shows a first order transition between the commensurate and incommensurate sohds [85,86]. Mixtures of Ar and Xe exhibit a large tendency to form commensurate alloys [87]. A first order commensurate-incommensurate phase transition is also observed in that case. 

Fig. 4. Reentrant fluid of Kr/graphite. High T region of the Kr/graphite phase diagram (from Ref. 30). The reentrant fluid (RF) phase is a domain wall fluid bounded by commensurate (C) and incommensurate (IC) regimes. S(23D) and L(3D) are the bulk solid and hquid phases. Sohd lines denote first-order transitions and dashed lines denote continuous transitions.

During the last decade the theoretical approach of the complex magnetic phase diagram, resulting from the competition of magnetic interactions in systems with strong magnetocrystalline anisotropy, has attracted much attention. In particular theoretical models focused on the transition between commensurate (C) and incommensurate (I) phases, and on the properties of the incommensurate phase. 

For a long time, there were major imcertainties about the commensurate-incommensurate phase transition, mainly because the experimental studies indicated a different order of that transition at high and low temperatures [113]. These uncertainties have been resolved by the proven existence of a reentrant fluid between the two solid regions [15,143]. The final proposed form for the phase diagram is shown in Fig. 5 [144], where the points are experimental data obtained from thermodynamic methods. 

With respect to the computer simulations of helium on graphite, we would only note that they reproduce the presence of fluid, commensurate and incommensurate solids, and a reentrant fluid phase [238,325]. The phase diagram obtained is similar to that proposed by Ecke and Dash [237], which differs from the more recent proposal of Greywall [106] (Fig. 7) and does not include a liquid-vapor transition. 

Crangle et al. (1995) indicate a complex magnetic diagram of DyPd2Sn below lOK. The powder neutron diffraction measurements reveal an incommensurate structure. At 5.2 K this structure undergoes a transition to a commensurate magnetic phase with the moment direction confined in or close to the (111) plane. 

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