Commensurate-incommensurate transition coverage

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 9. Adsorption isotherm [172, 189, 300] for N2 on graphite at 78 K showing the adsorption of the first layer (short dashes), the fluid to commensurate solid transition (solid line and blowup), and second-layer adsorption and/or commensurate to incommensurate transitions (long dashes) in terms of the coverage n measured in units of the complete Vs mono-layer. (Adapted from Fig. 1 of Ref. 91.)...

Figure 27. Reduced heat capacity of N2 films adsorbed on graphite for various coverages n as given in the figure the coverage is given in units of the complete /3-monolayer coverage. The vertical dashed lines at 28.1 K and 29.4 K mark the orientational transition temperatures in the commensurate and uniaxial incommensurate phases, respectively. (Adapted from Fig. 1 of Ref. 394.)...

Orientational ordering transitions [394] clearly occur in the commensurate phase (possibly in coexistence with the fluid) up to 1.101 monolayers at 28.1 K, as well as in the uniaxial compressed phase from 1.142 to 1.178 monolayers at 29-30 K based on adiabatic calorimetry [156] a heat capacity peak at 28.7 K was reported at a coverage of 1.109 which was interpreted as the transition to the uniaxially compressed incommensurate phase, whereas this peak is located near 27.5 K in the submonolayer regime. The ac heat capacity scans [394] in the triangular incommensurate phase at 1.200 and 1.302 monolayers show only very weak and broad features in the relevant temperature range from 22 K to 32 K. Thus, it is concluded [394] that their orientational order is only gradually lost as the temperature is increased... 

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 48. Semilogarithmic plot of the isothermal compressibility of N2 on boron nitride at 60.8 K as a function of the coverage in units of the complete /3 monolayer. The peak sequence starting at low coverages is attributed to the fluid to commensurate solid F-C and commensurate solid to reentrant fluid C-RF transitions and finally to second-layer growth RF-B (instead of a transition from the reentrant fluid to an incommensurate solid phase). (Adapted from Fig. 5 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.)...

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