Spectra of monolayers: (a) In the F phase ( and ), showing 3D gas peaks and a surface peak to the right of the corresponding gas peak. (b) In the UC phase ( and ), showing 3D gas peaks and a pair of surface peaks due to hybridization with the combination mode .
(a) Our “phase” diagram based on the qualitative characterization of the spectra together with the ellipsometric coverage. Monolayer phases are: open (upright commensurate: is dominant and locked to the substrate), open (tilted incommensurate: Both and are prominent), and short (flat: is dominant). Bilayer phases are: solid (upright: Two pairs of lines are dominant), open (mixed: Comparable and ), and long (flat: is dominant). (b). Comparison of our phase boundaries (light solid lines) with those reported by Knorr and co-workers based on heat capacity, x-ray diffraction, and ellipsometry (dashed lines). Heavy solid lines are 3D phase boundaries and bilayer boundaries. The two dash-dot lines are isobars. Open circles, shown in (a) and (b), are maxima of along isotherms.
(a) Calculated ratio of spectral peak areas as a function of molecular tilt angle for three different tilt orientations described in the text: Horizontal bars are the antiferro configuration AF II, open circles are “random” orientation, and solid circles are the all-parallel ferro orientation. These span the range of herringbone configurations. This calculation is for fixed lattice constant . It is seen that the inferred tilt angle is only weakly dependent on the tilt configuration. (b) Illustration of the herringbone configurations HB I and HB II.
(a) Model frequency as a function of tilt angle calculated for lattice constant and various orientational configurations described in the text: II, II 60°, II 30° (two branches), open , open I, solid I 60°, solid I 30°, and solid . (b). Frequency as a function of tilt angle calculated for and various configurations labeled as above. It is evident that the frequency is strongly configuration dependent when the dynamic dipole axis is tilted away from the surface normal.
Experimental frequencies (open triangles) and (solid squares) as functions of chemical potential (relative to coexistence with bulk bcc solid), along various isotherms ranging from on the left to on the right. These data include three monolayer phases: The horizontal band at the top is the UC phase, the less well defined band at the bottom is the beginning of the F phase, and the region of steeper slopes between is the TI phase.
Tilt angle as a function chemical potential. The tilt angle is derived from experimental spectral peak areas, as described in the text. The chemical potential is measured relative to the UC-TI phase boundary at the same temperature. The ranges of the TI and F phases are indicated.
Experimental frequency as a function of the chemical potential along various isotherms: Open , solid , open , , solid , , solid , open , , and open . The region of positive slope on the left is the liquid F phase, the common tangent line is solid F, and the region of stronger negative slope is the TI phase. The points near on the far right are from bilayer phases 2M and 2F.
(a) Relation between and . Solid squares are experimental data spanning the TI phase at . The other lines are calculated for various tilt configurations labeled by the same symbols as in Fig. 4, with the addition of HB II 45° (pluses) and three-sublattice antiferro (open triangles). Symbols are spaced at 5° increments in tilt angle , ranging from 5° at the top of the figure to 80° at the right end. Dashed lines represent the lower branch of , which is relatively strong for intermediate values of and . The heavy line is HB II 60°, which is recalculated more realistically for varying from for UC to at the F-TI boundary, instead of fixed . HB I configurations are all in the lower band, while HB II (upper branch) are in the upper right. The inset shows the centered rectangular unit cell and the HB II and HB I configurations. Arrow heads indicate the “up” end of the molecule. The splay angle in each case is measured from the average azimuth. (b) Expansion of the HB II region now with a chemical shift of of applied to the calculations. This brings the heavy line nearly into coincidence with the experimental data (squares).
(a) Temperature dependence of in the UC phase. Squares are from temperature scans and crosses are from pressure scans. The lower branch is a scan at a lower submonolayer coverage. (b) Temperature dependence of in the UC phase. Open triangles represent a second peak seen at submonolayer coverages.
(a) Frequencies vs temperature for phases seen at low temperatures. Open , solid bilayer, open and D1 dense monolayers, open dense monolayer, and solid trilayer (and also D3 monolayer). The two double lines for 3L represent hysteresis loops for the bottom layer and for the upper layers. (b) Frequencies vs temperature for the same spectra. The peaks for D2 are not resolved from the 3L bottom layer (see also Fig. 12).
Twelve successive spectra showing the evolution from UC (heavy line) to D1 at .
Ten successive spectra showing the evolution from mainly D1 to mainly D2 and 3L at .
Fermi resonance trajectory: Separation of the two -related peaks vs frequency of the high component. Solid circles are representative experimental data for various monolayer phases and for the range of the bottom layer of the 3L trilayer, all corrected as described in the text. The solid line is a theoretical two-parameter fit, which assumes that all of the polarizabilities are derived from the component. The broken line includes coupling to mode for fixed and varying tilt. The segment labeled “UC uncorr.” shows the spread of the uncorrected UC data.
Tilt orientations in a sample of the three-sublattice antiferro configuration with 30° rotation of the tilt azimuths from lines of nearest neighbors. Arrow heads indicate the “up” end of the molecule.
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