Rescaling of AQ/Cu(111) lattice based on STM measurements 23 to a new lattice shown by dashed lines. Open circles – copper atoms, elongated molecules mark AQ.
(a) Schematic representation of a pin-wheel honeycomb structure 333 on a new lattice. Long arrows mark the characteristic interaction distance of the 333 phase. Small double arrows with numbers 1, 2, 3 denote the three bond vectors of our model; (b) Allowed and forbidden short-range interactions of our model; (c) Illustration of different short-range interaction energies of AQ molecule in a state s = a surrounded by two molecules in states a and b: −ε1 − ε2 (bond vector orientation α = 2, left); −ε2 + ∞ (α = 1, center), and −ε1 + ∞ (α = 3, right).
Schematic representation of five porous pin-wheel phases: (a) 111, (b) 222, (c) 333, (d) 444, and (e) 555. Their concentrations are 3/4, 6/13, 9/28, 12/49, and 15/76, respectively.
Phase diagram in (A, μ) coordinates at ε d /ε1 = 0.047 and (a) k B T/ε1 = 0 and (b) 0.1. (c) Phase diagram in (A, ε d ) coordinates at μ/ε1 = 0.65 and k B T/ε1 = 0.1. The dots in (b) and (c) mark explored data points. The type of order in corresponding phases are shown above. The phases are distinguished by color and numbering (1–7).
Temperature dependences of (a) energy, (b) specific heat, and (c) molecular concentration close to the phase transition into the 333 phase obtained at μ/ε1 = 0.32 and A/ε1 = 0.38 and four values of ε d /ε1. Only the curves obtained for temperature decreasing from the disordered phase are presented, except for the curves 2 (ε d /ε1 = 0.047) in (a) which are taken to illustrate the energy hysteresis at T c point. Inset in (a) shows energy histogram at T c typical for the first-order phase transition (ε d /ε1 = 0.061).
Phase diagram in (T, ε d ) coordinates for transitions into the 333 phase and neighboring phases. Other parameters are: μ/ε1 = 0.32 and A/ε1 = 0.38. The names of phases are the same as in Fig. 4 .
Percentage of AQ molecules forming pin-wheel triangles or being directly attached to the triangle as a function of normalized AQ molecular coverage. The experimental data 23 are shown by dashed curve (1). Other curves are obtained by MC simulation: (2) (approach to 333 from disordered phase); (3) (approach to 333 from wave phase); (4) ; (5) ; (6) assuming the 333 phase is obtained via all sequence of nnn phases (N pw /N = 100% for n = 3 and 4/n × 100% for n > 3). Other parameters are: for curves 2 and 3, they are the same as in Fig. 4 and for the curves 4 and 5, A/ε1 = 0.35 and ε d /ε1 = 0.05.
The snapshots of structures occurring in calculations with characteristic distance of attractive interaction at : (a) disordered-333 phase separation, c m = 0.151 and A/ε1 = 0.25; (b) waves-333 phase separation, c m = 0.281 and A/ε1 = 0.38. Other parameters: ε d /ε1 = 0.05 and k B T/ε1 = 0.09.
The snapshots of structures occurring in calculations with characteristic distance of attractive interaction at : (a) c m = 0.14; (b) 0.21, (c) 0.24, and (d) 0.285. Other parameters: A/ε1 = 0.35, ε d /ε1 = 0.05, and k B T/ε1 = 0.09.
The structures obtained at A/ε1 = 0.35, ε d /ε1 = 0.05, and 0.09 ⩽ k B T/ε1 ⩽ 0.11 at different values of characteristic interaction length r d . The digits on the left denote the distance r d and those above the structure snapshot – the molecular concentration of this structure, c m .
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