Phasing circles

FIG. 2 Phase diagram in the M-z plane for a square lattice (MC) and for a Bethe lattice q = A). Dashed lines Exact results for the Bethe lattice for the transition lines from the gas phase to the crystal phase, from the gas to the demixed phase and from the crystal to the demixed phase full lines asymptotic expansions. Symbols for MC transition points from the gas phase to the crystal phase (circles), from the gas to the demixed phase (triangles) and from the crystal to the demixed phase (squares). (Reprinted with permission from Ref. 190, Fig. 7. 1995, American Physical Society.)... 

Under the simplifying assumption that the reflexions are independent of each other, K, can be written as a product over reflexions for which experimental structure factor amplitudes are available. For each of the reflexions, the likelihood gain takes different functional forms, depending on the centric or acentric character, and on the assumptions made for the phase probability distribution used in integrating over the phase circle for a discussion of the crystallographic likelihood functions we refer the reader to the description recently appeared in [51]. 

Figure 1 Phase diagram of the zigzag model (1). The solid line is the boundary between the ferromagnetic and singlet phases. Circles correspond to the special cases of the model. On the dotted line the ground state is a product of singlet pairs.

Figure 24. Variation in the percentage of the different phases of Ndo.5-SrasMnOj with temperature FMM phase (diamonds) orbitally ordered A-type AFM phase (circles) charge-ordered CE-type AFM phase (squares) (from Woodward et al.50),...

Figure 3.6 Typical kinetics of regulated proteins following neurotrophin treatment of SYSY-TrkA or SYSY-TrkB. The majority of proteins like for instance galectin-1 were regulated in the late stimulation phase. Circles (control) and triangles (neurotrophin-treated) represent single standardized...

Fig. 8 Fracture strengths, in terms of in-plane macrostress (triangles) and maximum "equivalent noni stress" in PSZ phase (circles), plotted against PSZ volume fraction. Solid and open markings refer to the cases with and without taking account of residual stresses.

Fig. 2.20. The total enthalpy of formation of the amorphous phase (squares) and equilibrium crystalline phase (circles) as obtained by DSC studies of multilayered Ni/Zr diffusion couples during SSAR. The experimental data are compared with the CALPHAD calculation (solid line) of Saunders and Miodownik [2.76]. The data points give the experimentally observed enthalpy of formation for diffusion couples of various overall compositions [2.6S]...

FIGURE 3 (a) Phase circle for a reflection with phase angle otp. (b) Phase circle for derivative 1 intersects native circle at A and B. (c) Phase circle for derivative 2 intersects native circle at A and C... 

F1GURE 7 Combined probability in Figure 6c plotted around phase circle. 

A3 corresponds to the white line and X2 to the minimum in/ ) and draw the corresponding phasing circles, we get a well-resolved unique phase (figure 9.10). The centres of these phasing circles are well separated and non-collinear this is necessary and sufficient for phasing (as has also been pointed out by Templeton et al (1980b), and by Ramaseshan and Narayan (1981)). 

Figure 9.10 The centres for the phasing circles in this Harker diagram are based on the Friedel equivalent pair at the white line (or just on the short A side of the edge) and one equivalent for the minimum off (i.e. two wavelengths in total). The centres are well separated and non-collinear and the unique phase is well resolved. From Flelliwell (1984) with the permission of the Institute of Physics.

The effect of a larger and larger <5A/A would gradually reduce the size of f and / so that the centres of the phase circles would move closer and the unique intersection of the phase circles could not be defined leading to a phasing error. Likewise, in the plot off versus/ (figure 9.2) the area of the loop decreases as <5A/A increases (Ramaseshan, pers. comm.). We... 

Figure 4. Log-log plot of the X-ray scattering intensity versus transverse scans at fixed for 4- and 34-layer H7F6EPP films. The films are in the SmA phase. Circles and crosses indicate positive and negative respectively. The values (in A" ) of q are 0.235 (a), 0.292 (b), 0.348 (c), 0.448 (d), 0.216 (e), 0.287 (0, 0.355 (g), and 0.429 (h), respectively. Data have been shifted for clarity. The solid lines are the best fits to the model. (Adapted from [9]).

Figure 19 Master plot of the layering transitions of water in five pores with water-wall interaction strength Uq = -4.62 kcal/mol (four cylindrical pores with i p = 12 to 25 A and one slit pore with = 24 A). The densities of the coexisting phases (circles) and the diameters (squares) are rescaled by the critical density (/ = 0.044 A ). The temperature is rescaled by the critical temperature. The solid lines represent fits of the average coexistence curve and of the average diameter to equations (4) and (5) with the critical exponent P = 0.125 and amplitude B = 1.55p. ...

Fig. 15a and b. Experimental 6 ( k) data for two samples of polyetbjdene (characteristics shown inTable2). Closed symbols fraction in concentrated phas open syndx fraction in dilute phase. Circles and squares refer to 1 and 2% initial concentration by weight, respectively. Solvent diphenylether... 

Figure 5.20 Experimental phase diagrams (a,c) of binary (AB) /(AB)p blends composed of S-I and I-EO diblock copolymers and corresponding theoretical predictions (b,d). In (a,b), the I fraction is about 0.5 in each copolymer, whereas this fraction is about 0.7 in (c,d). The experimental phase diagrams identify the conditions corresponding to macrophase separation (diamonds), microphase separation of the I-EO-rich phase (circles) and microphase separation of the S-I-rich phase (squares). The predicted phase diagrams show the binodal (solid hues) and spinodal (dotted lines) conditions, as well as microphase separation events (dashed hnes). (Compiled from Frielinghaus, H., Hermsdorf, N., Sigel, R., Almdal, K., Mortensen, K., Hamley, I. W., Messe, L., Corvazier, L., Ryan, A. J., van Dusschoten, D., Wilhelm, M., Floudas, G. and Fytas, G. Macromolecules 34, 4907, 2001, and reprinted with permission. Copyright (2001) American Chemical Society.)...

Fig. 15 An optical section taken at a level of 47.5 fim from the coverslip. The white phase corresponds to the PB phase, and the gray phase to the SBR phase. Circles with the radius of 4 fim, which corresponds to (R) obtained by the PSM, are shown...

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