Free contour plot

Figure B3.2.10. Contour plot of the electron density obtained by an orbital-free Hohenberg-Kolnr teclmique [98], The figure shows a vacancy in bulk aluminium in a 256-site cell containing 255 A1 atoms and one empty site, the vacancy. Dark areas represent low electron density and light areas represent high electron density. A Kolm-Sham calculation for a cell of this size would be prohibitively expensive. Calculations on smaller cell sizes using both techniques yielded densities that were practically identical.

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

Figure 7.22 shows the H NMR chromatogram (contour plot) of the separation of a 10% phthalate mixture in CH2CI2. The spectrum is almost free from interferences the NMR resolution is excellent, and it is possible to identify all plasticisers even at concentrations as low as 2%, which corresponds to 60 xg per component. In contrast, in on-line HPLC- H NMR separation the regions between 3.9-3.3 and 1.9-1.7 ppm are completely obscured by solvent signals. 

Figure 13-10. The potential of mean force (kcal/mol) as a function of D1 and D2 (A) shown as a 20-level contour plot and colored by the free energy values...

Fig. 3.3 Equivalent solution contour plots for solutions of and ethylenediamine [en] at 50°C. The curves represent conditions for a constant concentration of free Cd = 10 M. Bottom curve (solid line) [total Cd] against [ethylenediamine]. Top curve (dotted hne) the ratio of [ethylenediamine] to [total Cd] against [ethylenediamine]. (Adapted from Ref. 43.)...

Figure 7. The two-dimensional ground state free energy surfaces for (a) DNOA and (b) DONA. The straight-line reaction paths are shown on the contour plots as dashed lines, and the minima are labeled according to the dominant VB states. Note that the Zp solvent coordinate is scaled by a factor of approximately four. (Reproduced from Ref.

First, the presence of an additional minimum at r = 3 A along the reaction path is clearly discernible in the computer-simulated contour plot. The small energy barrier between this minimum and the minimum at r = 6 A is due to the molecularity of the solvent there is a free-energy cost associated with the making of the hole between the two fragments in order to fit in a water molecule. 

Figure 10 (a) Computer-simulated contour plot of the free-energy surface obtained by... 

The results are partially shown here as contour plots for NiCoCrAlY-alumina joints (Fig.4). These values are the mean ones of the respective tensor in certain direction (X or Y/Z). As far as the specimen is assumed to be free, the graded composition in X direction will be sufficient... 

Figure 17. Contour plot of a two-dimensional cut in the H2/Mg(100) PES for the configuration shown on the top right of the figure. The energies are relative to those of the free atoms. A is a barrier to molecular chemisorption. M is a molecular chemisorption well. D is a barrier to dissociation, and B is an atomic chemisorption well. The distance from the surface is measured from the first atomic layer, and the distance parallel to the surface is measured from the top site towards the bridge site. The figure is from Norskov et al. (1981) with permission.

More quantitative evidence for the charge transfer mechanism comes from self-consistent calculation of on Mg (Norskov et al 1981 Norskov and Besenbacher 1987). Calculated interaction energies are shown in the contour plot in Fig. 17. The vertical axis is Z and the horizonal axis is r. The energies in eV are calculated relative to those of the free H atoms. One immediately sees the various possible characteristics of a reactive PES ... 

In order to extend the above description to include the H-bond coordinate Q, we display a contour plot in Fig. 10.5 of the free energy of the PT system with the proton motion already quantized in its ground vibrational, zero point level, as a function of Q and the solvent coordinate AE. Reactant and product wells are... 

Figure 10.5 Contour plot of the PT system free energy versus the solvent coordinate, AE, and the H-bond coordinate separation Q for a symmetric reaction. Contour spacings are 1 kcal mol b...

The effect of substitutional impurities on the stability and aqueous solubility of a variety of solids is investigated. Stoichiometric saturation, primary saturation and thermodynamic equilibrium solubilities are compared to pure phase solubilities. Contour plots of pure phase saturation indices (SI) are drawn at minimum stoichiometric saturation, as a function of the amount of substitution and of the excess-free-energy of the substitution. SI plots drawn for the major component of a binary solid-solution generally show little deviation from pure phase solubility except at trace component fractions greater than 1%. In contrast, trace component SI plots reveal that aqueous solutions at minimum stoichiometric saturation can achieve considerable supersaturation with respect to the pure trace-component end-member solid, in cases where the major component is more soluble than the trace. 

Figure 2. Damage distribution and mean stress contour plot at 0.6 ms in computer simulation of Experiment 79-8. The contour level and plot dimensions are the same as in Figure 1. At this time, the detonation is complete. A shock wave is propagating upward toward the free surface. Extensive damage has occurred around the...

Figure B3.2.10. Contour plot of the electron density obtained by an orbital-free Hohenberg-Kohn technique...

Fig. 1 Contour plot of conversion of free fatty acid of tung oil during pretreatment (experiment 1)...

Figure 5. a, 2D exchange spectrum of heptamethylbenzenonium ion in 9.4 M HiSOi obtained by a 2D Fourier transformation from 64 free induction decays with t/ values ranging from 0 to 142 ms, and with = 280 ms (60-MHz proton resonance on a modified Varian DA60 spectrometer, 40°C sample temperature), b. Contour plot based on the same data as used for Figure 5a. Off-diagonal peaks indicate slow intramolecular exchange between the four nonequivalent groups of protons labeled 1 to 4. (Reproduced, with permission, from Ref. 26. Copyright 1979, American Institute of Physics.)...

Fig. 39a, b. Contour plot of relative surface free energy of Cu measured at T = 1200 K. Data are shown as a stereographic projection in the unit triangle of low-index orientations. All values are normalized to unity at the (100) orientation, (a) Clean Cu surfaces (b) oxygen covered Cu surfaces at a O2 partial pressure of lO mbar [70Hon2]. 

The contour plots presented in Fig. 6.43 show the free energy as a function of chain orientation expressed in terms of the average side-step number (6 60) y — corresponds to a perfect parallel arrangement of rigid rods) and polymer volume content (Vi). 

Figure 6.43 Contour plots showing the free energy (AG/RT) as a function of volume fraction (i>2) of rigid rod polymer (with different aspect ratios x as shown in the diagrams) and degree of orientation (y). Higher value of free energy is indicated by lighter colour.

---