Evolution phase

While it is not essential to the method, frozen Gaussians have been used in all applications to date, that is, the width is kept fixed in the equation for the phase evolution. The widths of the Gaussian functions are then a further parameter to be chosen, although it appears that the method is relatively insensitive to the choice. One possibility is to use the width taken from the harmonic approximation to the ground-state potential surface [221]. 

Fig. 4.2.5 Unaliased (A) and aliased (B) velocity images for a 0.6% aqueous carboxy-methylcellulose solution obtained by MRI. The vertical axes represent the data obtained in the velocity encoded direction and the horizontal axis represents data obtained in the spatially encoded direction. Aliasing is achieved by setting the velocity encode gradients so large that the maximum phase evolution of a given fluid element for a pulsed gradient step exceeds Ji or 2jt...

Inherent salt loadings in commercial grade anionic surfactants will influence observed phase evolution processes. 

The phase distribution observed in the alloys deposited from AlCb-NaCl is very similar to that of Mn-Al alloys electrodeposited from the same chloroaluminate melt [126 129], Such similarity may also be found between the phase structure of Cr-Al and Mn-Al alloys produced by rapid solidification from the liquid [7, 124], These observations are coincident with the resemblance of the phase diagrams for Cr-Al and Mn-Al, which contain several intermetallic compounds with narrow compositional ranges [20], inhibition of the nucleation and growth of ordered, often low symmetry, intermetallic structures is commonly observed in non-equilibrium processing. Phase evolution is the result of a balance between the interface velocity and... 

As previously, the phase evolution due to anisotropic terms is refocused if... 

Compared with the BSPS by a single PIP [Eq. (84)], the BSPS by a pair of complementary PIPs is reduced significantly and more importantly, it is now linearly proportional to the offset <5, making it possible to be eliminated completely. The minus sign in Eq. (91) implies that the actual phase evolution during the pulse is scaled by a factor of... 

FIGURE 2.10 The phase evolution of iron-doped zircon, ZrSi04, from zirconia, Zr02, silica, Si02, ferrous sulphate, FeS04, and sodium halide mineralisers. 

FIGURE 2.25 EXAFS patterns as a function of time illustrating the phase evolution of beta ferrosilicon from the alpha form when heated at 600°C. (Courtesy of Professor F.J.Beriy, Open University.)... 

Table 2 Phase evolution of the Ba-Al-0 system prepared via different preparation methods...

Fig. 6.5. Numerical simulation of quantum beats measurements of DLL mutant RCs of Rb. capsulatus with 80 fsec pump pulse. Two vibrational frequencies are included in the simulation. The box with broken line indicates the time region in which the phase evolution of the vibrational quantum beams can be seen clearly.

Fig. 1Gas phase evolution during the uv-irradiation of M/Ti02 suspensions (lMNaOH) a) original sample b) with 02 in the gas phase c) a fresh sample pre-reduced in H2 at 298K. 

Kolen ko YV, Amakawa K, Naumann d Alnoncourt R, Girgsdies F, Weinberg G, Schlogl R, Trunschke A. Unusual phase evolution in MoVTeNb oxide catalysts prepared by a novel acrylamide-gelation route. ChemCatChem. 2012 4(4) 495-503. 

The instrumentation must be constructed to be robust enough to allow continuous operation for many days time on stream without interruption. A typical example is the phase evolution of a partial oxidation catalyst that can easily take 100 h or more under steady-state flow conditions. Computer control of the gas feed and analysis instrumentation is mandatory for stable operation. In cases of nanostructure analysis when profiles of diffraction lines are required, the sheer data acquisition time can well exceed 24 h, during which steady-state operation of the system and the catalyst are mandatory to ensure that meaningful structural parameters are determined. 

Dutoit et al. (1995) IR Ti-Si xerogels Phase evolution, synthesis optimization + n.a. Mechanism of sol-gel chemistry in mixed oxides... 

Knobl et al. (2003) RAMAN, TGA MosOh, vanadium, tungsten substitution Phase evolution, solidification, + — n.a Multimethod phase formation... 

Moggridge et al. (1992) MnxOy Phase evolution, effect of structural promoters + + — Methane coupling... 

Moggridge et al. (1995) XAS Conversion electron detection Various systems Bulk vs. surface phase evolution + + - Various... 

Richter and Doppler (1997) Nickel and copper on supports Phase evolution, amorphous co-phases + + Reductive activation, various reactions... 

To partially address the problem of resonance offset artifacts, we can first separate the nuclear spin phase evolution induced by the gradient from the evolution induced by all other sources of resonance offset. Nobel Prize winner Richard Ernst introduced a form of imaging that uses pulsed gradients, in analogy... 

At the center of the echo all resonance offsets from interactions linear in the spin quantum number are canceled as long as these interactions operate for the full duration ofTE. Linear spin interactions include chemical shifts, heteronu-clear dipolar couplings, field inhomogeneity, field gradients, and transmitter frequency offsets but do not include quadru-polar and homonuclear dipolar couplings. There will however be a net phase evolution induced by an interaction to the extent its duration or intensity is not balanced with respect to the two halves of TE (that is, the balance with respect to amount of phase evolution on either side of the 180° pulse). 

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