Coherency phase matrix

Equation (41) is modelled qualitatively in Fig. 4 for the simplest MQMAS experiment involving two pulses (which can be easily adapted to STMAS experiment also). Four subspaces of the density matrix describe the phase accumulated by two arbitrary crystallites. From left to right, the first subspace, Fig. 4a, corresponds to the MQC m ( — m at time = 0 (or I — m >< ml, depending on Iml and /). When perfect excitation is assumed the coherence of all crystallites will have the same phase and amplitude. In Fig. 4b the same subspace is shown for time t = r, with a coherence phase accumulated according to Eq. (41). The two crystallites accumulate a different phase depending on their values. In Fig. 4c 1 the projection of the density matrix on to the CT subspace is shown following a conversion pulse. Ideally, this is similar in phase and amplitude to its predecessor and corresponds to time t2 = 0. Finally, in Fig. 4dl the phase accumulation at t2 = —i/l tx is shown. All crystallites refocus at the same k... 

From room temperature up to 150 °C the coherent Cu-rich Guinier-Preston zones I (GPI phase) form they are only one to two 001 layers thick and have a highly strained, coherent phase boundary with the cr-Al matrix phase. 

The simplest scheme that accounts for the destruction of phase coherence is the so-called stochastic interruption model [Nikitin and Korst 1965 Simonius 1978 Silbey and Harris 1989]. Suppose the process of free tunneling is interrupted by a sequence of collisions separated by time periods vo = to do After each collision the system forgets its initial phase, i.e., the off-diagonal matrix elements of the density matrix p go to zero, resulting in the density matrix p ... 

Two-dimensional constant matrix, transition state trajectory, white noise, 203-207 Two-pathway excitation, coherence spectroscopy atomic systems, 170-171 channel phases, 148-149 energy domain, 178-182 extended systems and dissipative environments, 177-185 future research issues, 185-186 isolated resonance, coupled continuum, 168-169... 

Lorentzian line shapes are expected in magnetic resonance spectra whenever the Bloch phenomenological model is applicable, i.e., when the loss of magnetization phase coherence in the xy-plane is a first-order process. As we have seen, a chemical reaction meets this criterion, but so do several other line broadening mechanisms such as averaging of the g- and hyperfine matrix anisotropies through molecular tumbling (rotational diffusion) in solution. 

The idea of back transformation of a three-dimensional NMR experiment involving heteronuclear 3H/X/Y out-and-back coherence transfer can in principle be carried to the extreme by fixing the mixing time in both indirect domains. Even if one-dimensional experiments of this kind fall short of providing any information on heteronuclear chemical shifts, they may still serve to obtain isotope-filtered 3H NMR spectra. A potential application of this technique is the detection of appropriately labelled metabolites in metabolism studies, and a one dimensional variant of the double INEPT 111/X/Y sequence has in fact been applied to pharmacokinetics studies of doubly 13C, 15N labelled metabolites.46 Even if the pulse scheme relied exclusively on phase-cycling for coherence selection, a suppression of matrix signals by a factor of 104 proved feasible, and it is easily conceivable that the performance can still be improved by the application of pulsed field gradients. 

In Ref. [4] we have studied an intense chirped pulse excitation of a molecule coupled with a dissipative environment taking into account electronic coherence effects. We considered a two state electronic system with relaxation treated as diffusion on electronic potential energy surfaces with respect to the generalized coordinate a. We solved numerically equations for the density matrix of a molecular system under the action of chirped pulses of carrier frequency a> with temporal variation of phase [Pg.131]

Internal nucleation and growth can occur coherently or incoherently while the reaction volume can be negative or positive. The severe constraints which the matrix crystal exerts on the internal reaction can lead to the formation of metastable (or even unstable) phases, which do not exist outside the matrix. Often, heavy plastic flow and anisotropic growth has been found. 

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