Single mean lifetime

Fig. 1. Mean lifetimes of a single water molecule in the first coordination sphere of a given metal ion, th2o> and the corresponding water exchange rate constants, h2o- The tall bars indicate directly determined values, and the short bars indicate values deduced from ligand substitution studies. References to the plotted values appear in the text.

A) Reorientation of a single polar molecule during the mean lifetime ror in a rather narrow intermolecular potential well considered in Section V in terms of the hat-curved (HC) model. 

The first picosecond laser spectroscopic study to examine charge carrier trapping and recombination dynamics was reported by Gratzel, Serpone and co-workers [15]. The mean lifetime of a single electron/hole pair was determined to be 30 15 ns at low occupancy of electron/hole pairs in the titanium dioxide particles. At high occupancies, where recombination followed second-order kinetics, the bulk rate coefficient for recombination was (3.2 1.4) x 10-11 cm3 s 1. 

In order to convert the measured lifetimes into dimensions (and shapes) of the pores, additional information is required. A basic shape of pores has to be assumed. The single parameter (lifetime) is not sufficient to determine a three dimensional object. Here simple spherical shapes for isolated pores and channels (tubes) with circular cross sections are assumed. The diameter of the pores can be related to the classical mean free path ( ) of a particle in such objects of volume V and surface area f [46],... 

In the simplest measurement, data collected for two energies can provide a measure of the escape depth, the porosity and the open porosity fraction. The values are extracted by comparing the measurements to a set of calibration curves. With a positron beam flux of 0.2 pA, 100 locations on a wafer could be checked in 30 minutes. Mean lifetime measurements can be carried out with a pulsed positron beam. An intermediate time resolution of about 1 ns will be sufficient. A single measurement can be accomplished in about 1 minute. 

Figure 5.75 shows the fluorescence decay function in a selected pixel of the recorded data array and a double exponential Levenberg-Marquardt fit. The decay is clearly double-exponential and cannot be reasonably approximated by a single exponential decay. For the lifetime image, both lifetime components were weighted with their amplitude coefficients. This mean lifetime" is displayed as colour in the lifetime image in Fig. 5.74, left. 

The intensity-weighted mean lifetime is a better approximation of the lifetime obtained by a single-exponential fit or by calculations based on the first moments [308]. The pile-up distorted r , ds... 

At very low temperatures the H NMR spectmm of a metal tetrahydroborate, M(BH4) , has two broad groups of resonances, of equal intensity, centered 500 Hz apart. On decoupling B the resonances sharpen, and each shows a small triplet coupling. On warming these resonances broaden, coalesce at 180 K, and eventually become a single sharp line, which becomes a 1 1 1 1 quartet when B is no longer decoupled. Account for these observations, and calculate the mean lifetimes in the protons two distinct positions at 180K. 

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