Zachariasen's theory of extinction is used to obtain the mean radius of the mosaic domain of a spherical lithium fluoride crystal. From consideration of the mosaic domain size obtained for a large thick crystal from the same specimen batch and of the crystal strain, it is deduced that this radius is physically unreasonable.

From consideration of the normal crystal strain in real crystals it is deduced that the value of mean domain size of a small sphere of sodium fluoride obtained by the application of Zachariasen's theory of extinction is physically meaningless and that no physical significance can be given to domain size so obtained Phys. Chem. Solids (1970). 31,[2689][2690][2691][2692][2693][2694][2695][2696][2697]. IntroductionIt has already been proven by Killean, Lawrence & Sharma (1972) that Zachariasen's theory for secondary extinction (Zachariasen, 1967) when applied to a small sphere of lithium fluoride gives a value of mean domain size which is physically unreasonable. These results are further supported by the application of Zachariasen's theory to a small sphere of sodium fluoride which is shown to exhibit secondary extinction. ExperimentalSmall cubes of sodium fluoride single crystal were ground into spheres and a sphere of approximate radius 0.10 mm chosen for intensity-data collection. A total of 61 independent reflexions were measured on a computer-controlled Siemens four-circle diffractometer using Mo K~ radiation [2(K~)=0.7107 A]. A fivepoint measuring cycle was employed using 0-20 scan. Measurement of three standard reflexions at regular intervals showed no significant changes in the intensities of these reflexions over a data collection period of three days. The counting statistics on most of the reflexions were kept below 1% of the integrated intensities. To minimize the lost counts to fewer than 0.5 % at the peak maxima one of a set of six attenuators was inserted in the main beam before the measurement of each reflexion.The integrated intensities were corrected for Lorentz and polarization factors and a set of relative observed structure factors deduced. No corrections were applied for photoelectric absorption and anomalous dispersion. The observed structure factors were adjusted to the calculated structure factors in the least-squares process using only high-order reflexions which were not suspected to be affected by extinction. The reflexions 200, 220, 222, 400, 420, 422, 440, 442 and 600 were excluded from the least-squares refinement. The * Present address: Department of Physics, University of Benin, Ekenwa Road, Benin City, Nigeria, least-squares minimization process was carried out using two thermal parameters and a scale factor and the atomic form factors used for the computation of calculated structure factors were those given in International Tables of X-ray Crystallography (1962). After the least-squares refinement, a comparison of the observed structure factors and the calculated structure factors showed that the observed structure factors were systematically smaller than the calculated structure factors for a few low-order reflexions, indicating extinction in the data.From a knowledge of the calculated structure factors and the extinction-affected observed structure factors values of r* were obtained for each of the extinguished reflexions using the method of Zacharia-, sen (1967). A fairly co...

In density functional-theoretic studies of photoionized water-based systems, the role of charge localization in proton-transfer dynamics is not well understood. This is due to the inherent complexity in extracting the contributions of coupled electron-nuclear nonadiabatic dynamics in the presence of exchange and correlation functional errors. In this work we address this problem by simulating a model system of ionized linear Hbonded water clusters using real-time time-dependent density functional theory-based Ehrenfest dynamics. Our aim is to understand how self-interaction error in semilocal exchange and correlation functionals affects the probability of proton transfer. In particular, we show that the proton-transfer probability is largely underestimated for short H-bonded chains but becomes comparable to that predicted by hybrid functionals for (H 2 O) + n chains with n > 3. This is because the formation of hemibonded-type geometries is largely suppressed in extended H-bonded structures. We also show how the degree of localization of the initial photo-hole is connected to the probability of a proton-transfer reaction, as well as to the hole-proton separation. These results are compared to those obtained with adiabatic dynamics where the initial wave function is allowed to relax to the ground state of the ion cluster, explaining why different functionals and dynamical approaches lead to quantitatively different results.

Water displaces potassium ions and initiates the formation of a homonuclear dimer ion (K²⁺) in the tunnels of hollandite.

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