Crystalline Environment

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].

Intrinsic defects (or native or simply defects ) are imperfections in tire crystal itself, such as a vacancy (a missing host atom), a self-interstitial (an extra host atom in an otherwise perfect crystalline environment), an anti-site defect (in an AB compound, tliis means an atom of type A at a B site or vice versa) or any combination of such defects. Extrinsic defects (or impurities) are atoms different from host atoms, trapped in tire crystal. Some impurities are intentionally introduced because tliey provide charge carriers, reduce tlieir lifetime, prevent tire propagation of dislocations or are otlierwise needed or useful, but most impurities and defects are not desired and must be eliminated or at least controlled. 

A calculation of tunneling splitting in formic acid dimer has been undertaken by Makri and Miller [1989] for a model two-dimensional polynomial potential with antisymmetric coupling. The semiclassical approximation exploiting a version of the sudden approximation has given A = 0.9cm" while the numerically exact result is 1.8cm" Since this comparison was the main goal pursued by this model calculation, the asymmetry caused by the crystalline environment has not been taken into account. 

ReflEXAES can be used for near-surface structural analysis of a wide variety of samples for which no other technique is appropriate. As with EXAES, ReflEXAES is particularly suited for studying the local atomic structure around particular atomic species in non-crystalline environments. It is, however, also widely used for the analysis of nanocrystalline materials and for studying the initial stages of crystallization at surfaces or interfaces. ReflEXAES was first proposed by Barchewitz [4.135], and after several papers in the early nineteen-eighties [4.136, 4.168-4.170] it became an established (although rather exotic) characterization technique. Most synchrotron radiation sources now have beam-lines dedicated to ReflEXAES experiments. 

The preparation and structural characterization of the ions HX2 has been an important feature of such work/ As expected, these H-bonded ions are much less stable than Hp2 though crystalline salts of all three anions and of the mixed anions HXY (except HBrI ) have been isolated by use of large counter cations, typically Cs+ and NR4+ (R = Me, Et, Bu") — see pp. 1313-21, of ref. 23 for further details. Neutron and X-ray diffraction studies suggest that [C1-H - C1] can be either centrosymmetric or non-centrosymmetric depending on the crystalline environment. An example of the latter mode involves interatomic distances of 145 and 178 pm respectively and a bond angle of -168 (Cl- -Cl 321.2pm).( >... 

Pelletier and Reber315 present new luminescence and low-energy excitation spectra of Pd(SCN)42 in three different crystalline environments, K2Pd(SCN)4, [K(18-crown-6)]2Pd(SCN)4, and (2-diethylammonium A -(2,6-dimethylphcnyl)acetamide)2Pd(SCN)4, and analyze the vibronic structure of the luminescence spectra, their intensities, and lifetimes as a function of temperature. The spectroscopic results are compared to the HOMO and LUMO orbitals obtained from density functional calculations to qualitatively illustrate the importance of the bending modes in the vibronic structure of the luminescence spectra. 

In the four isomorphous structures the different guest components are located in a similar crystalline environment. Since the species involved are of nearly identical... 

Fig 39a and b. Stereoviews of the crystalline environment around the phosphoric ester guest (+)-27a in its complexes with a (— )-26, and b +)-26. For clarity, the positions of the two adjacent guest moieties are shown schematically (taken from Ref.53>)... 

Caillet, J., P. Claverie, and B. Pullman. 1978. Effect of the Crystalline Environment upon the Rotational Conformation about the N-C and C-C Bonds ( and P) in Amides and Peptides. Theoret. Chim. Acta (Berl.) 47, 17-26. 

When a defect is introduced into a crystalline environment, crystal translational symmetry can no longer be invoked to transform the problem into tractable form as is done in band-structure calculations. Most of the computational treatments of defects in semiconductors rely on approximations to the defect environment that fall into one of three categories cluster, supercell (or cyclic cluster), and Green s function. 

These external fields can affect the physical properties and reactivity of the molecular systems. Such effects are especially important in ordered crystalline environments such as solid oxides and biological macromolecules [25-28]. These local electrostatic fields play an important role in catalytic functions and in governing the stabilization of many biomolecular systems [29-32]. These environmental effects cause dramatic changes in the reactivity, which can be different from the gas phase. 

Hitchman and his co-workers (121,122,151) have shown how the ground state wave function (in the form ax2 + by2 + cz2) can be obtained for rhombic copper(II) systems the coefficients a, b and c thus obtained are in reasonable agreement with those found by analysis of the e.s.r. spectrum. Marshall and James (123) have attempted an ambitious analysis of the optical and magnetic properties of [Cu(H20)6]2+ in several crystalline environments the AOM was used to parameterise the theoretical expressions for the various experimental properties, in order to see whether a great... 

This Lorentzian line-shape function has been sketched in Figure 1.4(b). The natural broadening is a type of homogeneous broadening, in which all the absorbing atoms are assumed to be identical and then to contribute with identical line-shape functions to the spectrum. There are other homogeneous broadening mechanisms, such as that due to the dynamic distortions of the crystalline environment associated with lattice vibrations, which are partially discussed in Chapter 5. 

Inhomogeneous broadening in solids typically occurs as a result of nonequivalent static distortions in the crystalline environment of an optically active center. As can happen with the paving stones in a floor, the crystal reticules are not perfectly equal there is a distribution of crystalline environments for the absorbing atom, and consequently a distribution of resonance frequencies. 

Strong crystalline field Hso < H e < Hqf- In this approach, the crystalline field term dominates over both the spin-orbit and the electron-electron interactions. This applies to transition metal ions in some crystalline environments (see Section 6.4). 

The low-temperature absorption spectrum of Nd + ions in LiNbOj crystals corresponding to the Ig/y Fj/2 transition consists of two peaks at 11 253 cm and 11 416 cm These two peaks are related to the split components of the 12 excited state. This excited state splits due to the crystalline environment of the Nd + ions (C3 symmetry). The high-energy absorption peak (11 416 cm )... 

If the transport process is rate-determining, the rate is controlled by the diffusion coefficient of the migrating species. There are several models that describe diffusion-controlled processes. A useful model has been proposed for a reaction occurring at the interface between two solid phases A and B [290]. This model can work for both solids and compressed liquids because it doesn t take into account the crystalline environment but only the diffusion coefficient. This model was initially developed for planar interface reactions, and then it was applied by lander [291] to powdered compacts. The starting point is the so-called parabolic law, describing the bulk-diffusion-controlled growth of a product layer in a unidirectional process, occurring on a planar interface where the reaction surface remains constant ... 

As shown in the chapter by French, Rowland and Allinger, when the same, relatively rigid glucose residue appears in numerous crystalline environments, there are substantial differences in the conformation. Of course, the errors in the experimental determination must also be considered. 

In the solid-state photochemical reaction of N,N-disubstituted a,(3-unsatu-rated thioamides 24, a crystal-to-crystal nature was observed in 24c furthermore, absolute asymmetric transformation in the chiral crystalline environment was performed in the photoreaction of 24b, 24c, and 24e. 

Example 12.4 Influence of the Environment on D i. Nitromethane is interesting to some people because it explodes. The reason is, of course, in the cleavage of the carbon-nitrogen bond. The monomer, compared to its trimer (taken as a model for the crystal), reveals that the C and N net charges change by A c — 8.7 and A n—1-1 me. respectively, on crystallization. Our bond energy formula and the appropriate parameters thus indicate that the crystalline environment reinforces the CN bond by 4.7 kcal/mol, which is significant at the local point of rupture, responsible for the reaction [251]. 

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