Positional disorder

C, Re, S and O atoms are represented by black, dark grey, medium grey and light grey balls, respectively. H atoms are omitted for clarity. The two disordered positions of the anions are represented. 

For the reaction aA + bB cC + t/D, the equilibrium constant is K = [C]l[D], /[A]"(B), Solute concentrations should be expressed in moles per liter gas concentrations should be in bars and the concentrations of pure solids, liquids, and solvents are omitted. If the direction of a reaction is changed. K = UK. If two reactions are added. A", = K, K-,. The equilibrium constant can be calculated from the free-energy change for a chemical reaction K = e AcrlRT. The equation AG = AH — TAS summarizes the observations that a reaction is favored if it liberates heat (exothermic, negative AH) or increases disorder (positive AS). Le Chatelier s principle predicts the effect on a chemical reaction when reactants or products are added or temperature is changed. The reaction quotient, Q, tells how a system must change to reach equilibrium. 

The overall lattice structure contains slightly kinked, but unobstructed, parallel tubes, and so (15)2- (THF) is a compound of the tubulate type. The THF guest molecules can occupy two alternate disorder positions within a tube, one only of these being illustrated in Figure 24. 

Because the diffraction experiment involves the average of a very large number of unit cells (of the order of 10 in a crystal used for X-ray diffraction analysis), minor static displacements of atoms closely simulate the effects of vibrations on the scattering power of the average atom. In addition, if an atom moves from one disordered position to another, it will be frozen in time during the X-ray diffraction experiment. This means that atomic motion and spatial disorder are difficult to separate from each other by simple experimental measurements of intensity falloff as a function of sm6/X. For this reason, atomic displacement parameter is considered a more suitable term than the terms that have been used historically, such as temperature factor, thermal parameter, or vibration parameter for each of the correction factors included in the structure factor equation. A displacement parameter may be isotropic (with equal displacements in all directions) or anisotropic (with different values in different directions in the crystal). 

FIGURE 15.16. The crystal structure of ice (hexagonal unit cell, a = b = 4.48 A, c = 7.31 A. Water molecules are drawn with four hydrogen atoms representing disordered positions. 

Only in a few measurements of salts 1 H+X was the NH proton found to lie strictly in a symmetry plane of the cation with averaged N—H bond lengths of ca 1.3 A. Nevertheless, the current standpoint is prone to accept that these results reflect a disordered position of the proton equilibrating rapidly between the two nitrogen atoms. This is supported by the fact that symmetrical H-bridges were mainly recorded when the measurements were conducted at ambient rather than at low temperature92. 

The letters o and d refer to molecules of fi-Sg at ordered and disordered positions, respectively... 

Ag has a three-fold disordered position around the three-fold axis, P and X do not. three-coordinate. 

Figiue 31 Structure of Sn(edaa), showing the two equivalent disordered positions of the edaa ligand... 

Figure 4 Crystal structures of clam-like CTC dimers encapsulating cations, with O O consistent with hydrogen bonding shown as dashed lines, (a) Rb" complex (b) NEt4+ complex with only one of two disordered positions of the cation shown.

On the basis of the nearly hexagonal symmetry of the a-cyclodextrin molecules in the krypton adducts one should assume that the included krypton atoms occupy at least six statistically disordered positions. Owing to the anisotropic environment of the a-cyclodextrin molecule in this crystal structure only five out of the six possible locations are occupied by krypton atoms, see Figure 9. The location near the most rotated glucose is empty - obviously the slight rotation of this glucose has prevented the krypton atom to fill that position. 

Since for most reactions the entropy change is negative, the thermodynamic efficiency is <100%, as can be seen in Table 1.2. However, in some cases the reaction results in an increase in disorder (positive AS) (e.g. formic acid) and the system takes heat in from the environment, so expressing an efficiency of greater than 100%, based on the thermal efficiency definition above. 

As a consequence of the reaction non-uniqueness which results in formation of either of two chain types, the polymerizing S2N2 phase is progressively disordered. The statistical alternation of these chain types is reflected in disordered positions which appear in the electron density maps for the final polymer crystals(23,24),... 

Fig. 19. The trisilacyclohexane skeleton showing bond lengths (left) and bond angles (right). Torsion angles of the skeleton are also given. The different labelling of atoms (below left and right) indicates the two disordered positions of the trisilacyclohexane rings of 402...

Figure 4 Section of the crystal structure of [Znfbtpjfdpedjj]. Only one disorder position is shown for each bridging ligand for the sake of clarity. The pendant alcohol groups directed into the MOF cavities can form R-O-M bonds with M = Li(I) and Mg(II)>o...

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