Average structures

The function W(X) is called the potential of mean force (PMF). The fundamental concept of the PMF was first introduced by Kirkwood [4] to describe the average structure of liquids. It is a simple matter to show that the gradient of W(X) in Cartesian coordinates is related to the average force. 

There is no guarantee that crack-free joints will automatically be obtained when fabricating weldable metals. This is a result of the fact that weldability is not a specific material property but a combination of the properties of the parent metals, filler metal (if used) and various other factors (Table 9.7) . The consequence of the average structural material possessing imperfect weldability is to produce a situation where defects may arise in the weld deposit or heat-affected zone (Table 9.8 and Fig. 9.27). 

Fig. 2 Average structure of the hairy or ramified region of an apectic substance, with a rhamnogalacturonan I backbone substituted at position 4 of the rhamnose units with arabinan and arabinogalactan type II side chains...

In order to discuss the various techniques we must distinguish between diffusive and non-diffusive systems (J8). Diffusive systems, such as liquids, are characterized by the eventual diffusion of particles over all of the available space non-diffusive systems such as solids, glasses and macromolecules with a definite average structure are characterized by time independent average positions around which the atoms fluctuate. 

Structural information about the metal-support interface is provided by EXAFS spectroscopy. The EXAFS data provide average structural information and are most informative when the samples are most nearly uniform. 

At this point it is essential to compare the calculated structure with both the experimental data and the results of the rMD run (6). On the one hand, the interatomic distances of the final model must match the NMR restraints additionally, the fMD-averaged structure should correspond with the refined conformation obtained by the rMD. Only if the rMD and the fMD simulations result in the same conformational model and no experimental restraints are severely violated the calculated structure can be presented as a 3D image (7). 

Among crystals with stacking faults the lack of a periodic order is restricted to one dimension this is called a one-dimensional disorder. If only a few layer positions occur and all of them are projected into one layer, we obtain an averaged structure. Its symmetry can be described with a space group, albeit with partially occupied atomic positions. The real symmetry is restricted to the symmetry of an individual layer. The layer is a three-dimensional object, but it only has translational symmetry in two dimensions. Its symmetry is that of a layer group there exist 80 layer-group types. 

Homoleptic complexes have been obtained also with tetrakis(l-pyrazolyl)borates, e.g., [ B(pz)4 2Cd] and [ B(3-Mepz)4 2Cd] (both P2 jc, Z = 2) in both compounds structure analyses the ligands have been shown to coordinate trihapto, i.e., with one pz ring free. In both cases Cd has a distorted octahedral environment, with averaged structural data very similar to those for the tris(l-pyrazolylhydridoborate complexes.201 Variable-temperature 3H NMR studies of these and of mixed complexes with tris- and bis(l-pyrazolylhydridoborates indicate fluxional behavior (coalescence temperatures and barriers for the dynamic processes are given). 

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