Observation distances

Consider next the experimental points for Csl, CsBr, and CsCl which, as already pointed out, lie quite near the diagonal in Fig. 57. At room temperature neither of those substances crystallizes in the NaCl type of lattice, but in a lattice where each ion has eight neighbors, instead of six. From the observed distance between the cesium nucleus and the halogen nucleus in each of these three crystals, one can easily calculate what... 

The size assigned to an atom or ion requires a decision about where an atom stops. From quantum mechanics we learn that an atom has no sharp boundaries or surfaces. Nevertheless, chemists find it convenient to assign sizes to atoms according to the observed distances between atoms. Thus, atomic size is defined operationally—it is determined by measuring the distance between atoms. 

In the foregoing treatment the assumption of additivity of interatomic distances in the compounds under discussion has been tacitly made. Examination of Table IV shows that this assumption is approximately substantiated by experiment. The agreement between the observed distances and the calculated radius sums is excellent in most cases. Aside from those just discussed, the exceptional crystals are AIN and SiC with observed interatomic distances slightly smaller than the radius sums. It seems doubtful that these deviations are to be attributed to a partially ionic character of the bonds, and the number of other factors which might conceivably be operative is so large that no single one can be selected with confidence as responsible. 

Observed distances between tetrahedral atoms in other crystals, given in Table V, are also in satisfactory agreement with the radius sums. One interesting crystal is Various investigators have suggested different... 

It seems probable also that, to within one or two percent, doublebond and triple-bond radii for various atoms should bear constant ratios to single-bond radii. We have chosen 0.79 for the triple-bond factor, which gives agreement with the observed distance in the N2 molecule, and 0.90 for the double-bond factor. The radii given in Table VI are obtained with these factors. 

Comparison of Radius Sums from Table VI with Observed Distances from Band Spectra. 

In Table VII radius sums from Table VI are compared with observed distances from band spectral data. Agreement to within 0.01 or 0.02 A is usually found in the exceptional case H2C0 the experimental value is not very accurate. In Table VIII a similar comparison is made with observed distances in crystals. These distances depend in all cases on... 

For the oxygen atoms in P4Oio that are bonded to only one phosphorus atom the predicted amount of ir-bond character, 1.02, leads to 1.45 A. for the P=0 distance. This is in only rough agreement with the observed distance, 1.39 0.02 A. 

The sodium salts also show the effect of double repulsion, the increase of the observed distances over the calculated being greatest (2.7%) for the iodide, for which f Na+/- i- is 0.44. 

In applying the metallic radii in the discussion of the structure of a metal or intermetallic compound either the observed distances may be used with the single-bond radii to calculate the bond numbers, the sums of which may then be compared with the expected valences, or the distances may be compared with the sums of radii for suitable coordination numbers, such as CN12. The correction to be added to i (CN12) to give the radius for another coordination number, the va-... 

Indeed, if the bond numbers are calculated from the observed distances, the following results are obtained... 

Equations (11a) and (12a) are based upon the values 1-399 and 1-430 for R sp3) for tin and lead, respectively, with slopes as indicated by the tetrahedral radii for the heavier elements. The value 1-430 for quadrivalent lead was obtained by adding to the radius for quadrivalent tin the difference 0-031A between the Mg-Pb distance in Mg2Pb and the Mg-Sn distance in Mg2Sn. The simple form of equations (116) and (126) was assumed in analogy with (106), and the equal values of the constant were obtained from the observed distances for silver and gold, both assumed to have valence 5 . 

CALCULATE OBSERVATION DISTANCE FROM TARGET AND ABSOLUTE VALUE OF THAT DIFFERENCE. difference = study day - target absdifference = abs(difference) ... 

Figure 8.46. Construction of observable distances (dal, Lf) in a paracrystal from its fundamental distances, L (not observable pseudo long-periods), and dcl (observable crystallite thicknesses). Advancing to the bottom the relations to the observable thicknesses of amorphous layers, dm, and the long periods, L , are sketched...

Bond Covalent sum8) Ionic sum8) Ionic sum1) Average observed distance )... 

This graph has several important features. It reaches saturation at d0bs of about 0.93, which means that the model predicts that one will never see a pair of proteins that are less than 7% identical. At this level of distance, a substitution will restore an amino acid identity just as likely as generate a new difference. Real sequences will sometimes exceed this level of observed distance and then the correction is not applicable. This is especially likely to occur with short sequences. If such distances are encountered in a real data set, then the sequences are so distant that the analysis will be difficult anyway. No matter what is done, it will be difficult to estimate the true number of substitutions. A further problem arises when one considers the possible variance or error of the distance estimates. A difference in the observed distance of just one identity more or less will have very little effect when dobs is small but will make an enormous difference to D when dobs is more than 0.80. 

The ice I model used to describe the structure of H20(as) 77 K/77 K does not predict any oxygen-oxygen distances in the region 2.76 A <7 <4.5 A and is hence not capable of explaining the observed distance spectrum and density of HoO(as) 10 K/10 K. We defer to a later section the discussion of an appropriate model for this high density H20(as). 

The natural way of analyzing this problem is to introduce the appropriate scales. They would come from the characteristic concentration c, the characteristic length Lr, the characteristic velocity Qr, the characteristic diffusivity Dr and the characteristic time Tr. The characteristic length Lr coincides in fact with the "observation distance". Setting... 

If the positions of the H ions are not known, one can make use of the observed distances between the donor and acceptor anions to search for potential hydrogen bonds. Donnay and Allmann (1970) have shown that it is possible to identify which atoms are donors and which are acceptors by considering the deficiency in the bond valence sums when the contributions of the hydrogen bonds are ignored. Donor anions will have a deficiency of around 0.8 vu while those with a smaller deficiency are likely acceptors. Identifying neighbouring donor and acceptor anions usually allows the hydrogen bond... 

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