Observation distances Distance

The c axis corresponds to both the short axis of the crystal and the axis along the molecular chain. The observed repeat distance in the c direction is what would be expected between successive substituents on a fully extended hydrocarbon chain with normal bond lengths and angles (see Sec. 1.2). 

The structure of lumazine has been studied more precisely by X-ray analysis (72AX(B)659). The crystal structure is built up of almost coplanar, hydrogen-bonded dimers of lumazine with the oxygens of the pyrimidine moiety in the keto form and the observed bond distances indicating the pyrazine ring electrons to be delocalized. 

Fig. 1. Schematic diagram illustrating the mechanical instability for (a) a weak spring (spring constant k) a distance D from the surface, experiencing an arbitrary surface force (after [19]) and (b) the experimentally observed force-distance curve relative to the AFM sample position (piezo displacement) for the same interaction.

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. 

We have constructed a number of sets of atomic radii for use in compounds containing covalent bonds. These radii have been obtained from the study of observed interatomic distances. They are not necessarily applicable only to crystals containing pure covalent bonds (it is indeed probable that very few crystals of this type exist) but also to crystals and molecules in which the bonds approach the covalent type more closely than the ionic or metallic type. The crystals considered to belong to this class are tetrahedral crystals, pyrite and marcasite-type crystals, and others which have been found on application of the various criteria discussed in the preceding section to contain covalent bonds or bonds which approach this extreme. 

In constructing this table, the radii for G, Si, Ge, and Sn were taken as half the observed interatomic distances in diamond-type crystals of the elements. It was next... 

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... 

Comparison of Tetrahedral Radius Sums with Observed Interatomic Distances in Other Crystals. 

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... 

Comparison of Observed Interatomic Distances with Radius Sums from Tables III and X. 

Calculated and observed interatomic distances are compared in Table XIY. The structure reported for pentlandite, (Ni,Fe)S, places four S atoms about each Ni atom at the corners of a flat pyramid this crystal is also tentatively included in Table XIY. 

Trigonal-Prism Radii. In molybdenite and the corresponding tungsten sulfide the metal atom is surrounded by six sulfur atoms at the corners of a right trigonal prism of axial ratio unity, the bond orbitals involved being those discussed in an earlier section. Prom the observed interatomic distances the values 1.37 and 1.44 A are calculated for Mo and IPIV in such crystals (Table XV). 

In the preceding sections it has been shown that in a large number of crystals containing covalent bonds, cited as examples, the number and distribution of the bonds are in good agreement with a classification deduced from quantum mechanical considerations, and, moreover, there exist regularities in the observed interatomic distances which may be expressed by assigning covalent radii to the atoms, dependent in a... 

The Use of the Interatomic Distance Function in Discussing the Electronic Structure of Molecules.—The observed interatomic distances listed in Table II are interpreted with the aid of the curve of Fig. 1 to lead to the assignment of fractional double bond character as given in the last column. It is seen that a single bond between conjugated double bonds (cyclopentadiene) or... 

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. 

In the past, ionic radii have often been compared with observed interatomic distances without much regard to the nature of the crystal from which they were derived. Recently several investigators19 have concluded that in many crystals the bond between atoms does not consist of the electrostatic attraction of only slightly deformed ions. Goldschmidt in particular has divided crystals into two classes, ionic and atomic crystals, and has shown that ionic radii (using Wasastjema s set) do not account for the observed inter-atomic distances in atomic crystals. In the following pages our crystal radii will be compared with the experimental dis-... 

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. 

The Fluorite Structure.—In Table XI are given the observed interatomic distances in crystals with the fluorite structure. There is good... 

It is indicated by the observed interatomic distances and shown by magnetic data that there occurs some deviation from this simple and attractive scheme in the middle region of the sequence. From chromium to cobalt the interatomic distances do not continue to decrease in value, as expected with increase in the number of bonds instead they remain nearly constant Cr, A2, 2.49A Mn, no simple structure Fe, A2, 2.48A, Al, 2.52A Co, Al, A3, 2.50-2.51A Ni,... 

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