Metal interatomic bond length

Another parameter of importance in metal nanoparticles is the change in interatomic bond length. Extended X-Ray absorption fine structure (EXAFS) showed this on many transition metal nanoparticles with diameters less than 5 nm [89, 90]. On Pd particles with a diameter 1.4 nm, the interatomic distance reduction was about 3%. Note that this is again in hne with surface observation. More generally, surfaces are submitted to tensile stress and ah initio calculations on 2D Pt models show a strong interatomic distance reduction by 6.6% and 9.1% for the (111) and (100) structures, respectively [91]. Of course, in nanopartides, the structure is not purely 2D and the coordination lowering is not as strong. 

What is the physical meaning of the critical amplitude of atomic vibrations in a melting metal Evidently, bond lengths can be stretched only in a frameworks of a certain stable structure. As shown by Goldschmidt, the relative interatomic distances in the structures of metals with different coordination munbers change as follows ... 

Mean cobalt-cobalt and nickel-nickel distances observed in these complexes are very close to interatomic distances determined at ambient temperatures in cobalt and nickel metals (Co-Co 2.489(7) A vs. 2.507 A in a-cobalt (33) Ni-Ni 2.469(6) A vs. 2.492 A in the metal (39)). The mean M-H bond lengths, as well as hydride displacements from M3 faces, are less for nickel in H3Ni4(Cp)4 than for cobalt in HFeCo3(CO)9(P(OMe)3)3. Although the differences are marginally significant within error limits (Ni-H 1.691(8) A vs. Co-H 1.734(4) A displacements from plane Ni3 0.90(3) A vs. Co3 0.978(3) A), they are in the expected direction since the covalent radius should vary inversely with atomic number within a transition series. However, other effects such as the number of electrons in the cluster also can influence these dimensions. 

In order to test the point-charge method experimentally measured dissociation energy and interatomic distance are required for each chemical bond. Dissociation energies for most homonuclear diatomic molecules have been measured spectroscopically and/or thermochemically. Interatomic distances for a large number of these are also known. However, for a large number of, especially metallic diatomic molecules, equilibrium interatomic distances have not been measured spectroscopically. In order to include these elements in the sample it is noted that for those metals with measured re, it is found to be related, on average, to 5, the distance of closest approach in the metal, by re = 0.78(5. On this assumption reference values of interatomic distance (d) become available for virtually all elements, as shown in the data appendix. In some special cases well-characterized dimetal bond lengths have also been taken into account for final assessment of interatomic distance. 

Covalent and metallic bondings suppose a strong overlap of the outermost atomic orbitals and so the atomic radii will be approximately the radii of the outermost orbitals. The atomic radii are empirically obtained from interatomic distances [59], For example, the length of the bond C-C is 154 pm in diamond, Si-Si is 234 pm in disilane, and so on. The consistency of this approach is shown by the agreement between the Si-C bond lengths determined experimentally and calculated from the corresponding atomic radii. The interatomic distances appreciably depend on the coordination. With decreasing coordination number, the bonds usually get shorter. For coordinations 8, 6, and 4, the bonds get shorter by about 2, 4, and 12%, respectively, as compared with the coordination number of 12. 

The Pd—Pd bond length lies between 2.61 A (for 84) and 2.72 A (for 57), varying surprisingly little for the different types of bridging ligands. This relatively short distance, comparable with the interatomic distance in metallic palladium (2.74 A), points to the existence of a direct metal-metal bond. 

An example of the Li—F interaction in the solid state of a fluoroaromatic compound is shown in Scheme 3.2. The two Li—F interatomic lengths are in the range of 2.27-2.39 A, both of which are in between dmm and dmax (see Table 3.3). A bond length threshold up to which CF-metal interactions are credible is summarized in Table 3.3 [10]. The threshold was used in a search for CF-metal interactions in the Cambridge Crystallographic Structure Database. 

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