Interatomic interaction

Thakkar A J and Smith V H Jr 1974 On a representation of the long range interatomic interaction potential J. Phys. B At. Moi. Phys. 7 L321... 

There are two basic physical phenomena which govern atomic collisions in the keV range. First, repulsive interatomic interactions, described by the laws of classical mechanics, control the scattering and recoiling trajectories. Second, electronic transition probabilities, described by the laws of quantum mechanics, control the ion-surface charge exchange process. 

This is better understood with a picture see figure B3.3.11. The discretized path-integral is isomorphic to the classical partition fiinction of a system of ring polymers each having P atoms. Each atom in a given ring corresponds to a different imaginary tune point p =. . . P. represents tire interatomic interactions... 

Fig. 4, top). In particular we asked, what interatomic interactions cause the experimentally observed unbinding forces. 

This expression relates the action-at-a-distance forces between atoms to the macroscopic deformations and dominated adhesion theoiy for the next several decades. The advent of quantum mechanics allowed the interatomic interactions giving rise to particle adhesion to be understood in greater depth. 

All the elements have stable electronic configurations (Is or ns np ) and, under normal circumstances are colourless, odourless and tasteless monatomic gases. The non-polar, spherical nature of the atoms which this implies, leads to physical properties which vary regularly with atomic number. The only interatomic interactions are weak van der Waals forces. These increase in magnitude as the polarizabilities of the atoms increase and the ionization energies decrease, the effect of both factors therefore being to increase the interactions as the sizes of the atoms increase. This is shown most directly by the enthalpy of vaporization, which is a measure of the energy required to overcome the... 

ANALYSIS OF THE EFFECTIVE INTERATOMIC INTERACTIONS IN METALLIC ALLOYS... 

The parameters of the semi-infinite alloy Ising Hamiltonian are the configurationally independent part of the alloy internal energy Eq, the on-site energies the interatomic pair interactions and generally, interatomic interactions of higher order. 

The interatomic interaction is described by an EAM potential specifically developed for NiAl in the B2 structure [12]. Compared to the older potential [16], which was used in most of the previous atomistic studies, our new potential gives considerably higher antiphase boundary (APB) energies = 0.82 J/m, yj pg = 1.06 J/m in good agreement with the APB... 

The Burgers vectors, glide plane and ine direction of the dislocations studied in this paper are given in table 1. Included in this table are also the results for the Peierls stresses as calculated here and, for comparison, those determined previously [6] with a different interatomic interaction model [16]. In the following we give for each of the three Burgers vectors under consideration a short description of the results. 

In linear molecules only the component of orbital momentum normal to the figure axis is destroyed, that along the figure axis being retained. In non-linear molecules with strong interatomic interactions the concept of orbital angular momentum loses its significance. 

Fig. 1. Electronic states [or iron-group atoms, showing number of states as qualitative [unction of electronic energy. Electrons in band A are paired with similar electrons of neighboring atoms to form bonds. Electrons in band B are d electrons with small interatomic interaction they remain unpaired until the band is half-filled. The shaded area represents occupancy of the states by electrons in nickel, with 0.6 electron lacking from a completely filled B band. (States corresponding to occupancy of bond orbitals by unshared electron pairs are not shown in the diagram.)...

Our knowledge of the properties of orbitals indicates that some of the 3d orbitals might be combined with the 45 and 4p orbitals to form bond orbitals in metals, the other 3d orbitals being unsuited to bond formation, but does not suffice to give a theoretical derivation of the number of d orbitals in each of these classes. Empirical evidence, outlined below, indicates that about 2.44 d orbitals (on the average) show only weak interatomic interactions, and that the remaining 2.56 d orbitals combine with the 5 orbital and the p orbitals to form hybrid bond orbitals. 

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

Both of the above approaches rely in most cases on classical ideas that picture the atoms and molecules in the system interacting via ordinary electrical and steric forces. These interactions between the species are expressed in terms of force fields, i.e., sets of mathematical equations that describe the attractions and repulsions between the atomic charges, the forces needed to stretch or compress the chemical bonds, repulsions between the atoms due to then-excluded volumes, etc. A variety of different force fields have been developed by different workers to represent the forces present in chemical systems, and although these differ in their details, they generally tend to include the same aspects of the molecular interactions. Some are directed more specifically at the forces important for, say, protein structure, while others focus more on features important in liquids. With time more and more sophisticated force fields are continually being introduced to include additional aspects of the interatomic interactions, e.g., polarizations of the atomic charge clouds and more subtle effects associated with quantum chemical effects. Naturally, inclusion of these additional features requires greater computational effort, so that a compromise between sophistication and practicality is required. 

The radii of the spheres in this figure are equal to the Van der Waals radii the high density of the atoms, obvious from this picture, is indicative of the large number of significant interatomic interactions in these systems. 

For technological applications it is highly desirable to be able to design self-assembling systems to have particular physico-chemical properties under a given set of experimental conditions. Using computer simulation, it is possible to construct an atomistic model of tapes, ribbons and fibrils to study all of the interatomic interactions within the system in a quantitative manner. Figure 13 shows atomistic... 

In 1987 Raevsky proposed to describe 3D structure by means of the spectra of interatomic interactions [24]. In this approach each pair of atoms in a molecule... 

H-bonding is an important, but not the sole, interatomic interaction. Thus, total energy is usually calculated as the sum of steric, electrostatic, H-bonding and other components of interatomic interactions. A similar situation holds with QSAR studies of any property (activity) where H-bond parameters are used in combination with other descriptors. For example, five molecular descriptors are applied in the solvation equation of Kamlet-Taft-Abraham excess of molecular refraction (Rj), which models dispersion force interactions arising from the polarizability of n- and n-electrons the solute polarity/polarizability (ir ) due to solute-solvent interactions between bond dipoles and induced dipoles overall or summation H-bond acidity (2a ) overall or summation H-bond basicity (2(3 ) and McGowan volume (VJ [53] ... 

The members of Class II in Table 1 present very small enthalpies of the mesophase-liquid transition [ AHml < 0.5 kJ/(mol of chain bonds)], suggesting that their mesophase is hardly stabilized by specific interatomic interactions. By contrast, we point out that in all cases the crystal-mesophase transition has a significant enthalpy value, mostly AHqm > 1 kJ/(mol of chain bonds). Consistent with their relatively flexible character, the polymers listed in the Tables have their glass transition below ambient temperature. 

Calculations of forces may be improved in several ways. One is to pursue efforts towards the development of accurate classical, atomic-level force fields. A promising extension along these lines is to add nonadditive polarization effects to the usual pairwise additive description of interatomic interactions. This has been attempted in the past [35-39], but has not brought the expected and long-awaited improvements. This is not so much because polarization effects are not important, or pairwise additive models can account for them accurately in an average sense in all, even highly anisotropic environments. Instead, it seems more likely that the previously developed nonadditive potentials were not sufficiently accurate to offer an enhanced description of those systems in which induction phenomena play a crucial role. 

Model of a molecular structure, which determines a mutual arrangement and interaction of atoms that form a molecule, molecular site, or a short-range order in a solid material. This is the area of molecular chemistry, stereochemistry, etc. A characteristic element of this level is the atom with prevailing interatomic interactions. 

FFs that are parameterized for high-pressure conditions can still lead to behavior that differs from that observed in experiments. For instance, it is common practice to treat the interatomic interactions with Lennard-Jones (LJ) potentials. Although this method is convenient from a computational standpoint, it is known that LJ potentials do not reproduce experimentally observed behavior such as necking, where a material attempts to minimize surface area and will break under large tensile stresses. Many other examples exist where particular types of FFs cannot reproduce properties of materials, and once again, we emphasize that one should ensure that the FF used in the simulation is sufficiently accurate. 

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