Subject using interatomic potentials

This approach is the most useful for engineering purposes since it expresses fracture events in terms of equations containing measurable parameters such as stress, strain and linear dimensions. It treats a body as a mechanical continuum rather than an assembly of atoms or molecules. However, our discussion can begin with the atomic assembly as the following argument will show. If a solid is subjected to a uniform tensile stress, its interatomic bonds will deform until the forces of atomic cohesion balance the applied forces. Interatomic potential energies have the form shown in Fig. 1 and consequently the interatomic force, whidi is the differential of energy with respect to linear separation, must pass throt a maximum value at the point of inflection, P in Fig. 1. 

An elementary approach for determining the structural energies of a solid is to eonstruct an algebraic representation of the interatomic force field. There are numerous obstacles to constructing such potentials. For example, changes in coordination, re-hybridization, charge transfer, and Jahn-Teller distortions are very difficult to incorporate in classical potentials. However, if the Coulomb forces play a dominant role in the chemical bonds present, it may be possible to obtain some useful results with interatomic potentials. This may be the case for materials subjected to high pressure situations. 

Already, chemistry is turning into a computerized subject, where mathematical modeling of molecules is just as important as molecular synthesis or chemical analysis. The structure of molecules can be worked out from the interatomic potentials using computer packages which are continuously under development at the large pharmaceutical companies (Section 5.3). The configurations of molecules, their reactions, and products will ultimately be predictable through the computer. 

A piezoelectric solid (e.g., quartz) acquires an electrical dipole moment upon mechanical deformation and, conversely, if it is subjected to an electric field E it becomes distorted by an amount proportional to the field strength E. The dipole moment disappears without the mechanical force. Piezoelectricity is only possible in lattices that do not have an inversion center. Electrostriction is also mechanical distortion in an electric field (strain proportional to E ) but ionic lattices that have a center of symmetry also show this effect. Figure 4.25 is a schematic representation of the source of these effects using the interatomic potential curve. A ferroelectric material is not only piezoelectric but its lattice has a permanent electric dipole moment (below its Curie temperature), which most other piezoelectric materials (such as quartz) do not have. 

Tunnelling up, on the other hand, there is the objection that chemistry as a subject is overall too complex for reductionism where quantum chemistry cannot predict accurately real world phenomena—take, for example, the chemical similarity of vanadium and niobium which have different electronic structures [27, 29]. The same argument can be made against simulations that rely on interatomic potentials rather than electronic structure calculations in either case the simulation will be too abstracted, too reduced from reality, to be useful. 

The subject of primary interest here is the role played by foreign atoms, molecnles, or ions in the processes of material fracture. These foreign atoms of the liquid medium penetrate into the predestruction zone of the solid, where they participate in interactions at the time when the chemical bonds are either broken or rearranged. The foreign atoms and molecules influence the interatomic interaction and participate in the compensation of newly formed bonds. A direct description of this process using the interaction potential of components is of a particular interest here. 

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