Lattice strain energy

These semiempirical models postulate that local strain associated with different atomic sizes of the elements is the major contribution to the solid-solution enthalpy of mixing. An estimate of lattice strain energy has been compared to fitted values of the enthalpy of mixing for several group III-V systems (156). The results led to a calculated enthalpy of mixing that was a... 

To account for this phenomenon of spinless conductivity, physicists have introduced the concept of transport via structural defects in the polymer chain. In a conventional semiconductor, an electron can be removed from the valence band and placed in the conduction band, and the structure can be assumed to remain rigid. In contrast, an electronic excitation in polymeric materials is accompanied by a distortion or relaxation of the lattice around the excitation, which minimizes the local lattice strain energy. The combined... 

Dopant is also called solute, which is dissolved as solid solution in polycrystalline solids. If there is an interaction potential for the solute to be attracted to or repelled from the grain boundary, the solute atoms or ions will have a nonuniform distribution at the grain boundaries. The interaction could be due to lattice strain energy caused by size mismatch between the solute and host ions and/or electrostatic potential energy for aliovalent solutes. 

Let us consider a system in which a small amount of a dopant (also referred to as the solute) is dissolved in solid solution in a polycrystalline solid (sometimes referred to as the host). If the solute is attracted to (or repelled from) the grain boundary due to an interaction potential, the solute ions will tend to have a nonuniform distribution in the grain boundary. The interaction between the boundary and the solute can arise from lattice strain energy due to size mismatch between the solute and host ions and, for aliovalent solutes, from electrostatic potential energy. 

Consider the vector percolation experiment shown in Fig. 11 applied to any 3D lattice in general. The stored strain energy density U in the lattice due to an... 

The stored strain energy can also be determined for the general case of multiaxial stresses [1] and lattices of varying crystal structure and anisotropy. The latter could be important at interfaces where mode mixing can occur, or for fracture of rubber, where f/ is a function of the three stretch rations 1], A2 and A3, for example, via the Mooney-Rivlin equation, or suitable finite deformation strain energy functional. 

When fracture is confined to a single plane of the lattice, the net solution collapses to the nail solution. Consider an atomically thin slab of dimension V = AL, where A is unit area and L is a bond length, the strain energy stored is U = a AL/lE and the energy dissipated is U = DoE p — / c). The VP model then predicts that Gic o- such that... 

Although a honeycomb lattice theoretically consists of sp2 atoms, the carbon s ability to represent intermediate states of hybridization leads to another kind of defect to counterbalance the strain energy induced by high curvature. This so-called rehybridization results in a higher n-character of the C-C bonds [24]. Furthermore, local sp3 hybridization can be induced though chemical treatment, such as after thermal elimination of functional groups. 

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