Interatomic separation equilibrium

Fig. 1-3. Schematic representation of the electron energy for Mg as a function of the interatomic separation, equilibrium distance.

The exponent n in eq. (1-1) is of the order of ten. For large interatomic separations, the total potential curve follows the coulombic law, and for small separations it follows the repulsive law of eq. (1-1). The equilibrium separation can be calculated from the total potential curve [5, 12]. 

Figure 2.3. Force and potential energy diagrams for a diatomic molecule, with respect to the interatomic separation. The equilibrium bond distance corresponds to the minimum of the potential energy well and the maximum attractive force between the two atoms. As the atoms are brought even closer together, the interatomic bonding becomes less stable due to exponential increases in repulsive forces and potential energy.

From a plot of interatomic separation versus force for two atoms/ions, the equilibrium separation corresponds to the value at zero force. 

Figure 6.7 Force versus interatomic separation for weakly and strongly bonded atoms. The magnitude of the modulus of elasticity is proportional to the slope of each curve at the equilibrium interatomic separation Tq.

Figure 11.3 Total squared spin angular momentum ((S ), a.u. soUd) and corresponding number of unpaired electrons (n dashed) at various interatomic separations (1 no) along the ground-state NO potential in UHF/6-311++G description, with vertical dotted line marking the calculated equilibrium geometry.

As we showed in Chapter 6 (on the modulus), the slope of the interatomic force-distance curve at the equilibrium separation is proportional to Young s modulus E. Interatomic forces typically drop off to negligible values at a distance of separaHon of the atom centres of 2rg. The maximum in the force-distance curve is typically reached at 1.25ro separation, and if the stress applied to the material is sufficient to exceed this maximum force per bond, fracture is bound to occur. We will denote the stress at which this bond rupture takes place by d, the ideal strength a material cannot be stronger than this. From Fig. 9.1... 

Figure 8 Left Schematic graph of the setup for the simulation of rubbing surfaces. Upper and lower walls are separated by a fluid or a boundary lubricant of thickness D. The outermost layers of the walls, represented by a dark color, are often treated as a rigid unit. The bottom most layer is fixed in a laboratory system, and the upper most layer is driven externally, for instance, by a spring of stiffness k. Also shown is a typical, linear velocity profile for a confined fluid with finite velocities at the boundary. The length at which the fluid s drift velocity would extrapolate to the wall s velocity is called the slip length A. Right The top wail atoms in the rigid top layer are set onto their equilibrium sites or coupled elastically to them. The remaining top wall atoms interact through interatomic potentials, which certainly may be chosen to be elastic.

Fig. 6. Schematic drawing of the shape of the Lennard-Jones 6-12 potential energy versus interatomic distance (r). The equilibrium separation distance occurs at the potential energy minimum and is defined to be twice the van der Waals radius if the two interacting atoms are identical.

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