![]() ![]() If we consider pulling two planes of atoms apart then the total force per unit area can be obtained by dividing F by r 0 2 We can define the stiffness of the bond, S 0, as the slope of this line: Young’s modulus is related to the interatomic bonding forces and, as you might expect, its magnitude depends on the slope of the force–distance curve at r 0.Ĭlose to r 0 the force–distance curve approximates a tangent when the applied forces are small the displacement of the atoms is small and proportional to the force. It is the same for both tension and compression. Young’s modulus (E) is a measure of the resistance to small changes in the separation of adjacent atoms ( modulus is Latin for “a small measure”). The force is attractive if A > 0 and negative if A r 0. This is the usual convention in materials science (and in Newton’s law of universal gravitation). The sign conventions for force : In Figure 4.1a the force is attractive when F is positive. ![]() The force will be zero at the equilibrium separation. ![]() 4.1 with respect to r, we obtain an equation that describes the resultant force F between a pair of atoms In discussing ceramics, we usually think of the material in terms of ions ions with the same sign always repel one another due to the Coulomb force. When the energy is a minimum the atoms are at their equilibrium separation ( r = r 0) the lowest energy state defines the equilibrium condition. The bond–energy curve can be plotted as shown in Figure 4.1a. Equation 4.1 indicates that attractive forces predominate when atoms are far apart and repulsive interactions predominate when the atoms are close together. Only when m > n will a minimum (equilibrium) value of E be possible. The first term is the attractive component the second is due to repulsion. Where r is the interatomic distance and A, B, n, and m are constants characteristic of the type of bonding. The simplest expression for the bond energy is In the next few sections we will briefly review the general characteristics of these bonds.Īll interatomic forces are electrostatic in origin. The types of primary and secondary bonds and their energy ranges are given in Table 4.1. We can divide interatomic bonds into two categories: ![]()
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