Question

1. For a Na+-Cl- ion pair, attractive and repulsive energies and , respectively, depends on the distance between the ions , according to and .
a) Determine the equilibrium spacing and the magnitude of the bonding energy .
b) Determine the theoretical elastic modulus. c) When the crystal is heated, constituent atom vibration increases and thus bonding becomes loose and the equilibrium distance lengthens. Plot the linear thermal expansion coefficient curve on the potential curve and derive the expression as a function of temperature. Suppose that this crystal melts when all atoms gain a quarter of the bonding energy .

Answer 1

1. The equilibrium separation for NaCl is 0.2361 nm.The mass of the sodium atom is 3.8176 x 10-26 kg. Chlorine has two stableisotopes, 35Cl(m 35Cl atom = 5.8068 x10-26 kg) and37Cl (m 37Cl atom = 6.1384 x 10-26 kg), that have different masses butidentical chemical properties.

If the electronegativity of one atom is much greater than another atom, then the more electronegative atom takes an electron almost completely away from the less electronegative atom and an almost purely ionic bond is formed. The atom that loses an electron becomes a positive ion and the atom that gains an electron becomes a negative ion. These ions are held together by the electrostatic force between the positive and negative charges. Ordinary table salt, NaCl, is held together by ionic bonds. The binding energy for NaCl is 7.97 eV per bond.

2. Zwicky proposed a method for calculating the theoretical strength of ionic crystals using the Madelung potential for alternating series. By this method he calculated the theoretical tensile strength of the sodium chloride crystal along the edge of the unit cube. This is a special case since the transverse compression deformation along the y- and z-axes is the same owing to the identical symmetry of the lattice in these directions. In the present paper the Zwicky method has been extended to other directions in tension, where the contractions in the mutually perpendicular directions are different. The theorretical tensile strength and Young's modulus along the body and face diagonals of the unit cell have been calculated for the sodium chloride crystal.