Imagine a cubic crystal like NaCl, with a negative charge at the center of a Cartesian coordinate
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Imagine a cubic crystal like NaCl, with a negative charge at the center of a Cartesian coordinate system with scale units equal to the interatomic distance.
(a) Show that an ion at a position r units along the x axis, s units along the y axis, and t units along the z axis has a charge of e(-1)r . (-1)s . (-1)t = e(-1)r + s + t, where e is the electron charge.
(b) Using Equation 10-2 as a guide, calculate the Madelung constant for a cube 2 units on a side. Do the same for cubes of sides 4, 6, 8, 10, 12, 16, and 20 units. (You will probably want to use a computer spreadsheet to write a program to do the calculations for the larger cubes.) Are your answers approaching the value a = 1.7476?
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