The interplant spacing between adjacent and parallel planes decreases as he values of h, k, and I increase. As values of the planar indices increase, the magnitude of the denominator in increases, with the result that the interplant spacing (deck) decreases.

4. 1 The surface energy of a single crystal depends on crystallographic orientation.

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Does this surface energy increase or decrease with an increase in planar density? Why? The surface energy of a single crystal depends on the planar density of the exposed surface plane because of the number of unsatisfied bonds. As the planar density increases, the number of nearest toms in the plane increases, which results in an increase in the number Of satisfied atomic bonds in the plane, and a decrease in the number of unsatisfied bonds.

Since the number of unsatisfied bonds diminishes, so also does the surface energy decrease.

4. 2 Does the grain size number (n of Equation 4. 16) increase or decrease with decreasing grain size? Why? Taking logarithms of Equation 4. 16 and then rearranging such that the grain size number n is the dependent variable leads to the expression n = 1 + log N log 2 Thus, n increases with increasing N. But as N increases the grain size decreases.