(a) With regard to the coincident site twist boundary on a {111} fcc metal plane shown in Fig. 6.25, show that using the Ranganathan relationships (Eqs. 6.21, 6.22 and 6.23), that a choice of x = 2 and y = 1 will also give this ?=7 boundary.

(b) To what angle of twist does x =2 and y = 1 correspond?
(c) Is the fact that x = 2 and y = 1 are able to produce an equivalent coincident site boundary to that in Fig. 6.25 related to the symmetry of the atomic arrangement on the {111} plane? Explain.


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(c) Use the cumulative distribution to show that P(X = 7 or 8) = 0.0. Even though this prob­ability is zero, the statement about X is that it can take on integer values of 1 to 10. How do you explain the apparent contradiction in these two statements?

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