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Chapter 3: Problem 39

For tetragonal crystals, cite the indices of directions that are equivalent to each of the following directions: (a) \([011]\) (b) \([100]\)

Short Answer

Expert verified
(a) [011] (b) [100] Answer: (a) The equivalent directions for [011] are: [011], [001], [110], [101], [0-11], [0-1-1], [1-10], and [1-01]. (b) The equivalent directions for [100] are: [100], [010], [001], [1-00], [0-10], and [0-01].

Step by step solution

01

(a) Equivalent directions for [011]

For the given direction [011], we can find equivalent directions using the symmetry rules of the tetragonal crystal system. As a = b, we can make all possible permutations by keeping the same magnitude of the index and switching the signs. The equivalent directions for [011] will have a permutation of (0,1,1), and their negative counterparts (-0,-1,-1) as: 1. [011] 2. [001] 3. [110] 4. [101] 5. [0-11] 6. [0-1-1] 7. [1-10] 8. [1-01]
02

(b) Equivalent directions for [100]

For the given direction [100], we can also find equivalent directions using the symmetry rules of the tetragonal crystal system. The equivalent directions for [100] will have a permutation of (1,0,0) and their negative counterparts (-1,0,0): 1. [100] 2. [010] 3. [001] 4. [1-00] 5. [0-10] 6. [0-01] Thus, we have the equivalent directions for the given directions in a tetragonal crystal system.

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Most popular questions from this chapter

(a) Derive planar density expressions for \(\mathrm{BCC}\) (100) and (110) planes in terms of the atomic radius \(R\). (b) Compute and compare planar density values for these same two planes for molybdenum (Mo).

Show for the body-centered cubic crystal structure that the unit cell edge length \(a\) and the atomic radius \(R\) are related through \(a=4 R / \sqrt{3}\).

For the HCP crystal structure, show that the ideal \(c / a\) ratio is \(1.633\).

Show that the atomic packing factor for \(\mathrm{BCC}\) is \(0.68\)

Would you expect a material in which the atomic bonding is predominantly ionic in nature to be more likely or less likely to form a noncrystalline solid upon solidification than a covalent material? Why? (See Section 2.6.)
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