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Chapter 3: Problem 55

Convert the (111) and (012) planes into the fourindex Miller-Bravais scheme for hexagonal unit cells.

Short Answer

Expert verified
Question: Convert the following hexagonal unit cell planes into the four-index Miller-Bravais scheme: (111) and (012). Answer: The four-index Miller-Bravais schemes for the given planes are (1 1 -2 1) for (111) and (0 1 -1 2) for (012).

Step by step solution

01

Remember the conversion rules.

To convert a three-index (hkl) plane into a four-index Miller-Bravais scheme (hkil), remember these rules: 1. i = -(h + k) 2. The sum of the first three indices (h, k, and i) must be zero (h + k + i = 0) 3. The last index, l, remains the same
02

Convert the (111) plane

Using the conversion rules, find the four-index Miller-Bravais scheme for the (111) plane: 1. h = 1, k = 1, l = 1 2. i = -(h + k) = -(1 + 1) = -2 3. Since h + k + i = 0, the given conversion is valid. 4. The four-index Miller-Bravais representation of the (111) plane is (1 1 -2 1).
03

Convert the (012) plane

Using the conversion rules, find the four-index Miller-Bravais scheme for the (012) plane: 1. h = 0, k = 1, l = 2 2. i = -(h + k) = -(0 + 1) = -1 3. Since h + k + i = 0, the given conversion is valid. 4. The four-index Miller-Bravais representation of the (012) plane is (0 1 -1 2). In summary, the four-index Miller-Bravais schemes for the given planes are: (111) converts to (1 1 -2 1) (012) converts to (0 1 -1 2)

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Most popular questions from this chapter

Iron (Fe) undergoes an allotropic transformation at \(912^{\circ} \mathrm{C}:\) upon heating from a \(\mathrm{BCC}\) ( \(\alpha\) phase) to an FCC \((\gamma\) phase). Accompanying this transformation is a change in the atomic radius of \(\mathrm{Fe}-\) from \(R_{\mathrm{BCC}}=\) \(0.12584 \mathrm{~nm}\) to \(R_{\mathrm{FCC}}=0.12894 \mathrm{~nm}-\) and, in addition, a change in density (and volume). Compute the percentage volume change associated with this reaction. Does the volume increase or decrease?

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