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Chapter 12: Problem 8

The zinc blende crystal structure is one that may be generated from close- packed planes of anions. (a) Will the stacking sequence for this structure be FCC or HCP? Why? (b) Will cations fill tetrahedral or octahedral positions? Why? (c) What fraction of the positions will be occupied?

Short Answer

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Question: Identify the following properties of the zinc blende crystal structure: (a) the stacking sequence, (b) whether cations fill tetrahedral or octahedral positions, and (c) the fraction of positions that will be occupied by the cations. Explain your answers.

Step by step solution

01

(a) Stacking Sequence and Why

The zinc blende crystal structure is generated from the close-packed planes of anions. The two types of close-packed planes are Face-Centered Cubic (FCC) and Hexagonal Close-Packed (HCP). For zinc blende, the stacking sequence is FCC. This is because in FCC, the third layer matches the first layer, creating a repeating ABABAB sequence, whereas in HCP, the stacking follows an ABAB pattern. This FCC pattern allows for the tetrahedral positions to be occupied by cations, resulting in the well-known zinc blende structure found in compounds like ZnS, GaAs, and others.
02

(b) Tetrahedral or Octahedral Positions

In the zinc blende crystal structure, cations fill tetrahedral positions. The reason behind this is due to the fact that each anion in the close-packed crystal structure is surrounded by four cations, forming a tetrahedral arrangement. This pattern is maintained throughout the crystal, resulting in a 1:1 ratio between cations and anions, characteristic of the zinc blende structure.
03

(c) Fraction of Positions Occupied

To determine the fraction of positions occupied by the cations, we need to consider the available amount of tetrahedral positions in the FCC crystal structure. In an FCC lattice, the total number of tetrahedral interstitial sites is double the number of lattice points, as each FCC lattice point contributes to four tetrahedral positions. However, in the zinc blende structure, only half of these tetrahedral sites are occupied, since the formula is AB, where A represents cations and B represents anions. Therefore, the fraction of positions occupied by cations in the zinc blende structure is 1/2, or 50%.

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Most popular questions from this chapter

In your own words, briefly define the term stoichiometric.

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