Open Question
When spheres of radius r are packed in a body-centered cubic arrangement, they occupy 68.0% of the available volume. Use the fraction of occupied volume to calculate the value of a, the length of the edge of the cube, in terms of r.
Ch.12 - Solids and Modern Material
Chapter 12, Problem 87
What is a tetrahedral site in a closest-packed lattice formed by?
Verified step by step guidance1
Understand that a closest-packed lattice refers to the arrangement of atoms in a crystal structure where they are packed as closely as possible.
Recognize that in a closest-packed structure, there are two main types of interstitial sites: tetrahedral and octahedral.
A tetrahedral site is formed when four atoms are arranged in a tetrahedron, creating a small space or void in the center.
Visualize that in a face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice, the tetrahedral sites are located between the layers of atoms.
Remember that these sites are important because they can be occupied by smaller atoms or ions, influencing the properties of the material.
Related Practice
Open Question
Potassium chloride crystallizes in the rock salt structure. Estimate the density of potassium chloride using the ionic radii provided in Chapter 8.
Textbook Question
Calculate the fraction of empty space in cubic closest packing to five significant figures.
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Textbook Question
X-ray diffractometers often use metals that have had their core electrons excited as a source of X-rays. Consider the 2p → 1s transition for copper, which is called the K⍺ transition. Calculate the wavelength of X-rays (in Å) given off by the K⍺ transition if the energy given off by a mole of copper atoms is 7.77⨉105 kJ.(1Å = 10-10 m)
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Open Question
Why is it necessary to use the Kα transition (2p → 1s) in copper (see Problem 88) to generate X-rays? Why not use, for example, the 4s → 3p transition?