10.6 Lattice Structures in Crystalline Solids
Unit cells for simple, body-centered, and face-centered packing, ionic radii computed from cell dimensions, and X-ray diffraction measurements.
16 exercises
10.6 Exercise 1
Describe the crystal structure of iron, which crystallizes with two equivalent metal atoms in a cubic unit cell.
10.6 Exercise 3
What is the coordination number of a chromium atom in the body-centered cubic structure of chromium?
10.6 Exercise 5
Cobalt metal crystallizes in a hexagonal closest packed structure. What is the coordination number of a cobalt atom?
10.6 Exercise 7
Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 3.165 Å.
(a) What is the atomic radius of tungsten in this structure?
(b) Calculate the density of tungsten.
10.6 Exercise 9
Barium crystallizes in a body-centered cubic unit cell with an edge length of 5.025 Å
(a) What is the atomic radius of barium in this structure?
(b) Calculate the density of barium.
10.6 Exercise 11
The density of aluminum is 2.7 g/cm3; that of silicon is 2.3 g/cm3. Explain why Si has the lower density even though it has heavier atoms.
10.6 Exercise 13
Cadmium sulfide, sometimes used as a yellow pigment by artists, crystallizes with cadmium, occupying one-half of the tetrahedral holes in a closest packed array of sulfide ions. What is the formula of cadmium sulfide? Explain your answer.
10.6 Exercise 15
What is the formula of the magnetic oxide of cobalt, used in recording tapes, that crystallizes with cobalt atoms occupying one-eighth of the tetrahedral holes and one-half of the octahedral holes in a closely packed array of oxide ions?
10.6 Exercise 17
A compound of thallium and iodine crystallizes in a simple cubic array of iodide ions with thallium ions in all of the cubic holes. What is the formula of this iodide? Explain your answer.
10.6 Exercise 19
What is the percent by mass of titanium in rutile, a mineral that contains titanium and oxygen, if structure can be described as a closest packed array of oxide ions with titanium ions in one-half of the octahedral holes? What is the oxidation number of titanium?
10.6 Exercise 21
As minerals were formed from the molten magma, different ions occupied the same cites in the crystals. Lithium often occurs along with magnesium in minerals despite the difference in the charge on their ions. Suggest an explanation.
10.6 Exercise 23
One of the various manganese oxides crystallizes with a cubic unit cell that contains manganese ions at the corners and in the center. Oxide ions are located at the center of each edge of the unit cell. What is the formula of the compound?
10.6 Exercise 25
At temperatures above ~175 °C, thallium(I) iodide crystallizes with the same structure as CsCl. The edge length of the unit cell of TlI is 4.20 Å. Assuming contact between the body-centered Tl+ ion and the cube-corner I− ions of a unit cell, calculate the ionic radius of TI+. (The ionic radius of I− is 2.16 Å.)
10.6 Exercise 27
What is the spacing between crystal planes that diffract X-rays with a wavelength of 1.541 Å at an angle θ of 15.55° (first order diffraction)?
10.6 Exercise 29
A metal with spacing between planes equal to 0.4164 nm diffracts X-rays with a wavelength of 0.2879 nm. What is the diffraction angle for the first order diffraction peak?
10.6 Exercise 31
When an electron in an excited molybdenum atom falls from the L to the K shell, an X-ray is emitted. These X-rays are diffracted at an angle of 7.75° by planes with a separation of 2.64 Å. What is the difference in energy between the K shell and the L shell in molybdenum assuming a first order diffraction?
Adapted from General Chemistry © 2019 Rice University. Licensed under CC BY 4.0. Sources: Chemistry 2e, Chemistry: Atoms First 2e. Imported at revision 32c7196.