Question

Materials containing the elements Y, Ba, Cu, and O that are superconductors (electrical resistance equals zero) at temperatures above that of liquid nitrogen were recently discovered. The structures of these materials are based on the perovskite structure. Were they to have the ideal perovskite structure, the superconductors would have thestructure shown in part (a) of the accompanying figure.

a. What is the formula of this ideal perovskite material?

b. How is this structure related to the perovskite structure discussed in Exercise 78? These materials, however, do not act as superconductors unless they are deficient in oxygen. The structure of theactual superconducting phase appears to be that shown in part (b) of the figure.

c. What is the formula of this material?

Short answer

a) Y: 1 Y in the center; Ba: 2 Ba in the center

$\begin{array}{c}\mathrm{Cu}:8\mathrm{corners}\mathrm{x}(1/8\mathrm{Cu})/\mathrm{corners}=1\mathrm{Cu},\\ \\ 8\mathrm{edges}\times (1/4)/\mathrm{edge}=2\mathrm{Cu},\mathrm{total}=3\mathrm{Cu}\mathrm{atoms}\\ \\ \mathrm{O}:20\mathrm{edges}\times (1/4\mathrm{O})/\mathrm{edges}=5\mathrm{oxygen},\\ 8\mathrm{faces}\times (1/2\mathrm{O})/\mathrm{faces}=4\mathrm{oxygen},\mathrm{total}=9\mathrm{O}\mathrm{atoms}\\ \\ \mathrm{Formula}:{\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_9\\ {}_{}\end{array}$

b)The structure of this superconductor material follows the alternative perovskite structure. The YBa₂Cu₃O₉structure is three of these cubic perovskite unit cells stacked on top of each other. The oxygen atoms are in the same places, Cu takes the place of Ti, two calcium atoms are replaced by two barium atoms, and one Ca is replaced by Y.

c)Y, Ba, and Cu are the same. Some oxygen atoms are missing.

$\begin{array}{c}12\mathrm{edges}\times (1/4\mathrm{O})/\mathrm{edges}=3\mathrm{O}\\ 8\mathrm{faces}\times (1/4\mathrm{O})/\mathrm{faces},\mathrm{total}=7\mathrm{O}\mathrm{atoms}.\\ \mathrm{Super}\mathrm{conductor}\mathrm{formula}={\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7.}\\ \\ \end{array}$

Step-by-step solution

Perovskite material

Perovskite is a calcium titanium oxide mineral with a chemical formula .

Perovskite is mainly found in the Earth's mantle, and it has been mined by different types of countries. Each variety of perovskite has a different chemical makeup because of different physical characteristics.

Superconductors

Superconductors are materials which transport electric charge without resistance1 and with the display of associated macroscopic quantum phenomena, such as persistent electrical currents and magnetic flux quantization.

Cubic unit cell

The cubic unit cell is known as the smallest repeating unit, and it applies when all angles are 90⁰and all the lengths are equal, with each axis being defined by a coordinate.

The simple cubic unit cell is denoted by eight atoms, which are marked with the actual cube.

Explanation

a) Y: 1 Y in the center; Ba: 2 Ba in the center

$\begin{array}{c}\mathrm{Cu}:8\mathrm{corners}\mathrm{x}(1/8\mathrm{Cu})/\mathrm{corners}=1\mathrm{Cu},\\ \\ 8\mathrm{edges}\times (1/4)/\mathrm{edge}=2\mathrm{Cu},\mathrm{total}=3\mathrm{Cu}\mathrm{atoms}\\ \\ \mathrm{O}:20\mathrm{edges}\times (1/4\mathrm{O})/\mathrm{edges}=5\mathrm{oxygen},\\ 8\mathrm{faces}\times (1/2\mathrm{O})/\mathrm{faces}=4\mathrm{oxygen},\mathrm{total}=9\mathrm{O}\mathrm{atoms}\\ \\ \mathrm{Formula}:{\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_9\\ {}_{}\end{array}$

b)The structure of this superconductor material follows the alternative perovskite structure. The YBa₂Cu₃O₉structure is three of these cubic perovskite unit cells stacked on top of each other. The oxygen atoms are in the same places, Cu takes the place of Ti, two calcium atoms are replaced by two barium atoms, and one Ca is replaced by Y.

c)Y, Ba, and Cu are the same. Some oxygen atoms are missing.

$\begin{array}{c}12\mathrm{edges}\times (1/4\mathrm{O})/\mathrm{edges}=3\mathrm{O}\\ 8\mathrm{faces}\times (1/4\mathrm{O})/\mathrm{faces},\mathrm{total}=7\mathrm{O}\mathrm{atoms}.\\ \mathrm{Superconductor}\mathrm{formula}={\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7.}\\ \\ \end{array}$