The memory metal, nitinol, is an alloy of nickel and titanium. It is called a memory metal because after being deformed, a piece of nitinol wire will return to its original shape. The structure of nitinol consists of a simple cubic array of \(\mathrm{Ni}\) atoms and an inner penetrating simple cubic array of Ti atoms. In the extended lattice, a Ti atom is found at the center of a cube of \(\mathrm{Ni}\) atoms; the reverse is also true. a. Describe the unit cell for nitinol. b. What is the empirical formula of nitinol? c. What are the coordination numbers (number of nearest neighbors) of Ni and Ti in nitinol?

The problem states that the nitinol structure consists of a simple cubic array of \(\mathrm{Ni}\) atoms and an inner penetrating simple cubic array of Ti atoms. In an extended lattice, a Ti atom is found at the center of a cube of \(\mathrm{Ni}\) atoms, and the reverse is also true, which means that a \(\mathrm{Ni}\) atom is found at the center of a cube formed by Ti atoms. With this information, we can derive that the unit cell for nitinol is a face-centered cubic (fcc) arrangement, where \(\mathrm{Ni}\) atoms are located at the corners of the unit cell, and Ti atoms are located at the center of each face. This lattice also applies vice versa, with Ti atoms at the corners and \(\mathrm{Ni}\) atoms at the center of each face.

To find the empirical formula of nitinol, we need to determine the ratio of \(\mathrm{Ni}\) to Ti atoms in the unit cell. In the face-centered cubic arrangement, there are: - 8 corner atoms, where each contributes 1/8 of an atom to the total (8*(1/8) = 1 atom) - 6 face-centered atoms, where each contributes 1/2 of an atom to the total (6*(1/2) = 3 atoms) When considering the positions of \(\mathrm{Ni}\) and Ti atoms in the unit cell, we can conclude that the ratio of \(\mathrm{Ni}\) to Ti atoms is 1:1. Therefore, the empirical formula of nitinol is \(\mathrm{NiTi}\).

The coordination number is the number of nearest neighbors of an atom (how many atoms are immediately surrounding a given atom). In the nitinol lattice, since it is face-centered cubic: - Each \(\mathrm{Ni}\) atom is surrounded by Ti atoms: 4 are on the same horizontal plane (north, south, east, and west) and 1 is above and another 1 is below, giving us a coordination number of 6 for \(\mathrm{Ni}\). - The same applies to the Ti atoms, as they are also surrounded by 6 \(\mathrm{Ni}\) atoms. Thus, in nitinol, the coordination number for both \(\mathrm{Ni}\) and Ti is 6.