Problem 85 - Chemistry

Question

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 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 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?

Step-by-Step Solution

Answer

The unit cell for nitinol consists of 8 Ni atoms at the corners of a cube and a Ti atom at the center of the cube, and vice versa for another unit cell with 8 Ti atoms at the corners and an Ni atom at the center. The empirical formula of nitinol is NiTi. The coordination number of both Ni and Ti in nitinol is 8, as each atom is surrounded by 8 nearest neighbors of the opposite element.

Step 1: a. Describe the unit cell for nitinol

Nitinol consists of a simple cubic array of Ni atoms, with an inner penetrating simple cubic array of Ti atoms. In the extended lattice, there is a Ti atom at the center of a cube of Ni atoms and vice versa. So, the unit cell consists of 8 Ni atoms at the 8 corners of the cube, and a Ti atom at the center of the cube. Similarly, there is another unit cell with 8 Ti atoms at the corners of the cube and an Ni atom at the center of the cube.

Step 2: b. What is the empirical formula of nitinol?

To find the empirical formula, we first need to find the number of Ni and Ti atoms in a unit cell. In each unit cell, there is: - 1 Ti atom at the center of the cube surrounded by 8 Ni atoms at the corners. - 1 Ni atom at the center of the cube surrounded by 8 Ti atoms at the corners. As both Ni and Ti atoms are equally distributed in the unit cell, we get the empirical formula as NiTi.

Step 3: c. What are the coordination numbers of Ni and Ti in nitinol?

Coordination number is the number of nearest neighboring atoms to an atom in a crystal structure. For nitinol: - A Ni atom is at the center of a cube surrounded by 8 Ti atoms on each corner of the cube. So, the coordination number of a Ni atom is 8. - A Ti atom is also at the center of a cube surrounded by 8 Ni atoms on each corner of the cube. So, the coordination number of a Ti atom is also 8. In conclusion, the coordination number of both Ni and Ti is 8 in the nitinol crystal structure.

Key Concepts

Nitinol

Nitinol is a fascinating alloy that brings together nickel and titanium. It's renowned for its unique property called "shape memory." This means it can "remember" its original shape after being bent or deformed. When heated, nitinol will spontaneously return to this original form.

This property is incredibly useful in various applications. For instance, nitinol is often used in medical devices like stents and guidewires because it can change shape inside the human body. It's also used in eyeglass frames and other products where flexibility and return to shape are beneficial.

• Nickel (Ni) and titanium (Ti) are the key components in nitinol.
• The ratio for an equal balance between these elements is important for its shape-memory ability.
• Different ratios can also influence the temperature range at which nitinol "remembers" its shape.

Unit Cell

The concept of a unit cell is fundamental in understanding crystal structures. In nitinol, the unit cell is a simple yet elegantly balanced arrangement that gives the material its unique properties.

Visualize the unit cell as a cube. In the case of nitinol, there are two important configurations. There is one where nickel atoms are at the corners, and a titanium atom is at the center.

• This arrangement means there are 8 nickel atoms on the corners and 1 titanium atom at the center.

Then, you can flip this model to imagine a second unit cell that has titanium atoms at the corners and a nickel atom in the center.

• Similarly, this consists of 8 titanium atoms on the corners with a single nickel atom centrally.

This particular layout is essential because it ensures that each atom type experiences the same environments and neighboring atoms, affecting how the alloy behaves as a whole.

Empirical Formula

The empirical formula of a compound gives the simplest integer ratio of the constituent elements. For nitinol, determining this formula involves understanding the balance between nickel (Ni) and titanium (Ti) within the unit cell.

In each unit cell, the elements are arranged such that there is an equal number of nickel and titanium atoms. Despite the apparent complexity of the arrangements, the counts are simple in nature:

• 1 nickel in the center surrounded by 8 titanium atoms at the corners in one configuration.
• Switch the arrangement to have 1 titanium at the center surrounded by 8 nickels.

Because of this symmetry, there is no preferential abundance of one element over the other, leading us to the straightforward empirical formula of NiTi. This indicates perfect balance and equal proportions of nickel and titanium.

Coordination Number

The coordination number in a crystal structure is the total number of nearest neighboring atoms surrounding a given atom. It's a crucial factor that influences the stability and characteristics of the structure.

In nitinol, both nickel and titanium atoms have the same coordination number due to their reciprocal arrangements in the unit cell.

• A nickel atom, located at the center of a cubic unit, is surrounded by 8 titanium atoms placed at the corners of the cube.
• Similarly, a titanium atom at the cube's center is surrounded by 8 nickel atoms.

This setup ensures that both Ni and Ti have a coordination number of 8. Such high coordination numbers are indicative of strong and extensive bonds throughout the nitinol structure, contributing to its durable and stress-resistant nature.