Problem 38 - Chemistry The Central Science

Question

For each of the following alloy compositions indicate whether you would expect it to be a substitutional alloy, an interstitial alloy, or an intermetallic compound: (a) \(\mathrm{Cu}_{0.66} \mathrm{Zn}_{0.34},\) (b) \(\mathrm{Ag}_{3} \mathrm{Sn}\) (c) \(\mathrm{Ti}_{0.99} \mathrm{O}_{0.01}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{Cu}_{0.66} \mathrm{Zn}_{0.34}\) is a substitutional alloy, as Copper (Cu) and Zinc (Zn) are both transition metals with similar sizes and compatible lattice structures. (b) \(\mathrm{Ag}_{3} \mathrm{Sn}\) is an intermetallic compound, as Silver (Ag) and Tin (Sn) are metals with different lattice structures and form compounds in well-defined stoichiometric proportions. (c) \(\mathrm{Ti}_{0.99} \mathrm{O}_{0.01}\) is an interstitial alloy, as Titanium (Ti) is a base metal and Oxygen (O) is a non-metal with a much smaller size, occupying the interstitial sites within the metal lattice.

Step 1: (a) Cu0.66Zn0.34 Alloy Type

Copper (Cu) and Zinc (Zn) are both transition metals with similar sizes and compatible lattice structures (face-centered cubic). The small-size difference and the fact that they are both metals indicate that this will likely be a substitutional alloy. Therefore, \(\mathrm{Cu}_{0.66} \mathrm{Zn}_{0.34}\) is a substitutional alloy.

Step 2: (b) Ag3Sn Alloy Type

Silver (Ag) and Tin (Sn) are metals but have different lattice structures, and they don't share a continuous solubility range. However, they form compounds in well-defined stoichiometric proportions. In this case, we have \(\mathrm{Ag}_3\mathrm{Sn}\) with a fixed ratio of elements, indicating that this is an intermetallic compound.

Step 3: (c) Ti0.99O0.01 Alloy Type

In this case, we have Titanium (Ti) as the base metal and Oxygen (O) as the alloying element. Oxygen is a non-metal and much smaller in size than Titanium. The small fraction of Oxygen atoms can occupy the interstitial sites within the metal lattice. Thus, \(\mathrm{Ti}_{0.99} \mathrm{O}_{0.01}\) is an interstitial alloy.

Key Concepts

Substitutional Alloy

Substitutional alloys are formed when atoms of a solute element take the place of solvent atoms in the crystal lattice. This substitution occurs because the atoms of the two different elements are of comparable size—usually within about 15% of each other in radius—and the elements are mutually soluble in each other. The solute atoms essentially 'substitute' for the solvent atoms in the lattice positions.

Examples of substitutional alloys include brass, which is made up of copper and zinc atoms. As identified in the original exercise \textbf{(a) \(\mathrm{Cu}_{0.66} \mathrm{Zn}_{0.34}\)}, the copper-zinc alloy's structure permits zinc atoms to replace some of the copper atoms in a copper-based lattice, forming a solid solution.

Factors that influence the formation of substitutional alloys include atomic size, electronegativity, and valency. As mentioned in the solution, because copper and zinc have similar atomic radii and are both transition metals, they typically form substitutional alloys. To ensure an effective formation of these alloys, the elements are melted together, allowing the atoms to mix thoroughly and occupy the substitutional sites upon cooling and solidification.

Intermetallic Compound

Intermetallic compounds are a unique type of alloy where the component elements come together to form a new phase with a distinct, ordered crystal structure and composition. These compounds have a fixed stoichiometry and very different properties from their constituent metals—often being harder and more brittle. They are also typically less electrically conductive than typical alloys.

The common feature in intermetallic compounds, like the \textbf{(b) \(\mathrm{Ag}_{3}\mathrm{Sn}\)} from our exercise, lies in their definite proportioning of elements as opposed to a mixed solution. This rigid ordering distinguishes them from other types of alloys. Intermetallic compounds are generally useful in situations where high strength at elevated temperatures is required, such as in aerospace and other high-performance applications.

An important factor to note is that intermetallic compounds form when the metals involved have significantly different electronegativities or atomic sizes, resulting in limited solubility in each other. These compounds have well-defined melting points and are usually formed via a controlled reaction process.

Interstitial Alloy

Interstitial alloys occur when the small atoms of one element fit into the interstitial spaces (the gaps) within a crystal lattice of a larger metal atom. These small atoms are usually non-metallic, such as carbon or nitrogen, which is why interstitial alloys are sometimes characterized by a metal-base with a small amount of a non-metal element. The smaller atoms do not replace the metal atoms in the lattice but instead occupy the spaces between them, which can lead to a distortion of the lattice and an increase in the hardness and strength of the alloy.

Steel, an iron-carbon alloy, is a classic example of an interstitial alloy, where carbon atoms fit into the interstices of the iron lattice. In the provided exercise, \textbf{(c) \(\mathrm{Ti}_{0.99} \mathrm{O}_{0.01}\)} represents an interstitial alloy with titanium as the base metal and oxygen as the small, interstitially-positioned non-metal. Interstitial alloys often demonstrate improved characteristics over the base metal, such as increased tensile strength and resistance to dislocation movement, making them extremely useful in a wide range of industrial applications.