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) \(\mathrm{Fe}_{0.97} \mathrm{Si}_{0.03}\), (b) \(\mathrm{Fe}_{0.60} \mathrm{Ni}_{0,40}\), (c) \(\mathrm{Cu}_{3} \mathrm{~A} \mathbf{u}\).

Short answer

(a) The alloy \(\mathrm{Fe}_{0.97} \mathrm{Si}_{0.03}\) is a substitutional alloy due to the similar atomic radii and cubic crystal structures of Fe and Si. (b) The alloy \(\mathrm{Fe}_{0.60} \mathrm{Ni}_{0.40}\) is also a substitutional alloy as Fe and Ni share similar atomic radii and both possess face-centered cubic (FCC) structures. (c) The alloy \(\mathrm{Cu}_{3} \mathrm{Au}\) is an intermetallic compound because of the similar electronegativities and face-centered cubic (FCC) structures of Cu and Au.

Step-by-step solution

(a) Fe0.97 Si0.03 alloy type

In order to determine the type of alloy for \(\mathrm{Fe}_{0.97} \mathrm{Si}_{0.03}\), let us consider the atomic radii and crystal structures of these elements. Iron (Fe) has a body-centered cubic (BCC) structure and an atomic radius of 124 pm, while Silicon (Si) has a diamond cubic structure and an atomic radius of 117 pm. Since their atomic radii are relatively close and their crystal structures are both cubic, we would expect this alloy to be a substitutional alloy. The Si atoms can easily replace some Fe atoms in the lattice without causing significant distortion. The alloy for (a) is a substitutional alloy.

(b) Fe0.60 Ni0.40 alloy type

Now let's look at the alloy \(\mathrm{Fe}_{0.60} \mathrm{Ni}_{0.40}\). Iron (Fe) and Nickel (Ni) share similar atomic radii (Iron at 124 pm and Nickel at 125 pm) and both possess face-centered cubic (FCC) structures. Due to the similarity in both their atomic radii and crystal structures, the alloy would form as a substitutional alloy, with Ni atoms substituting some Fe atoms in the lattice. The alloy for (b) is a substitutional alloy.

(c) Cu3Au alloy type

Lastly, we will analyze the alloy \(\mathrm{Cu}_{3} \mathrm{Au}\). Copper (Cu) and Gold (Au) both have face-centered cubic (FCC) structures, although their atomic radii are different (Copper at 128 pm and Gold at 144 pm). However, these elements have similar electronegativities (Cu with a value of 1.90 and Au with a value of 2.54). The similarities in both their crystal structures and electronegativities lead to strong bonds formed between Cu and Au atoms, resulting in the formation of an intermetallic compound with a well-defined stoichiometry represented as \(\mathrm{Cu}_{3} \mathrm{Au}\). The alloy for (c) is an intermetallic compound.

Key concepts

Substitutional Alloy

Substitutional alloys occur when atoms of the alloying element replace some atoms in the original metal's lattice. This is possible when the two elements have similar atomic radii and compatible crystal structures. Because of these similarities, the substitution doesn’t disrupt the host metal’s lattice too much.
For example, in the alloy \(\mathrm{Fe}_{0.97}\ \mathrm{Si}_{0.03}\), iron (Fe) and silicon (Si) have closely matched atomic radii (124 pm for Fe and 117 pm for Si), making it feasible for Si atoms to take the place of Fe atoms. Both elements also have cubic structures, which further supports a seamless substitution without significant lattice disruption.

Here are a couple of key features of substitutional alloys:

• The alloying element’s atoms replace the base metal's atoms.
• Essential compatibility in terms of atomic size and lattice structure is needed.
• Common in systems where the base and alloying metals have similar properties.

Examples of typical substitutional alloys include brass (copper and zinc) and bronze (copper and tin).

Interstitial Alloy

Interstitial alloys form when smaller atoms fit into the spaces or "interstices" between the larger atoms in a metal lattice. This type of alloying is feasible when the secondary element has significantly smaller atomic size compared to the host metal.
Elements like carbon, boron, and nitrogen are often part of interstitial alloys, as their small atomic sizes allow them to securely snuggle into the interstices of larger metallic lattices like iron.

Notable characteristics of interstitial alloys comprise:

• Smaller atoms occupy gaps present within the metal lattice.
• A more rigid lattice structure compared to the original metal.
• Often results in improved hardness and strength.

Steel, which is an alloy of iron and carbon, is a classic example of an interstitial alloy, where carbon atoms fit into the gaps of the iron lattice.

Intermetallic Compound

Intermetallic compounds are formed when two or more metals, or a metal and a non-metal, come together to form a new compound with a distinct crystal structure and fixed stoichiometry. Unlike substitutional or interstitial alloys, intermetallic compounds possess a specific structural arrangement, meaning the elements bind in a precise stoichiometric ratio.
One example is the compound \(\mathrm{Cu}_{3}\ \mathrm{Au}\), where copper (Cu) and gold (Au) share similar crystal structures which allows them to interact strongly, despite having different atomic radii (128 pm for Cu and 144 pm for Au). Their similar electronegativities play a crucial role here, ensuring the formation of strong bonds and a stable compound.

Important features of intermetallic compounds include:

• A new and distinct crystal structure emerges.
• Fixed compositional ratio between the constituent elements.
• Generally high melting points and are often brittle.

Intermetallics like \(\mathrm{AlNi}\) and \(\mathrm{TiAl}\) are valued in aerospace and high-temperature applications for their unique properties.