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: $$ (a)\mathrm{Cu}_{0.66} \mathrm{Zn}_{0.34}, \quad(\mathbf{b}) \mathrm{Ag}_{3} \mathrm{Sn}, \quad(\mathbf{c}) \mathrm{Ti}_{0.99} \mathrm{O}_{0.01} $$

Short answer

The three alloy compositions can be classified as follows: 1. Substitutional alloy: \(Cu_{0.66}Zn_{0.34}\) - due to similar atomic radii and crystal structures. 2. Intermetallic compound: \(Ag_3Sn\) - due to its fixed stoichiometry ratio of 3:1 and different crystal structures. 3. Interstitial alloy: \(Ti_{0.99}O_{0.01}\) - because of the small percentage of Oxygen atoms and their significantly smaller atomic radius compared to Titanium, occupying interstitial spaces.

Step-by-step solution

(a) Cu0.66Zn0.34 Analysis

Copper (Cu) and Zinc (Zn) have similar atomic radii and crystal structures; both adopt face-centered cubic (FCC) structures and have less than a 15% difference in atomic radii. This suggests that this composite is likely to be a substitutional alloy.

(b) Ag3Sn Analysis

Silver (Ag) and Tin (Sn) create a compound with a fixed stoichiometry ratio of 3:1, consistent with an intermetallic compound. It is worth noting that Ag and Sn also have different crystal structures, providing more evidence that this compound cannot be a substitutional alloy.

(c) Ti0.99O0.01 Analysis

Titanium (Ti) and Oxygen (O) create a composite in which only a small percentage of Oxygen atoms (0.01) are embedded in a Titanium matrix. Oxygen has a significantly smaller atomic radius compared to Titanium, suggesting that the Oxygen atoms might occupy interstitial spaces in the Titanium lattice. This behavior indicates that the composite is likely an interstitial alloy. 1. Substitutional alloy: Cu0.66Zn0.34 2. Intermetallic compound: Ag3Sn 3. Interstitial alloy: Ti0.99O0.01

Key concepts

Substitutional Alloy

A substitutional alloy is a combination of two or more elements where the atoms of one replace or occupy the positions of the atoms of another element within the crystal lattice. The alloy composition of \textbf{Cu}\(_{0.66}\)\textbf{Zn}\(_{0.34}\) is an example of this type of alloy. These alloys often form between elements that have similar atomic sizes, typically less than a 15% difference in atomic radius, and identical crystal structures. The elements copper (Cu) and zinc (Zn) satisfy these conditions as they both have face-centered cubic (FCC) structures.

When creating a substitutional alloy, the properties of the resulting material can be significantly different from those of the pure components, thus offering versatility in their applications. These properties include changes in ductility, strength, and resistance to corrosion. Substitutional alloys are widely used in various industries, including the production of coins, jewelry, and structural materials.

Intermetallic Compound

Intermetallic compounds are a unique type of alloy where the elements involved combine to form a specific stoichiometry and often exhibit a distinct crystal structure. The example provided, \textbf{Ag}\(_3\)\textbf{Sn}, represents a compound where the atoms of silver (Ag) and tin (Sn) bond in a fixed ratio, which is characteristic of intermetallics.

Unlike substitutional alloys, intermetallic compounds do not necessarily require the elements to have similar atomic sizes or crystal structures. They are known for their high melting points, hardness, and brittleness. These compounds can exhibit unique magnetic, electrical, and thermal properties, which are critical in high-tech applications, such as aerospace, electronics, and advanced coating technologies. The precise order and bonding of atoms in intermetallic compounds often result in materials with superior performance in specific applications but can also lead to difficulties in processing and limited ductility.

Interstitial Alloy

An interstitial alloy is formed when the small atoms of one element fit into the spaces, or 'interstices,' between the larger atoms of the host metal's crystal lattice. In the Ti\(_{0.99}\)O\(_{0.01}\) example, the small oxygen (O) atoms are situated in the interstitial spaces of the titanium (Ti) lattice. These alloys typically involve non-metallic elements such as hydrogen, carbon, nitrogen, or, in this case, oxygen, which have significantly smaller atomic radii than the host metal.

The presence of interstitial atoms can lead to an increase in the hardness and strength of the metal, making interstitial alloys particularly valuable in applications requiring materials with high strength-to-weight ratios. A widely recognized interstitial alloy is steel, where carbon atoms occupy interstitial spaces within iron's crystal structure. The small amount of oxygen in Ti\(_{0.99}\)O\(_{0.01}\) suggests a minimal but impactful alteration of the titanium's mechanical properties, possibly enhancing strength without compromising ductility too much.