Question

Would you expect an alloy of iron and vanadium to be substitutional or interstitial? Explain your choice. Create a phase diagram for the binary alloy of iron and vanadium based on the tabulated data provided. $$ \begin{array}{cc} \% \mathrm{~V} & \text { Melting Point } \\ 0 & 1530 \\ \hline 20 & 1480 \\ \hline 40 & 1470 \\ \hline 60 & 1560 \\ \hline 80 & 1720 \\ \hline 100 & 1900 \end{array} $$

Short answer

The iron-vanadium alloy is likely to be substitutional given their similar atomic sizes. To create the phase diagram, plot the given compositions and melting points on a graph and connect the points to illustrate the melting behavior at various compositions.

Step-by-step solution

Understand Alloy Types

There are two main types of alloys: substitutional and interstitial. In a substitutional alloy, atoms of the solute replace atoms of the solvent in the lattice, which typically occurs when the two atomic radii differ by less than 15%. In interstitial alloys, smaller atoms fit into the spaces (interstices) between the larger atoms in the lattice, usually when the atomic radii differ significantly (more than 15%).

Assess the Atomic Radii of Iron and Vanadium

Iron (Fe) and vanadium (V) are neighboring elements in the periodic table, meaning their atomic sizes are relatively similar. Since their atomic radii do not differ by more than 15%, we would expect the alloy to be substitutional, with vanadium atoms substituting iron atoms in the metal lattice structure.

Plot the Phase Diagram

Begin by plotting the given data points on a graph with the percentage of V on the x-axis and the melting point on the y-axis. Connect the points to form a curve representing the melting point of the alloy at different compositions.

Analyze the Phase Diagram

The phase diagram can provide information on the liquidus and solidus lines, which indicate the temperatures at which the alloy is completely liquid or solid, respectively. The eutectic point can also be observed if present, which is the composition with the lowest melting point where the solid and liquid phases can coexist at equilibrium.

Key concepts

Substitutional Alloy

Alloys significantly enhance the properties of pure metals, and understanding how they are formed is essential in materials science. A substitutional alloy occurs when atoms of one element replace atoms of another in the crystal lattice. The criterion for the formation of a substitutional alloy is primarily based on the atomic radii of the component elements; specifically, it's more likely to occur if the difference in atomic radii between the solute and solvent atoms is less than 15%. This small difference allows the solute atoms to fit comfortably in the lattice positions normally occupied by the solvent atoms, maintaining the crystal structure.

Given their similar atomic sizes, an iron-vanadium (Fe-V) alloy is a perfect example of a substitutional alloy. Here, the vanadium atoms would replace some of the iron atoms in the crystal lattice. This type of alloy results in a homogeneous mixture with properties that might vary uniformly across the material. Substitutional alloys are common in systems where the two metals are close in size and have similar crystal structures, as is the case with iron and vanadium.

Interstitial Alloy

Departing from substitutional alloys, interstitial alloys offer a different mechanism of mixing elements. In interstitial alloys, smaller atoms fit into the spaces, or interstices, between larger host atoms in the crystal lattice. This type of alloy forms when there is a considerable size difference between the atoms – typically when the smaller atoms are less than 59% the size of the larger atoms, which often corresponds to a difference in atomic radii of more than 15%.

These smaller atoms, such as carbon or nitrogen, do not replace the host metal atoms but instead squeeze into the gaps within the metallic structure. This imparts distinctive properties to the alloy; for instance, steel, which is an interstitial alloy of iron and carbon, is markedly stronger and harder than pure iron due to the presence of carbon atoms within its crystal lattice. However, since iron and vanadium have a small difference in atomic radii, an iron-vanadium alloy wouldn't typically form an interstitial alloy.

Melting Point of Alloys

The melting point of an alloy offers valuable insight into its behavior under thermal conditions. It is influenced by the alloy's composition and the type of atomic bonding that occurs between the constituent elements. In general, alloys tend to have a melting point that is lower than the pure metals that constitute them. This is due to the introduction of a second element which disrupts the regular lattice structure and hence reduces the thermal energy required to overcome the metallic bonding forces.

Looking at a phase diagram, like the one for the iron-vanadium system, one can observe the gradual change in melting points with varying compositions. Phase diagrams graphically illustrate the temperature at which an alloy transitions from a solid to a liquid (melting point) and can show the presence of special points like eutectic points, where a particular mixture will have a melting point lower than either of the pure metals. These diagrams are crucial for materials engineering, as they help in selecting the appropriate alloy composition for a given application based on its melting point.

Atomic Radii

The atomic radius is a measure of the size of an atom, usually the average distance from the nucleus to the boundary of the surrounding electron cloud. Atomic radii play a pivotal role in determining the structure and type of alloys that can be formed between elements. When two metallic elements with similar atomic radii are combined, as in the case of iron and vanadium, they are likely to form a substitutional alloy.

In a binary alloy system, if one element has a significantly smaller atomic radius (usually more than 15% smaller), it can lead to the formation of an interstitial alloy. Variations in atomic radii can impact the crystal structure, physical properties, and overall behavior of the alloy formed. Therefore, understanding atomic radii can provide fundamental insights into the nature of different alloy systems and predict how these materials will interact at an atomic level when combined.