Chemistry
Chemistry
Problem
A metallurgical microscope image is translated into the following textual diagram of a single solid that contains two distinct regions separated by a grain boundary. • Region 1: A face-centered cubic lattice in which 15 % of the lattice sites are occupied by Zn atoms and the remaining sites by Cu atoms. The Cu and Zn spheres are drawn almost the same size. • Region 2: A body-centered cubic lattice of Fe atoms with small C atoms drawn in 5 % of the interstitial spaces between the Fe atoms. No lattice sites are substituted. Assume the grain boundary does not significantly impede electron flow. Respond to the following prompts. (a) Identify the type of alloy present in Region 1 and the type present in Region 2. (b) Region 1 and Region 2 each occupy exactly half of the macroscopic sample volume. Which region contributes more free (delocalized) electrons per unit volume? Justify your answer qualitatively without numerical calculation. (c) The mass densities of pure Cu, pure Zn, and pure Fe are 8.96 g cm, 7.14 g cm, and 7.87 g cm, respectively. Assuming ideal mixing and neglecting the mass of carbon, estimate the overall density of the entire sample to two significant figures. (d) If the concentration of carbon in Region 2 were increased to occupy all available interstitial sites, predict qualitatively how the mechanical brittleness of Region 2 would change and explain the structural reason for your prediction.Intuitive explanation
This problem asks you to recognize two fundamentally different types of solid solutions and how they affect material properties. Region 1 is a substitutional solid solution where Zn atoms replace Cu atoms on the lattice itself, while Region 2 is an interstitial solid solution where C atoms occupy the gaps between Fe atoms without displacing them. The key insight is that these different arrangements—one changing the lattice composition, the other filling empty spaces—produce distinct effects on electrical conductivity and mechanical behavior, and you'll need to think about how each type of impurity disrupts the regular crystal structure differently.
Intuitive explanation
This problem asks you to recognize two fundamentally different types of solid solutions and how they affect material properties. Region 1 is a substitutional solid solution where Zn atoms replace Cu atoms on the lattice itself, while Region 2 is an interstitial solid solution where C atoms occupy the gaps between Fe atoms without displacing them. The key insight is that these different arrangements—one changing the lattice composition, the other filling empty spaces—produce distinct effects on electrical conductivity and mechanical behavior, and you'll need to think about how each type of impurity disrupts the regular crystal structure differently.