Ch.12 - Solids and Modern Materials

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.12 - Solids and Modern Materials

Problem 106

Chapter 12, Problem 106

Pure iron crystallizes in a body-centered cubic structure, shown in the figure. but small amounts of impurities can stabilize a facecentered cubic structure. Which form of iron has a higher density?

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Identify the two types of crystal structures mentioned: body-centered cubic (BCC) and face-centered cubic (FCC).

Recall the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).

Determine the number of atoms per unit cell for each structure: BCC has 2 atoms per unit cell, and FCC has 4 atoms per unit cell.

Calculate the volume of the unit cell for each structure using the lattice parameter \( a \): For BCC, \( a = \frac{4r}{\sqrt{3}} \), and for FCC, \( a = \frac{4r}{\sqrt{2}} \), where \( r \) is the atomic radius.

Compare the densities by considering the mass of the atoms in the unit cell and the calculated volume for each structure.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Crystal Structure

Crystal structure refers to the orderly arrangement of atoms in a crystalline material. In body-centered cubic (BCC) structures, atoms are located at the corners of a cube with one atom at the center, while in face-centered cubic (FCC) structures, atoms are at the corners and the centers of each face of the cube. The arrangement affects properties like density and packing efficiency.

Density Calculation

Density is defined as mass per unit volume (density = mass/volume). The density of a crystalline material can be influenced by its atomic arrangement and the mass of the atoms involved. In general, FCC structures tend to have higher packing efficiency than BCC structures, which can lead to differences in density between the two forms of iron.

Effect of Impurities

Impurities in a material can alter its crystal structure and properties. In the case of iron, small amounts of certain impurities can stabilize the FCC structure, which typically has a higher density than the BCC structure. Understanding how impurities affect the arrangement of atoms is crucial for predicting changes in physical properties like density.

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Textbook Question

Which statement correctly describes a difference between graphene and graphite? (a) Graphene is a molecule but graphite is not. (b) Graphene is a single sheet of carbon atoms and graphite contains many, and larger, sheets of carbon atoms. (c) Graphene is an insulator but graphite is a metal. (d) Graphite is pure carbon but graphene is not. (e) The carbons are sp2 hybridized in graphene but sp3 hybridized in graphite.

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Textbook Question

Imagine the primitive cubic lattice. Now imagine pushing on top of it, straight down. Next, stretch another face by pulling it to the right. All angles remain 90°. What kind of primitive lattice have you made?

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Textbook Question

Energy bands are considered continuous due to the large number of closely spaced energy levels. The range of energy levels in a crystal of copper is approximately 1×10−19 J. Assuming equal spacing between levels, one can approximate the spacing between energy levels by dividing the range of energies by the number of atoms in the crystal. b. Determine the average spacing in J between energy levels in the copper metal in part (a).

Textbook Question

Silicon carbide, SiC, has the three-dimensional structure shown in the figure.

(b) Would you expect the bonding in SiC to be predominantly ionic, metallic, or covalent?

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