Ch.12 - Solids and Modern Materials

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

Ch.12 - Solids and Modern Materials

Problem 105

Chapter 12, Problem 105

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?

Verified step by step guidance

Step 1: Identify the initial structure as a primitive cubic lattice, where all sides are equal, and all angles are 90°.

Step 2: Apply pressure from the top, which compresses the lattice along one axis, reducing the height of the unit cell.

Step 3: Stretch the lattice by pulling one face to the right, which increases the length of the unit cell along that axis.

Step 4: Observe that all angles remain 90°, but the unit cell now has different lengths along the three axes.

Step 5: Conclude that the resulting lattice is a tetragonal lattice, characterized by two equal axes and one different axis, with all angles remaining 90°.

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Key Concepts

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

Primitive Cubic Lattice

A primitive cubic lattice is a type of crystal structure where atoms are located at the corners of a cube. Each unit cell contains one atom, as the corner atoms are shared among adjacent cells. This lattice is characterized by its simple geometry and is the basis for understanding more complex structures.

Deformation of Lattices

Deformation of lattices refers to the changes in the arrangement of atoms in a crystal structure due to external forces, such as pressure or tension. In this scenario, pushing down on the lattice compresses it, while pulling on a face stretches it, resulting in a new arrangement of atoms while maintaining right angles between the axes.

Types of Crystal Systems

Crystal systems categorize crystals based on their symmetry and lattice parameters. The transformation described in the question leads to a body-centered cubic (BCC) structure, where an additional atom is added to the center of the cube, resulting in a more complex arrangement while preserving the cubic symmetry.

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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

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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Textbook Question

CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (c) What about red light?

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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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