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Ch.12 - Solids and Modern Materials
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?
Illustration showing transformation of a simple cubic unit cell under pressure and stretching.

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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.
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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.
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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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Related Practice
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

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

Selected chlorides have the following melting points: NaCl (801 °C), MgCl2 (714 °C), PCl3 (-94 °C), SCl2 (-121 °C) (a) For each compound, indicate what type its solid form is (molecular, metallic, ionic, or covalent-network).

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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
Introduction of carbon into a metallic lattice generally results in a harder, less ductile substance with lower electrical and thermal conductivities. Explain why this might be so.
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Textbook Question
For each of the intermetallic compounds shown in Figure 12.17 determine the number of each type of atom in the unit cell. Do your answers correspond to the ratios expected from the empirical formulas: Ni3Al?

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