Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 24

Imagine the primitive cubic lattice. Now imagine grabbing opposite corners and stretching it along the body diagonal while keeping the edge lengths equal. The three angles between the lattice vectors remain equal but are no longer \(90^{\circ}\) . What kind of primitive lattice have you made?

Short Answer

Expert verified
After stretching the primitive cubic lattice along the body diagonal while maintaining equal edge lengths and equal angles, the resulting lattice is a rhombohedral (or trigonal) lattice which belongs to the hexagonal crystal system. This lattice has equal edge lengths (a = b = c) and equal angles between the lattice vectors, but the angles are no longer \(90^{\circ}\).

Step by step solution

01

Identify key features of the initial primitive cubic lattice

A primitive cubic lattice has three lattice vectors (a, b, and c) that are mutually perpendicular, meaning all the angles between them are \(90^{\circ}\). The edge lengths of the unit cell are all equal: a = b = c.
02

Visualize the transformation

Now, we need to stretch the lattice along the body diagonal while maintaining equal edge lengths. This means that we will still have a = b = c, but the angles between the lattice vectors will no longer remain \(90^{\circ}\).
03

Identify the type of lattice after the transformation

After the transformation, we still have equal edge lengths a = b = c, and the angles between the lattice vectors are no longer \(90^{\circ}\) but remain equal. This type of lattice structure is known as a "rhombohedral" (or "trigonal") lattice which belongs to the hexagonal crystal system. So, the resulting primitive lattice after the transformation is a rhombohedral lattice.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An element crystallizes in a face-centered cubic lattice. The edge of the unit cell is 4.078\(\hat{A}\) , and the density of the crystal is 19.30 \(\mathrm{g} / \mathrm{cm}^{3} .\) Calculate the atomic weight of the element and identify the element.

Calculate the volume in \(\hat{A}^{3}\) of each of the following types of cubic unit cells if it is composed of atoms with an atomic radius of 1.82 A. (a) primitive (b) face-centered cubic.

Unlike metals, semiconductors increase their conductivity as you heat them (up to a point). Suggest an explanation.

For each of the following pairs of semiconductors, which one will have the larger band gap: (a) CdS or CdTe, (b) GaN or InP, ( c) GaAs or InAs?

What evidence supports the notion that buckyballs are actual molecules and not extended materials? $$ \begin{array}{l}{\text { (a) Buckyballs are made of carbon. }} \\ {\text { (b) Buckyballs have a well-defined atomic structure and }} \\ {\text { molecular weight. }} \\ {\text { (c) Buckyballs have a well-defined melting point. }} \\ {\text { (a) Buckyballs are semiconductors. }} \\ {\text { (e) More than one of the previous choices. }}\end{array} $$
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation

Physical Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free