Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 14

Discuss the methods for designation of planes of a crystal.

Short Answer

Expert verified
There are three primary methods for the designation of crystal planes: Miller Indices, which uses reciprocals of intercepts; Intercepts Method, which uses ratios of intercepts; and Reciprocal Method, which uses shortest non-zero distances from origin.

Step by step solution

01

Miller Indices

Miller Indices refers to a notation system in crystallography for planes in crystal structures and directions in such planes. First, determine the intercepts of the set of planes with the crystallographic axes in terms of the lattice parameters, a, b, and c. Next, take the reciprocals of these numbers and reduce these to the smallest integers, if necessary. The resulting set of three integers are written in parentheses without commas to represent a plane – this is the Miller Index (hkl) of the plane.
02

Intercepts Method

The Intercepts method is a more practical approach towards identification of lattice planes. Start by determining the intercepts of the planes along the three coordinate axes. Afterwards, measure the ratios of these intercepts and express them in terms of the lattice parameters. H, K, and L would be calculated as, \( H = a/Intercept along X \), \( K = b/Intercept along Y \), \( L = c/Intercept along Z \).
03

Reciprocal Method

In the reciprocal method, determine the shortest non-zero distance from the origin to the plane, following the reciprocal of each of the three coordinates. Reduce these reciprocals to the smallest possible whole numbers – these would be the Miller indices (hkl) of the plane. The plane can be denoted by (hkl), where h, k, and l are either integers or fractions.

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

Discuss the structure of the following ionic crystal types: (a) Rock salt type structure (b) Fluorite-type structure (c) Zinc-blende-type structure

Discuss the splitting of \(d\) -orbitals in octahedral ligand field environment on the basis of group theory.

Determine the irreducible representation for the following: (a) \(\mathrm{C}_{2 v}\) point group (b) Set of \(p\) -orbitals

Derive Born-Lande equation and hence prove that lattice energy of an ionic crystal is inversely proportional to the interionic distances.

How does coordination number vary with radius ratio? How does it affect the geometry of the ionic crystal?
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Inorganic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Ionic and Molecular Compounds

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