Explanation MgO has lattice parameter of 0 .396 nm a 0 = 0 .396 nm Since, r Mg +2 = 0 .66×10 -8 cm r O -2 = 1 .32×10 -8 cm Representation of planes in cubic unit cell. Mg+2 ions are present on the plane ( 111 ) and O-2 ions are present on the plane (222) A cubic cell with the plane ( 111 ) can be represented as: There are two atoms per face and 3 half atoms and 3 one-sixth atoms per lattice parameter. Planer density is defined as a ratio of plane area to the number of atoms occupied by plane. Planer density for plane ( 111 ) = Atoms/plane/Area of plane =2/[ 2 a 0 /2][ 3 a 0 / 2 ] =2/[ 3 /2 a 0 2 ] =2/[ 3 /2 ( 0 .396 ) 2 ] nm 2 =2/[ 3 /2 ( 0 .396×10 -7 ) 2 ] cm 2 =2/1 .358×10 -15 =1 .4727×10 15 /cm 2 The fraction of plane ( 111 ) = Area of atom/plane/Area of plane = 2 π r 2 / ( 2 a 0 / 2 ) ( 3 a 0 / 2 ) = 2 × π × 0

Essentials of Materials Science and Engineering, SI Edition

4th Edition

ISBN: 9781337672078

Author: ASKELAND, Donald R., WRIGHT, Wendelin J.

Publisher: Cengage Learning

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Question

Chapter 3, Problem 3.92P

Interpretation Introduction

Interpretation:

The plane density and planar packing fraction for the plane (111) and plane (222) of MgO needs to be determined. Also, the icons which are present on the planes needs to be determined.

Concept introduction:

MgO has a sodium chloride structure with a lattice parameter of 0.396 nm. Planar density is the ratio of the area of the plane to the number of atoms in a plane.

Expert Solution & Answer

Chapter 3 Solutions

Essentials of Materials Science and Engineering, SI Edition

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