Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
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Chapter 2, Problem 2.12P
To determine

The planar atom density of the {100} -type planes and {111} -type planes and to compare their atom density.

Expert Solution & Answer
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Answer to Problem 2.12P

The planar density of {100} -plane is 15.35×1018atoms/m2 and the planar density of {111} -plane is 17.746×1018atoms/m2. {111} -plane is more closely packed.

Explanation of Solution

Given:

Lattice parameter of FCC structure of copper is 0.361nm.

Formula used:

The planar density of a plane is given as,

PD=Number of atoms contributed to planeArea of plane   ...... (I)

Here, PD is planar density.

The area of {100} -plane is given by

Area of {100}-plane=(a0)2   ...... (II)

Here, a0 is lattice parameter.

Calculation:

The area of {100} -plane in FCC structure has two atoms.

Substitute 0.361nm for a0 in equation (II) to find the area of {100} -plane,

Area of {100}-plane=(0.361nm)2=(0.361 nm× 10 9 m 1 nm)2=0.1303×1018 m2

Substitute 0.1303×1018 m2 for Area of plane and 2 atoms for Number of atoms contributed to plane in equation (I) to find the planar density of {100} -plane,

PD=2 atoms0.1303× 10 18  m2=15.35×1018atoms/m2

Draw {111} -plane of FCC crystal.

Materials Science And Engineering Properties, Chapter 2, Problem 2.12P

Figure (1)

Calculate the plane area.

Area of plane=12bh

Here, b is breadth and h is height of the triangle.

From figure (1),

Substitute 2a0 for b and 32a0 for h in the above expression to find the expression for the area of plane.

Area of plane=12(2a0)(32a0)

Substitute 0.361nm for a0 in the above equation to find area of the plane.

Area of plane=12[2(0.361nm)][ 3 2(0.361nm)]=12(0.51nm)(0.4421nm)=(0.1127 nm2)( 10 9  m 1 nm)2=0.1127×1018 m2

The area of {111} -plane in FCC structure has two atoms.

Substitute 0.1127×1018 m2 for Area of plane and 2 atoms for Number of atoms contributed to plane in equation (I) to find the planar density of {111} -plane.

PD=2 atoms0.1127× 10 18  m2=17.746×1018atoms/m2

Compare the planar density of {100} -plane and the planar density of {111} -plane, it can be observed that {111} -plane is more closely packed.

Conclusion:

Therefore, the planar density of {100} -plane is 15.35×1018atoms/m2 and the planar density of {111} -plane is 17.746×1018atoms/m2. {111} -plane is more closely packed.

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Chapter 2 Solutions

Materials Science And Engineering Properties

Ch. 2 - Prob. 11CQCh. 2 - Prob. 12CQCh. 2 - Prob. 13CQCh. 2 - Prob. 14CQCh. 2 - Prob. 15CQCh. 2 - Prob. 16CQCh. 2 - Prob. 17CQCh. 2 - Prob. 18CQCh. 2 - Prob. 19CQCh. 2 - Prob. 20CQCh. 2 - Prob. 21CQCh. 2 - Prob. 22CQCh. 2 - Prob. 23CQCh. 2 - Prob. 24CQCh. 2 - Prob. 25CQCh. 2 - Prob. 26CQCh. 2 - Prob. 27CQCh. 2 - Prob. 28CQCh. 2 - Prob. 29CQCh. 2 - Prob. 30CQCh. 2 - Prob. 31CQCh. 2 - Prob. 32CQCh. 2 - Prob. 33CQCh. 2 - Prob. 34CQCh. 2 - Prob. 35CQCh. 2 - Prob. 36CQCh. 2 - Prob. 37CQCh. 2 - Prob. 38CQCh. 2 - Prob. 39CQCh. 2 - Prob. 40CQCh. 2 - Prob. 41CQCh. 2 - Prob. 42CQCh. 2 - Prob. 43CQCh. 2 - Prob. 44CQCh. 2 - Prob. 45CQCh. 2 - Prob. 46CQCh. 2 - Prob. 47CQCh. 2 - Prob. 48CQCh. 2 - Prob. 49CQCh. 2 - Prob. 50CQCh. 2 - Prob. 51CQCh. 2 - Prob. 52CQCh. 2 - Prob. 1ETSQCh. 2 - Prob. 2ETSQCh. 2 - Prob. 3ETSQCh. 2 - Prob. 4ETSQCh. 2 - Prob. 5ETSQCh. 2 - Prob. 6ETSQCh. 2 - Prob. 7ETSQCh. 2 - Prob. 8ETSQCh. 2 - Prob. 9ETSQCh. 2 - Prob. 10ETSQCh. 2 - Prob. 11ETSQCh. 2 - Prob. 12ETSQCh. 2 - Prob. 13ETSQCh. 2 - Prob. 1DRQCh. 2 - Prob. 2DRQCh. 2 - Prob. 3DRQCh. 2 - Prob. 4DRQCh. 2 - Prob. 5DRQCh. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - Prob. 2.3PCh. 2 - Prob. 2.4PCh. 2 - Prob. 2.5PCh. 2 - Prob. 2.6PCh. 2 - Prob. 2.7PCh. 2 - Prob. 2.8PCh. 2 - Prob. 2.9PCh. 2 - Prob. 2.10PCh. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - Prob. 2.14PCh. 2 - Prob. 2.15PCh. 2 - Prob. 2.16PCh. 2 - Prob. 2.17PCh. 2 - Prob. 2.18PCh. 2 - Prob. 2.19PCh. 2 - Prob. 2.20PCh. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - Prob. 2.23PCh. 2 - Prob. 2.24PCh. 2 - Prob. 2.25PCh. 2 - Prob. 2.26P
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Materials Science And Engineering Properties
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ISBN:9781111988609
Author:Charles Gilmore
Publisher:Cengage Learning