Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
Question
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Chapter 2, Problem 2.8P
To determine

(a)

The numbers of atoms in Silicon FCC unit cell.

Expert Solution
Check Mark

Answer to Problem 2.8P

The numbers of atoms in Silicon FCC unit cell is 8.

Explanation of Solution

Given:

Silicon is atom at 0,0,0 and an atom at 14,14,14.

Lattice parameter of silicon is 0.543nm.

Density of the silicon atoms is 2.33×103kg/m3.

Calculation:

Draw the crystal structure of silicon atoms.

Materials Science And Engineering Properties, Chapter 2, Problem 2.8P

Figure (1)

FCC (Face-Centered structure) of Silicon has 4 atoms. Other atoms are placed at 14,14,14 as shown in figure (1). It can be concluded that after placing four new atoms in existing FCC structure, the total atoms in this FCC unit cell is 8atoms.

Conclusion:

Therefore, the numbers of atoms in Silicon FCC unit cell is 8.

To determine

(b)

The numbers of atoms per unit volume for the unit cell of Silicon.

Expert Solution
Check Mark

Answer to Problem 2.8P

The numbers of atoms per unit volume for the unit cell of Silicon is 0.50×1029atoms/m3.

Explanation of Solution

Formula used:

Write the expression to find the number of atoms per unit volume.

na=Numberofatomsa3      ......... (I)

Here, na is the number of atoms per unit volume, a is the lattice parameter and Numberofatoms is the numbers of atoms in a unit cell.

Calculation:

Silicon has Face Centered Cubic (FCC) structure with 8 number of atoms.

Substitute 8atoms for Numberofatoms and 0.543nm for a in equation (I) to find na.

na=8atoms ( 0.543 )3=8atoms ( 0.543nm× 10 9 m 1nm )3=8atoms0.16× 10 27m3=0.50×1029atoms/m3

Conclusion:

Therefore, the numbers of atoms per unit volume for the unit cell of Silicon is 0.50×1029atoms/m3.

To determine

(c)

The number of atoms per unit volume by using the density of silicon.

Expert Solution
Check Mark

Answer to Problem 2.8P

The number of atoms per unit volume is 0.50×1029atoms/m3

Explanation of Solution

Formula used:

Write the formula to find the atoms per unit volume.

NV=ργSi×NAMSi      ......... (III)

Here, NV is the atom per unit volume, ργSi is thedensity of Silicon, MSi is the molecular weight of Silicon and NA is the Avogadro’s number.

Calculation:

The molecular weight of Silicon is 28.09×103kg/mole.

The density of Silicon is 2.33×103kg/m3.

Avogadro’s number is 6.02×1023atoms/mole.

Substitute 2.33×103kg/m3 for ργSi, 28.09×103kg/mole for MSi and 6.02×1023atoms/mole for NA in equation (II) to find NV.

NV=2.33× 103kg/ m 3×6.02× 10 23atoms/mole28.09× 10 3kg/mole=0.50×1029atoms/m3

Conclusion:

Therefore, the number of atoms per unit volume is 0.50×1029atoms/m3.

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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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