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 2.6P
To determine

(a)

The density of FCC iron.

Expert Solution
Check Mark

Answer to Problem 2.6P

The density of FCC iron is 8.027g/cm3.

Explanation of Solution

Given:

The density of BCC iron at room temperature is listed as 7.87g/cm3.

At temperature above 912°C iron has the FCC (γ) structure.

The lattice parameter is 0.3589nm.

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 and the Numberofatoms is the numbers of atoms in a unit cell.

Write the formula to find the density of silver.

ργFe=na×MFeNA …… (II)

Here, ργFe is thedensity of FCC iron, MFe is the molecular weight of iron, and NA is the Avogadro’s number.

Calculation:

Gama phase iron has theFace Centered Cubic (FCC) structure with 4 number of atoms.

Substitute 4atoms for Numberofatoms and 0.3589nm for a in the equation (I) to find na.

na=4atoms ( 0.3589nm )3=4atoms ( 0.3589nm× 10 9 m 1nm )3=4atoms0.04623× 10 27m3=86.52×1027atoms/m3

The molecular weight of silver is 55.85×103kg/mole.

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

Substitute 86.52×1027atoms/m3 for na, 55.85×103kg/mole for MFe and 6.02×1023atoms/mole for NA in equation (II) to find ργFe.

ργFe=86.52× 10 27atoms/ m 3×55.85× 10 3kg/mole6.02× 10 23atoms/mole=8.027×103kgm3×( 10g kg)×( 10 6 cm 3 m 3 )=8.027g/cm3

Conclusion:

Therefore, the density of FCC iron is 8.027g/cm3.

To determine

(b)

The difference in the density of the FCC phase relative to the BCC phase of iron.

Expert Solution
Check Mark

Answer to Problem 2.6P

The density of the obtained FCC phase is higher than the BCC phase of iron.

Explanation of Solution

Calculation:

The obtained density of FCC iron is 8.027g/cm3, and the density of BCC iron at room temperature is listed as 7.87g/cm3.

Compare the obtained density of FCC iron at 912°C temperature with the density of iron at room temperature.The obtained density of Face Centered Cubic (FCC) iron is greater than the density of Body Centered Cubic (BCC) iron at room temperature. This implies that theBCCiron structure is loosely packed when compared with FCC gamma phase iron.

Conclusion:

Therefore, the density of the obtainedFCC phase is higherthan the BCC phaseof iron.

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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