Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 4.8, Problem 56SEP

(a)

To determine

Estimate the density of a 75 wt% copper25 wt% Ni alloy.

(a)

Expert Solution
Check Mark

Answer to Problem 56SEP

The density of copper and nickel alloy is 8.94g/cm3.

Explanation of Solution

Express the density of alloy.

 ρalloy=(wt%Cu)(ρCu)+(wt%Ni)(ρNi)                                              (I)

Here, density of copper and nickel is ρCuandρNi respectively.

Conclusion:

Write the density of copper and nickel and also write the number of atom per mole or Avogadro number.

 ρCu=8.96g/cm3ρNi=8.9g/cm3N=6.02×1023atoms

Write the molar or atomic mass of copper and nickel.

 MCu=63.55gMNi=58.69g

Substitute 25g for wt%Ni, 75g for wt%Cu, 8.96g/cm3 for ρCu and 8.9g/cm3 for ρNi in Equation (I).

 ρalloy=(0.75)(8.96g/cm3)+(0.25)(8.9g/cm3)=8.94g/cm3

Hence, the density of copper and nickel alloy is 8.94g/cm3.

(b)

To determine

The most probable crystal structure for this copper and nickel alloy.

(b)

Expert Solution
Check Mark

Answer to Problem 56SEP

The most probable crystal structure for this copper and nickel alloy is FCC.

Explanation of Solution

Write the information data for copper and nickel as in Table (1).

ElementCrystal structure
CopperFCC
NickelFCC

As both of the copper and nickel have similar FCC crystal structure, then the formed alloy will also have the FCC structure.

Hence, the most probable crystal structure for this copper and nickel alloy is FCC.

(c)

To determine

The mass in grams of the atoms inside a unit cell of the copper nickel alloy.

(c)

Expert Solution
Check Mark

Answer to Problem 56SEP

The mass in grams of the atoms inside a unit cell of the copper nickel alloy is 4.13×1022g.

Explanation of Solution

Consider the mass of alloy as 100g.

Express the total atoms of copper.

 nCu=(wt%Cu)NMCu                                                                           (II)

Here, atomic mass of copper is MCu and number of atom per mole or Avogadro number is N.

Express the total atoms of nickel.

 nNi=(wt%Ni)NMNi                                                                          (III)

Here, atomic mass of nickel is MNi.

Express the mass in grams of the atoms inside a unit cell of the copper nickel alloy.

 mcell=nCuMcuN+nNiMNiN                                                                     (IV)

Conclusion:

Consider the mass of the alloy be 100g.

Substitute 75g for wt%Cu, 6.02×1023atoms for N and 63.55g for MCu in Equation (II).

 nCu=(75g)(6.02×1023atoms)63.55g=7.10×1023atoms                                                (V)

Substitute 25g for wt%Ni, 6.02×1023atoms for N and 58.69g for MCu in Equation (III).

 nNi=(25g)(6.02×1023atoms)58.69g=2.56×1023atoms                                            (VI)

Thus from Equations (V) and (VI), it is observed that there are 73%Cuatomsto27%Niatoms. Hence, there will be 4atoms per unit cell based on the calculations that is 3 copper atoms to 1 atom in each cell.

 nCu=3atomsnNi=1atoms

Substitute 3atoms for nCu, 1atoms for nNi, 6.02×1023atoms for N, 63.55g for MCu, and 58.69g for MCu in Equation (IV).

 mcell=(3atoms)[63.55g6.02×1023atoms]+(1atoms)[58.69g6.02×1023atoms]=4.13×1022g

Hence, the mass in grams of the atoms inside a unit cell of the copper nickel alloy is 4.13×1022g.

(d)

To determine

The lattice constant for the copper nickel alloy.

(d)

Expert Solution
Check Mark

Answer to Problem 56SEP

The lattice constant for the copper nickel alloy is 3.58×108cm.

Explanation of Solution

Express the lattice constant for the copper nickel alloy.

 a=mcellρalloy                                                                               (VII)

Conclusion:

Substitute 4.13×1022g for mcell and 8.94g/cm3 for ρalloy in Equation (VII).

 a=4.13×1022g8.94g/cm3=3.58×108cm

Hence, the lattice constant for the copper nickel alloy is 3.58×108cm.

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Chapter 4 Solutions

Foundations of Materials Science and Engineering

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