Explanation Given: The length of unit cell, a is 0.4759 nm . The height of the unit cell, c is 1.2989 nm . The density of the material ρ is 3.99 g / cm 3 . Refer the Table 12.3, The radius of cation ( Al 3 + ) r c is 0.053 nm . The radius of anion ( O 2 − ) r A is 0.140 nm . Write the expression for Explanation: Write the expression for the base area for HCP. A = 6 [ a 2 ] 2 3 (I) Here, the base area of HCP structure is A . Write the expression for the unit cell volume. V c = A × c (II) Here, the unit cell volume is V c . Write the expression for density of Al 2 o 3 ρ = n ( 2 A C + 2 A A ) V C N A (III) Here, Here, Avogadro’s number ( 6.022 × 10 23 atoms/mol ) is N A , number of atom with in atom is n , the atomic weight is A and the density of Al 2 o 3 . Write the expression for the volume occupied by the cations. V C = 4 3 π r c 3 (IV) Here, the volume occupied by the cations is V C . Write the expression for the volume occupied by the anions. V A = 4 3 π r A (V) Here, the volume occupied by the anions is V A . Write the expression for the volume of spherical particle. V S = N c V c + N A V A (VI) Here, the volume of spherical particle is V S . Write the expression for the Atomic Packing Factor. A P F = V S V c (VII) Conclusion: Substitute 0.4759 nm for a in equation (I). A = 6 [ 0.4759 nm ( 10 − 7 cm 1 nm ) 2 ] 2 3 = 5.88 × 10 − 15 cm 2 Substitute 1.2989 nm for c and 5.88 × 10 − 15 cm 2 for A in equation (II). V c = ( 5.88 × 10 − 15 cm 2 ) × ( 1.2989 nm ( ( 10 − 7 cm 1 nm ) ) ) = 7.64 × 10 − 22 cm 3 Substitute 7.64 × 10 − 22 cm 3 for V c , 6.022 × 10 23 atoms/mol for N A , 26.98 g / mol for A C , 16 g / mol for A A and 3

Fundamentals of Materials Science and Engineering, Binder Ready Version: An Integrated Approach

5th Edition

ISBN: 9781119175483

Author: William D. Callister Jr., David G. Rethwisch

Publisher: WILEY

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Question

Chapter 3.21, Problem 29QP

To determine

The Atomic Packing Factor for Al2o3 .

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Chapter 3.21, Problem 28QP

Chapter 3.21, Problem 30QP

Chapter 3 Solutions

Fundamentals of Materials Science and Engineering, Binder Ready Version: An Integrated Approach

Ch. 3.21 - Prob. 1QP Ch. 3.21 - Prob. 2QP Ch. 3.21 - Prob. 3QP Ch. 3.21 - Prob. 4QP Ch. 3.21 - Prob. 5QP Ch. 3.21 - Prob. 6QP Ch. 3.21 - Prob. 7QP Ch. 3.21 - Prob. 8QP Ch. 3.21 - Prob. 9QP Ch. 3.21 - Prob. 10QP

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