Circuits 34 Tutorials - Electrical and Electronics Material PDF

Preview

Summary

Electrical and Electronics Tutorial...

Description

Chapter 3 & 4 Fundamentals of Crystallography & Structure of Crystalline Solids

Question 1 Calculate the radius of a vanadium atom, given that V has a BCC crystal structure, a density of 5.96 g/cm3, and an atomic weight of 50.9 g/mol. Solution This problem asks for us to calculate the radius of a vanadium atom. For BCC, n = 2 atoms/unit cell, and ( Since

(

√

√

)

√

)

Solving for R from the previous equation, (

√

( √ )( ) * ( (

(

(

⁄

+

Question 2 A hypothetical metal has the simple cubic crystal structure. If its atomic weight is 70.6 g/mol and the atomic radius is 0.128 nm, compute its density. Solution For the simple cubic crystal structure, the value of n is unity since there is only a single atom associated with each unit cell. Furthermore, for the unit cell edge length, a = 2R. Therefore,

(

and incorporating values of the other parameters provided in the problem statement leads to

{[( (

1|Page

( ] (

( }(

Question 3 Rhenium has an HCP crystal structure, an atomic radius of 0.134 nm, and a c/a ratio of 1.615. Compute the volume of the unit cell for Re. Solution In order to compute the volume of the unit cell for Re, it is necessary to use the equation: √ The problem states that c = 1.615a, and a = 2R. Therefore (

( √)

(

( √ )(

Question 4 For a ceramic compound, what are the two characteristics of the component ions that determine the crystal structure? Solution The two characteristics of component ions that determine the crystal structure of a ceramic compound are: 1) the magnitude of the electrical charge on each ion, and 2) the relative sizes of the cations and anions.

Question 5 The metal iridium has an FCC crystal structure. If the angle of diffraction for the (220) set of planes occurs at 69.20 o (first-order reflection) when monochromatic x-radiation having a wavelength of 0.154 nm is used, compute the interplanar spacing for this set of planes. Solution From the data given in the problem, and realizing that

, the interplanar spacing

for the (220) set of planes for iridium may be computed using ( (

( (

)

Question 6 The metal rubidium has a BCC crystal structure. If the angle of diffraction for the (321) set of planes occurs at 27.00o (first-order reflection) when monochromatic x-radiation having a wavelength of 0.071 nm is used, compute the interplanar spacing for this set of planes.

2|Page

Solution From the data given in the problem, and realizing that

, the interplanar spacing

for the (321) set of planes for Rb may be computed using ( (

( (

)

Question 7 What is the difference between crystal structure and crystal system? Solution A crystal structure is described by both the geometry of, and atomic arrangements within, the unit cell, whereas a crystal system is described only in terms of the unit cell geometry. For example, face-centered cubic and body-centered cubic are crystal structures that belong to the cubic crystal system.

Question 8 Do non-crystalline materials display the phenomenon of allotropy (or polymorphism)? Why or why not? Solution Non-crystalline materials do not display the phenomenon of allotropy; since a non-crystalline material does not have a defined crystal structure, it cannot have more than one crystal structure, which is the definition of allotropy.

3|Page...