Topic XII: Materials Science/Structure of Matter
Diagnostic Examination for Materials Science/Structure of Matter
Chapter 36 Chrystallography and Atomic Bonding
Chapter 37 Material Testing
Chapter 38 Metallurgy
Diagnostic Examination
TOPIC XII: MATERIALS SCIENCE/STRUCTURE OF MATTER
TIME LIMIT: 45 MINUTES
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Degrees 0° 30° 45° 60° 90° 180° 270° 360°
√2 À
Greek alphabet
Αα Alpha Νν Nu
Ββ Beta Ξξ Xi
Γγ Gamma Οο Omicron
Δδ Delta Ππ Pi
Εε Epsilon Ρρ Rho
Ζζ Zeta Σσς Sigma
Ηη Eta Ττ Tau
Θθ Theta Υυ Upsilon
Ιι Iota Φφ Phi
Κκ Kappa Χχ Chi
Λλ Lambda Ψψ Psi
Μμ Mu Ωω Omega
Obsolete letters
Digamma Qoppa
San Sampi
Other characters
Stigma Sho
Heta
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1. How many atoms per cell are in the base-centered orthorhombic crystal shown?
Solution 1:
Each corner atom is shared by eight cells, while each base atom is shared by two cells.
(1/8)(8) + (1/2)(2) = 2
2. What is the packing factor for the body-centered tetragonal crystal with the dimensions shown?(Assume atoms are hard spheres and have a radius of r.)
Solution 2:
The packaging factor is the volume of the atoms divided by the cell volume.
The number of atoms per cell is:
(1/8)(8) + 1 = 2
The packing actor is
PF = [(2 atoms)((4/3)Πr^3]/(2r)(2r)(2√2)r =
Π/(3√2) = 0.74
3. At a particular temperature, iron exhibits a body-centered cubic crystal structure with a cell dimension of 2.86 A. What is the theoretical atomic radius of iron? (Assume atoms are hard spheres and have a radius of r.)
Solution 3:
The atoms are touching along the cell diagonal. The length of the cell diagonal is four atomic radii.
(√2a)^2 + a^2 = (4r)^2
r^2 = (3/16)a^2
r = (√3/4)a
= (√3/4)(2.86 À)
= 1.24 A
4. what are the Miller indices of the cplane shown in its cubic crystallographic cell?
Solution 4:
The intercepts of the x-,y-, and z- axes are ∞, 1/2,and ∞, respectively. The Miller indices are the reciprocals of the intercepts, normalized to the lowest possible integer values. For this plane, the Miller indices are (0 2 0).
5. Which of the following planes is a member of the family of equivalent planes containing (1 0 1)?
Soltion 5:
