Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 3.15, Problem 82SEP
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Explain why the iron and tungsten being BCC have different atomic radius but same atomic packing factor.
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A hypothetical metal has the BCC crystal structure, a density of 7.24 g/cm, and an atomic weight of 48.9
g/mol. Please calculate the atomic radius of this metal. Some useful equations are provided below.
a= 2R/2
a = 2R3
!!
nA
VNA
O 0.122 nm
O 0.567 nm
0.745 nm
1.23 nm
Sodium chloride (NaCl) has the rock salt crystal structure and a density of 2.17 g/cm³. The atomic weights of sodium and chlorine are
22.99 g/mol and 35.45 g/mol, respectively.
(a) Determine the unit cell edge length.
nm
(b) Determine the unit cell edge length from the radii in the table below assuming that the Nat and Cl- ions just touch each other along
the edges.
nm
Cation
Mg2+
Fe2+
Na+
Ionic Radius (nm)
0.072
0.077
0.102
Anion Ionic Radius (nm)
CI-
0²-
0.181
0.140
Fe has a BCC structure and an atomic radius of 0.126 nm. The atomic mass of Fe is 55.85 g/mol & Avogadro's No. is 6.023 x 1023. Calculate the density of Fe.
Chapter 3 Solutions
Foundations of Materials Science and Engineering
Ch. 3.15 - Prob. 1KCPCh. 3.15 - Prob. 2KCPCh. 3.15 - Prob. 3KCPCh. 3.15 - Prob. 4KCPCh. 3.15 - Prob. 5KCPCh. 3.15 - Prob. 6KCPCh. 3.15 - Prob. 7KCPCh. 3.15 - Prob. 8KCPCh. 3.15 - Prob. 9KCPCh. 3.15 - Prob. 10KCP
Ch. 3.15 - Prob. 11KCPCh. 3.15 - Prob. 12KCPCh. 3.15 - Prob. 13KCPCh. 3.15 - Prob. 14KCPCh. 3.15 - Prob. 15KCPCh. 3.15 - Prob. 16KCPCh. 3.15 - Prob. 17KCPCh. 3.15 - Prob. 18KCPCh. 3.15 - Prob. 19KCPCh. 3.15 - Prob. 20KCPCh. 3.15 - Prob. 21KCPCh. 3.15 - Prob. 22KCPCh. 3.15 - Prob. 23KCPCh. 3.15 - Prob. 24AAPCh. 3.15 - Prob. 25AAPCh. 3.15 - Prob. 26AAPCh. 3.15 - Prob. 27AAPCh. 3.15 - Prob. 28AAPCh. 3.15 - Prob. 29AAPCh. 3.15 - Prob. 30AAPCh. 3.15 - Prob. 31AAPCh. 3.15 - Prob. 33AAPCh. 3.15 - A direction vector passes through a unit cube from...Ch. 3.15 - Prob. 36AAPCh. 3.15 - Prob. 37AAPCh. 3.15 - Prob. 38AAPCh. 3.15 - Prob. 41AAPCh. 3.15 - Prob. 42AAPCh. 3.15 - Prob. 43AAPCh. 3.15 - Prob. 44AAPCh. 3.15 - Prob. 45AAPCh. 3.15 - Prob. 46AAPCh. 3.15 - Prob. 47AAPCh. 3.15 - Rodium is FCC and has a lattice constant a of...Ch. 3.15 - Prob. 49AAPCh. 3.15 - Prob. 50AAPCh. 3.15 - Prob. 51AAPCh. 3.15 - Prob. 52AAPCh. 3.15 - Prob. 53AAPCh. 3.15 - Prob. 54AAPCh. 3.15 - Prob. 55AAPCh. 3.15 - Determine the Miller-Bravais direction indices of...Ch. 3.15 - Determine the Miller-Bravais direction indices of...Ch. 3.15 - Prob. 58AAPCh. 3.15 - Prob. 59AAPCh. 3.15 - Prob. 60AAPCh. 3.15 - Prob. 61AAPCh. 3.15 - Prob. 62AAPCh. 3.15 - Prob. 63AAPCh. 3.15 - Prob. 64AAPCh. 3.15 - Prob. 65AAPCh. 3.15 - Prob. 66AAPCh. 3.15 - Prob. 67AAPCh. 3.15 - Prob. 68AAPCh. 3.15 - Prob. 69AAPCh. 3.15 - Prob. 70AAPCh. 3.15 - Prob. 71AAPCh. 3.15 - Prob. 72AAPCh. 3.15 - Prob. 73AAPCh. 3.15 - Prob. 74SEPCh. 3.15 - Prob. 75SEPCh. 3.15 - Prob. 76SEPCh. 3.15 - Assuming that the volume of an HCP metal cell...Ch. 3.15 - Prob. 79SEPCh. 3.15 - Prob. 80SEPCh. 3.15 - Prob. 81SEPCh. 3.15 - Prob. 82SEPCh. 3.15 - Prob. 83SEPCh. 3.15 - Prob. 84SEPCh. 3.15 - Prob. 85SEPCh. 3.15 - Prob. 86SEPCh. 3.15 - Prob. 87SEPCh. 3.15 - Prob. 88SEPCh. 3.15 - Prob. 89SEPCh. 3.15 - Prob. 90SEPCh. 3.15 - Prob. 91SEPCh. 3.15 - Prob. 92SEPCh. 3.15 - Prob. 93SEPCh. 3.15 - Prob. 94SEPCh. 3.15 - Prob. 95SEPCh. 3.15 - Prob. 96SEP
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- Consider two hypothetical metallic crystal structures A and B. A has an fcc and B a bcc lattice structure. Both have the same unit cell volume. The Atomic Packing Factor for A is 0.740 and that for B is 0.680. What is the ratio of the fcc to bcc atomic radii? (This question has only one correct answer) a. 0.82 b. 0.63 c. 0.92 d. 0.44 e. 1.21 Clear my choicearrow_forward1. When Au comes into contact with Ag, it creates a solid solution that is called a substitutional solid solution. Calculate the amount of Au atoms per cubic centimeter in an Ag–Au alloy with 10% Au and 90% Ag. Pure Au has a density of 19.32 g/cm3 and pure Ag has a density of 10.49 g/cm3. 2. What is the atomic radius of nickel (in A) if it follows an FCC crystal structure, given that Nickel has a density of 8.9 g/mL and an atomic weight of 58.7 g/mol. 3. If 25 grains per square inch are measured at 100x magnification, what is the ASTM grain size number of the metal specimen?arrow_forwardA hypothetical metal has the SC crystal structure, a density of 7.08 g/cm3, and an atomic weight of 51.63 g/mol. The atomic radius of this metal in nanometer isarrow_forward
- Iron exhibits an allotropic behavior change of solid state structure in such a way that when it is heated to 910 C it undergoes a structure change from body-centered cubic BCC to face-centered cubic FCC considering that the atomic radius of iron increases to 0.1241 nm or 0.126 nm more when said temperature is reached obtainThe volume change experienced by the structure when the temperature of 910 C is reachedarrow_forwardVanadium (V) has a BCC crystal structure. The atomic radius is R = 0.132 nm and the atomic mass is M = 50.94 g/mole. What is the density of Vanadium in g/mm3? Given: Avogadro’s Number NA = 0.6023 × 1024 (atoms/mole) Select one: a. 1.5 b. 0.021 c. 0.011 d. 0.0087 e. 0.00597arrow_forwardSilver Ag has the fcc crystal structure as shown in the figure below. Determine its atomic packing factor APF? Given: The radius of Germanium: r(Ag)= 0.144 nm.  Select one: a. 0.14 b. 0.34 c. 0.68 d. 0.12 e. 0.4 f. 0.51 g. 0.74 h. 0.21arrow_forward
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