Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 3.15, Problem 8KCP
To determine
State the location of the atomic positions in cubic unit cells.
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How many atoms constitute one unit cell of a face centered cubic crystal?
3 Copper Unit Cell Uniqueness
Here's a weird way to describe the structure of copper: Cu falls into the tetragonal crystal system with
a = 0.256 nm, c = 0.362 nm = a√√2, and atoms located at 000 and. Its density is 8.94 g/cc at room
temperature.
(a) Draw a few adjacent units cells of the structure as described in this "weird" way. You should be able
to see that there is a much more convenient way to describe the structure. What is it? (The point I
wish to make is that there are many different unit cells that can be used to describe any given crystal,
so we usually choose the one that is easiest to visualize.)
(b) Calculate the radius of a copper atom using the above information.
(c) Calculate the lattice parameter of the "better" unit cell of Cu.
1- The density of the elemental magnesium crystal structure, which is in the face centered cubic structure, is 1,738 g / cm3. Specify the side lengths of the crystal lattice.
2-Polonium is an element with a simple cubic crystal arrangement. Find the radius of the polonium atoms in this structure with a density of 9.4 g / cm3 and a weight of 209 g / atom.
3- A wire with a diameter of 9.6 mm is pulled with a force of 18,000 N. With this loading, the initial length of the wire that grows 1.5 mm is 400 mm. Find the engineering voltage.
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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- Question-7 Calculate the volume in cubic nanometers of the titanium crystal structure unit cell. Lattice constants for titanium at 20°C are a = 0.29504 nm and c = 0.46833 nm.arrow_forwardQuestion-10 Platinum has a lattice constant of 0.39239 nm and its atomic mass is 195.09 g/mol. Calculate a value for its density in grams per cubic centimeter.arrow_forwardWhat is the angle between the [110] and [111] directions in the cubic system? Select one: a. 65.1° O b. 31.4° O c. 35.3 O d. 45.2 Calcium has the Face-Centered Cubic (FCC crystal. structure shown in the figure below. room temperature (20 C). Calculate the edge length "a" of the unit cellarrow_forward
- Problem #4 a) Find the indices for the directions indicated by the two vectors in the shown sketch below 0.5 mm 0.4 mm 0.7 mm Direction 1 Direction 2 ty b) Sketch the following directions within a cubic unit cell: (a) [123], (b) [211], (c) [102], (d) [133]. c) Sketch the following planes within a cubic unit cell: (a) (011), (b) (102), (c) (112), and (d) (131)arrow_forwardThe spacing between two adjacent (123) planes in a simple cubic crystal with the lattice parameter a=0.4 nm is _______ (nm). Draw [322] in a body centered cubic crystal. Draw (202) in a face centered cubic crystal. The planar density of (003) should be higher than that of (002) in a body centered cubic crystal. Ture___ or False____. You need to justify why to the answer.arrow_forward2- The unit cell for tin (sn) has tetragonal symmetry, with a and c lattice parameters of 0.583 and 0.318 nm, respectively. If its density, atomic weight, and atomic radius are 7.30 g/cm3, 118.69 g/mol, and 0.152 nm, respectively, compute the atomic packing factor.arrow_forward
- Question 3: a) Draw the following planes in a cubic cell: (102), (131) and (013) b) Draw the following crystallographic directions in a cubic lattice: [11], [012], [103].1arrow_forwardCalculate the density (in g/cm3) of the atomic structure with a radius of 0.267 nm and an atomic weight of 52.1g/mol. It has an FCC crystal structure. Use 3 decimal place accuracy and ONLY enter a number answer. Answer:arrow_forwardThe face-centered cubic cell has atoms: (select all that apply) In the middle of each side of the unit cell In the middle of each edge of the unit cell On the corners of the unit cell In the center of the unit cellarrow_forward
- You are given the density of a metal as 4.22 g/cm3. You are advised the crystallographic structure is fcc, and the atomic mass is 28.9 g/mol. What is the atomic radius of the metal? a. 0.15 nm b. 0.09 nm c. 0.13 nm d. 0.10 nmarrow_forwardQuestion-6 Gold has a lattice constant of 0.40788 nm. Calculate a value for the atomic radius of a gold atom in nanometers. Compare this value with the standard atomic radius of gold. Question-7 Calculate the volume in cubic nanometers of the titanium crystal structure unit cell. Lattice constants for titanium at 20°C are a 0.29504 nm and c 0.46833 nm.arrow_forwardTop of graph represents the atomic percentage of zinc. Bottom axis is the weight percentage of zincarrow_forward
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