Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 3.15, Problem 11KCP
To determine
Explain the crystallographic directions for a family or form and state their general notation.
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what are the properties of monoclinic crystal structure
For the images shown below, which Miller indices for crystallographic planes are included?
lu
C.
Z
Select one or more:
a. (111)
b. (230)
(211)
d. (110)
e. (100)
b
y
X
a/2
Z
b
Z
2b/3
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.
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 j620 Find the Miller indices of each crystallographic planearrow_forwardA hypothetical tetrahedral crystal has the following lattice parameters: a = b = 0.40 nm, c = 0.5 nm, a = B = y = 90°. Please write the indices of all planes/directions that belong to the family of (i) {100} and (ii)arrow_forwardSometimes, in the equation for resolved shear stress in a single crystal, the term cos cos is termed the Schmid factor. Determine the magnitude of the Schmid factor for an FCC single crystal oriented with its [100] direction parallel to the loading axis.arrow_forward
- Vanadium (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_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/mm ? Given: Avogadro's Number NA = 0.6023 x 1024 (atoms/mole) Select one: O a, 0.021 O b. 0.011 Oc.1.5 d. 0.0087 e. 0.00597 Potassium (K) has the Body-Centered Cubic (BC) crystal structune. The edge length is a = 0.533 nm. What is the linear density in atoms/nm along direction (01112 Select one: O ENG O O 0 00arrow_forwardA half a plane of atoms are inserted into the crystal lattice is known as_ O Screw Dislocation O Edge Dislocation O Surface Imperfections O Grain Boundary Imperfectionsarrow_forward
- 1. A crystal has a basis of one atom per lattice point and a set of primitive translation vectors are (in À): b = 3j: where i, j, and k are unit vectors in the x, y and z directions of a cartesian coordinate system. a = 3i; c = 1.5(i + j + k); What is the Bravais lattice type of this crystal, and what are the Miller indices of the set of planes most densely populated with atoms? Calculate the volumes of the primitive unit cell and the conventional unit cell.arrow_forwardConsider the following face-centered-cubic dislocation reaction: a/2 [110] → a/6 [211] + a/6 [121] a. Prove that the reaction will occur. b. What kind of dislocations are the (a/6)<121>? c. What kind of crystal imperfection results from this dislocation reaction? d. What determines the distance of separation of the (a/6)[211] and the (a/6)[121] dislocations?arrow_forward1- 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.arrow_forward
- 1 Aluminum Slip System Identification Aluminum has a lattice parameter of 0.405 nm and a density of 2.71 g/cc at room temperature. (a) Based on this information, and taking into account the atomic weight, demonstrate that Al has an FCC crystal structure. (b) Draw a unit cell of Al. Identify and draw a plane in the {100} family that is neither (100) nor (100). What is the planar density of this family of planes? (c) Draw another unit cell of Al. Identify and draw a plane in the {101} family that is neither (101) nor (101). What is the planar density of this family of planes? (d) Draw another unit cell of Al. Identify and draw a plane in the {111} family that is neither (111) nor (111). What is the planar density of this family of planes? (e) of the three planes you just drew, which one is close-packed? In this plane, what family of directions has the highest linear density? (The densest direction of the densest plane of a crystal structure form something called a slip system, which will…arrow_forwardb. Figure 2 shows another ball-and-stick model of a very small crystal of a- Polonium, but this crystal contains one edge dislocation. Answer the questions. Figure 2: If the edge dislocation moves by slip or glide by one unit of b from left to right, how many bonds will be broken to achieve this outcome? Answer: To move the dislocation from its current position (Fig. 2) to the far right (so that a small step of size b appears at the right-side face), how many bonds will be broken? Answer: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_forward
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