Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 3.15, Problem 68AAP
To determine
The lattice constant
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For which set of crystallographic planes will a first-order diffraction peak occur at a diffraction angle of 44.53° for FCC nickel (Ni) when
monochromatic radiation having a wavelength of 0.1542 nm is used? The atomic radius for Ni is 0.1246 nm.
(
When the iron metal sample with a density of 7.87 g cm³ was placed in an X-ray diffractometer
using incoming X-rays with a wavelength of 0.1541 nm, a diffraction from the (110) planes was
obtained at an angle of 22.35 °
(i) Using the defined axes as shown below, sketch the (110) crystallographic plane in a 3-
dimension primitive cubic lattice.
y
(ii)
What type of cubic lattice does this metal sample have if the order of diffraction, n=1?
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For FCC iron, calculate the diffraction angle for the (220) set of planes. The lattice parameter for Fe is 0.3571 nm. Assume that monochromatic radiation having a wavelength of 0.1540 nm is used, and the order of reflection is 1.
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- For which set of crystallographic planes will a first-order diffraction peak occur at a diffrac- tion angle of 46.21° for BCC iron when mono- chromatic radiation having a wavelength of 0.0711 nm is used?arrow_forwardThe metal niobium has a BCC crystal structure. If the angle of diffraction for the (211) set of planes occurs at 75.99° (first-order reflection) when monochromatic x-radiation having a wavelength of 0.1659 nm is used, compute the following: (a) The interplanar spacing for this set of planes i nm (b) The atomic radius for a Nb atom nmarrow_forwarda) Draw the [11 0], [-1 1 0], [ 0-1-1] directions for FCC and prove they are crystallographically equivalent. The family of directions is shown with these brackets. So we can say these directions are part of the family of directions. b) Draw the (1 o 0), (-1 0 0), (0 -1 0), and (00-1) planes for FCC and prove they are crystallographically equivalent. The family of directions is shown with {} these brackets. So we can say these planes are part of the {10 0} family of planes. h me Note that I cannot put a bar as the minus sign.arrow_forward
- Consider a unit cell with lattice dimensions a, b, and c in the x-, y and z directions. Which of the following sets of Miller indices can represent a crystallographic plane with intercepts of b and (c/4) along the y- and z-axes respectively? (more than one answer is possible for this question. marks will only be awarded for the question if all the correct options are selected (i.e. 'all or nothing' marking scheme). a. b. C. d. (214) (421) (114) e. (412)arrow_forward2 Miscellaneous I (a) A certain metal has a BCC crystal structure, a density of 5.96 g/cm³, and an atomic weight of 50.9 g/mol. Calculate the atomic radius. (b) Compute the interplanar spacing for the (111) set of planes for this metal. Are these planes close- packed? (c) Determine the expected diffraction angle for this (111) set of planes when monochromatic radiation of wavelength 0.154 nm is used. (d) What is the metal used in this problem?arrow_forwardQuestion-2. BCC Tantalum has an atomic radius of 0.1430 nm. Answer the following questions: (a) Calculate the lattice parameter a, b, c of the BCC structure. (b) Determine the interplanar spacings of (110), (200), (211), and (220) planes (c) Determine the expected angles for the first-order reflection of (110), (200), (211), and (220) planes when monochromatic x-ray radiation of a wavelength 0.1542 nm is used.arrow_forward
- ( 100] Problem 4. Calculate a value for the density of FCC platinum in grams per cubic centimeter from its lattice constant a of 0.36263 nm and its atomic mass of 195.09 g/mol. (pts 15)arrow_forwardThe distance between the two (111) planes in the FCC crystal structure is 0.2 nm. Find out the atomic radius in nm.arrow_forwardNickel has the fcc crystal structure and a lattice parameter of a = 0.3517 nm. Using this information, determine the atomic radius of Ni in angstroms.arrow_forward
- b) The spacing between successive (100) planes in NaCl is 2.82 Å. X-ray incident upon the surface of this crystal and it is found that it gives rise to the first order Bragg reflection at a grazing angle of 8°35¢. (i) Calculate the wavelength of X-ray (ii) Find the angle at which the 2nd order Bragg reflection would occur.arrow_forward(b) Draw the following direction vectors in a cubic unit cell: [212] and [101] Draw the following crystallographic planes in a cubic unit cell: (111) and (121) "oin 2/2 Page 1 of 2arrow_forwardFor BCC metal X, compute the interplanar spacing for the 212 set of planes. The lattice parameter for Fe is 0.2194 nm. Round your answer to 2 decimal places.arrow_forward
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