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(a) Consider an area formed by the close packing of circles. Calculate the area fraction of circles in a close-packed layer, a portion of which is shown below. Each circle has a radius R. Note: This is similar in principle to the atomic packing factor, but instead calculated in two dimensions; compute the fraction of area that the circles occupy of the total area. (b) Calculate the area fraction of a close-packed layer of circles of radius R with smaller atoms of radius r in each interstitial site. Note: r occupies a triangular interstitial site; therefore, r = 0.155R. :**

(a) Consider an area formed by the close packing of circles. Calculate the area fraction of circles in a close-packed layer, a portion of which is shown below. Each circle has a radius R. Note: This is similar in principle to the atomic packing factor, but instead calculated in two dimensions; compute the fraction of area that the circles occupy of the total area. (b) Calculate the area fraction of a close-packed layer of circles of radius R with smaller atoms of radius r in each interstitial site. Note: r occupies a triangular interstitial site; therefore, r = 0.155R. :**

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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(a) Consider an area formed by the close packing of circles. Calculate the area fraction of circles in a close-packed layer, a portion of which is shown below. Each circle has a radius R. Note: This is similar in principle to the atomic packing factor, but instead calculated in two dimensions; compute the fraction of area that the circles occupy of the total area. • (b) Calculate the area fraction of a close-packed layer of circles of radius R with smaller atoms of radius r in each interstitial site. Note: r occupies a triangular interstitial site; therefore, r = 0.155R. :**
Transcribed Image Text:(a) Consider an area formed by the close packing of circles. Calculate the area fraction of circles in a close-packed layer, a portion of which is shown below. Each circle has a radius R. Note: This is similar in principle to the atomic packing factor, but instead calculated in two dimensions; compute the fraction of area that the circles occupy of the total area. • (b) Calculate the area fraction of a close-packed layer of circles of radius R with smaller atoms of radius r in each interstitial site. Note: r occupies a triangular interstitial site; therefore, r = 0.155R. :**
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