Revere Homework 3 SOLUTIONS

Revere Homework 3 SOLUTIONS - P A UL REV ERE: TO UG H A S N...

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PAUL REVERE: TOUGH AS NAILS The Stuff of History + Materials Science and Solid State Chemistry Homework 3 Solutions M A T E R I A L S S C I E N C E PROBLEMS Practice Problems 1. Askeland Problem 3-34. Beryllium has a hexagonal crystal structure, with a o = 0.22858 nm and c o = 0.35842 nm. The atomic radius is 0.1143 nm, the density is 1.848 g/cm 3 , and the atomic weight is 9.01 g/mol. Determine a. The number of atoms in each unit cell; and b. The packing factor in the unit cell 2. Askeland Problem 3-78. Explain why most often polycrystalline materials exhibit isotropic properties. Most polycrystalline materials consist of randomly arranged crystals or “grains.” Although individual grains have different orientations and behave anisotropically by themselves, at a larger scale the material behavior is determined by the sum of many grain orientations, and the bulk material acts in an isotropic manner. There are some notable exceptions to this generalization. If the crystals or grains in a solid material are all aligned in the same or similar directions (called “columnar” orientation of grains), as is the case in some turbine blades, the crystal will exhibit anisotropic behavior. 3. Crystallographic planes. Sketch an fcc unit cell. Within the unit cell, sketch and label the following: a. ( 0 0 1 ) b. 2 0 1 () c. 1 2 0 [] Well, I didn’t include the atomic positions in all these sketches, but I think you get the idea… x z y ±²³

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4. Crystallographic planes and directions. Sketch a bcc unit cell. Within the unit cell, sketch and label the following: a. [ 0 1 0 ] b. [ 2 2 1 ] c. ( 0 0 1 ) 5. Nickel has the fcc structure and a lattice parameter of a = 0.3517 nm. a. Determine the atomic radius in nm. Compare this value to that shown in the front of your textbook. o R = a/(2 ± 2) = 0.124 nm b. Determine the atomic volume ± in nm 3 (assume a spherical atom shape). o Assuming a spherical atoms, ± = 4 ² R 3 /3 = .000805 nm 3 = 8.05 x 10 -3 nm 3 c. Determine the density in g/cm 3 and compare this answer to the Ni density value given in the table at the front of your textbook. o Book value for nickel density is 8.90 g/cm 3 , so the values are very close (hard sphere model is pretty good). [010] [221] r = nA V c N A = 4 atoms/cell ± 58 . 693 g/mol 0.3517 nm () 3 ± 6 . 023 ² 10 23 atoms/mol = 8 . 96 ² 10 -21 g/nm 3 = 8 . 96 g/cm 3
6. Sketch an fcc unit cell.

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This note was uploaded on 09/28/2010 for the course MECHENG 382 taught by Professor Thouless during the Winter '08 term at University of Michigan.

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Revere Homework 3 SOLUTIONS - P A UL REV ERE: TO UG H A S N...

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