Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 4.8, Problem 40AAP
To determine
Consider an aluminum lattice with an excessive average of one vacancy in every100 unit cells. What will be its density and compare this to the theoretical density of aluminum (must calculate this using a perfect model of the unit cell) and what is your conclusion.
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Magnesium (Mg) has an HCP crystal structure and a density of 1.74 g/cm' and AMg 24.3
g/mol. (a) What is the volume of its unit cell in cubic centimeters?
(b) If the cla ratio is 1.624, compute the values of c and a.
BCC Iron has a lattice parameter of .2866 nm. Calculate its planar density on (111).
The accompanying figure shows a unit cell for a hypothetical metal.
(a) To which crystal system does this unit cell belong?
(b) What would this crystal structure be called?
(c) Calculate the density of the material, given that its atomic weight is 145 g/mol.
+2
90°i
0.40 nm
+y
90°
90°
0.30 nm
- 0.30 nm
Chapter 4 Solutions
Foundations of Materials Science and Engineering
Ch. 4.8 - Prob. 1KCPCh. 4.8 - Define the homogeneous nucleation process for the...Ch. 4.8 - In the solidification of a pure metal, what are...Ch. 4.8 - In the solidification of a metal, what is the...Ch. 4.8 - During solidification, how does the degree of...Ch. 4.8 - Distinguish between homogeneous and heterogeneous...Ch. 4.8 - Describe the grain structure of a metal ingot that...Ch. 4.8 - Distinguish between equiaxed and columnar grains...Ch. 4.8 - How can the grain size of a cast ingot be refined?...Ch. 4.8 - Prob. 10KCP
Ch. 4.8 - Prob. 11KCPCh. 4.8 - Prob. 12KCPCh. 4.8 - Distinguish between a substitutional solid...Ch. 4.8 - What are the conditions that are favorable for...Ch. 4.8 - Prob. 15KCPCh. 4.8 - Prob. 16KCPCh. 4.8 - Prob. 17KCPCh. 4.8 - Prob. 18KCPCh. 4.8 - Describe the structure of a grain boundary. Why...Ch. 4.8 - Describe and illustrate the following planar...Ch. 4.8 - Prob. 21KCPCh. 4.8 - Describe the optical metallography technique. What...Ch. 4.8 - Prob. 23KCPCh. 4.8 - Prob. 24KCPCh. 4.8 - Prob. 25KCPCh. 4.8 - Prob. 26KCPCh. 4.8 - Prob. 27KCPCh. 4.8 - Prob. 28KCPCh. 4.8 - Prob. 29KCPCh. 4.8 - Prob. 30KCPCh. 4.8 - Prob. 31KCPCh. 4.8 - Calculate the size (radius) of the critically...Ch. 4.8 - Prob. 33AAPCh. 4.8 - Prob. 34AAPCh. 4.8 - Calculate the number of atoms in a critically...Ch. 4.8 - Prob. 36AAPCh. 4.8 - Prob. 37AAPCh. 4.8 - Prob. 38AAPCh. 4.8 - Prob. 39AAPCh. 4.8 - Prob. 40AAPCh. 4.8 - Prob. 41AAPCh. 4.8 - Prob. 42AAPCh. 4.8 - Determine, by counting, the ASTM grain-size number...Ch. 4.8 - Prob. 44AAPCh. 4.8 - For the grain structure in Problem 4.43, estimate...Ch. 4.8 - Prob. 46AAPCh. 4.8 - Prob. 47SEPCh. 4.8 - Prob. 48SEPCh. 4.8 - Prob. 49SEPCh. 4.8 - Prob. 50SEPCh. 4.8 - In Chapter 3 (Example Problem 3.11), we calculated...Ch. 4.8 - Prob. 52SEPCh. 4.8 - Prob. 53SEPCh. 4.8 - Prob. 54SEPCh. 4.8 - Prob. 55SEPCh. 4.8 - Prob. 56SEPCh. 4.8 - Prob. 57SEPCh. 4.8 - Prob. 58SEPCh. 4.8 - Prob. 59SEPCh. 4.8 - Prob. 60SEPCh. 4.8 - Prob. 61SEPCh. 4.8 - Prob. 62SEPCh. 4.8 - Prob. 63SEPCh. 4.8 - Prob. 64SEPCh. 4.8 - Prob. 65SEPCh. 4.8 - Prob. 66SEP
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- EXAMPLE SHOT ON POCO X3 Theoretical Density Computation for Copper. Copper has an atomic radius of 0.128 nm, an FCC crystal structure, and an atomic weight of 63.5 g/mol.compute its theoretical density, and compare the answer with its measured density.arrow_forwardIron has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic weight of 55.85 g/mol. Compute its theoretical density and compare with its experimental density, which is 7.87 g/cm3. Which one is higher? O Experimental density is higher. O Not enough information to compute the theoretical density. O Theoretical density is higher. O Neither. Both are equal.arrow_forward3. Molybdenum has a BCC crystal structure, an atomic radius of 0.1363 nm, and an atomic weight of 95.94 g/mol. Compute its theoretical density.arrow_forward
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- Nickel has face -centered (FCC) cubic structure and atomic mass is 58.69. The atomic radius of nickel is given by 1.243*10^-10m. Calculate the density of Nickel crystal.arrow_forwardIron(Fe) is unusual in that it transforms from a BCC to an FCC structure at high temperature. Calculate the ratio of the densities of FCC-iron and BCC-iron . find the value of the expression shownarrow_forwardThe density of a sample of HCP beryllium is 1.844 g/cm 3 , and the lattice parameters are a 0 = 0.22858 nm and c 0 = 0.35842 nm. Calculate (a) the fraction of the lattice points that contains vacancies: and (b) the total number of vacancies in a cubic centimetre of Bearrow_forward
- The accompanying figure shows a unit cell for a hypothetical metal. (a) To which crystal system does this unit cell belong? (b) What would this crystal structure be called? (c) Calculate the density of the material, given that its atomic weight is 145 g/mol. +2 90°i 0.40 nm +y 90° 90° 0.30 nm 0.30 nm +Xarrow_forwardCalculate the radius of the atomic structure with a density of 0.541g/cm^3 and an atomic weight of 63.4g/mol It has an FCC crystal structure. Your answer should be in nm and 3 decimal places. Enter ONLY the number as an answer. Answer:arrow_forwardWith the information on its molar volume and lattice parameter, a, determine the crystal structure of Puterium. Sketch the crystal structure indicating the atoms arrangement. DATA: molar volume, Vmol = 5.90 cm/mol; lattice parameter, a = 2.15 Å = 2.15 x 10-8 cmarrow_forward
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