HW 5 Solutions

# HW 5 Solutions - HW 5 ENMA 300 5.1 5.12 Some hypothetical...

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HW 5 ENMA 300 5.1 5.12 Some hypothetical alloy is composed of 25 wt% of metal A and 75 wt% of metal B. If the densities of metals A and B are 6.17 and 8.00 g/cm 3 , respectively, whereas their respective atomic weights are 171.3 and 162.0 g/mol, determine whether the crystal structure for this alloy is simple cubic, face-centered cubic, or body-centered cubic. Assume a unit cell edge length of 0.332 nm. 5.22 Determine the ASTM grain size number if 25 grains per square inch are measured at a magnification of 75. 5.D1 Aluminum–lithium alloys have been developed by the aircraft industry to reduce the weight and improve the performance of its aircraft. A commercial aircraft skin material having a density of 2.47 g/cm 3 is desired. Compute the concentration of Li (in wt%) that is required. 5.D2 Gallium arsenide (GaAs) and indium arsenide (InAs) both have the zinc blende crystal structure and are soluble in each other at all concentrations. Determine the concentration in weight percent of InAs that must be added to GaAs to yield a unit cell edge length of 0.5820 nm. The densities of GaAs and InAs are 5.316 and 5.668 g/cm 3 , respectively. Solutions: HW 5. IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS Vacancies and Self-Interstitials 5.1 Calculate the fraction of atom sites that are vacant for copper at its melting temperature of 1084°C (1357 K). Assume an energy for vacancy formation of 0.90 eV/atom. Solution In order to compute the fraction of atom sites that are vacant in copper at 1357 K, we must employ Equation 5.1. As stated in the problem, Q v = 0.90 eV/atom. Thus, N v N = exp - Q v kT = exp - 0.90 eV/atom ( 8.62 × 10 - 5 eV/atom- K ) (1357 K) = 4.56 × 10 - 4

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5.12 Some hypothetical alloy is composed of 25 wt% of metal A and 75 wt% of metal B. If the densities of metals A and B are 6.17 and 8.00 g/cm 3 , respectively, whereas their respective atomic weights are 171.3 and 162.0 g/mol, determine whether the crystal structure for this alloy is simple cubic, face-centered cubic, or body-centered cubic. Assume a unit cell edge length of 0.332 nm.
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