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Masters Engineering

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MASTERS ENGINEERING 4.1. The equilibrium fraction of lattice sites that are vacant in gold at 800C is 2.5  10−5. Calculate the number of vacancies (per meter cubed) at 800C. Assume a density of 18.45 g/cm3 for Au (at 800C). GIVEN: 𝑁𝐴 = 6.022 𝑥 1023 𝑎𝑡𝑜𝑚𝑠/𝑚𝑜𝑙 𝐴𝐴𝑔 = 196.97 𝑔/𝑚𝑜𝑙 ρ = 18.45 𝑔/𝑐𝑚3 Au = 800C FORMULA: 𝑁𝐴𝑔 = 𝑁𝐴 ρ𝐴𝑔 𝐴𝐴𝑔 𝑁𝑣 = (2.5 𝑥 10−5 )𝑁𝐴𝑔 SOLUTION: 𝑔3 𝑎𝑡𝑜𝑚𝑠 𝑐𝑚3 ) (18.45 𝑐𝑚 ) (106 3 ) 𝑚𝑜𝑙 𝑚 𝑔 196.97 𝑚𝑜𝑙 𝑎𝑡𝑜𝑚𝑠 𝑚3 (6.022 𝑥 1023 𝑁𝐴𝑔 = 𝑁𝐴𝑔 = 5.64 𝑥 1028 𝑁𝑣 = (2.5 𝑥 10−5 ) (5.64 𝑥 1028 ∴ 𝑁𝑣 = 1.41 𝑥 1024 𝑎𝑡𝑜𝑚𝑠 ) 𝑚3 𝑣𝑎𝑐𝑎𝑛𝑐𝑖𝑒𝑠 𝑚3 4.38. For a BCC single crystal, would you expect the surface energy for a (100) plane to be greater or less than that for a (110) plane? Why? (Note: You may want to consult the solution to Problem 3.60 at the end of Chapter 3.) ANSWER: Depending on the planar or packing density, surface energy can be calculated. To increase the planar or packing density, atomic forces must be activated, which results in more neighboring atoms being formed. Surface energy at a lower level will be completed at this point. GIVEN: (BCC Unit = 100) Unit Cell's Edge = 4𝑅 √3 Area = 16𝑅2 √3 FORMULA: 𝑃𝐷100 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡? ...
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