Download 6 Questions on Engineering Science Materials - Quiz 3 | ENSC 3313 and more Quizzes Materials science in PDF only on Docsity! ENSC 3313, Fall 2012 Quiz 3 -KEY Name __________________ Answer ONLY 4 of the following 6 questions. Show all work. 1 point each Grade:______/4 1. Given the following data, rank the elements listed from most to least soluble in copper as a substitutional solid solution. Explain your reasoning. Note: DC=diamond cubic Element Atom radius (nm) radius % difference relative to Cu Crystal structure Electro- negativity Valence Rank 1= most soluble Copper 0.128 0% FCC 1.8 +2 -- Zinc 0.133 +3.9% HCP 1.7 +2 2 Lead 0.175 +36.7% FCC 1.6 +2, +4 6 Silicon 0.117 -8.6% DC 1.8 +4 3 Nickel 0.125 -2.3% FCC 1.8 +2 1 Aluminum 0.143 +11.7% FCC 1.5 +3 4 Beryllium 0.144 -10.9% HCP 1.5 +2 5 Similarity in size, crystal structure, etc. make Ni the clear winner. Zn is second based largely on size. Pb is obviously least soluble based on size alone. Si, Al, and Be all have a similar mismatch in size though Si has a slight advantage. Crystal structure breaks the tie favoring FCC over HCP or DC. 2. The fraction of vacant lattice sites in a copper crystal increases with temperature by: Nv /Vo = e − EA kBT " # $ % & ' , where kB=8.62×10-5 eV/K. If at 500oC the fraction of vacancies is Nv / No =1.4×10 −6 , at what temperature would we expect 0.01% of the lattice sites to be vacant? First, calculate the energy to create a vacancy: ( ) eV9.0E104.1ln7731062.8 N NlnTkE A 65 o V BA =→×⋅⋅×−=⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ −= −− Next, find T at Nv/No=0.0001: ( ) )C860(K1134T 0001.0ln1062.8 9.0 N Nlnk ET o5 o V B A =→ ×− = ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − = − Note: Tm=1358oC 3. Due to the difference in atomic size and crystal structure Cu can only dissolve a limited amount of Zn as a substitutional solute atom. Which characterization technique (optical microscopy, scanning electron microscopy, transmission electron microscopy, or x-ray diffraction) could a scientist use to monitor the distorting effect of dissolving Zn into the Cu lattice? Explain! X-ray diffraction. Recall that x-ray diffraction measures specific planes within a crystal structure by recording peaks that satisfy the Bragg equation ( θ=λ sind2 ) where d is the plane spacing. Hence, by monitoring the 2θ value of say the (111) peak, one could calculate the lattice parameters of the crystal with the plane spacing formula ( θ λ =→ ++ = sin2 3a lkh ad 222hkl ) where a is the unit cell dimension and λ is the wavelength of the x-rays.
