Understanding X-Ray Diffraction in Materials Science
School
IIT Kanpur**We aren't endorsed by this school
Course
ESO 225
Subject
Material Science
Date
Dec 11, 2024
Pages
2
Uploaded by ChiefFerret4580
ESO225, Introduction to Materials Science and EngineeringDue: 07-11-2024Assignment 9Total: 60 Marks Answer all the questions!1.You have a mixture of 50 grams of pure silver powder and 50 grams of pure copper powder at room temperature. a) Make a quantitatively correct x-ray diffraction pattern of the powder mixture showing the two theta locations of the (111) and (200) you expect to observe (you may assume that all peak intensities are the same). Assume that you are using Cu Kα x-rays (λ = 0.154 nm) to collect your XRD data.b) The powder mixture is heated to 1000°C and held there until all of the powder has melted. The resulting liquid is cooled to 800°C and then held at that temperature. If you perform x-ray diffraction using Cu Kα x-rays (λ = 0.154 nm) on the alloy held at 800°C, describe in words how the resulting diffraction pattern will be different from the pattern in part a).aAu=0.407nm, aCu=0.362nm [15]2.If the free energy per unit area of the {100} is smaller than the free energy per unit area associated with all of the other atomic planes (referred to below as γsv(isotropic))the equilibrium shape of the particles would be cubes rather than spheres. Calculate the ratio of solid-vapor interfacial energies γsv(isotropic)/γ sv{100} such that there will be a driving force for solid spherical particles of a given material to transform into cube-shaped particles. The term γsv(isotropic) refers to the case where the solid-vapor interfacial energy per unit area is independent of crystallographic orientation. [15]3.During nucleation, atoms come together forming crystal-like clusters that often break apart before they can form a stable
nucleus. Use the equations below to make two quantitative plots, as a function of undercooling, of the number of crystal-like clusters (nr) composed of 100 atoms that you would expect to find in 50,000 cm3 of copper. Your undercooling (∆T) should range from 0-250K (forcopper, this means temperatures ranging from 1356 down to 1106K). Assume that the clusters of atoms are spherical in shape.Plot 1: Use a linear scale for both nr (y-axis) and T (x-axis).Plot 2: Use a natural logarithm (ln) scale for nr (y-axis) and a linear scale for T (x-axis).The following data for copper will be useful: The atomic volume of liquid copper is 1.6 x 10-29m3/atom, γis 0.177 J/m2, ∆Hv=209 J/g, ρ=9g/cm3, k= 1.38 x 10-23J/atom-K, Tm=1356K.nr is the number of spherical clusters of radius r and n0 is the total number of atoms in the system. [20]4.A brass alloy is known to have a yield strength of 275 MPa, a tensile strength of 380 MPa, and an elastic modulus of 103 GPa. A cylindrical specimen of this alloy 12.7 mm in diameter and 250 mm long is stressed in tension and found to elongate 7.6 mm.On the basis of the information given, is it possible to compute the magnitude of the load that is necessary to produce this change in length? If so, calculate the load. If not,explain why you cannot calculate the load. [10]