Vegard's Law states that the lattice parameter of many simple alloys is expected to follow simple...
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Vegard's Law states that the lattice parameter of many simple alloys is expected to follow simple rule of mixtures in which the lattice parameter of the alloy is a simple weighted average of the lattice parameter of the two end members. An example of this relationship is show below in the phase diagram for the Cu-Ni system. 0363. 0362- 0.361- 0360 - 0350 0358- 0.357 0356- 0.355- 0354 - 0.353 - 0.352- 0.3514 10 20 30 40 50 60 70 80 90 100 110 Cu content (atom%) Figure 2.53 Lattice parameter as a function of Cu content in a Ni-Cu alloy. The following diffraction pattern of unknown Cu-Ni was taken using monochromatic radiation with a wavelength of 0.0709 nm. Diffraction Pattern of Unknown Ni-Cu Alloy (331) 50.98° (420) 52.41° (422) 57.86° 50 52 54 56 58 60 Two Theta (Degrees) a) Use Bragg's Law to calculate the d-spacing of each of the peaks in the diffraction pattern above. b) Using the hkl indices provided (peaks are labeled), calculate the lattice parameter, a, of the unknown alloy from each of the diffraction peaks Recall for a cubic crystal structure: a drkl = Vh2 + k2 + [² c) Using an average of the above lattice parameters and the phase diagram above estimate the composition of the Cu-Ni alloy. Intensity (Arb Units) Lattice parameter (nm) Vegard's Law states that the lattice parameter of many simple alloys is expected to follow simple rule of mixtures in which the lattice parameter of the alloy is a simple weighted average of the lattice parameter of the two end members. An example of this relationship is show below in the phase diagram for the Cu-Ni system. 0363. 0362- 0.361- 0360 - 0350 0358- 0.357 0356- 0.355- 0354 - 0.353 - 0.352- 0.3514 10 20 30 40 50 60 70 80 90 100 110 Cu content (atom%) Figure 2.53 Lattice parameter as a function of Cu content in a Ni-Cu alloy. The following diffraction pattern of unknown Cu-Ni was taken using monochromatic radiation with a wavelength of 0.0709 nm. Diffraction Pattern of Unknown Ni-Cu Alloy (331) 50.98° (420) 52.41° (422) 57.86° 50 52 54 56 58 60 Two Theta (Degrees) a) Use Bragg's Law to calculate the d-spacing of each of the peaks in the diffraction pattern above. b) Using the hkl indices provided (peaks are labeled), calculate the lattice parameter, a, of the unknown alloy from each of the diffraction peaks Recall for a cubic crystal structure: a drkl = Vh2 + k2 + [² c) Using an average of the above lattice parameters and the phase diagram above estimate the composition of the Cu-Ni alloy. Intensity (Arb Units) Lattice parameter (nm)
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Related Book For
Fundamentals of Analytical Chemistry
ISBN: 978-0495558286
9th edition
Authors: Douglas A. Skoog, Donald M. West, F. James Holler, Stanley R. Crouch
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