Relationship between directions and planes for cubic

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Relationship between directions and planesFor cubic crystal structures,the [xyz] direction is normalto the (xyz) plane.
MSE160H1 Molecules and MaterialsWinter 2016MSE160H1 Molecules and MaterialsWinter 201621Crystallographic PlanesWe want to examine the atomic packing ofcrystallographic planesIron foil can be used as a catalyst. The atomicpacking of the exposed planes is important.a)Draw (100) and (111) crystallographic planes for Fe.b)Calculate the planar density for each of these planes.
MSE160H1 Molecules and MaterialsWinter 2016MSE160H1 Molecules and MaterialsWinter 201622Linear DensityLinear Density of Atoms{LD =ex:linear density of Al in [110]directiona= 0.405 nma[110]Unit length of direction vectorNumber of atoms# atomslength13.5 nma22LD-==
MSE160H1 Molecules and MaterialsWinter 2016MSE160H1 Molecules and MaterialsWinter 201623Atomic density along crystallographic planesPlanar Density:Crystallographic planes that are equivalent have the same atomic planardensity. The plane of interest is positioned so as to pass through atomcenters.Planar density is the fraction of total crystallographic plane area that isoccupied by atoms.ExampleWe want to examine the atomic packing of crystallographic planesIron foil can be used as a catalyst. The atomic packing of theexposed planes is important.a)Draw (100) and (111) crystallographic planes for Fe.b)Calculate the planar density for each of these planes.
MSE160H1 Molecules and MaterialsWinter 2016MSE160H1 Molecules and MaterialsWinter 201624Planar Density of (100) IronSolution:At T < 912 C iron has the BCC structure.(100)Radius of ironR= 0.1241 nmR334a=2D repeat unit=Planar Density =a21atoms2D repeat unit=nm2atoms12.1m2atoms= 1.2 x 101912R334area2D repeat unit
MSE160H1 Molecules and MaterialsWinter 2016MSE160H1 Molecules and MaterialsWinter 201625Planar Density of (111) Iron(111) planes1 atom in plane/ unit surface cellatoms in planeatoms above planeatoms below planeah23=a21==nm2atoms7.0m2atoms0.70 x 101932R316Planar Density =atoms2D repeat unitarea2D repeat unit33322R316R342a3ah2area====
MSE160H1 Molecules and MaterialsWinter 2016MSE160H1 Molecules and MaterialsWinter 201626X-Ray DiffractionA diffraction grating must have a spacing comparable to the wavelengthof the diffracted radiationto cause scattering and constructiveinterference for the electromagnetic radiation (beam)cannot resolve spacings±λfor x-ray diffraction, the grating is a crystal, and the spacing is thedistance between parallel planes of atoms.
MSE160H1 Molecules and MaterialsWinter 2016MSE160H1 Molecules and MaterialsWinter 201627X-Rays to Determine Crystal StructureX-rayintensity(fromdetector)θθcd=nλ2 sinθcMeasurement ofcritical angle,Tc,allows computation ofthe planar spacing,d.Incoming X-raysdiffractfrom crystal planes.reflections mustbe in phase fora detectable signalspacingbetweenplanesdθλθextradistancetravelledby wave2
MSE160H1 Molecules and MaterialsWinter 2016MSE160H1 Molecules and MaterialsWinter 201628X-RayDiffraction Pattern(110)(200)(211)zxyabcDiffraction angle 2θDiffraction pattern for polycrystallineα-iron (BCC)Intensity (relative)zxyabczxyabc

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Term
Spring
Professor
N/A
Tags
Crystallography, Crystal, Crystal system, Atomic packing factor, crystallographic planes

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