3.40 Lecture Summary - MIT OpenCourseWare
9/21/20093.40 Lecture SummarySeptember 16, 2009Basic CrystallographyBCC, FCC, and HCP Crystals1BCC2FCC3HCPBCC MetalsFCC MetalsHCP MetalsFe, W, V, MoCu, Ag, Au, Pt, Al, Ni, PbTi,Zr, Mg, Zn, Be, CdAt high temps: Ti, ZrAt high temps: Fe‐‐[1] Li, J. Modeling Simul. Mater. Sci. Eng. 11 (2003) 173. (AtomEye Visualization Software)[2] NRL. Lattice Crystal Structures (2008) http://cst‐www.nrl.navy.mil/lattice/ .[3] Abbaschian, R. et al. Physical Metallurgy Principles 4th ed. (2009).11
9/21/2009Basic CrystallographyMiller Indices1 Cubic Lattices2 Hexagonal Lattices(010)abc–(1010)a1 a2a3cIntercept Length 1 Intercept Length1 ‐1 Reciprocal010Reciprocal10‐102[1] Li, J. Modeling Simul. Mater. Sci. Eng. 11 (2003) 173. (AtomEye Visualization Software)Basic CrystallographyCrystal Symmetry1 Cubic Lattice Symmetryo Crystallographic families2 Hexagonal Lattice Symmetryo Why (hkil) indexing scheme? Directions: hkl Allows permutation rule! Plane: {hkl} (hkil) Implies permutation rule Permute over (hki)Equivalent Directions 110 –Equivalent Planes: {1010}[1] Li, J. Modeling Simul. Mater. Sci. Eng. 11 (2003) 173. (AtomEye Visualization Software)32
9/21/2009Basic CrystallographyCrystal Symmetry and Stereographic Projection1 What symmetry exists in cubic crystals?o Rotational 2 fold ‐Image removed due to copyright restrictions.Please see p. 3 in Schlom, Darrell G."Stereographic Projection."MatSE535 Course Notes, 2009. 3 fold ‐ 4 fold –2 What symmetry exists in hexagonal crystals?o Rotational 6 foldf ld –3 How do we keep track of crystal symmetries?o Answer: Stereographic ProjectionImage removed due to copyright restrictions.Please see Fig 16.4in Henderson, David, and Daina Taimina.Experiencing Geometry: Euclidean and Non-Euclidean With History.3rd Ed. Upper Saddle River, NJ: Prentice-Hall, 2005.[4]Schlom, D. G. Stereographic Projection Notes. http://www.ems.psu.edu/ schlom/MatSE535/StereoProjection.pdf .[5] Henderson, D. W. (1999) http://www.math.cornell.edu/ dwh/books/eg99/Ch16/Ch16.html4Basic CrystallographyStereographic Projection of Crystal DirectionsImage removed due to copyright restrictions.Please see p. 3, 10 in Schlom, Darrell G."Stereographic Projection."MatSE535 Course Notes, 2009.[1] www.ems.psu.edu/ schlom/MatSE535/StereoProjection.pdf53
9/21/2009Basic CrystallographyStereographic Projection of Crystal Planes[110](110)6[1] ex.phpBasic CrystallographyReading a Stereographic Projection023012013113014001014013012123The plane is 90 degreesfrom the pole directionon a longitudinal line2The directions on aplane are in the plane3Symmetry markersreflect the pointsymmetry of the crystal023104 114011103113 123102112213 112133032133032213 203122122132101 313021212021132212111111121031031121312 313 302 312131131201041041211 221231221 211141141231311 301401 311331 321321 331100110 120 140410 210140 120 110210 410010010310 320230 130130 230320 310311 321 331331301231231311141211141221 321041201221041211 312131131302 312031121031121111 313 101 212111132132021212313021122122213 203133032032213 112112133102113113 123103123011011114 104 114023023(110)0120120130130140140010111114113[1] Abbaschian, R. et al. Physical Metallurgy Principles4thed. (2009).Figure by MIT OpenCourseWare.Adapted from Fig. 1.33 in Reed-Hill and Abbaschian,Physical Metallurgy Principles74
9/21/2009Basic CrystallographySymmetry on the Stereographic 13212001104103014013012114113 123023011102213 112032133203313133122132101 313021021132212111111313 302121031031121312312131131201041041211 221231221 211141141231331311 301401 311331331 321321100110 120 140410 210140 120 110210 410010010310 320230 130130 230320 310311 321 331331 331331301231231311141211141221 321041201221041211 312131131302 312031121031121111 313 101 212111132132021212313021122122213 203313133032032213 112112133102113113 123103123011011114 104 114023023012012013013014014001032[1] Abbaschian, R. et al. Physical Metallurgy Principles 4th ed. (2009).Adapted from Fig. 1.33 inReed-Hill and Abbaschian,Physical MetallurgyPrinciples8Figure by MIT OpenCourseWare.Image courtesy of U.S. Naval Research Laboratory.5
9/21/2009Basic CrystallographyOther Resources"The Stereographic Projection."DoITPoMS, University of Cambridge.[1] ex.php106
MIT OpenCourseWarehttp://ocw.mit.edu3.40J / 22.71J / 3.14 Physical MetallurgyFall 2009For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Physical Metallurgy Principles 7. 9/21/2009 Basic Crystallography Symmetry on the Stereographic Projection [1] Abbaschian, R. et al. Physical Metallurgy Principles 4th ed. (2009). 5 014 013 012 023 011 032 021 031 041 010 041 031 021 032 011 023 012 123 114 113 112 213 212 113 133 132 122 121 131 141 140 130 120 230 231 231
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