Welcome to 3.091

Lecture 15 October 14, 2009

Introduction to Crystallography Images by Inductiveload at Wikipedia. The Big Picture electronic structure  bonding  state of aggregation

Bohr atom primary: gas Bohr-Sommerfeld  ionic liquid quantum numbers  covalent solid Aufbau principle  metallic  multielectron atoms  van der Waals 3.091  Periodic Table patterns octet stability secondary:  dipole-dipole  London dispersion  hydrogen solid : that which is dimensionally stable, i.e., has a volume of its own classifications of solids:  bonding type  atomic arrangement classifications of solids:  bonding type  atomic arrangement

white

Tetragonal Sn a = b = c, � = � = � =90o

1.40 7.03 a b

1.62 290.4 c 16.31 301.25 � � 3.67/7.7 0.228 �

11.50oC 0.668

Image by MIT OpenCourseWare. Photo by Will Wysong on Flickr.

Figure 12.4 Figure 12.4 4 Lattice Types

Bravais Simple Volume Base Face Parameters Lattice (P) Centered (I) Centered (C) Centered (F)

a = a = a Triclinic 1 2 3 �12 = �23 = �31

a1 = a2 = a3 0 Monoclinic �23 = �31 = 90 0 �12 = 90

a1 = a2 = a3 Orthorhombic 0 �12 = �23 = �31 = 90

a1 = a2 = a3 Tetragonal 0 �12 = �23 = �31 = 90 7 Crystal Classes

a1 = a2 = a3 Trigonal 0 �12 = �23 = �31 < 120

a1 = a2 = a3 Cubic 0 �12 = �23 = �31 = 90

a1 = a2 = a3 a3 0 a Hexagonal �12 = 120 2 0 �23= �31= 90 a1

Image by MIT OpenCourseWare.

Courtesy of National Academy of Sciences, U. S. A. Used with permission. Source: Caspar, Donald L. D., and Eric Fontano. "Five-fold Symmetry in Crystalline Quasicrystal Lattices." PNAS 93 (December 1996): 14271-14278. Copyright © 1996 National Academy of Sciences, U.S.A. Figure 12.5

Averill, B., and P. Eldredge. Chemistry: Principles, Patterns, and Applications. Flat World Knowledge, 2011. ISBN: 9781453331224.

Figure 12.5c

Averill, B., and P. Eldredge. Chemistry: Principles, Patterns,and Applications. Flat WorldKnowledge, 2011. ISBN: 9781453331224. Figure 12.10

Image by Eloy at Wikipedia. © Pearson. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. Source: Fig. 10.24 in McMurry, John, and Robert C. Fay. Chemistry. 4th ed. Upper Saddle River, NJ: Pearson/Prentice-Hall, 2004. ISBN: 0131402218. © Pearson. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. Source: Fig. 10.24 in McMurry, John, and Robert C. Fay. Chemistry. 4th ed. Upper Saddle River, NJ: Pearson/Prentice-Hall, 2004. ISBN: 0131402218. © Pearson. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. Source: Fig. 10.24 in McMurry, John, and Robert C. Fay. Chemistry. 4th ed. Upper Saddle River, NJ: Pearson/Prentice-Hall, 2004. ISBN: 0131402218. © Pearson. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. Source: Fig. 10.24 in McMurry, John, and Robert C. Fay. Chemistry. 4th ed. Upper Saddle River, NJ: Pearson/Prentice-Hall, 2004. ISBN: 0131402218. All M. C. Escher works © 2010 The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com. All M. C. Escher works © 2010 The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com. All M. C. Escher works © 2010 The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com. Figure 12.5a

Averill, B., and P. Eldredge. Chemistry: Principles, Patterns,and Applications. Flat World Knowledge, 2011. ISBN: 9781453331224.

All M. C. Escher works © 2010 The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com. All M. C. Escher works © 2010 The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com All M. C. Escher works © 2010 The M. C. Escher Company – The Netherlands. All rights reserved. www.mcescher.com a = f(r) 2r 4r/√3 2√2r or 4r = √4 a √3 a √2 a packing density 0.5 0.68 0.74 3 1 8 x = 1 1 2 8 1 6 x = 3 1 2 2 4 3 = 4 lattice FCC points/unit cell

Averill, B., and P. Eldredge. Chemistry: Principles, Patterns, and Applications. Flat World Knowledge, 2011. ISBN: 9781453331224.

4r a = 407 pm

a

Image by MIT OpenCourseWare. Adapted from Fig. 5 in Aquaro, Donato. "Thermal Mechanical Analysis of a Solid Breeding Blanket." Fusion Engineering and Design 69 (2003): 511-518. Courtesy of Elsevier, Inc., http://www.sciencedirect.com. Used with permission. Houses at L’Estaque

Georges Braque

1908 Courtesy of Rod Nave/HyperPhysics. Used with permission. Courtesy of Rod Nave/HyperPhysics. Used with permission. Colored Golds: FCC with zest pure Au yellow

Cu(low) yellow

Cu(high) pink Ni white Al purple In blue Cr green MIT OpenCourseWare http://ocw.mit.edu

3.091SC Introduction to Solid State Chemistry Fall 2009

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