Crystal Structure, Important - Solid State Physics - Lecture Slides, Slides of Solid State Physics

Download Crystal Structure, Important - Solid State Physics - Lecture Slides and more Slides Solid State Physics in PDF only on Docsity! THE “MOST IMPORTANT” CRYSTAL STRUCTURES B.C. WHO CAN GIVE ME AN EXAMPLE Fe eM ie A Pee OF A" SCIENTIFIC BREAKTHROUGH" ? A _An infinite number of mathematiqgans walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You're all idiots”, and pours two beers. — Randgruppenhumor cont'd docsity.com THE “MOST IMPORTANT” CRYSTAL STRUCTURES docsity.com NaCl Structure docsity.com docsity.com • This structure can also be considered as a face-centered-cubic Bravais lattice with a basis consisting of a sodium ion at 0 and a chlorine ion at the center of the conventional cell, at position • LiF, NaBr, KCl, LiI, have this structure. • The lattice constants are of the order of 4-7 Angstroms. )(2/   zyxa docsity.com 2 - CsCl Structure B2 (CsCl Structure • Cesium Chloride, CsCl, crystallizes in a cubic lattice. The unit cell may be depicted as shown. (Cs+ is teal, Cl- is gold) • Cesium Chloride consists of equal numbers of Cs and Cl ions, placed at the points of a body-centered cubic lattice so that each ion has eight of the other kind as its nearest neighbors. 2 - CsCl Structure docsity.com • The translational symmetry of this structure is that of the simple cubic Bravais lattice, and is described as a simple cubic lattice with a basis consisting of a Cs ion at the origin 0 and a Cl ion at the cube center • CsBr & CsI crystallize in this structure.The lattice constants are of the order of 4 angstroms. )(2/   zyxa CsCl Structure docsity.com The Ancient “Periodic Table” (a. GG AIR in ZN) WATER fs Lf. 1, NA) FIRE. a A. EART 4 ® “The periodic table.” 4 - Diamond Structure • The Diamond Lattice consists of 2 interpenetrating FCC Lattices. • There are 8 atoms in the unit cell. Each atom bonds covalently to 4 others equally spaced about a given atom. • The Coordination Number = 4. • The diamond lattice is not a Bravais lattice. C, Si, Ge & Sn crystallize in the Diamond structure. docsity.com Diamond Lattice The Cubic Unit Cell Diamond Lattice docsity.com Zincblende (ZnS) Lattice Zincblende Lattice The Cubic Unit Cell docsity.com Diamond & Zincblende Structures A brief discussion of both of these structures & a comparison. • These two are technologically important structures because many common semiconductors have Diamond or Zincblende Crystal Structures • They obviously share the same geometry. • In both structures, the atoms are all tetrahedrally coordinated. That is, atom has 4 nearest-neighbors. • In both structures, the basis set consists of 2 atoms. In both structures, the primitive lattice  Face Centered Cubic (FCC). • In both the Diamond & the Zincblende lattice there are 2 atoms per fcc lattice point. In Diamond: The 2 atoms are the same. In Zincblende: The 2 atoms are different. docsity.com Diamond & Zincblende Lattices Diamond Lattice The Cubic Unit Cell Zincblende Lattice The Cubic Unit Cell Other views of the cubic unit cell docsity.com The Wurtzite Lattice Wurtzite Lattice  Hexagonal Close Packed (HCP) Lattice + 2 atom basis View of tetrahedral coordination & the 2 atom basis. docsity.com Diamond & Zincblende crystals • The primitive lattice is FCC. The FCC primitive lattice is generated by r = n1a1 + n2a2 + n3a3. • The FCC primitive lattice vectors are: a1 = (½)a(0,1,0), a2 = (½)a(1,0,1), a3 = (½)a(1,1,0) NOTE: The ai’s are NOT mutually orthogonal! Diamond: 2 identical atoms per FCC point Zincblende: 2 different atoms per FCC point Primitive FCC Lattice cubic unit cell docsity.com Wurtzite Crystals • The primitive lattice is HCP. The HCP primitive lattice is generated by r = n1a1 + n2a2 + n3a3. • The hcp primitive lattice vectors are: a1 = c(0,0,1) a2 = (½)a[(1,0,0) + (3)½(0,1,0)] a3 = (½)a[(-1,0,0) + (3)½(0,1,0)] NOTE! These are NOT mutually orthogonal! Wurtzite Crystals 2 atoms per HCP point Primitive HCP Lattice: Hexagonal Unit Cell Primitive Lattice Points docsity.com Inversion • A center of inversion: A point at the center of the molecule. (x,y,z) --> (-x,-y,-z) • A center of inversion can only occur in a molecule. It is not necessary to have an atom in the center (benzene, ethane). Tetrahedral, triangles, pentagons don't have centers of inversion symmetry. All Bravais lattices are inversion symmetric. Mo(CO)6 docsity.com • A plane in a cell such that, when a mirror reflection in this plane is performed, the cell remains invariant. Rotational Invariance & Invariance on Reflection Through a Plane Rotational Invariance about more than one axis Invariance on Reflection through a plane docsity.com Examples • A triclinic lattice has no reflection plane. • A monoclinic lattice has one plane midway between and parallel to the bases, and so forth. docsity.com Axes of Rotation docsity.com Axes of Rotation 6 1-fold 6 9 2-fold 6 © 6 @® 9 9 9 6-fold “nN Objects wi a identity h symmetry: Z cS ot pom docsity.com This type of symmetry is not allowed because it can not be combined with translational periodicity! 5-Fold Symmetry docsity.com