PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Introduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering1How do atoms arrange themselves to form solids?•Fundamental concepts and language•Unit cells•Crystal structures Face-centered cubic Body-centered cubic Hexagonal close-packed•Close packed crystal structures•Density computations•Types of solidsSingle crystalPolycrystallineAmorphous3.7–3.11 Crystallography – Not Covered / Not Tested3.16 Diffraction – Not Covered / Not Tested Learning objectives #5, #6 - Not Covered / Not TestedChapter OutlineIntroduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering2Types of SolidsCrystalline material: periodic arraySingle crystal: periodic array over the entire extent of the materialPolycrystalline material: many small crystals or grainsAmorphous: lacks a systematic atomic arrangementCrystalline AmorphousSiO2Introduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering3Crystal structureIt is useful to consider atoms as being hard spheres with a radius. The shortest distance between two like atoms is one diameter.We can also consider crystalline structure as a lattice of points at atom/sphere centers.Introduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering4Unit CellThe unit cell is the building block for the crystal structure. Repetition of the unit cell generates the entire crystal.Different choices of unit cells possible, generally choose parallelepiped unit cell with highest level of symmetryExample: 2D honeycomb net can be represented by translation of adjacent atoms that form a unit cell for this 2D crystalline structureExample of 3D crystalline structure:Introduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering5Metallic Crystal StructuresMetals are usually polycrystalline; although formation of amorphous metals is possible by rapid coolingThe atomic bonding in metals is non-directional  large number of nearest neighbors and dense atomic packingAtom (hard sphere) radius, R, defined by ion core radius - typically 0.1 - 0.2 nm The most common types of unit cells are the Faced-centered cubic (FCC)Body-centered cubic (BCC) Hexagonal close-packed (HCP).Introduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering6Face-Centered Cubic (FCC) Crystal Structure (I)Atoms are located at each of the corners and on the centers of all the faces of cubic unit cellCu, Al, Ag, Au have this crystal structureTwo representations of the FCC unit cellIntroduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering7The hard spheres (atom cores) touch along diagonal the cube edge length, a= 2R2The coordination number, CN = the number of closest neighbors to which an atom is bonded = number of touching atoms, CN = 12Number of atoms per unit cell, n = 4. In FCC unit cell we have:6 face atoms shared by two cells: 6 x 1/2 = 38 corner atoms shared by eight cells: 8 x 1/8 = 1Atomic packing factor, APF = fraction of volume occupied by hard spheres = (Sum of atomic volumes)/(Volume of cell) = 0.74 (maximum possible)Face-Centered Cubic Crystal Structure (II)RaIntroduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering8Atomic Packing FractionAPF= Volume of Atoms/ Volume of CellVolume of Atoms = n (4/3) R3Volume of Cell = a3Introduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering9  = mass/volume = (atoms in the unit cell, n ) x (mass of an atom, M) / (the volume of the cell, Vc) Density ComputationsAtoms in the unit cell, n = 4 (FCC)Mass of an atom, M = A/NA A = Atomic weight (in amu or g/mol) Avogadro number NA = 6.023  1023 atoms/molThe volume of the cell, Vc = a3 (FCC)a = 2R2 (FCC)R = atomic radius AcNVnAIntroduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering10Density ComputationsAcNVnAIntroduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering11The hard spheres touch one another along cube diagonal  the cube edge length, a= 4R/3The coordination number, CN = 8Number of atoms per unit cell, n = 2Center atom (1) shared by no other cells: 1 x 1 = 18 corner atoms shared by eight cells: 8 x 1/8 = 1Atomic packing factor, APF = 0.68Corner and center atoms are equivalentBody-Centered Cubic Crystal Structure (II)aIntroduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering12Hexagonal Close-Packed Crystal Structure (I)HCP is one more common structure of metallic crystals Six atoms form regular hexagon, surrounding one atom in center. Another plane is situated halfway up unit cell (c-axis), with 3 additional atoms situated at interstices of hexagonal (close-packed) planesCd, Mg, Zn, Ti have this crystal structureIntroduction To Materials Science, Chapter 3, The structure of crystalline solidsUniversity of Virginia, Dept. of Materials Science and Engineering13Unit cell has two lattice parameters a and c. Ideal ratio c/a = 1.633The coordination number, CN = 12 (same as in FCC)Number of atoms per unit cell, n = 6. 3 mid-plane atoms shared by no other cells: 3 x 1 = 312 hexagonal corner atoms shared by 6 cells: 12 x 1/6 = 22 top/bottom plane center atoms shared by 2 cells: 2 x 1/2 = 1Atomic packing factor, APF = 0.74 (same as in FCC) All atoms are equivalent