http://www.mse.ncsu.edu/zhu Materials Science & Engineering Objectives/Outcomes: •Describe crystal lattices and the unit cell. •Describe the principal metallic crystal structures: the body-centered cubic, the face-centered cubic, and the hexagonal close-packed structures.•Determine directions in the cubic system. MSE200 Lecture 3 (CHAPTER 3.1-3.5) Crystal Structures and Crystal Geometry Instructor: Yuntian Zhuhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering The Space Lattice and Unit Cells • Atoms, arranged in repetitive 3-D pattern in long range order give rise to crystal structure • Why do we care? • An imaginary network of lines, with points at intersections, representing the arrangement of atoms is called space lattice. Unit Cell Space Lattice • Unit cell. • Amorphous materialshttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Crystal Systems and Bravais Lattice • Only 7 different types of unit cells are necessary to create all point lattices. • According to Bravais: 14 standard unit cells.http://www.mse.ncsu.edu/zhu Materials Science & Engineering Types of Unit Cells • Type 1: Cubic Unit Cell  a = b = c   = =  = 900 • Type 2: Tetragonal  a =b  c   = =  = 900 Simple Body Centered (bcc) Face centered (fcc) Simple Body Centeredhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Types of Unit Cells (Cont..) • Type 3: Orthorhombic  a  b  c   = =  = 900 • Type 4: Rhombohedral  a =b = c   = =   900 Simple Base Centered Face Centered Body Centered Simple Figure 3.2http://www.mse.ncsu.edu/zhu Materials Science & Engineering Types of Unit Cells (Cont..) • Type 5: Hexagonal  a = b  c   = = 900  = 1200 • Type 6: Monoclinic  a  b  c   =  = 900  • Type 7: Triclinic  a  b  c       900 Simple Simple Simple Base Centered Figure 3.2http://www.mse.ncsu.edu/zhu Materials Science & Engineering Principal Metallic Crystal Structures • 90% of the metals have either Body Centered Cubic (BCC), Face Centered Cubic (FCC) or Hexagonal Close Packed (HCP) crystal structure. • HCP is denser version of simple hexagonal crystal structure. BCC Structure FCC Structure HCP Structure http://www.youtube.com/watch?v=Co550Yn7QVc&feature=relatedhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Body Centered Cubic (BCC) Crystal Structure • Represented as one atom at each corner of cube and one at the center of cube. • coordination number: • Examples :-  Chromium (a=0.289 nm)  Iron (a=0.287 nm)  Sodium (a=0.429 nm) Figure 3.4 a&bhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering BCC Crystal Structure (Cont..) • # of atoms in the unit cell • Atoms contact each other at cube diagonal 34RLattice constant a = Packing factor: Example 3.1http://www.mse.ncsu.edu/zhu Materials Science & Engineering Face Centered Cubic (FCC) Crystal Structure • FCC structure: 1 atom at each corner and face center • Coordination number: • Atomic Packing Factor: • Examples :-  Aluminum (a = 0.405)  Gold (a = 0.408) Figure 3.6 a&bhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering FCC Crystal Structure (Cont..) • # of atoms in a unit cell 24RLattice constant a =http://www.mse.ncsu.edu/zhu Materials Science & Engineering Hexagonal Close-Packed Structure • The HCP structure is represented as an atom at each of 12 corners of a hexagonal prism, 2 atoms at top and bottom face and 3 atoms in between top and bottom face. • The coordination number is 12, packing factor = 0.74.http://www.mse.ncsu.edu/zhu Materials Science & Engineering HCP Crystal Structure (Cont..) • # of atoms in each HCP unit cell: • Examples:-  Zinc (a = 0.2665 nm, c/a = 1.85)  Cobalt (a = 0.2507 nm, c/a = 1.62) • Ideal c/a ratio is 1.633.http://www.mse.ncsu.edu/zhu Materials Science & Engineering Atom Positions in Cubic Unit Cells • In a cubic unit cell  • Atom positions are located using unit distances along the axes.http://www.mse.ncsu.edu/zhu Materials Science & Engineering Find Direction Indices (0,0,0) z x yhttp://www.mse.ncsu.edu/zhu Materials Science & Engineering Homework • Example Problems (both 4th and 5th versions): 3.1, 3.2, 3.4, 3.5, 3.6, • Regular Problems: see the separate problem file • Reading assignment for the next class (both versions):