MSE200 Lecture 3 CHAPTER 3 1 3 5 Crystal Structures and Crystal Geometry Instructor Yuntian Zhu 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 http 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 Space Lattice Unit cell Amorphous materials Unit Cell http 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 Simple Body Centered bcc Face centered fcc Type 2 Tetragonal a b c 900 Simple http www mse ncsu edu zhu Body Centered Materials Science Engineering Types of Unit Cells Cont Type 3 Orthorhombic a b c 900 Simple Base Centered Body Centered Face Centered Type 4 Rhombohedral Figure 3 2 a b c 900 Simple http www mse ncsu edu zhu Materials Science Engineering Types of Unit Cells Cont Type 5 Hexagonal a b c 900 1200 Simple Type 6 Monoclinic a b c Base Centered 900 Simple Figure 3 2 Type 7 Triclinic a b c 900 Simple http 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 http www youtube com watch v Co550Yn7QVc feature related BCC Structure http www mse ncsu edu zhu FCC Structure HCP Structure 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 b http 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 Lattice constant a 4R 3 Example 3 1 Packing factor http 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 b http www mse ncsu edu zhu Materials Science Engineering FCC Crystal Structure Cont of atoms in a unit cell Lattice constant 4R a 2 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 z 0 0 0 y x http 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 3 6 3 11 http www mse ncsu edu zhu Materials Science Engineering