Crystal Structures - Basic Concepts PDF

SCI 401 GENERAL CHEMISTRY Chemistry of Engineering Materials Basic Concepts of Crystal Structures CRYSTAL STRUCTURES UNIT CELLS DENSITY COMPUTATIONS TYPES OF CRYSTALS AMORPHOUS SOLIDS  LEARNING OBJECTIVES ► Describe the basic structural unit or building bloc...

SCI 401 GENERAL CHEMISTRY Chemistry of Engineering Materials Basic Concepts of Crystal Structures CRYSTAL STRUCTURES UNIT CELLS DENSITY COMPUTATIONS TYPES OF CRYSTALS AMORPHOUS SOLIDS  LEARNING OBJECTIVES ► Describe the basic structural unit or building block of the crystal structure. ► Determine to compute the density of a solid given its unit cell. ► Classify the four types of crystals. ► Describe the characteristics of amorphous solids.  SOLIDS A solid is defined as a state of matter with a definite shape and volume. The particles in a solid (atoms, molecules, ions) are tightly- packed compared to liquids and gases. The arrangement may be a regular lattice called a crystal or an irregular arrangement called an amorphous solid. CATEGORIES OF SOLIDS CATEGORIES OF SOLIDS CRYSTAL STRUCTURES  Chemistry of Engineering Materials: Basic Concepts of Crystal Structures CRYSTAL STRUCTURES UNIT CELLS DENSITY COMPUTATIONS TYPES OF CRYSTALS AMORPHOUS SOLIDS UNIT CELLS https://www.youtube.com/watch?v=qAeaHYSX0hs Three Types of Unit Cells 1. Simple Cubic or Primitive (SC) 2. Body-Centered Cell (BCC) 3. Face-Centered Cell (FCC)  The Simple Cubic Crystal Structure The possibility of a unit cell that consists of atoms placed only at the corners of a cube do exist and it is called the simple cubic (SC) crystal structure. Polonium, a metalloid or a semi-metal is the only simple-cubic element that has a relatively low atomic packing factor. SEVEN TYPES OF PRIMITIVE UNIT CELLS The Face-Centered Cubic Crystal Structure The Face-Centered Cubic Crystal Structure  The Face-Centered Cubic Crystal Structure Example 1. Calculate the volume of an FCC unit cell in terms of atomic radius R. The Face-Centered Cubic Crystal Structure The Face-Centered Cubic Crystal Structure Important Characteristics of a Crystal Structure Important Characteristics of a Crystal Structure For FCCs, the coordination number is 12. Front face atoms has four nearest neighboring atoms around it, four face atoms that are link from behind, and four other equivalent face atoms positioned in the next unit cell to the front which is not shown. Atomic Packing Factor Atomic Packing Factor The Body-Centered Cubic Crystal Structure A body-centered cubic (BCC) is another common metallic crystal structure that also has a cubic unit cell with atoms located at all eight corners and a single atom at the center of the cube. Corner atoms and center touch one another along with the diagonal of the cube, and unit cell length a and atomic radius R are related by the way of The Body-Centered Cubic Crystal Structure From Equation 2, the number of atoms per BCC is 2. The BCC crystal structure has 8 coordination number. The atomic packing factor for BCC 0.68 which is lower than for FCC, since BCC has lesser coordination number. Edge Length and Atomic Radius Relationships The Hexagonal Close-Packed Crystal Structure The final common metallic crystal structure is the hexagonal close-packed (HCP). The top and bottom faces of the unit cell consist six atoms that form regular hexagons and surround a single atom in the center. Between the top and bottom planes, there is another plane that provides three additional atoms to the unit cell. The atoms in this midplane have as nearest neighbors atoms in both of the adjacent two planes. The Hexagonal Close-Packed Crystal Structure The Hexagonal Close-Packed Crystal Structure To compute the number of atoms per unit cell for HCP crystal structure, the formula is shown below: One-sixth of each corner atom is designated to a unit cell instead of 8 as with the cubic structure. This is because, HCP has 6 corner atoms in each of the top and bottom faces for a total of 12 corner atoms, 2 face center atoms (one from each of the top and bottom faces), and 3 midplane interior atoms. Using Equation 5, the value of N for HCP can be found. The Hexagonal Close-Packed Crystal Structure Crystal Structure  Chemistry of Engineering Materials: Basic Concepts of Crystal Structures CRYSTAL STRUCTURES UNIT CELLS DENSITY COMPUTATIONS TYPES OF CRYSTALS AMORPHOUS SOLIDS  Density Computations A theoretical density (ρ) can be computed with a knowledge of the crystal structure of a metallic solid through the relationship Where n = number of atoms associated with each unit cell A = atomic weight VC = volume of the unit cell NA = Avogadro’s number (6.022 x 1023 atoms/mol) Density Computations Density Computations Density Computations Density Computations  Chemistry of Engineering Materials: Basic Concepts of Crystal Structures CRYSTAL STRUCTURES UNIT CELLS DENSITY COMPUTATIONS TYPES OF CRYSTALS AMORPHOUS SOLIDS  Types of Crystals In determining the structures and properties of crystals, such as melting point, density, and hardness it is important to consider the kinds of forces that hold the particles together. The classification of any crystal has four types: ionic, covalent, molecular, or metallic.  Ionic Crystals There are two important characteristics of ionic crystals and they are as follows: (1) They are composed of charged species (2) anions and cations are generally quite different in size. The radii of the ions must be known because it is helpful in understanding the structure and stability of these compounds. It is hard to measure the radius of an individual ion but sometimes it is possible to come up with an estimation.  Ionic Crystals For example, the crystal which has a FCC lattice shows that the edge length of the unit cell of NaCl is twice the sum of the ionic radii of Na+ and Cl-. Getting the values of ionic radius given in some references: Na+=95pm Cl-=181pm We can calculate the length of the edge to: 2*(95+181)pm = 552pm  Ionic Crystals The edge length shown was determined experimentally and has a value of 564pm. Ionic Crystals Ionic Crystals Ionic Crystals Covalent Crystals Covalent Crystals Covalent Crystals Molecular Crystals Molecular Crystals Molecular Crystals SO2 Molecular Crystals Metallic Crystals Metallic Crystals Metallic Crystals Metallic Crystals General Properties of Crystals  Chemistry of Engineering Materials: Basic Concepts of Crystal Structures CRYSTAL STRUCTURES UNIT CELLS DENSITY COMPUTATIONS TYPES OF CRYSTALS AMORPHOUS SOLIDS Amorphous Solids Amorphous Solids Amorphous Solids Amorphous Solids