Crystal Structure Lab: Understanding Properties of Ionic and Covalent Solids, Lab Reports of Materials science

Download Crystal Structure Lab: Understanding Properties of Ionic and Covalent Solids and more Lab Reports Materials science in PDF only on Docsity! Page 1 of 8 – version 4/14/06 LAB II CRYSTAL STRUCTURE Study Questions: 1. What properties of a strongly bonded covalent solid like diamond can be attributed to its bond type? 2. Explain why covalent bonds are directional but ionic bonds are not. 3. Show the electron notation of Cu, Cu+1, and Cu+2. 4. Explain why a simple ionic crystal like CsCl cannot crystallize into a BCC structure. 5. Graphite is very anisotropic; that is, its properties are dependent on crystallographic direction. Given a cross-section of graphite, try to explain why the electrical conductivity of graphite is 100 times greater in the horizontal direction than in the vertical. 6. Consider an FCC unit cell with the lattice parameter ‘a’. Calculate the diameter of the atoms making up this unit cell. 7. For a cubic crystal system, how many 〈110〉 directions are contained in the (111) plane? 8. For a cubic crystal system, label the following: [100], (112), [123], and (123). _______________________________________________________________ Lab: I. Crystal Structure A lattice is a regular array of points repeated through space. The Bravais lattices are the14 different lattices possible in 3-dimensional space. A crystal structure is a three dimensional arrangement of atoms or groups of atoms in space that can follow any of the 14 Bravais lattices. A primary unit cell is the smallest repeating unit of a crystal structure. Unit cells are parallelograms in two dimensions and parallelepipeds in three dimensions. The size and shape of a unit cell is described, in three dimensions, by the lengths of the three edges (a, b, and c) and the angles between the edges (α, β, and γ). These quantities are referred to as the lattice parameters of the unit cell. For a cubic unit cell, a=b=c and α=β=γ=90°. Note that although different materials may have the same unit cell and crystal structure, they will not have the same lattice parameters. I.1 What would explain the difference in lattice parameters between materials with the same crystal structure (e.g., BCC)? Page 2 of 8 – version 4/14/06 The selection of a unit cell is not unique; the corners of a unit cell may actually be any where within the space of the lattice, provided that repeated translations of this chosen cell will fill all of the space of the lattice. Conventional practice is to choose the smallest, simplest, most expressive and symmetric unit cell for the lattice. I.2 Here is a two-dimensional grid of dots. Draw 3 unique unit cells on this grid, with cell corners on dots, labeling the unit cells as A, B, and C, respectively. Next, determine each cell’s lattice parameters a, b, and α (here, the smallest angle between any a and b). Finally, give the number of dots in each cell (assuming that any lines intersect the exact middle of dots, so a dot on a line will not be a whole dot!). • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • The horizontal distance between adjacent dots is ‘x’ and the vertical distance between adjacent dots is ‘y’. Express ‘a’, ‘b’, and ‘α’ (if necessary) in terms of these. unit cell a b α # dots in unit cell A B C I.3 Other than not having its corners on dots, would the following cell be a valid unit cell? If not, why not? .• • • • • • • • • • • • • • • • • • • • • • • • • • • • Page 5 of 8 – version 4/14/06 III. Three - Dimensional Packing The four most basic crystal structures are: - Simple cubic (SC) - Body centered cubic (BCC) - Face centered cubic (FCC) - Hexagonal close packed (HCP) You should develop a complete understanding of the geometry and atomic arrangement of each of these structures. Make a sketch of each of these structures below. III.1 Simple Cubic III.2 Body Centered Cubic III.3 Face Centered Cubic III.4 Hexagonal Close Packed Page 6 of 8 – version 4/14/06 Now construct each of these four crystal structures using Styrofoam balls and toothpicks. You should strive to completely understand the atomic packing and geometry of each of these structures. Begin by creating the individual layers, and then stack each layer together to compose the structure. To test your understanding you should discuss the similarities and differences between the structures in your team. Be sure that you can completely visualize each structure. III.5 For each structure determine the following: Structure atoms/cell coordination # APF a = f(r) SC BCC FCC HCP Which two structures show the greatest similarities? _________ and ________ Page 7 of 8 – version 4/14/06 Consider the BCC and FCC structures you have built: III.6 Which crystal has the largest interstitial site? _________ III.7 Does the size of the interstitial sites in each crystal type correlate with APF? (i.e., does a higher APF mean smaller interstitial sites?) _________ III.8 There are 2 different types of interstitial sites for BCC crystals. How many of each type are there? Indicate in a sketch where each is. III.9 There are 2 different types of interstitial sites for FCC crystals. How many of each type are there? Indicate in a sketch where each is. III.10 If material properties (tensile strength, conductivity, etc) are a function of crystal structure, will the measured properties of some materials vary with crystal orientation? How can you explain this?