Crystalline Solids Revised: 4/28/15 CRYSTALLINE SOLIDS. Adapted from Experiments by A.B. Ellis et al, ICE LABORATORY NOTEBOOK

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1 CRYSTALLINE SOLIDS Adapted from Experiments by A.B. Ellis et al, ICE LABORATORY NOTEBOOK All work for this experiment must be recorded, attached, or answered in the ELN. Create a Pre/InLab page in this week s Experiment folder. An objectives and observations (data) sections are required, chemical/equipment tables and procedures are NOT required. No Post Lab page is required for this experiment. INTRODUCTION Many exciting discoveries are found at the interfaces between traditional scientific disciplines such as the interaction between researchers in chemistry, physics, and engineering that has led to the emerging field of material science: the study of the synthesis, composition, and properties of solids. In this experiment we will investigate the composition and properties of one class of material crystalline solids containing cube-like building blocks called cubic unit cells. Primitive and body centered cubic unit cells are created from two different arrangements of square array layers. Layering of close packed arrays creates face centered cubic unit cells. (You should read Crystal Structures with Cubic Unit Cells before proceeding further.) Students will investigate models to determine composition and observe the properties of actual samples of a metal alloy called nitinol and a superconductor with the formula YBa 2 Cu 3 O 7. Nitinol (NiTi) Smart materials have the ability to respond to physical stimulus in a predictable, preprogrammed way. One such material, the metal alloy NiTi, is called a memory metal because it can be twisted or bent without causing crystal defects and returns to its original shape when heated. This alloy is referred to as "nitinol", a name derived from the lab where it was discovered in 1965: Nickel Titanium - Naval Ordinance Laboratory. At high temperatures, the atoms of the nitinol are arranged in the orderly crystalline austenite form that resists distortion. At low temperatures, the atoms of nitinol are arranged in the more disordered martensite form that can easily be twisted and bent. The difference between the two forms can be understood by looking at the unit cell of each: austenite has a regular body centered cubic structure while 1

2 martensite has a related, but distorted structure. During the process of cooling, the high temperature austenite exists until the transition temperature (the point where the solid-solid transition occurs between austenite and martensite) is reached. At this temperature the distortion to the martensite form can be seen by rotating the body center cubic unit cell of the austenite form on a diagonal and then pulling the middle layer of atoms (outlined in blue) to the right while pushing the top and bottom layers to the left (Figure 1). 45 o rotation high temperature austenite form beginning of distortion at transition temperature Figure 1. The distortion of the austenite form of NiTi. If the alloy is bent while in the lower temperature martensite phase, gentle heating of the metal above the transition temperature (into the austenite phase) restores the original shape. If a new permanent shape is desired, the metal can be annealed (programmed) at very high temperatures (in a flame) to retain the "memory" of a new shape. Slightly altering the one to one ratio of Ni to Ti (i.e., Ni 0.99 Ti 1.01 ) changes the transition temperature. Therefore, at room temperature one sample of nitinol can be in the martensite form, while another can be in the austenite form. The Superconductor (YBa 2 Cu 3 O 7 ) This superconductor is commonly called "1-2-3" because of the yttrium, barium, copper atom ratio. The three dimensional structure of the superconductor is very similar to that of perovskite, CaTiO 3 (Figure 2). The perovskite structure can be found by starting at a face centered cubic unit cell then moving down ½ the cell s edge length and over ½ the face diagonal s length. The smaller cations (Ti 4+ ) in the octahedral holes of the fcc body center become the corner spheres and the larger cations (Ca 2+ ) that were on the fcc corner are now the body center. The anions (O 2- ) that were in the fcc face center are now on the edges. 2

3 shift vertically 1 / 2 edge length & over 1 / 2 a face diagonal Ti 4+ face centered cubic unit cell Ca 2+ O 2- perovskite structure Figure 2. The unit cell of CaTiO 3. The unit cell of YBa 2 Cu 3 O 7 is created by stacking three pervoskite unit cells. The calcium ions (Ca 2+ ) are replaced by Ba 2+ in the 1 st and 3 rd unit cells and Y 3+ in the 2 nd unit cell while the titanium ions (Ti 4+ ) are replaced by Cu 2+ and/or Cu 3+. Two oxide ions (O 2- ) are omitted from the 1 st and 3 rd unit cells and four oxides are omitted from the 2 nd unit cell. (Figure 3). Cu 2+ /Cu 3+ Ba 2+ O 2- Y 3+ Figure 3. The unit cell of YBa 2 Cu 3 O 7. 3

4 In this experiment the interaction between a cooled superconductor and a magnet will be observed. Understanding this and other properties of superconductors requires knowledge of band theory. "Band theory" is a bonding model for solids that explains conductivity by assuming that a higher energy level exists above valence electrons called a "conduction band". The electrons in this band are not attached to (localized on) individual atoms, but are free to move (delocalized) throughout the entire solid. The "band gap" is the energy needed to promote an electron from the lower energy valence band to the higher energy conduction band (Figure 4). Electrons cannot cross the large band gap of insulators (nonmetals), thus no electrical current can be produced. Depending on conditions, electrons can cross the moderately sized band gap in semiconductors (semimetals) to create a current. Electrons can always cross the small band gap of conductors (metals) with the input of ordinary thermal energy (at room temp) to create a current. Raising the temperature of a metal results in thermally excited atoms that cause electron scattering in the conduction band and thus, lower conductivity (higher resistance). In ordinary metals resistance decreases as the temperature decreases but still remains greater than zero because of scattering of electrons caused by defects in crystals. However, at very low temperatures, some Figure 4. Band Theory for solids. metals (or metal oxides) undergo a solid-solid transition and the resistance drops to zero, allowing electrical current to flow without hindrance. This remarkable phenomenon is called "superconductivity". In superconductors, current flows indefinitely and is caused by pairs of electrons called "Cooper pairs". The combined momentum of Cooper pairs is not affected by 4

5 electron scattering and resistance drops to zero below some critical phase transition temperature (T c ). Above T c, the Cooper pairs dissociate, superconductivity ceases, and the solid becomes normal conducting material. The Tc for YBa 2 Cu 3 O 7 is 95 K. In this experiment, a Samarium containing magnet will be brought near the YBa 2 Cu 3 O 7 superconductor cooled in N 2 (l) (77 K). When the magnet s magnetic field lines penetrate the superconductor a current is induced. This current creates an opposing magnetic field in the superconductor which repels the magnet and leads to its levitation. (Figure 5) magnet super conductor perpendicular current induced in superconductor magnetic field induced in superconductor (perpendicular to current & antiparallel to magnet's field Figure 5. Induced current and magnetic field of the superconductor. The height at which the magnet is levitated reflects the tendency to minimize the total energy of the system: The internal energy of the superconductor increases as the magnet moves closer to the surface and the gravitational potential energy increases as the magnet moves further away from the surface. The levitation height reflects the minimum total energy based on the sum of these two opposing forces. In this experiment students will inspect models of monoatomic and polyatomic solids containing cubic unit cells to gain a clear understanding of their three dimensional structure. The memory and acoustic properties of nitinol will be observed and compared with the cubic unit cell models of the austenite and martensite forms. The YBa 2 Cu 3 O 7 superconductor will be cooled so the levitation of a rare earth magnet can be observed and its model will be investigated. 5

6 SAFETY PRECAUTIONS Safety goggles and lab aprons must be worn in lab at all times. Liquid nitrogen is extremely cold ( 321 F!). Contact with skin may result in severe frostbite. If any liquid nitrogen spills on clothing, remove the clothing immediately, as the trapped liquid will cause severe frostbite to the skin beneath the clothing. Do not touch any metal dipped into liquid nitrogen until it has warmed to room temperature. Do not place liquid nitrogen in a closed container; it can rapidly expand and explosively shatter a container that is not properly vented. Use plastic tweezers to handle superconductors and rare earth magnets; the solids may be toxic. The solid state models contain small spheres and rods - if any are dropped on the floor, pick them up to prevent slips or falls. Wash your hands before leaving lab. Report any spills, accidents, or injuries to your TA. Before starting the experiment, the TA will asks you to do a quick demonstration or talk-through one of the following: 1) How to remove a rod that has been in liquid nitrogen? 2) Assemble the superconductor setup for this experiment (without the liquid nitrogen) Make sure you watch the videos on the course website and read the documents to prepare. These demonstrations will be done every week. Everyone will have presented at least one topic by the end of the quarter. The demonstrations should be short (>1 min) and will be graded. PROCEDURES Because of limitations with the number of models, you will probably need to perform the parts of this experiment out of the order indicated. All ELN entries should be in complete sentences that fully convey the information obtained in lab. Part A: Solids with Square Array Layers 1. The following questions pertain to the primitive, body centered cubic (bcc), CsCl, and NaTl models. Using the Sketch editor on the ELN, sketch the cubes and spheres to create the unit cells for primitive, body centered cubic, CsCl, and NaTl. a. Use colorless and darkened spheres to indicate the different atoms or ions for CsCl and NaTl. 6

7 b. Provide the arrangement of metal atoms for the two cubes that when repeated create the unit cell of NaTl. Choose the correct response for each of the following. 2. The tiny pink sphere is in a cubic / tetrahedral / octahedral hole in the primitive cubic model. cubic / tetrahedral / octahedral hole in the body centered cubic model. 3. The unit cell of CsCl is primitive / body centered cubic. The holes in this unit cell are cubic / tetrahedral / octahedral. 4. The unit cell of NaTl is based on the repetition of a primitive / body centered cubic structure. The holes in this unit cell are cubic / tetrahedral / octahedral. 5. How many of each of the two cubes drawn for NaTl are required to create its unit cell? (Hint: The face of one unit cell is also the face of another unit cell. Therefore, faces on opposite sides of a unit cell should be superimposable.) 6. Calculate the empirical formula for CsCl and NaTl using their unit cells or coordination numbers. All work must be shown to receive credit. Nitinol Record all observations, no prompts are given below. 1. Warm some water to C using a hot plate. Obtain a piece of NiTi wire and bend it into a new shape. Drop the wire into the warm water. Try it again when the wire is cool. 2. Grasp the ends of the wire and place the center of the wire in a candle flame. Bend the wire into a V shape with the point of the V in the flame. (The wire will resist bending initially, but will deform when hot.) Once the V shape forms, remove the wire from the flame and wave it in the air to cool. Bend the wire into a new shape and then dip it into warm water. 3. Obtain two different NiTi rods. Drop each one on the floor. 4. Put the martensite rod into warm water (70-80 C) for a few minutes. Remove the rod with tongs (do not touch, it may be too hot to handle) and drop it on the floor. 7

8 Crystalline Solids Revised 12/12/13 5. Put austenite rod in a styrofoam cup containing N 2 (l) for a few minutes, remove the rod with tongs and drop it on the lab bench. (Caution: N 2 (l) is extremely cold ( 321 F!) and can cause severe frostbite!) 6. Slowly warm the martensite rod in a water bath, taking it out occasionally (every 5-10 C) and dropping it on the floor. Record the sound as a "ring", "intermediate", or "thud" for each temperature measurement (in C). 7. Inspect the models for the two forms of nitinol labeled Model #1 & Model #2. Which is austenite and which is martensite? What is the unit cell of the austenite form? DISCUSSION Choose the correct response for each of the following. 1. At room temperature the wire is in the (martensite / austenite) phase. At C the wire is in the (martensite / austenite) phase. 2. The wire is in the (martensite / austenite) phase in the flame. Why can the wire be bent at room temperature, but returns to the V shape when warmed? 3. The room temperature austenite rod makes a (thud / intermediate / ring) sound at room temperature. Why? 4. What sound does the room temperature martensite rod make when it warms? Why? What sound does the room temperature austenite rod make when it cools? Why? 5. What is the temperature range where the solid-solid transition occurs? PROCEDURES Part B: Solids with Close Packed Layers The following questions pertain to the cubic close packed (ccp), face centered cubic (fcc), NaCl, and CaTiO 3 models. Choose the correct response for each of the following. (1) The packing order of the cubic close packed model is: A-A / A-B-A / A-B-C. The tiny pink sphere is in a: cubic / tetrahedral / octahedral hole. The tiny black sphere is in a: cubic / tetrahedral / octahedral hole. (2) For the face centered cubic model 8

9 Crystalline Solids Revised 12/12/13 the tiny pink sphere is in a: cubic / tetrahedral / octahedral hole. the tiny black sphere is in a: cubic / tetrahedral / octahedral hole. (3) Sketch the cubes and spheres to create the unit cells for primitive, body centered cubic, CsCl, and NaTl. Use labeled colorless and darkened spheres to indicate the different atoms or ions for NaCl and CaTiO 3. (4) Fill in the coordination number for each of the following: a. Any sphere in the face centered cubic model. b. Ions of the NaCl model: Na + Cl (5) Calculate the empirical formula for NaCl and CaTiO 3 using their unit cells or coordination numbers. All work must be shown to receive credit. (6) What type of holes are filled in a. in NaCl? cubic / tetrahedral / octahedral. b. in CaTiO 3 (fcc)? cubic / tetrahedral / octahedral. Superconductor 1. Check out a magnet from your TA. (Loss of magnet will result in a 5 point deduction from lab report score.) 2. Using plastic tweezers, place the larger superconductor pellet on a stack of pennies in the center of a cutoff Styrofoam cup. The pellet should be level with the top edge of the cup. (Scrape off loose material from the pellet with a spatula. If the pellet is broken, use the largest piece, flat side up.) Use plastic tweezers to place the smaller magnet on the superconductor. 3. Carefully pour N 2 (l) into the cup, covering the pennies and the bottom of the pellet. Touch the magnet gently with tweezers - it should spin. Allow the N 2 (l) to evaporate so the pellet and magnet warm back to room temperature. (To avoid frostbite, do not touch pellet or magnet until warmed.) 4. Inspect the models for the superconductor. Which model is face centered cubic? Which is perovskite? How many units cells are present in model #2? Calculate the empirical formula 9

10 Crystalline Solids Revised 12/12/13 from the perovskite model. (The atoms are represented by the following spheres: Y: red; Ba: black; Cu: blue; O: colorless.) 10